Finite Group Databasebeta

← #35197444

Subgroups — #35197444

Order 20224.

7082 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777511C212yesmaximal, complemented
2#23777485C212yesmaximal, complemented
3#23777468C216yesmaximal, complemented
4#23777439C216yesmaximal, complemented
5#23777411C212yesmaximal, complemented
6#23777393C212yesmaximal, complemented
7#23777361C216yesmaximal, complemented
8#23777342C216yesmaximal, complemented
9#23777303C213yesmaximal, complemented
10#23777297C213yesmaximal, complemented
11#23777213C211yesmaximal, characteristic, complemented
12#23777194C211yesmaximal, characteristic, complemented
13#23777142C213yesmaximal, complemented
14#23777136C213yesmaximal, complemented
15#23777073C211yesmaximal, characteristic, complemented
16#23777070C211yesmaximal, characteristic, complemented
17#23776833C213yesmaximal, complemented
18#23776816C213yesmaximal, complemented
19#23776785C213yesmaximal, complemented
20C2×#19099185C213yesmaximal, complemented
21C4×#14579207C211yesmaximal, characteristic, complemented
22#23776599C211yesmaximal, characteristic, complemented
23C4×2−1+4×C79C211yesmaximal, characteristic, complemented
24C2×#14579207C2211yescharacteristic
25C2×#41×D79C2211yescharacteristic
26#19099298C2216yescomplemented
27#19099298C2216yescomplemented
28Q8×Dic158C2212yescomplemented
29#19099289C2212yescomplemented
30#19099286C2216yescomplemented
31#19099285C2216yescomplemented
32#19099285C2216yescomplemented
33#19099281C2216yescomplemented
34#19099276C2216yescomplemented
35#19099276C2216yescomplemented
36#19099273C2216yescomplemented
37#19099272C2216yescomplemented
38#19099268C2216yescomplemented
39#19099262C22112yescomplemented
40#19099261C2216yescomplemented
41#19099257C2216yescomplemented
42#19099254C2216yescomplemented
43#19099254C2216yescomplemented
44#19099246C22112yescomplemented
45#19099242C22112yescomplemented
46#19099237C22112yescomplemented
47#19099237C22112yescomplemented
48#19099237C22112yescomplemented
49#19099235C2212yes—
50D4×Dic158C2216yescomplemented
51Q8×C22⋊D79C2212yescomplemented
52#19099225C2212yes—
53#19099224C2212yescomplemented
54#19099224C2212yescomplemented
55#19099224C2212yescomplemented
56#19099222C22112yescomplemented
57#19099214C2216yescomplemented
58#19099214C2216yescomplemented
59#19099212C2216yescomplemented
60#19099209C22112yescomplemented
61#19099208C2216yes—
62#19099201C2216yescomplemented
63#19099201C2216yescomplemented
64#19099201C2216yescomplemented
65D4×D316C2216yes—
66#19099194C2213yescomplemented
67#19099191C2213yescomplemented
68#19099185C2213yescomplemented
69#19099185C2216yescomplemented
70#19099185C2216yescomplemented
71#19099185C2216yescomplemented
72#19099185C2216yescomplemented
73#19099185C2216yescomplemented
74#19099185C2216yescomplemented
75#19099185C2216yescomplemented
76#19099185C2213yescomplemented
77#19099185C2216yescomplemented
78#19099184C2216yescomplemented
79#19099178C2211yescharacteristic, complemented
80#19099178C2213yescomplemented
81#19099171C2213yescomplemented
82#19099171C2213yescomplemented
83#19099171C2216yescomplemented
84#19099168C2216yescomplemented
85#19099164C2213yescomplemented
86#19099164C2213yescomplemented
87#19099160C22112yescomplemented
88#19099155C2216yescomplemented
89#19099155C2216yescomplemented
90#19099146C2216yescomplemented
91#19099146C2216yescomplemented
92#19099146C22112yescomplemented
93#19099144C2213yes—
94#19099141C2213yescomplemented
95#19099137C2213yescomplemented
96#19099137C2213yescomplemented
97#19099132C2213yes—
98#19099127C2213yescomplemented
99#19099117C2216yescomplemented
100#19099117C2216yescomplemented
101#19099116C2213yescomplemented
102#19099113C2216yescomplemented
103#19099110C2216yescomplemented
104#19099109C2213yescomplemented
105C2×#14579160C2213yescomplemented
106#19099100C2216yescomplemented
107#19099100C2216yescomplemented
108#19099100C2216yescomplemented
109#19099097C2216yescomplemented
110#19099097C2216yescomplemented
111#19099097C2216yescomplemented
112#19099097C22112yescomplemented
113#19099091C2216yescomplemented
114#19099091C2216yescomplemented
115C2×#14579155C2216yescomplemented
116C2×#14579150C2213yescomplemented
117C2×#14579149C2216yescomplemented
118#19099075C2213yes—
119#19099072C22112yescomplemented
