Finite Group Databasebeta

← #33994429

Subgroups — #33994429

Order 18688.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624018C212yesmaximal, complemented
2#22623967C216yesmaximal, complemented
3#22623939C212yesmaximal, complemented
4#22623896C216yesmaximal, complemented
5#22623840C213yesmaximal, complemented
6#22623816C213yesmaximal, complemented
7#22623744C211yesmaximal, characteristic, complemented
8#22623712C211yesmaximal, characteristic, complemented
9#22623685C213yesmaximal, complemented
10#22623677C213yesmaximal, complemented
11#22623611C211yesmaximal, characteristic, complemented
12#22623547C212yesmaximal, complemented
13#22623543C216yesmaximal, complemented
14Q8×#11924027C212yesmaximal, complemented
15#22623482C216yesmaximal, complemented
16#22623359C213yesmaximal, complemented
17#22623355C213yesmaximal, complemented
18#22623223C213yesmaximal, complemented
19C2×#17989139C213yesmaximal, complemented
202−1+4×Dic73C211yesmaximal, characteristic, complemented
21#22623142C211yesmaximal, characteristic, complemented
22C2×#41×Dic73C211yesmaximal, characteristic, complemented
23C73×#3489C211yesmaximal, characteristic, complemented
24C2×#14556638C2211yescharacteristic
25Q8×Dic146C2212yescomplemented
26#17989313C2212yescomplemented
27#17989312C2216yescomplemented
28#17989312C2216yescomplemented
29#17989308C2216yescomplemented
30#17989308C2216yescomplemented
31#17989307C2216yescomplemented
32#17989306C2216yescomplemented
33#17989306C2216yescomplemented
34#17989301C2216yescomplemented
35#17989296C2216yescomplemented
36#17989295C2216yes—
37#17989295C2216yescomplemented
38#17989294C2216yes—
39#17989280C22112yescomplemented
40#17989279C2216yes—
41#17989277C2216yes—
42#17989277C2216yescomplemented
43#17989274C22112yescomplemented
44#17989274C22112yescomplemented
45#17989274C22112yescomplemented
46#17989272C22112yescomplemented
47#17989271C2216yescomplemented
48#17989268C22112yes—
49#17989263C22112yes—
50D4×Dic146C2216yescomplemented
51Q8×C22⋊D73C2212yes—
52Q8×C22⋊D73C2212yescomplemented
53Q8×C22⋊D73C2212yescomplemented
54#17989244C2212yes—
55#17989243C22112yescomplemented
56#17989237C2216yescomplemented
57#17989236C2216yes—
58#17989236C2216yescomplemented
59#17989236C2216yescomplemented
60#17989231C2216yes—
61#17989218C2213yescomplemented
62#17989215C2213yescomplemented
63#17989210C2216yescomplemented
64#17989206C2216yescomplemented
65#17989204C2216yescomplemented
66#17989204C2216yescomplemented
67#17989198C2216yescomplemented
68#17989197C2216yescomplemented
69#17989197C2216yescomplemented
70#17989197C2216yescomplemented
71#17989182C22112yescomplemented
72#17989181C22112yescomplemented
73#17989165C2213yes—
74#17989161C2213yescomplemented
75#17989158C2213yes—
76#17989158C2213yescomplemented
77#17989142C2216yescomplemented
78#17989140C2213yescomplemented
79#17989139C2216yes—
80#17989139C2216yes—
81#17989139C2216yes—
82#17989139C2213yes—
83#17989139C2216yescomplemented
84#17989139C2216yescomplemented
85#17989139C2213yescomplemented
86#17989139C2216yescomplemented
87#17989139C2216yescomplemented
88#17989139C2216yescomplemented
89#17989133C2213yescomplemented
90#17989132C2211yescharacteristic
91#17989132C2213yescomplemented
92C2×#14556590C2213yescomplemented
93C2×#14556589C2213yescomplemented
94#17989123C2213yes—
95#17989123C2213yescomplemented
96#17989118C2213yes—
97#17989118C22112yescomplemented
98#17989118C2216yescomplemented
99#17989118C2213yescomplemented
