Finite Group Databasebeta

← #35196819

Subgroups — #35196819

Order 20224.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C212yesmaximal, complemented
2#23777192C214yesmaximal, complemented
3#23777189C214yesmaximal, complemented
4#23777182C214yesmaximal, complemented
5#23777175C214yesmaximal, complemented
6#23777169C214yesmaximal, complemented
7#23777163C214yesmaximal, complemented
8#23777161C218yesmaximal, complemented
9#23776883C2116yesmaximal, complemented
10#23776733C211yesmaximal, characteristic, complemented
11#23776727C214yesmaximal, complemented
12C2×#19099109C212yesmaximal, complemented
13#532×D79C214yesmaximal, complemented
14C2×#19099031C211yesmaximal, characteristic, complemented
15C79×#3449C211yesmaximal, characteristic, complemented
16#19099399—232no—
17C2×#14579209C2214yescomplemented
18C2×#14579208C2214yescomplemented
19C2×#14579208C2214yescomplemented
20C2×#14579207C2214yescomplemented
21C2×#14579207C2214yescomplemented
22C2×#14579206C2218yescomplemented
23C2×#14579206C2214yescomplemented
24C22×#11929624C2211yescharacteristic
25C22×#11929624C2218yescomplemented
26C22×#11929624C2212yescomplemented
27C2×#41×D79C2218yescomplemented
28C2×#41×D79C2218yescomplemented
29#19099231C22116yescomplemented
30#19099226C22116yescomplemented
31#19099223C22116yescomplemented
32#19099219C22116yescomplemented
33#19099215C22116yescomplemented
34#19099211C22132yescomplemented
35#19099210C22116yescomplemented
36#19099205C22132yescomplemented
37#19099204C22116yescomplemented
38#19099200C22132yescomplemented
39#19099197C22116yescomplemented
40#19099195C22132yescomplemented
41#19099144C2214yescomplemented
42#19099140C22116yescomplemented
43#19099139C2214yescomplemented
44#19099138C2218yescomplemented
45#19099133C2218yescomplemented
46#19099132C2214yescomplemented
47#19099131C2218yescomplemented
48#19099126C2218yescomplemented
49#19099125C2214yescomplemented
50#19099121C22116yescomplemented
51#19099114C2214yescomplemented
52#19099113C2214yescomplemented
53#19099112C2218yescomplemented
54#19099111C2214yescomplemented
55#19099110C22116yescomplemented
56#19099109C2218yescomplemented
57#19099109C2218yescomplemented
58#19099109C2214yescomplemented
59#19099109C2214yescomplemented
60#19099109C2214yescomplemented
61#19099109C2214yescomplemented
62#19099108C22116yescomplemented
63C2×#14579159C2212yescomplemented
64C4⋊Q8×D79C2214yescomplemented
65C2×#14579157C2212yescomplemented
66#127×D79C2214yescomplemented
67C2×#14579150C2212yescomplemented
68C2×#14579148C2212yescomplemented
69#124×D79C2218yescomplemented
70#19099075C2218yescomplemented
71#19099072C22132yescomplemented
72C2×#14579133C2218yescomplemented
73#121×D79C22116yescomplemented
74#19099031C2218yescomplemented
75#19099031C2214yescomplemented
76#19099031C2214yescomplemented
77C2×#14579126C2212yescomplemented
78C2×#14579123C2212yescomplemented
79C2×C4×C22⋊D79C2218yescomplemented
80C2×(C22⋊D79)⋊C4C2214yescomplemented