120#19099070C2213yescomplemented
121C2×#14579146C2216yescomplemented
122C2×#14579139C2216yescomplemented
123C2×#14579137C2213yescomplemented
124C2×#14579136C2213yes—
125#19099046C2211yescharacteristic
126#19099045C2211yescharacteristic, complemented
127#19099045C2211yescharacteristic, complemented
128#19099045C2212yescomplemented
129#19099043C2213yescomplemented
130#19099042C2213yescomplemented
131#19099042C2213yescomplemented
132#19099039C2211yescharacteristic, complemented
133#19099039C2211yescharacteristic, complemented
134#19099037C2213yescomplemented
135#19099035C2213yescomplemented
136#19099035C2213yescomplemented
137#19099035C2216yescomplemented
138#41×Dic79C2211yescharacteristic
139C4×#11929625C2212yescomplemented
140C4×#11929624C2213yescomplemented
141C4×#11929624C2213yescomplemented
142#19099031C2213yescomplemented
143C2×C4×D316C2213yescomplemented
144C4×D4×D79C2216yescomplemented
145C2×#14579118C2213yescomplemented
146#117×D79C2213yescomplemented
147C2×2−1+4×C79C2211yescharacteristic
148#520×C79C2211yescharacteristic
149#520×C79C2213yescomplemented
150#520×C79C2216yescomplemented
151#519×C79C2213yescomplemented
152#519×C79C2212yescomplemented
153C4×#41×C79C2211yescharacteristic
154C4×#41×C79C2213yescomplemented
155C4×#41×C79C2216yescomplemented
156C2×C4×Q8×C79C2213yescomplemented
157C2×C4×Q8×C79C2212yescomplemented
158#14579207—28no—
159C2×#11929625C2312yes—
160C2×#11929625C2311yescharacteristic
161C2×#11929624C2313yes—
162C2×#11929624C2313yes—
163C2×#11929624C23112yes—
164C2×#11929623C2313yes—
165#41×D79—28no—
166C22×Dic158C2316yes—
167C2×Q8×D79C2311yescharacteristic
168C22×D316C2313yes—
169C22×D316C2316yes—
170C2×D4×D79C2316yes—
171C2×D4×D79C2313yes—
172C22×C4×D79C2313yes—
173C22×C4×D79C2316yes—
174#14579161C2316yes—
175#14579160C2313yes—
176#14579160C2311yescharacteristic
177#14579160C2316yes—
178#14579160C2316yes—
179#14579160C2316yes—
180#14579160C2316yes—
181#14579159C2313yes—
182#14579159C2316yes—
183#14579158C2316yes—
184#14579157C2313yes—
185#14579156C2316yes—
186#14579156C2316yes—
187#14579156C23112yes—
188#14579156C23112yes—
189#14579155C23112yes—
190#14579155C2316yes—
191#14579155C2316yes—
192#14579155C2316yes—
193#14579155C2316yes—
194#14579155C23112yes—
195#14579155C23112yes—
196#14579154C2312yes—
197#14579154C2316yes—
198#14579153C2316yes—
199#14579153C2316yes—
200#14579153C2316yes—
201#14579152C2313yes—
202#14579152C2313yes—
203#14579152C2316yes—
204#14579151C2316yes—
205#14579151C2316yes—
206#14579151C23112yes—
207#14579150C2316yes—
208#14579150C2316yes—
209#14579150C2313yes—
210#14579150C2316yes—
211#14579150C2316yes—
212#14579149C2316yes—
213#14579149C23112yes—
214#14579149C2316yes—
215#14579149C2316yes—
216#14579149C23112yes—
217#14579149C23112yes—
218#14579148C2311yescharacteristic
219#14579147C2312yes—
220#14579147C2316yes—
221#14579147C23112yes—
222#14579146C23112yes—
223#14579146C2316yes—
224#14579146C2316yes—
225#14579146C23112yes—
226#14579146C23112yes—
227#14579146C23112yes—
228#14579146C23112yes—
229#14579145C2316yes—
230#14579144C23112yes—
231#14579144C23112yes—
232#14579144C2312yes—
233#14579144C2316yes—
234#14579144C2316yes—
235#14579144C2316yes—
236#14579143C2316yes—
237#14579143C2316yes—
238#14579142C2316yes—
239#14579141C2313yes—
240#14579141C2316yes—
241#14579141C2311yescharacteristic
242#14579140C2316yes—
243#14579140C2312yes—
244#14579140C2316yes—
245#14579140C23112yes—
246#14579139C2316yes—
247#14579139C2316yes—
248#14579139C23112yes—
249#14579139C23112yes—
250#14579139C23112yes—
251#14579139C23112yes—
252#14579138C2316yes—
253#14579138C2316yes—
254#14579138C23112yes—
255#14579137C2313yes—
256#14579137C2316yes—
257#14579137C2316yes—
258#14579137C2316yes—
259#14579137C2313yes—
260#14579137C2316yes—
261#14579137C2316yes—
262#14579136C2316yes—
263#14579136C2316yes—
264#14579136C2313yes—
265#14579136C2313yes—
266#14579136C2316yes—
267#14579136C2316yes—
268#14579135C2316yes—
269#14579135C23112yes—
270#14579135C2316yes—
271#14579135C2316yes—
272#14579135C2316yes—
273#14579135C2316yes—
274#14579134C2316yes—
275#14579134C2316yes—
276#14579134C23112yes—
277#14579133C23112yes—
278#14579133C2316yes—
279#14579133C2316yes—
280#14579132C2313yes—
281#14579132C2311yescharacteristic