100#17989117C2216yes—
101#17989117C2216yescomplemented
102#17989116C2216yescomplemented
103#17989114C2216yescomplemented
104#17989114C22112yescomplemented
105#17989114C2216yescomplemented
106C2×#14556581C2216yescomplemented
107#17989098C2213yes—
108#17989093C2216yes—
109#17989093C2216yes—
110C2×#14556570C2213yes—
111C2×#14556568C2216yes—
112#17989070C2211yescharacteristic
113#17989070C2213yescomplemented
114#17989070C2216yescomplemented
115#17989068C2213yescomplemented
116#17989066C2216yescomplemented
117#17989065C2212yescomplemented
118#17989065C2213yescomplemented
119#17989064C2213yescomplemented
120#17989063C2212yescomplemented
121#41×Dic73C2211yescharacteristic
122#41×Dic73C2213yes—
123#41×Dic73C2211yescharacteristic
124#41×Dic73C2213yes—
125#41×Dic73C2213yes—
126#41×Dic73C2213yes—
127#41×Dic73C2211yescharacteristic
128#41×Dic73C2211yescharacteristic
129#41×Dic73C2216yescomplemented
130#41×Dic73C2213yescomplemented
131#17989055C2213yescomplemented
132C4×#11924027C2216yes—
133C4×#11924027C2216yescomplemented
134C4×#11924027C2216yescomplemented
135C2×Q8×Dic73C2211yescharacteristic
136C2×Q8×Dic73C2211yescharacteristic
137C2×Q8×Dic73C2212yescomplemented
138C2×Q8×Dic73C2213yescomplemented
139C2×#14556556C2216yescomplemented
140C2×#14556556C2213yescomplemented
141C4×Q8×D73C2212yescomplemented
142C2×D4×Dic73C2213yes—
143C2×D4×Dic73C2213yes—
144C2×#14556550C2213yes—
145C2×#14556547C2216yes—
146C22×C4×Dic73C2213yes—
147C2×2−1+4×C73C2211yescharacteristic
148C22×#41×C73C2211yescharacteristic
149D4×Q8×C73C2212yes—
150#548×C73C2212yes—
151#547×C73C2216yes—
152#546×C73C2216yes—
153#537×C73C2213yes—
154#536×C73C2213yes—
155#525×C73C2213yes—
156C2×C22⋊Q8×C73C2213yes—
157#520×C73C2211yescharacteristic
158#14556638—28no—
159C2×#11924028C2313yes—
160C2×#11924027C2312yes—
161C2×#11924027C2316yes—
162C2×#11924027C2316yes—
163C22×Dic146C2313yes—
164C22×Dic146C2316yes—
165C2×Q8×D73C2312yes—
166C23×Dic73C2313yes—
167C23×Dic73C2313yes—
168#14556591C2316yes—
169#14556590C2313yes—
170#14556590C2316yes—
171#14556590C2316yes—
172#14556590C2316yes—
173#14556590C2311yescharacteristic
174#14556590C2316yes—
175#14556589C2313yes—
176#14556589C2316yes—
177#14556589C2316yes—
178#14556589C2316yes—
179#14556589C2316yes—
180#14556587C2311yescharacteristic
181#14556586C2316yes—
182#14556586C2316yes—
183#14556586C23112yes—
184#14556584C23112yes—
185#14556584C2316yes—
186#14556584C23112yes—
187#14556584C23112yes—
188#14556584C23112yes—
189#14556584C23112yes—
190#14556584C2316yes—
191#14556583C2316yes—
192#14556582C2313yes—
193#14556582C2313yes—
194#14556582C23112yes—
195#14556582C23112yes—
196#14556582C2316yes—
197#14556581C2316yes—
198#14556581C23112yes—
199#14556581C23112yes—
200#14556581C23112yes—
201#14556581C23112yes—
202#14556581C2316yes—
203#14556581C23112yes—
204#14556580C2313yes—
205#14556578C2313yes—
206#14556578C2316yes—
207#14556578C23112yes—
208#14556577C2312yes—
209#14556577C2316yes—
210#14556577C23112yes—
211#14556575C2316yes—
212#14556575C2316yes—
213#14556574C23112yes—
214#14556574C2316yes—
215#14556573C23112yes—
216#14556572C23112yes—
217#14556572C23112yes—
218#14556572C2316yes—
219#14556572C23112yes—
220#14556572C2316yes—
221#14556571C23112yes—
222#14556570C2313yes—
223#14556570C2316yes—
224#14556570C2316yes—
225#14556570C2316yes—
226#14556570C2313yes—
227#14556570C2316yes—
228#14556570C2316yes—
229#14556570C23112yes—
230#14556568C2316yes—
231#14556568C23112yes—