81C4×D4×D79C22116yescomplemented
82C2×#14579118C2212yescomplemented
83C22×C4×Dic79C2211yescharacteristic, complemented
84C2×C42×D79C2212yescomplemented
85C22×#41×C79C2212yescomplemented
86#537×C79C2214yescomplemented
87#536×C79C2214yescomplemented
88#535×C79C2214yescomplemented
89#534×C79C2214yescomplemented
90#532×C79C2214yescomplemented
91#525×C79C2218yescomplemented
92C2×#117×C79C2211yescharacteristic, complemented
93#14579209—232no—
94#14579208—232no—
95#14579208—232no—
96#14579207—232no—
97#14579207—232no—
98#14579206—232no—
99#14579206—264no—
100C2×#11929625C2318yes—
101C2×#11929625C2318yes—
102C2×#11929624—216no—
103C2×#11929624—264no—
104C2×#11929624D4116yescomplemented
105C2×#11929624C2314yes—
106C2×#11929624C23116yes—
107C2×#11929624C2314yes—
108C2×#11929624C2318yes—
109C2×#11929624C2318yes—
110C2×#11929624C23116yes—
111C2×#11929624C2314yes—
112C2×#11929624C2314yes—
113C2×#11929624C2314yes—
114C2×#11929624C2314yes—
115C2×#11929623C23116yes—
116C2×#11929623C23116yes—
117C2×#11929623C2318yes—
118C2×#11929623C2318yes—
119#41×D79—264no—
120#41×D79—264no—
121C22×Dic158C2312yes—
122C22×Dic158C2318yes—
123C22×Dic158C2311yescharacteristic
124C2×Q8×D79C2318yes—
125C2×Q8×D79C2318yes—
126C22×D316C2318yes—
127C22×D316C2312yes—
128C22×D316C2311yescharacteristic
129C22×C22⋊D79C23116yes—
130C22×C22⋊D79C2314yes—
131C22×C22⋊D79C2318yes—
132C22×C22⋊D79C2312yes—
133C2×D4×D79C23116yes—
134C2×D4×D79C2318yes—
135C2×D4×D79C23116yes—
136C2×D4×D79C2318yes—
137C2×D4×D79C23116yes—
138C23×Dic79C2312yes—
139C22×C4×D79C23116yes—
140C22×C4×D79C2314yes—
141C22×C4×D79C2314yes—
142C22×C4×D79C2312yes—
143#14579161C2314yes—
144#14579160C23116yes—
145#14579159C2314yes—
146#14579159C2318yes—
147#14579159C2314yes—
148#14579158C2314yes—
149#14579157C23116yes—
150#14579157C2318yes—
151#14579157C2314yes—
152#14579157C2314yes—
153#14579150C2314yes—
154#14579150C2318yes—
155#14579150C2314yes—
156#14579149C2318yes—
157#14579148C2318yes—
158#14579148C2314yes—
159#14579148C2314yes—
160#14579147C23132yes—
161#14579146C23132yes—
162#14579145C23116yes—
163#14579143C23132yes—
164#14579141C23116yes—
165#14579139C23132yes—
166#14579138C23132yes—
167#14579136C23116yes—
168#14579136C23116yes—
169#14579135C23116yes—
170#14579134C23132yes—
171#14579134C23132yes—
172#14579133C23116yes—
173#14579133C23132yes—
174#14579133C23116yes—
175#14579133C23116yes—
176#14579133C23116yes—
177#14579132C23116yes—
178#14579131C23116yes—
179#14579131C23132yes—
180#14579129C23132yes—
181#14579126C2318yes—
182#14579126C2318yes—
183C4×D316C23116yes—
184D4×Dic79C23116yes—
185#14579123C2318yes—
186#14579123C2318yes—
187#14579123C23116yes—
188C4×C22⋊D79C23116yes—
189C4×C22⋊D79C23116yes—
190C4×C22⋊D79C23116yes—
191C4×C22⋊D79C23116yes—
192(C22⋊D79)⋊C4C23116yes—
193(C22⋊D79)⋊C4C23132yes—
194(C22⋊D79)⋊C4C23116yes—
195#14579118C2318yes—
196#14579118C2318yes—
197C2×Dic79⋊C4C2314yes—
198C2×Dic79⋊C4C2318yes—