282#14579131C2316yes—
283#14579131C23112yes—
284#14579129C2316yes—
285#14579129C23112yes—
286Q8×Dic79C2311yescharacteristic
287Q8×Dic79C2311yescharacteristic
288Q8×Dic79C2312yes—
289C4×Dic158C2311yescharacteristic
290C4×Dic158C2313yes—
291C4×Dic158C2313yes—
292C4×Dic158C2313yes—
293C4×Dic158C23112yes—
294C4×Dic158C2316yes—
295C4×Dic158C2316yes—
296#14579126C2313yes—
297#14579126C2313yes—
298C4×D316C2313yes—
299C4×D316C2313yes—
300C4×D316C2313yes—
301C4×D316C2316yes—
302C4×D316C2316yes—
303C4×D316C2316yes—
304C4×D316C2313yes—
305C4×D316C2316yes—
306C4×D316C2316yes—
307C4×D316C23112yes—
308C4×D316C23112yes—
309D4×Dic79C2313yes—
310D4×Dic79C2313yes—
311D4×Dic79C2316yes—
312#14579123C2313yes—
313#14579123C2316yes—
314#14579123C2316yes—
315#14579123C2313yes—
316C4×C22⋊D79C2316yes—
317C4×C22⋊D79C2316yes—
318C4×C22⋊D79C2316yes—
319C4×C22⋊D79C2316yes—
320C4×C22⋊D79C2316yes—
321C4×C22⋊D79C2316yes—
322C4×C22⋊D79C2316yes—
323C4×C22⋊D79C2316yes—
324C4×C22⋊D79C23112yes—
325(C22⋊D79)⋊C4C2316yes—
326(C22⋊D79)⋊C4C23112yes—
327(C22⋊D79)⋊C4C2316yes—
328#14579120C2313yes—
329#14579120C2313yes—
330#14579119C2313yes—
331#14579119C2316yes—
332#14579119C2313yes—
333#14579118C2313yes—
334#14579118C2313yes—
335#14579118C2316yes—
336#14579118C2311yescharacteristic
337#14579118C2313yes—
338#14579118C2313yes—
339#14579118C2313yes—
340#14579118C2313yes—
341#14579118C2313yes—
342#14579118C23112yes—
343#14579118C23112yes—
344#14579118C23112yes—
345#14579117C2316yes—
346C2×C4⋊Dic79C2313yes—
347C2×Dic79⋊C4C2313yes—
348C2×Dic79⋊C4C2313yes—
349C2×Dic79⋊C4C2316yes—
350C2×Dic79⋊C4C2316yes—
351C4⋊C4×D79C2313yes—
352C4⋊C4×D79C2316yes—
353C4⋊C4×D79C2313yes—
354C2×(C2×D79)⋊C4C2313yes—
355C2×(C2×D79)⋊C4C2313yes—
356C2×(C2×D79)⋊C4C2316yes—
357C2×(C2×D79)⋊C4C2316yes—
358C2×(C2×D79)⋊C4C2316yes—
359C2×(C2×D79)⋊C4C2316yes—
360C2×(C2×D79)⋊C4C2316yes—
361C22⋊C4×D79C2316yes—
362C22⋊C4×D79C23112yes—
363C2×C4×Dic79C2313yes—
364C42×D79C2316yes—
365C42×D79C2316yes—
3662−1+4×C79—28no—
367C2×#41×C79C2313yes—
368C2×#41×C79C2316yes—
369C2×#41×C79C2311yescharacteristic
370C22×Q8×C79C2313yes—
371C22×Q8×C79C2312yes—
372C4×Q8×C79C2313yes—
373C4×Q8×C79C2316yes—
374C4×Q8×C79C2313yes—
375C4×Q8×C79C2316yes—
376C4×Q8×C79C2316yes—
377C4×Q8×C79C2312yes—
378C4×Q8×C79C2311yescharacteristic
379C4×Q8×C79C2316yes—
380C4×Q8×C79C2311yescharacteristic
381C4×Q8×C79C2316yes—
382C4×D4×C79C2316yes—
383C4×D4×C79C2316yes—
384C4×D4×C79C2311yescharacteristic
385C4×D4×C79C2313yes—
386C4×D4×C79C2316yes—
387C4×D4×C79C23112yes—
388C4×D4×C79C2313yes—
389C4×D4×C79C2313yes—
390#117×C79C2316yes—
391#117×C79C2313yes—
392#117×C79C2313yes—
393#117×C79C23112yes—
394#117×C79C2316yes—
395C2×C4⋊C4×C79C2313yes—
396C2×C4⋊C4×C79C2316yes—
397C2×C4⋊C4×C79C2316yes—
398C2×C42×C79C2313yes—
399C2×C42×C79C2316yes—
400C2×C42×C79C2316yes—
401C23×D79C2413yes—
402C23×D79C2416yes—
403#11929625—24no—
404#11929625—28no—
405#11929624—212no—
406#11929624—212no—
407#11929624—812no—
408#11929623—212no—
409C2×Dic158—86no—
410C2×Dic158C2413yes—
411C2×Dic158C2411yescharacteristic
412C2×Dic158C2416yes—
413C2×Dic158C24112yes—
414C2×Dic158C2412yes—
415Q8×D79—24no—
416C2×D316—212no—
417C2×D316—86no—
418C2×D316C2413yes—
419C2×D316C2413yes—
420C2×D316C2416yes—
421C2×D316C24112yes—
422C2×D316C2416yes—
423C2×D316C2416yes—
424C2×C22⋊D79C2416yes—
425C2×C22⋊D79C2416yes—
426C2×C22⋊D79C2416yes—
427C2×C22⋊D79C2416yes—
428C2×C22⋊D79C2412yes—
429C2×C22⋊D79C2416yes—
430D4×D79—212no—
431D4×D79—224no—
432C22×Dic79C2413yes—
433C22×Dic79C2413yes—
434C22×Dic79C2416yes—
435C22×Dic79C2413yes—
436C2×C4×D79—212no—
437C2×C4×D79—86no—
438C2×C4×D79C2413yes—
439C2×C4×D79C2413yes—
440C2×C4×D79C2413yes—
441C2×C4×D79C2416yes—
442C2×C4×D79C2411yescharacteristic
443C2×C4×D79C2416yes—
444C2×C4×D79C24112yes—
445C2×C4×D79C2416yes—
446C2×C4×D79C2416yes—
447C2×C4×D79C2416yes—
448C4⋊Dic79C2416yes—
449C4⋊Dic79C2413yes—
450C4⋊Dic79C2413yes—
451C4⋊Dic79C2413yes—
452C4⋊Dic79C2411yescharacteristic
453C4⋊Dic79C2412yes—
454C4⋊Dic79C2416yes—
455C4⋊Dic79C2416yes—
456C4⋊Dic79C2416yes—
457Dic79⋊C4C2413yes—
458Dic79⋊C4C2413yes—
459Dic79⋊C4C2416yes—
460Dic79⋊C4C2411yescharacteristic
461Dic79⋊C4C2411yescharacteristic
462Dic79⋊C4C2416yes—
463Dic79⋊C4C2416yes—
464Dic79⋊C4C2413yes—
465Dic79⋊C4C2413yes—
466Dic79⋊C4C2413yes—
467Dic79⋊C4C2413yes—
468Dic79⋊C4C24112yes—
469Dic79⋊C4C24112yes—
470Dic79⋊C4C2412yes—
471Dic79⋊C4C2416yes—
472Dic79⋊C4C2416yes—
473Dic79⋊C4C2416yes—
474Dic79⋊C4C2416yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2412yes—
477C22⋊Dic79C2416yes—
478C22⋊Dic79C2416yes—
479C22⋊Dic79C2416yes—
480C22⋊Dic79C2412yes—
481C22⋊Dic79C2412yes—
482C22⋊Dic79C2412yes—
483(C2×D79)⋊C4C2413yes—
484(C2×D79)⋊C4C2413yes—
485(C2×D79)⋊C4C2416yes—
486(C2×D79)⋊C4C24112yes—
487(C2×D79)⋊C4C2411yescharacteristic
488(C2×D79)⋊C4C2411yescharacteristic
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C2416yes—
491(C2×D79)⋊C4C2416yes—
492(C2×D79)⋊C4C2416yes—
493(C2×D79)⋊C4C2416yes—
494(C2×D79)⋊C4C2413yes—
495(C2×D79)⋊C4C2413yes—
496(C2×D79)⋊C4C2413yes—
497(C2×D79)⋊C4C2413yes—
498(C2×D79)⋊C4C24112yes—
499(C2×D79)⋊C4C24112yes—
500(C2×D79)⋊C4C24112yes—
501(C2×D79)⋊C4C24112yes—
502(C2×D79)⋊C4C2416yes—
503(C2×D79)⋊C4C2416yes—
504(C2×D79)⋊C4C2416yes—
505(C2×D79)⋊C4C2412yes—
506C4×Dic79C2412yes—
507C4×Dic79C2413yes—
508C4×Dic79C2416yes—
509C4×Dic79C2416yes—
510C4×Dic79C2416yes—
511C4×Dic79C2416yes—
512C4×Dic79C2411yescharacteristic
513C4×Dic79C2413yes—
514C4×Dic79C2413yes—
515#41×C79—224no—
516#41×C79—212no—
517#41×C79#4118yescomplemented
518C2×Q8×C79—28no—
519C2×Q8×C79—212no—
520C2×Q8×C79C2413yes—
521C2×Q8×C79C2416yes—
522C2×Q8×C79C2411yescharacteristic
523C2×D4×C79C2416yes—
524C2×D4×C79C2411yescharacteristic
525C2×D4×C79C2413yes—
526C22×C4×C79C2416yes—
527C22×C4×C79C2416yes—
528C22×C4×C79C2416yes—
529C22×C4×C79C2416yes—
530C22×C4×C79C2413yes—
531C22×C4×C79C2412yes—
532C22×C4×C79C2413yes—
533C22×C4×C79C2413yes—
534C4⋊C4×C79C2413yes—
535C4⋊C4×C79C2413yes—
536C4⋊C4×C79C2416yes—
537C4⋊C4×C79C2416yes—
538C4⋊C4×C79C24112yes—
539C4⋊C4×C79C2413yes—
540C4⋊C4×C79C2411yescharacteristic
541C4⋊C4×C79C2416yes—
542C22⋊C4×C79C2416yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2412yes—
545C22⋊C4×C79C2416yes—
546C42×C79C2411yescharacteristic
547C42×C79C2413yes—
548C42×C79C2416yes—
549C42×C79C2413yes—
550C42×C79C2413yes—
551C42×C79C2416yes—
552C42×C79C24112yes—
553C42×C79C2416yes—
554C23×C79C2512yes—
555C23×C79C2513yes—
556C22×D79—26no—
557C22×D79—212no—
558C22×D79—46no—
559C22×D79—43no—
560C22×D79—43no—
561C22×D79—46no—
562C22×D79C2511yescharacteristic
563C22×D79C2516yes—
564C22×D79C2513yes—
565Q8×C79—212no—
566Q8×C79—26no—
567Q8×C79C2×#4114yes—
568D4×C79—212no—
569D4×C79—22no—
570D4×C79C2×#41112yes—
571C2×C4×C79—212no—
572C2×C4×C79—212no—
573C2×C4×C79—43no—
574C2×C4×C79—46no—
575C2×C4×C79—46no—
576C2×C4×C79—42no—
577C2×C4×C79—43no—
578C2×C4×C79C2×#41112yes—
579C2×C4×C79C2513yes—
580C2×C4×C79C2511yescharacteristic
581C2×C4×C79C2513yes—
582C2×C4×C79C2511yescharacteristic
583C2×C4×C79C2516yes—
584C2×C4×C79C2512yes—
585C2×C4×C79C2516yes—
586C2×C4×C79C2513yes—
587C2×C4×C79C2511yescharacteristic
588C22⋊D79—212no—
589C22⋊D79—212no—
590C22⋊D79—46no—
591C22⋊D79—42no—
592C22⋊D79—46no—
593C22⋊D79—46no—
594C2×Dic79—26no—
595C2×Dic79—46no—
596C2×Dic79—43no—
597C2×Dic79—43no—
598C2×Dic79C2511yescharacteristic
599C2×Dic79C2511yescharacteristic
600C2×Dic79C2512yes—
601C2×Dic79C2513yes—
602C2×Dic79C2513yes—
603C2×Dic79C2513yes—
604C2×Dic79C2512yes—
605C2×Dic79C2516yes—
606C2×Dic79C2511yescharacteristic
607D316—212no—
608D316—26no—
609D316—26no—
610D316—46no—
611D316—412no—
612D316—46no—
613C4×D79—22no—
614C4×D79—26no—
615C4×D79—26no—
616C4×D79—26no—
617C4×D79—212no—
618C4×D79—46no—
619C4×D79—412no—
620C4×D79—46no—
621C4×D79—46no—
622C4×D79—46no—
623Dic158—26no—
624Dic158—22no—
625Dic158—46no—
626Dic158—412no—
627Dic158—42no—
628C22×C79—23no—
629C22×C79—23no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79—22no—
633C22×C79C22×#4116yes—
634C22×C79C2611yescharacteristic
635C2×D79—23no—
636C2×D79—26no—
637C2×D79—21no—
638C2×D79—23no—
639C2×D79—26no—
640C2×D79—21no—
641C2×D79—21no—
642C2×D79—26no—
643C2×D79—23no—
644C2×D79—86no—
645C2×D79—812no—
646C4×C79—26no—
647C4×C79—26no—
648C4×C79—21no—
649C4×C79—23no—
650C4×C79—21no—
651C4×C79—22no—
652C4×C79—23no—
653C4×C79C22×#4116yes—
654C4×C79C22×#4112yes—
655Dic79—22no—
656Dic79—23no—
657Dic79—21no—
658Dic79—23no—
659Dic79—26no—
660Dic79—21no—
661Dic79—23no—
662Dic79—22no—
663Dic79—21no—
664#62857—791nomaximal, Sylow
665C2×C79—26no—