199C4⋊C4×D79C23116yes—
200C2×C22⋊Dic79C2318yes—
201C2×(C2×D79)⋊C4C2318yes—
202C2×(C2×D79)⋊C4C2314yes—
203C22⋊C4×D79C23132yes—
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2311yescharacteristic
207C2×C4×Dic79C2314yes—
208C2×C4×Dic79C2312yes—
209C2×C4×Dic79C2312yes—
210C2×C4×Dic79C2312yes—
211C42×D79C2318yes—
212C42×D79C2314yes—
213C42×D79C2314yes—
214C2×#41×C79—216no—
215C2×#41×C79C2314yes—
216C2×#41×C79C2314yes—
217C2×#41×C79C2314yes—
218C2×#41×C79C2314yes—
219C22×Q8×C79C2312yes—
220C22×D4×C79C2314yes—
221C22×D4×C79C2312yes—
222C23×C4×C79C2314yes—
223C23×C4×C79C2311yescharacteristic
224C4⋊Q8×C79C2314yes—
225#127×C79C2314yes—
226#124×C79C2318yes—
227#123×C79C23116yes—
228C22⋊Q8×C79C23116yes—
229#121×C79C23116yes—
230#121×C79C23116yes—
231#120×C79C23116yes—
232C4×D4×C79C23116yes—
233#117×C79C2314yes—
234#117×C79C2314yes—
235C2×C4⋊C4×C79C2312yes—
236C2×C22⋊C4×C79C2312yes—
237C2×C42×C79C2312yes—
238C23×D79C24116yes—
239C23×D79C2414yes—
240C23×D79C2412yes—
241#11929625—232no—
242#11929625—232no—
243#11929624—232no—
244#11929624—264no—
245#11929624—232no—
246#11929624—216no—
247#11929624—216no—
248#11929624—216no—
249#11929624—216no—
250#11929624—264no—
251#11929624C2×D4132yescomplemented
252#11929624C2×D4132yescomplemented
253#11929623—264no—
254#11929623—232no—
255#11929623—232no—
256#11929623—264no—
257C2×Dic158—232no—
258C2×Dic158—28no—
259C2×Dic158C2×D418yescomplemented
260C2×Dic158C24116yes—
261C2×Dic158C2414yes—
262C2×Dic158C2414yes—
263C2×Dic158C2414yes—
264Q8×D79—232no—
265Q8×D79—232no—
266C2×D316—232no—
267C2×D316—28no—
268C2×D316C2×D418yescomplemented
269C2×D316C2414yes—
270C2×D316C24116yes—
271C2×D316C2414yes—
272C2×D316C24116yes—
273C2×D316C2414yes—
274C2×C22⋊D79—216no—
275C2×C22⋊D79—264no—
276C2×C22⋊D79—416no—
277C2×C22⋊D79C2×D4116yescomplemented
278C2×C22⋊D79C24116yes—
279C2×C22⋊D79C2418yes—
280C2×C22⋊D79C24116yes—
281C2×C22⋊D79C2418yes—
282C2×C22⋊D79C24116yes—
283C2×C22⋊D79C24116yes—
284C2×C22⋊D79C2418yes—
285D4×D79—232no—
286D4×D79—232no—
287D4×D79—264no—
288D4×D79—264no—
289D4×D79—432no—
290C22×Dic79—44no—
291C22×Dic79C2414yes—
292C22×Dic79C24116yes—
293C22×Dic79C2412yes—
294C22×Dic79C2414yes—
295C22×Dic79C2414yes—
296C22×Dic79C2412yes—
297C22×Dic79C2412yes—
298C2×C4×D79—264no—
299C2×C4×D79—216no—
300C2×C4×D79—48no—
301C2×C4×D79C2×D4116yescomplemented
302C2×C4×D79C24116yes—
303C2×C4×D79C24116yes—
304C2×C4×D79C2418yes—
305C2×C4×D79C2418yes—
306C2×C4×D79C2418yes—
307C2×C4×D79C2418yes—
308C2×C4×D79C2414yes—
309C2×C4×D79C2414yes—
310C4⋊Dic79C24116yes—
311Dic79⋊C4C24116yes—
312Dic79⋊C4C24116yes—
313Dic79⋊C4C24116yes—
314C22⋊Dic79C24116yes—
315C22⋊Dic79C24116yes—
316(C2×D79)⋊C4C24116yes—
317(C2×D79)⋊C4C24132yes—
318(C2×D79)⋊C4C24116yes—
319(C2×D79)⋊C4C24116yes—
320C4×Dic79C2412yes—
321C4×Dic79C2411yescharacteristic
322C4×Dic79C2411yescharacteristic
323C4×Dic79C2418yes—
324C4×Dic79C2418yes—
325C4×Dic79C2412yes—
326C4×Dic79C2412yes—