666C2×C79—42no—
667C2×C79C23×#4111yescharacteristic
668C2×C79H(7,𝔽2)11yescharacteristic
669C2×C792−1+611yescharacteristic
670D79—43no—
671D79—46no—
672D79—41no—
673#3524—792no—
674#3522—792no—
675#3521—796no—
676#3520—796no—
677#3518—792no—
678#3516—792no—
679#3514—796no—
680#3513—796no—
681#3511—793no—
682#3510—793no—
683#3503—791no—
684#3500—791no—
685#3495—793no—
686#3494—793no—
687#3489—791no—
688#3488—791no—
689#3461—793no—
690#3460—793no—
691#3455—793no—
692C2×#542—793no—
693C4×2−1+4D7911yescharacteristic, complemented
694C4×H(5,𝔽2)—791no—
695#3428—791no—
696C79#6285711yescharacteristic, complemented, Sylow
697C2×2−1+4C2×D7911yescharacteristic
698C2×H(5,𝔽2)—791no—
699C22×#41—791no—
700#559—796no—
701#559—796no—
702Q82—792no—
703#557—792no—
704#556—796no—
705#556—796no—
706#556—796no—
707#556—796no—
708#555—796no—
709#555—796no—
710#554—796no—
711#554—796no—
712#554—796no—
713#553—7912no—
714#553—796no—
715#553—796no—
716#552—796no—
717#552—796no—
718#552—7912no—
719#551—7912no—
720#551—7912no—
721#551—7912no—
722#551—7912no—
723#550—792no—
724D4×Q8—792no—
725D4×Q8—796no—
726#548—792no—
727#548—792no—
728#548—792no—
729#548—792no—
730#548—7912no—
731#547—796no—
732#547—796no—
733#547—796no—
734#546—796no—
735#546—796no—
736#546—796no—
737#546—796no—
738#546—7912no—
739D42—796no—
740#544—793no—
741#544—793no—
742#542—793no—
743#542—796no—
744#542—796no—
745#542—796no—
746#542—796no—
747#542—796no—
748#542—796no—
749#542—796no—
750#542—793no—
751#542—796no—
752#542—791no—
753#542—793no—
754#542—796no—
755#541—793no—
756#541—793no—
757#541—796no—
758#540—793no—
759#540—793no—
760#540—796no—
761#539—796no—
762#539—796no—
763#539—7912no—
764#538—796no—
765#538—796no—
766#538—7912no—
767#537—793no—
768#537—793no—
769#536—793no—
770#536—793no—
771#535—793no—
772#535—793no—
773#533—796no—
774#533—796no—
775#533—793no—
776#532—793no—
777#532—796no—
778#532—796no—
779C2×C4⋊Q8—793no—
780#529—796no—
781#529—796no—
782#529—796no—
783#529—796no—
784#529—796no—
785#529—796no—
786#529—796no—
787#529—796no—
788#529—7912no—
789C2×#126—796no—
790C2×#124—793no—
791C2×#124—796no—
792#525—793no—
793#525—7912no—
794#525—793no—
795C2×#123—796no—
796C2×C22⋊Q8—793no—
797C2×C22⋊Q8—796no—
798C2×#121—793no—
799#520—791no—
800#520—791no—
801#520—791no—
802#520—792no—
803#520—793no—
804#520—793no—
805#520—793no—
806#520C2×D7911yescharacteristic
807#520C2×D7913yescomplemented
808#520C2×D7916yescomplemented
809#519—791no—
810#519—791no—
811#519C2×D7913yescomplemented
812#519C2×D7912yescomplemented
813#518—793no—
814#518—793no—
815#518—796no—
816#518—793no—
817C4×#41—791no—
818C4×#41—792no—
819C4×#41—793no—
820C4×#41—793no—
821C4×#41—793no—
822C4×#41C2×D7911yescharacteristic
823C4×#41C2×D7913yescomplemented
824C4×#41C2×D7916yescomplemented
825C2×C4×Q8C2×D7913yescomplemented
826C2×C4×Q8C2×D7912yescomplemented
827C2×C4×D4—796no—
828C2×C4×D4—793no—
829C2×#117—793no—
830C2×#117—793no—
8312−1+4—28no—
832H(5,𝔽2)—1588no—
833C2×#41—792no—
834C2×#41—791no—
835C2×#41—793no—
836C2×#41—7912no—
837C2×#41—793no—
838C2×#41—793no—
839C2×#41—1588no—
840C2×#41C22×D7913yes—
841C2×#41C22×D7916yes—
842C2×#41C22×D7911yescharacteristic
843C22×Q8—791no—
844C22×Q8—796no—
845C22×Q8C22×D7913yes—
846C22×Q8C22×D7912yes—
847C22×D4—796no—
848C22×D4—793no—
849C22×D4—796no—
850C22×D4—793no—
851C23×C4—796no—
852C23×C4—793no—
853C4⋊Q8—793no—
854C4⋊Q8—796no—
855C4⋊Q8—793no—
856C4⋊Q8—796no—
857C4⋊Q8—796no—
858C4⋊Q8—796no—
859C4⋊Q8—791no—
860C4⋊Q8—796no—
861C4⋊Q8—796no—
862#127—793no—
863#127—796no—
864#126—796no—
865#126—796no—
866#126—7912no—
867#126—7912no—
868#126—792no—
869#126—796no—
870#126—796no—
871#126—7912no—
872#126—7912no—
873#126—7912no—
874#126—796no—
875#126—796no—
876#126—796no—
877#125—793no—
878#125—793no—
879#125—796no—
880#125—796no—
881#125—796no—
882#125—7912no—
883#125—796no—
884#125—796no—
885#125—796no—
886#124—793no—
887#124—796no—
888#124—796no—
889#124—796no—
890#124—796no—
891#124—791no—
892#124—792no—
893#124—796no—
894#124—7912no—
895#124—796no—
896#124—7912no—
897#124—7912no—
898#124—7912no—
899#124—796no—
900#124—796no—
901#123—796no—
902#123—792no—
903#123—796no—
904#123—7912no—
905#123—7912no—
906#123—796no—
907#123—796no—
908#123—796no—
909#123—7912no—
910#123—7912no—
911#123—7912no—
912#123—7912no—
913#123—796no—
914#123—7912no—
915#123—796no—
916#123—796no—
917#123—796no—
918C22⋊Q8—793no—
919C22⋊Q8—796no—
920C22⋊Q8—796no—
921C22⋊Q8—796no—
922C22⋊Q8—793no—
923C22⋊Q8—796no—
924C22⋊Q8—796no—
925C22⋊Q8—792no—
926C22⋊Q8—796no—
927C22⋊Q8—796no—
928C22⋊Q8—7912no—
929C22⋊Q8—796no—
930C22⋊Q8—7912no—
931C22⋊Q8—7912no—
932C22⋊Q8—7912no—
933C22⋊Q8—791no—
934C22⋊Q8—793no—
935C22⋊Q8—796no—
936C22⋊Q8—796no—
937C22⋊Q8—7912no—
938C22⋊Q8—7912no—
939C22⋊Q8—796no—
940C22⋊Q8—796no—
941#121—791no—
942#121—793no—
943#121—7912no—
944#121—796no—
945#121—796no—
946#121—796no—
947#121—796no—
948#121—7912no—
949#121—796no—
950#121—796no—
951#121—796no—
952#121—793no—
953#121—796no—
954#121—796no—
955#121—796no—
956#121—793no—
957#121—796no—
958#121—796no—
959#121—796no—
960#121—7912no—
961#120—7912no—
962#120—796no—
963#120—7912no—
964#120—796no—
965C4×Q8—791no—
966C4×Q8—791no—
967C4×Q8—792no—
968C4×Q8—793no—
969C4×Q8—793no—
970C4×Q8—791no—
971C4×Q8—793no—
972C4×Q8—793no—
973C4×Q8—793no—
974C4×Q8—796no—
975C4×Q8—796no—
976C4×Q8—7912no—
977C4×Q8C22×D7911yescharacteristic
978C4×Q8C22×D7913yes—
979C4×Q8C22×D7916yes—
980C4×Q8C22×D7912yes—
981C4×Q8C22×D7916yes—
982C4×Q8C22×D7916yes—
983C4×Q8C22×D7916yes—
984C4×Q8C22×D7911yescharacteristic
985C4×Q8C22×D7913yes—
986C4×Q8C22×D7916yes—
987C4×D4—796no—
988C4×D4—793no—
989C4×D4—793no—
990C4×D4—796no—
991C4×D4—796no—
992C4×D4—796no—
993C4×D4—796no—
994C4×D4—796no—
995C4×D4—796no—
996C4×D4—7912no—
997C4×D4—796no—
998C4×D4—796no—
999C4×D4—796no—
1000C4×D4—796no—
1001C4×D4—793no—
1002C4×D4—793no—
1003C4×D4—7912no—
1004C4×D4—796no—
1005C4×D4—796no—
1006C4×D4—796no—
1007C4×D4—793no—
1008C4×D4—796no—
1009C4×D4—796no—
1010C4×D4—793no—
1011C4×D4—793no—
1012C4×D4—793no—
1013C4×D4—796no—
1014C4×D4—796no—
1015C4×D4—7912no—
1016C4×D4—7912no—
1017C4×D4C22×D7913yes—
1018C4×D4C22×D7913yes—
1019C4×D4C22×D7916yes—
1020C4×D4C22×D7911yescharacteristic
1021C4×D4C22×D7916yes—
1022C4×D4C22×D7916yes—
1023C4×D4C22×D7913yes—
1024C4×D4C22×D79112yes—
1025#117—793no—
1026#117—793no—
1027#117—793no—
1028#117—793no—
1029#117—796no—
1030#117—796no—
1031#117—793no—
1032#117—791no—
1033#117—793no—
1034#117—793no—
1035#117—793no—
1036#117—793no—
1037#117—793no—
1038#117—793no—
1039#117—796no—
1040#117—7912no—
1041#117—7912no—
1042#117—7912no—
1043#117C22×D7913yes—
1044#117C22×D7913yes—
1045#117C22×D7916yes—
1046#117C22×D79112yes—
1047#117C22×D7916yes—
1048C2×C4⋊C4—793no—
1049C2×C4⋊C4—793no—
1050C2×C4⋊C4—793no—
1051C2×C4⋊C4—796no—
1052C2×C4⋊C4—796no—
1053C2×C4⋊C4—793no—
1054C2×C4⋊C4—793no—
1055C2×C4⋊C4—796no—
1056C2×C4⋊C4C22×D7913yes—
1057C2×C4⋊C4C22×D7916yes—
1058C2×C4⋊C4C22×D7916yes—
1059C2×C22⋊C4—793no—
1060C2×C22⋊C4—793no—
1061C2×C22⋊C4—796no—
1062C2×C22⋊C4—796no—
1063C2×C22⋊C4—796no—
1064C2×C22⋊C4—796no—
1065C2×C22⋊C4—796no—
1066C2×C22⋊C4—796no—
1067C2×C22⋊C4—7912no—
1068C2×C42—793no—
1069C2×C42—796no—
1070C2×C42—796no—
1071C2×C42C22×D7913yes—
1072C2×C42C22×D7916yes—
1073C2×C42C22×D7916yes—
1074C24—796no—
1075C24—793no—
1076#41—224no—
1077#41—212no—
1078#41—63212no—
1079#41—1584no—
1080#41—1588no—
1081#41—15812no—
1082#41—15812no—
1083#41—15812no—
1084#41#1192962418yescomplemented
1085C2×Q8—28no—
1086C2×Q8—212no—
1087C2×Q8—792no—
1088C2×Q8—796no—
1089C2×Q8—7912no—
1090C2×Q8—793no—
1091C2×Q8—791no—
1092C2×Q8—6326no—
1093C2×Q8—1584no—
1094C2×Q8C23×D7913yes—
1095C2×Q8C23×D7916yes—
1096C2×Q8C23×D7911yescharacteristic
1097C2×D4—792no—
1098C2×D4—796no—
1099C2×D4—796no—
1100C2×D4—796no—
1101C2×D4—796no—
1102C2×D4—796no—
1103C2×D4—796no—
1104C2×D4—796no—
1105C2×D4—7912no—
1106C2×D4—793no—
1107C2×D4—796no—
1108C2×D4—793no—
1109C2×D4—6326no—
1110C2×D4—15812no—
1111C2×D4—15824no—
1112C2×D4—15812no—
1113C2×D4C23×D7916yes—
1114C2×D4C23×D7911yescharacteristic
1115C2×D4C23×D7913yes—
1116C22×C4—793no—
1117C22×C4—793no—
1118C22×C4—796no—
1119C22×C4—796no—
1120C22×C4—796no—
1121C22×C4—796no—
1122C22×C4—796no—
1123C22×C4—7912no—
1124C22×C4—793no—
1125C22×C4—793no—
1126C22×C4—796no—
1127C22×C4—793no—
1128C22×C4—793no—
1129C22×C4—791no—
1130C22×C4—6326no—
1131C22×C4—15812no—
1132C22×C4C23×D7916yes—
1133C22×C4C23×D7916yes—
1134C22×C4C23×D7913yes—
1135C22×C4C23×D7912yes—
1136C22×C4C23×D7913yes—
1137C22×C4C23×D7916yes—