327C4×Dic79C2414yes—
328C4×Dic79C2414yes—
329C24×C79C2414yes—
330C24×C79C2411yescharacteristic
331#41×C79—216no—
332#41×C79—216no—
333#41×C79—216no—
334#41×C79—216no—
335C2×Q8×C79—28no—
336C2×Q8×C79C2414yes—
337C2×Q8×C79C2414yes—
338C2×D4×C79—216no—
339C2×D4×C79—28no—
340C2×D4×C79C2418yes—
341C2×D4×C79C2418yes—
342C2×D4×C79C2414yes—
343C2×D4×C79C2414yes—
344C2×D4×C79C24116yes—
345C22×C4×C79—216no—
346C22×C4×C79C2×D418yescomplemented
347C22×C4×C79C2418yes—
348C22×C4×C79C2414yes—
349C22×C4×C79C2418yes—
350C22×C4×C79C2414yes—
351C22×C4×C79C2411yescharacteristic
352C22×C4×C79C2412yes—
353C22×C4×C79C2411yescharacteristic
354C22×C4×C79C2412yes—
355C4⋊C4×C79C2418yes—
356C4⋊C4×C79C24116yes—
357C22⋊C4×C79C2418yes—
358C22⋊C4×C79C24132yes—
359C42×C79C2414yes—
360C42×C79C2414yes—
361C23×C79—28no—
362C23×C79—42no—
363C23×C79—48no—
364C23×C79C22×D414yes—
365C23×C79C2518yes—
366C23×C79C2512yes—
367C23×C79C2511yescharacteristic
368C22×D79—28no—
369C22×D79—232no—
370C22×D79—44no—
371C22×D79—432no—
372C22×D79—48no—
373C22×D79C22×D418yes—
374C22×D79C2518yes—
375C22×D79C2514yes—
376Q8×C79—28no—
377Q8×C79—28no—
378D4×C79—216no—
379D4×C79—216no—
380D4×C79—28no—
381D4×C79—28no—
382D4×C79—416no—
383C2×C4×C79—28no—
384C2×C4×C79—216no—
385C2×C4×C79—216no—
386C2×C4×C79—44no—
387C2×C4×C79C22×D418yes—
388C2×C4×C79C22×D414yes—
389C2×C4×C79C22×D418yes—
390C2×C4×C79C22×D414yes—
391C2×C4×C79C2518yes—
392C2×C4×C79C2518yes—
393C2×C4×C79C2511yescharacteristic
394C2×C4×C79C2512yes—
395C2×C4×C79C2511yescharacteristic
396C22⋊D79—216no—
397C22⋊D79—216no—
398C22⋊D79—232no—
399C22⋊D79—232no—
400C22⋊D79—232no—
401C22⋊D79—416no—
402C22⋊D79C22×D4132yes—
403C2×Dic79—28no—
404C2×Dic79—232no—
405C2×Dic79—24no—
406C2×Dic79—28no—
407C2×Dic79—42no—
408C2×Dic79—44no—
409C2×Dic79C22×D418yes—
410C2×Dic79C2512yes—
411C2×Dic79C2514yes—
412C2×Dic79C2518yes—
413C2×Dic79C2514yes—
414C2×Dic79C2512yes—
415D316—232no—
416D316—28no—
417D316—28no—
418D316—416no—
419D316C22×D4116yes—
420C4×D79—232no—
421C4×D79—216no—
422C4×D79—216no—
423C4×D79—232no—
424C4×D79—216no—
425C4×D79—48no—
426C4×D79C22×D4116yes—
427C4×D79C22×D4116yes—
428Dic158—28no—
429Dic158—28no—
430Dic158—232no—
431Dic158C22×D4116yes—
432C22×C79—22no—
433C22×C79—24no—
434C22×C79—28no—
435C22×C79—216no—
436C22×C79—44no—
437C22×C79—88no—
438C22×C79C23×D412yes—
439C22×C79C23×D414yes—
440C22×C79C2611yescharacteristic
441C2×D79—28no—
442C2×D79—28no—
443C2×D79—216no—
444C2×D79—48no—
445C2×D79—832no—
446C2×D79—88no—
447C2×D79C23×D418yes—
448C4×C79—28no—
449C4×C79—28no—
450C4×C79C23×D412yes—
451C4×C79C23×D414yes—
452C4×C79C23×D412yes—
453Dic79—28no—
454Dic79—24no—
455Dic79—22no—
456Dic79C23×D418yes—
457Dic79#58514yescomplemented
458#62812—791nomaximal, Sylow
459C2×C79—22no—
460C2×C79—24no—
461C2×C79—48no—
462C2×C79C24×D411yescharacteristic
463C2×C79C2×#58512yes—
464D79—28no—
465D79—48no—
466C2×#585—792no—
467#3500—794no—
468#3500—794no—
469#3499—794no—
470#3498—794no—
471#3497—794no—
472#3496—794no—
473#3496—798no—
474D4×#41—7916no—
475#3449—794no—
476#3449—791no—
477#3449D7911yescharacteristic, complemented
478C2×#532—792no—
479C2×#532—794no—
480C2×C4×#41—791no—
481C79#6281211yescharacteristic, complemented, Sylow
482#585—15832no—
483C2×2−1+4—794no—
484C2×2−1+4—794no—
485C2×2−1+4—794no—
486C2×H(5,𝔽2)—794no—
487C2×H(5,𝔽2)—794no—
488C2×H(5,𝔽2)—798no—
489C2×H(5,𝔽2)—794no—
490C22×#41—798no—
491C22×#41—798no—
492C22×#41—791no—
493C22×#41—792no—
494C22×#41—798no—
495C22×#41C2×D7912yescomplemented
496#550—7916no—
497D4×Q8—7916no—
498#548—7916no—
499#548—7916no—
500#547—7932no—
501#547—7916no—
502#546—7932no—
503#546—7916no—
504#546—7916no—
505#546—7932no—
506D42—7916no—
507D42—7932no—
508#537—7916no—
509#537—794no—
510#537C2×D7914yescomplemented
511#536—798no—
512#536—798no—
513#536—794no—
514#536C2×D7914yescomplemented
515#535—798no—
516#535—798no—
517#535—794no—
518#535C2×D7914yescomplemented
519#534—7916no—
520#534—794no—
521#534C2×D7914yescomplemented
522#532—794no—
523#532—794no—
524#532—798no—
525#532—798no—
526#532—794no—
527#532—794no—
528#532—794no—
529#532—794no—
530#532—798no—
531#532—7916no—
532#532—7916no—
533#532—794no—
534#532C2×D7914yescomplemented
535C2×C4⋊Q8—792no—
536C2×C4⋊Q8—794no—
537C2×#127—792no—
538C2×#127—794no—
539C2×#124—792no—
540C2×#124—792no—
541C2×#124—798no—
542#525—7932no—
543#525—798no—
544#525C2×D7918yescomplemented
545C2×#121—798no—
546C2×#121—7916no—
547C4×#41—798no—
548C4×#41—794no—
549C4×#41—794no—
550C2×C4×Q8—792no—
551C2×C4×D4—798no—
552C2×C4×D4—7916no—
553C2×C4×D4—792no—
554C2×C4×D4—794no—
555C2×#117—792no—
556C2×#117C2×D7911yescharacteristic, complemented
557C22×C42—791no—
558C22×C42—792no—
5592−1+4—15832no—
5602−1+4—15832no—
5612−1+4—15832no—
562H(5,𝔽2)—15864no—
563H(5,𝔽2)—15832no—
564H(5,𝔽2)—15832no—
565H(5,𝔽2)—15832no—
566C2×#41—216no—
567C2×#41—798no—
568C2×#41—798no—
569C2×#41—798no—
570C2×#41—7916no—
571C2×#41—7916no—
572C2×#41—798no—
573C2×#41—7916no—
574C2×#41—794no—
575C2×#41—794no—
576C2×#41—7916no—
577C2×#41—794no—
578C2×#41—794no—
579C2×#41—794no—
580C2×#41—794no—
581C2×#41—798no—
582C2×#41—7916no—
583C2×#41—798no—
584C2×#41—15864no—
585C2×#41—15864no—
586C2×#41—15864no—
587C2×#41—15816no—
588C2×#41C22×D7914yes—
589C2×#41C22×D7914yes—
590C2×#41C22×D7914yes—
591C2×#41C22×D7914yes—
592C22×Q8—798no—
593C22×Q8—798no—
594C22×Q8—791no—
595C22×Q8—792no—
596C22×Q8—798no—
597C22×Q8C22×D7912yes—
598C22×D4—798no—
599C22×D4—7916no—
600C22×D4—792no—
601C22×D4—794no—
602C22×D4—7916no—
603C22×D4—7916no—
604C22×D4—798no—
605C22×D4—7916no—
606C22×D4—798no—
607C22×D4—791no—
608C22×D4—792no—
609C22×D4—798no—
610C22×D4C22×D7914yes—
611C22×D4C22×D7912yes—
612C23×C4—792no—
613C23×C4—794no—
614C23×C4—792no—
615C23×C4—7916no—
616C23×C4—794no—
617C23×C4C22×D7914yes—
618C23×C4C22×D7911yescharacteristic
619C4⋊Q8—794no—
620C4⋊Q8—794no—
621C4⋊Q8—798no—
622C4⋊Q8—7916no—