1138C22×C4C23×D7916yes—
1139C22×C4C23×D7913yes—
1140C4⋊C4—791no—
1141C4⋊C4—793no—
1142C4⋊C4—791no—
1143C4⋊C4—793no—
1144C4⋊C4—796no—
1145C4⋊C4—796no—
1146C4⋊C4—796no—
1147C4⋊C4—793no—
1148C4⋊C4—793no—
1149C4⋊C4—793no—
1150C4⋊C4—793no—
1151C4⋊C4—7912no—
1152C4⋊C4—7912no—
1153C4⋊C4—792no—
1154C4⋊C4—796no—
1155C4⋊C4—796no—
1156C4⋊C4—796no—
1157C4⋊C4—796no—
1158C4⋊C4—796no—
1159C4⋊C4—792no—
1160C4⋊C4—796no—
1161C4⋊C4—793no—
1162C4⋊C4—793no—
1163C4⋊C4—793no—
1164C4⋊C4—791no—
1165C4⋊C4—792no—
1166C4⋊C4—796no—
1167C4⋊C4—796no—
1168C4⋊C4—796no—
1169C4⋊C4C23×D7913yes—
1170C4⋊C4C23×D7913yes—
1171C4⋊C4C23×D7913yes—
1172C4⋊C4C23×D7916yes—
1173C4⋊C4C23×D7916yes—
1174C4⋊C4C23×D79112yes—
1175C4⋊C4C23×D7911yescharacteristic
1176C4⋊C4C23×D7916yes—
1177C22⋊C4—796no—
1178C22⋊C4—796no—
1179C22⋊C4—796no—
1180C22⋊C4—792no—
1181C22⋊C4—792no—
1182C22⋊C4—792no—
1183C22⋊C4—793no—
1184C22⋊C4—793no—
1185C22⋊C4—791no—
1186C22⋊C4—791no—
1187C22⋊C4—796no—
1188C22⋊C4—7912no—
1189C22⋊C4—796no—
1190C22⋊C4—796no—
1191C22⋊C4—796no—
1192C22⋊C4—796no—
1193C22⋊C4—796no—
1194C22⋊C4—793no—
1195C22⋊C4—793no—
1196C22⋊C4—793no—
1197C22⋊C4—793no—
1198C22⋊C4—7912no—
1199C22⋊C4—7912no—
1200C22⋊C4—7912no—
1201C22⋊C4—7912no—
1202C22⋊C4—796no—
1203C22⋊C4—796no—
1204C22⋊C4—792no—
1205C22⋊C4—796no—
1206C22⋊C4C23×D7916yes—
1207C22⋊C4C23×D7916yes—
1208C22⋊C4C23×D7912yes—
1209C22⋊C4C23×D7916yes—
1210C42—791no—
1211C42—793no—
1212C42—792no—
1213C42—796no—
1214C42—796no—
1215C42—796no—
1216C42—796no—
1217C42—793no—
1218C42—793no—
1219C42C23×D7913yes—
1220C42C23×D7913yes—
1221C42C23×D7911yescharacteristic
1222C42C23×D7913yes—
1223C42C23×D7916yes—
1224C42C23×D7916yes—
1225C42C23×D79112yes—
1226C42C23×D7916yes—
1227C23—3166no—
1228C23—3163no—
1229C23—3163no—
1230C23—3166no—
1231C23—791no—
1232C23—796no—
1233C23—793no—
1234C23—1586no—
1235C23—15812no—
1236C23C24×D7912yes—
1237C23C24×D7913yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—3166no—
1241Q8—31612no—
1242Q8—3162no—
1243Q8—1586no—
1244Q8—1582no—
1245Q8C2×#1192962414yes—
1246D4—212no—
1247D4—22no—
1248D4—3166no—
1249D4—31612no—
1250D4—3166no—
1251D4—3166no—
1252D4—3162no—
1253D4—3166no—
1254D4—3166no—
1255D4—15812no—
1256D4—15812no—
1257D4—15812no—
1258D4—1586no—
1259D4—1586no—
1260D4C2×#11929624112yes—
1261C2×C4—212no—
1262C2×C4—212no—
1263C2×C4—43no—
1264C2×C4—43no—
1265C2×C4—42no—
1266C2×C4—46no—
1267C2×C4—46no—
1268C2×C4—3166no—
1269C2×C4—31612no—
1270C2×C4—3166no—
1271C2×C4—3166no—
1272C2×C4—3166no—
1273C2×C4—3166no—
1274C2×C4—3163no—
1275C2×C4—3163no—
1276C2×C4—791no—
1277C2×C4—791no—
1278C2×C4—792no—
1279C2×C4—793no—
1280C2×C4—793no—
1281C2×C4—793no—
1282C2×C4—792no—
1283C2×C4—796no—
1284C2×C4—791no—
1285C2×C4—1586no—
1286C2×C4—1582no—
1287C2×C4—1586no—
1288C2×C4—1586no—
1289C2×C4—1586no—
1290C2×C4—15812no—
1291C2×C4C2×#11929624112yes—
1292C2×C4C24×D7913yes—
1293C2×C4C24×D7911yescharacteristic
1294C2×C4C24×D7913yes—
1295C2×C4C24×D7911yescharacteristic
1296C2×C4C24×D7912yes—
1297C2×C4C24×D7916yes—
1298C2×C4C24×D7916yes—
1299C2×C4C24×D7913yes—
1300C2×C4C24×D7911yescharacteristic
1301C22—23no—
1302C22—23no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—6326no—
1307C22—63212no—
1308C22—1581no—
1309C22—1583no—
1310C22—1586no—
1311C22—1586no—
1312C22—1583no—
1313C22—1581no—
1314C22—1583no—
1315C22—1586no—
1316C22—1581no—
1317C22C22×#1192962416yes—
1318C22C25×D7911yescharacteristic
1319C4—26no—
1320C4—21no—
1321C4—23no—
1322C4—26no—
1323C4—21no—
1324C4—23no—
1325C4—22no—
1326C4—1581no—
1327C4—1582no—
1328C4—1583no—
1329C4—1586no—
1330C4—1583no—
1331C4—1581no—
1332C4—1583no—
1333C4—1582no—
1334C4—1581no—
1335C4C22×#1192962416yes—
1336C4C22×#1192962412yes—
1337C2—26no—
1338C2—42no—
1339C2—3161no—
1340C2—3166no—
1341C2—3163no—
1342C2C23×#1192962411yescharacteristic
1343C2#2377821111yescharacteristic
1344C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62857
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777511C2semidirect
2. #23777485C2semidirect
3. #23777468C2semidirect
4. #23777439C2semidirect
5. #23777411C2semidirect
6. #23777393C2semidirect
7. #23777361C2semidirect
8. #23777342C2semidirect
9. #23777303C2semidirect
10. #23777297C2semidirect
11. #23777213C2semidirect
12. #23777194C2semidirect
13. #23777142C2semidirect