623C4⋊Q8—794no—
624C4⋊Q8C22×D7914yes—
625#127—794no—
626#127—794no—
627#127—798no—
628#127—7916no—
629#127—794no—
630#127C22×D7914yes—
631#124—794no—
632#124—794no—
633#124—798no—
634#124—794no—
635#124—794no—
636#124—798no—
637#124—7932no—
638#124—798no—
639#124C22×D7918yes—
640#123—7932no—
641#123—7932no—
642#123—7916no—
643#123C22×D79116yes—
644C22⋊Q8—7932no—
645C22⋊Q8—7916no—
646C22⋊Q8—7932no—
647C22⋊Q8C22×D79116yes—
648#121—7916no—
649#121—7916no—
650#121—7916no—
651#121—7916no—
652#121—7916no—
653#121—7932no—
654#121—7916no—
655#121—7916no—
656#121—7916no—
657#121—7932no—
658#121—7932no—
659#121C22×D79116yes—
660#121C22×D79116yes—
661#120—7932no—
662#120—7932no—
663#120—7916no—
664#120C22×D79116yes—
665C4×Q8—798no—
666C4×Q8—798no—
667C4×D4—7916no—
668C4×D4—7916no—
669C4×D4—7916no—
670C4×D4—7916no—
671C4×D4—7916no—
672C4×D4—798no—
673C4×D4—798no—
674C4×D4—7916no—
675C4×D4—7916no—
676C4×D4—7916no—
677C4×D4—7932no—
678C4×D4—7916no—
679C4×D4C22×D79116yes—
680#117—798no—
681#117—798no—
682#117C22×D7914yes—
683#117C22×D7914yes—
684C2×C4⋊C4—794no—
685C2×C4⋊C4—798no—
686C2×C4⋊C4—7916no—
687C2×C4⋊C4C22×D7912yes—
688C2×C22⋊C4—798no—
689C2×C22⋊C4—794no—
690C2×C22⋊C4—798no—
691C2×C22⋊C4—7932no—
692C2×C22⋊C4C22×D7912yes—
693C2×C42—791no—
694C2×C42—794no—
695C2×C42—792no—
696C2×C42—794no—
697C2×C42—792no—
698C2×C42—792no—
699C2×C42—791no—
700C2×C42—798no—
701C2×C42—794no—
702C2×C42—794no—
703C2×C42C22×D7912yes—
704C24—792no—
705C24—7916no—
706C24—794no—
707C24C23×D7914yes—
708C24C23×D7911yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—7932no—
714#41—7932no—
715#41—15864no—
716#41—15864no—
717#41—15832no—
718#41—15832no—
719#41—15864no—
720#41—15832no—
721#41—15832no—
722#41—15864no—
723#41—15832no—
724#41—15832no—
725#41—15816no—
726#41—15816no—
727#41—15816no—
728#41—15816no—
729C2×Q8—28no—
730C2×Q8—794no—
731C2×Q8—7916no—
732C2×Q8—794no—
733C2×Q8—794no—
734C2×Q8—798no—
735C2×Q8—15832no—
736C2×Q8—15832no—
737C2×Q8—15832no—
738C2×Q8—1588no—
739C2×Q8C23×D7914yes—
740C2×Q8C23×D7914yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—31632no—
744C2×D4—31616no—
745C2×D4—7916no—
746C2×D4—798no—
747C2×D4—7916no—
748C2×D4—7916no—
749C2×D4—7916no—
750C2×D4—798no—
751C2×D4—798no—
752C2×D4—7916no—
753C2×D4—7916no—
754C2×D4—794no—
755C2×D4—7916no—
756C2×D4—794no—
757C2×D4—794no—
758C2×D4—798no—
759C2×D4—15832no—
760C2×D4—15832no—
761C2×D4—15864no—
762C2×D4—15832no—
763C2×D4—15864no—
764C2×D4—15864no—
765C2×D4—15816no—
766C2×D4—1588no—
767C2×D4C23×D7918yes—
768C2×D4C23×D7918yes—
769C2×D4C23×D7914yes—
770C2×D4C23×D7914yes—
771C2×D4C23×D79116yes—
772C22×C4—216no—
773C22×C4—3168no—
774C22×C4—3164no—
775C22×C4—794no—
776C22×C4—792no—
777C22×C4—798no—
778C22×C4—792no—
779C22×C4—794no—
780C22×C4—794no—
781C22×C4—7916no—
782C22×C4—792no—
783C22×C4—794no—
784C22×C4—794no—
785C22×C4—7916no—
786C22×C4—798no—
787C22×C4—7916no—
788C22×C4—7916no—
789C22×C4—798no—