14. #23777136C2semidirect
15. #23777073C2semidirect
16. #23777070C2semidirect
17. #23776833C2semidirect
18. #23776816C2semidirect
19. #23776785C2semidirect
20. C2×#19099185C2semidirect
21. C4×#14579207C2semidirect
22. #23776599C2semidirect
23. C4×2−1+4×C79C2semidirect
26. #19099298C22semidirect
27. #19099298C22semidirect
28. Q8×Dic158C22semidirect
29. #19099289C22semidirect
30. #19099286C22semidirect
31. #19099285C22semidirect
32. #19099285C22semidirect
33. #19099281C22semidirect
34. #19099276C22semidirect
35. #19099276C22semidirect
36. #19099273C22semidirect
37. #19099272C22semidirect
38. #19099268C22semidirect
39. #19099262C22semidirect
40. #19099261C22semidirect
41. #19099257C22semidirect
42. #19099254C22semidirect
43. #19099254C22semidirect
44. #19099246C22semidirect
45. #19099242C22semidirect
46. #19099237C22semidirect
47. #19099237C22semidirect
48. #19099237C22semidirect
50. D4×Dic158C22semidirect
51. Q8×C22⋊D79C22semidirect
53. #19099224C22semidirect
54. #19099224C22semidirect
55. #19099224C22semidirect
56. #19099222C22semidirect
57. #19099214C22semidirect
58. #19099214C22semidirect
59. #19099212C22semidirect
60. #19099209C22semidirect
62. #19099201C22semidirect
63. #19099201C22semidirect
64. #19099201C22semidirect
66. #19099194C22semidirect
67. #19099191C22semidirect
68. #19099185C22semidirect
69. #19099185C22semidirect
70. #19099185C22semidirect
71. #19099185C22semidirect
72. #19099185C22semidirect
73. #19099185C22semidirect
74. #19099185C22semidirect
75. #19099185C22semidirect
76. #19099185C22semidirect
77. #19099185C22semidirect
78. #19099184C22semidirect
79. #19099178C22semidirect
80. #19099178C22semidirect
81. #19099171C22semidirect
82. #19099171C22semidirect
83. #19099171C22semidirect
84. #19099168C22semidirect
85. #19099164C22semidirect
86. #19099164C22semidirect
87. #19099160C22semidirect
88. #19099155C22semidirect
89. #19099155C22semidirect
90. #19099146C22semidirect
91. #19099146C22semidirect
92. #19099146C22semidirect
94. #19099141C22semidirect
95. #19099137C22semidirect
96. #19099137C22semidirect
98. #19099127C22semidirect
99. #19099117C22semidirect
100. #19099117C22semidirect
101. #19099116C22semidirect
102. #19099113C22semidirect
103. #19099110C22semidirect
104. #19099109C22semidirect
105. C2×#14579160C22semidirect
106. #19099100C22semidirect
107. #19099100C22semidirect
108. #19099100C22semidirect
109. #19099097C22semidirect
110. #19099097C22semidirect
111. #19099097C22semidirect
112. #19099097C22semidirect
113. #19099091C22semidirect
114. #19099091C22semidirect
115. C2×#14579155C22semidirect
116. C2×#14579150C22semidirect
117. C2×#14579149C22semidirect
119. #19099072C22semidirect
120. #19099070C22semidirect
121. C2×#14579146C22semidirect
122. C2×#14579139C22semidirect
123. C2×#14579137C22semidirect
126. #19099045C22semidirect
127. #19099045C22semidirect
128. #19099045C22semidirect
129. #19099043C22semidirect
130. #19099042C22semidirect
131. #19099042C22semidirect
132. #19099039C22semidirect
133. #19099039C22semidirect
134. #19099037C22semidirect
135. #19099035C22semidirect
136. #19099035C22semidirect
137. #19099035C22semidirect
139. C4×#11929625C22semidirect
140. C4×#11929624C22semidirect
141. C4×#11929624C22semidirect
142. #19099031C22semidirect
143. C2×C4×D316C22semidirect
144. C4×D4×D79C22semidirect
145. C2×#14579118C22semidirect
146. #117×D79C22semidirect
149. #520×C79C22semidirect
150. #520×C79C22semidirect
151. #519×C79C22semidirect
152. #519×C79C22semidirect
154. C4×#41×C79C22semidirect
155. C4×#41×C79C22semidirect
156. C2×C4×Q8×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
517. #41×C79#41semidirect
693. C4×2−1+4D79semidirect
696. C79#62857semidirect
807. #520C2×D79semidirect
808. #520C2×D79semidirect
811. #519C2×D79semidirect
812. #519C2×D79semidirect
823. C4×#41C2×D79semidirect
824. C4×#41C2×D79semidirect
825. C2×C4×Q8C2×D79semidirect
826. C2×C4×Q8C2×D79semidirect
1084. #41#11929624semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237775112
#237774852
#237774682
#237774392
#237774112
#237773932
#237773612
#237773422
#237773032
#237772972
#237772132
#237771942
#237771422
#237771362
#237770732
#237770702
#237768332
#237768162
#237767852
C2×#190991852
C4×#145792072
#237765992
C4×2−1+4×C792
#6285779