790C22×C4—798no—
791C22×C4—15864no—
792C22×C4—15816no—
793C22×C4D4×D7918yescomplemented
794C22×C4C23×D7914yes—
795C22×C4C23×D7918yes—
796C22×C4C23×D7918yes—
797C22×C4C23×D7914yes—
798C22×C4C23×D7911yescharacteristic
799C22×C4C23×D7912yes—
800C22×C4C23×D7911yescharacteristic
801C22×C4C23×D7912yes—
802C4⋊C4—7916no—
803C4⋊C4—7916no—
804C4⋊C4—7916no—
805C4⋊C4—7916no—
806C4⋊C4C23×D79116yes—
807C4⋊C4C23×D7918yes—
808C22⋊C4—7916no—
809C22⋊C4—7916no—
810C22⋊C4—7916no—
811C22⋊C4—7916no—
812C22⋊C4—7916no—
813C22⋊C4—7932no—
814C22⋊C4C23×D79132yes—
815C22⋊C4C23×D7918yes—
816C42—791no—
817C42—791no—
818C42—792no—
819C42—798no—
820C42—794no—
821C42—798no—
822C42—794no—
823C42—792no—
824C42—792no—
825C42C23×D7914yes—
826C42C23×D7914yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—3164no—
831C23—3168no—
832C23—31632no—
833C23—798no—
834C23—794no—
835C23—798no—
836C23—15832no—
837C23—1588no—
838C23C2×D4×D7914yes—
839C23C24×D7918yes—
840C23C24×D7912yes—
841C23C24×D7911yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—7916no—
845Q8—15832no—
846Q8—1588no—
847Q8—1588no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—31616no—
854D4—31616no—
855D4—7932no—
856D4—7916no—
857D4—15832no—
858D4—15832no—
859D4—15832no—
860D4—15832no—
861D4—15816no—
862D4—15816no—
863D4—1588no—
864D4—1588no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—3168no—
870C2×C4—3164no—
871C2×C4—3162no—
872C2×C4—792no—
873C2×C4—794no—
874C2×C4—798no—
875C2×C4—7916no—
876C2×C4—7916no—
877C2×C4—792no—
878C2×C4—794no—
879C2×C4—798no—
880C2×C4—15816no—
881C2×C4—15832no—
882C2×C4—15832no—
883C2×C4—1584no—
884C2×C4—1588no—
885C2×C4—15832no—
886C2×C4—1588no—
887C2×C4—15816no—
888C2×C4—15816no—
889C2×C4C2×D4×D7918yes—
890C2×C4C2×D4×D7914yes—
891C2×C4C2×D4×D7918yes—
892C2×C4C2×D4×D7914yes—
893C2×C4C24×D7918yes—
894C2×C4C24×D7918yes—
895C2×C4C24×D7911yescharacteristic
896C2×C4C24×D7912yes—
897C2×C4C24×D7911yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—3168no—
905C22—798no—
906C22—6328no—
907C22—63232no—
908C22—1588no—
909C22—15816no—
910C22—1588no—
911C22C22×D4×D7914yes—
912C22C22×D4×D7912yes—
913C22C25×D7911yescharacteristic
914C4—28no—
915C4—28no—
916C4—798no—
917C4—794no—
918C4—1588no—
919C4—1582no—
920C4—1584no—
921C4C22×D4×D7912yes—
922C4C22×D4×D7914yes—
923C4C22×D4×D7912yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—3168no—
928C2—1588no—
929C2C23×D4×D7911yescharacteristic
930C2#585×D7912yes—
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC79×#3449C2
hypercenter#3449D79
hypocenterC79#62812
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. #23777192C2semidirect
3. #23777189C2semidirect
4. #23777182C2semidirect
5. #23777175C2semidirect
6. #23777169C2semidirect
7. #23777163C2semidirect
8. #23777161C2semidirect
9. #23776883C2semidirect
10. #23776733C2semidirect
11. #23776727C2semidirect
12. C2×#19099109C2semidirect
13. #532×D79C2semidirect
14. C2×#19099031C2semidirect
15. C79×#3449C2semidirect
17. C2×#14579209C22semidirect
18. C2×#14579208C22semidirect
19. C2×#14579208C22semidirect
20. C2×#14579207C22semidirect
21. C2×#14579207C22semidirect
22. C2×#14579206C22semidirect
23. C2×#14579206C22semidirect
25. C22×#11929624C22semidirect
26. C22×#11929624C22semidirect
27. C2×#41×D79C22semidirect
28. C2×#41×D79C22semidirect
29. #19099231C22semidirect
30. #19099226C22semidirect
31. #19099223C22semidirect
32. #19099219C22semidirect
33. #19099215C22semidirect
34. #19099211C22semidirect
35. #19099210C22semidirect
36. #19099205C22semidirect
37. #19099204C22semidirect
38. #19099200C22semidirect
39. #19099197C22semidirect
40. #19099195C22semidirect
41. #19099144C22semidirect
42. #19099140C22semidirect
43. #19099139C22semidirect
44. #19099138C22semidirect
45. #19099133C22semidirect
46. #19099132C22semidirect
47. #19099131C22semidirect
48. #19099126C22semidirect
49. #19099125C22semidirect
50. #19099121C22semidirect
51. #19099114C22semidirect
52. #19099113C22semidirect
53. #19099112C22semidirect
54. #19099111C22semidirect
55. #19099110C22semidirect
56. #19099109C22semidirect
57. #19099109C22semidirect
58. #19099109C22semidirect
59. #19099109C22semidirect
60. #19099109C22semidirect
61. #19099109C22semidirect
62. #19099108C22semidirect
63. C2×#14579159C22semidirect
64. C4⋊Q8×D79C22semidirect
65. C2×#14579157C22semidirect
66. #127×D79C22semidirect
67. C2×#14579150C22semidirect
68. C2×#14579148C22semidirect
69. #124×D79C22semidirect
70. #19099075C22semidirect
71. #19099072C22semidirect
72. C2×#14579133C22semidirect
73. #121×D79C22semidirect
74. #19099031C22semidirect
75. #19099031C22semidirect
76. #19099031C22semidirect
77. C2×#14579126C22semidirect
78. C2×#14579123C22semidirect
79. C2×C4×C22⋊D79C22semidirect
80. C2×(C22⋊D79)⋊C4C22semidirect
81. C4×D4×D79C22semidirect
82. C2×#14579118C22semidirect
83. C22×C4×Dic79C22semidirect
84. C2×C42×D79C22semidirect
85. C22×#41×C79C22semidirect
86. #537×C79C22semidirect
87. #536×C79C22semidirect
88. #535×C79C22semidirect
89. #534×C79C22semidirect
90. #532×C79C22semidirect
91. #525×C79C22semidirect
92. C2×#117×C79C22semidirect
104. C2×#11929624D4semidirect
251. #11929624C2×D4semidirect
252. #11929624C2×D4semidirect
259. C2×Dic158C2×D4semidirect
268. C2×D316C2×D4semidirect
277. C2×C22⋊D79C2×D4semidirect
301. C2×C4×D79C2×D4semidirect
346. C22×C4×C79C2×D4semidirect
457. Dic79#585semidirect
477. #3449D79semidirect
481. C79#62812semidirect
495. C22×#41C2×D79semidirect
510. #537C2×D79semidirect
514. #536C2×D79semidirect
518. #535C2×D79semidirect
521. #534C2×D79semidirect
534. #532C2×D79semidirect
544. #525C2×D79semidirect
556. C2×#117C2×D79semidirect
793. C22×C4D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993992
#237771922
#237771892
#237771822
#237771752
#237771692
#237771632
#237771612
#237768832
#237767332
#237767272
C2×#190991092
#532×D792
C2×#190990312
C79×#34492
#6281279