232#14556568C23112yes—
233#14556568C23112yes—
234#14556568C23112yes—
235#14556568C2316yes—
236#14556568C2316yes—
237#14556568C2316yes—
238#14556568C23112yes—
239#14556567C2316yes—
240#14556567C2316yes—
241#14556567C2316yes—
242#14556565C2311yescharacteristic
243#14556565C2313yes—
244#14556563C2312yes—
245#14556563C2316yes—
246#14556563C2316yes—
247#14556563C2316yes—
248#14556563C23112yes—
249#14556562C2316yes—
250#14556560C2316yes—
251Q8×Dic73C2313yes—
252Q8×Dic73C2313yes—
253Q8×Dic73C2316yes—
254Q8×Dic73C2316yes—
255Q8×Dic73C2316yes—
256Q8×Dic73C2313yes—
257Q8×Dic73C2313yes—
258Q8×Dic73C2312yes—
259Q8×Dic73C2311yescharacteristic
260Q8×Dic73C2311yescharacteristic
261Q8×Dic73C2316yes—
262Q8×Dic73C2316yes—
263Q8×Dic73C2313yes—
264Q8×Dic73C2311yescharacteristic
265Q8×Dic73C2313yes—
266Q8×Dic73C2311yescharacteristic
267C4×Dic146C2316yes—
268C4×Dic146C2316yes—
269C4×Dic146C2316yes—
270C4×Dic146C2316yes—
271#14556556C23112yes—
272#14556556C2316yes—
273#14556556C2316yes—
274#14556556C2313yes—
275#14556556C2316yes—
276#14556556C2316yes—
277#14556556C23112yes—
278#14556556C23112yes—
279#14556556C2313yes—
280#14556556C2316yes—
281D4×Dic73C2311yescharacteristic
282D4×Dic73C2313yes—
283D4×Dic73C2316yes—
284D4×Dic73C2316yes—
285D4×Dic73C2313yes—
286D4×Dic73C2316yes—
287D4×Dic73C2313yes—
288D4×Dic73C2313yes—
289D4×Dic73C2313yes—
290D4×Dic73C2316yes—
291D4×Dic73C23112yes—
292D4×Dic73C2316yes—
293D4×Dic73C2316yes—
294D4×Dic73C2313yes—
295D4×Dic73C2313yes—
296D4×Dic73C2313yes—
297D4×Dic73C2316yes—
298D4×Dic73C2313yes—
299D4×Dic73C2316yes—
300D4×Dic73C2316yes—
301#14556553C2313yes—
302#14556553C2311yescharacteristic
303C4×C22⋊D73C2316yes—
304C4×C22⋊D73C2316yes—
305C4×C22⋊D73C2316yes—
306C4×C22⋊D73C2316yes—
307C4×C22⋊D73C23112yes—
308#14556551C2316yes—
309#14556551C2316yes—
310#14556551C2312yes—
311#14556551C2316yes—
312#14556551C2316yes—
313#14556551C2316yes—
314#14556550C2313yes—
315#14556550C2313yes—
316#14556550C2316yes—
317#14556550C2316yes—
318#14556550C23112yes—
319#14556550C2313yes—
320#14556550C2316yes—
321#14556550C2316yes—
322#14556550C2313yes—
323#14556550C2313yes—
324#14556549C2316yes—
325#14556549C2316yes—
326#14556549C2316yes—
327#14556548C2316yes—
328#14556547C2316yes—
329#14556547C23112yes—
330#14556547C23112yes—
331#14556547C23112yes—
332#14556547C2316yes—
333#14556547C2316yes—
334#14556547C23112yes—
335#14556547C2316yes—
336C2×C4⋊Dic73C2313yes—
337C2×C4⋊Dic73C2316yes—
338C2×C4⋊Dic73C2316yes—
339C2×C4⋊Dic73C2313yes—
340C2×C4⋊Dic73C2313yes—
341C2×#11924007C2316yes—
342C2×#11924007C2316yes—
343C2×#11924007C2316yes—
344C2×#11924007C2316yes—
345C2×#11924007C2316yes—
346C4⋊C4×D73C2316yes—
347C2×C22⋊Dic73C2316yes—
348C2×C22⋊Dic73C2316yes—
349C2×C4×Dic73C2313yes—
350C2×C4×Dic73C2313yes—
351C2×C4×Dic73C2313yes—
352C2×C4×Dic73C2311yescharacteristic
353C2×C4×Dic73C2313yes—
354C2×C4×Dic73C2313yes—
355C2×C4×Dic73C2313yes—
356C2×C4×Dic73C2313yes—
357C2×C4×Dic73C2313yes—
358C2×C4×Dic73C2316yes—
359C2×C4×Dic73C2313yes—
360C2×C4×Dic73C2313yes—
361C2×C4×Dic73C2313yes—
362C2×C4×Dic73C2316yes—
363C2×C4×Dic73C2316yes—
364C42×D73C2316yes—
3652−1+4×C73—28no—
366C2×#41×C73—28no—
367C2×#41×C73C2313yes—
368C2×#41×C73C2313yes—
369C2×#41×C73C2313yes—
370C2×#41×C73C2316yes—
371C2×#41×C73C2311yescharacteristic
372C2×#41×C73C2311yescharacteristic
373C22×Q8×C73C2313yes—
374C22×Q8×C73C2311yescharacteristic
375C22×Q8×C73C2312yes—
376C22×D4×C73C2313yes—
377C23×C4×C73C2313yes—
378C4⋊Q8×C73C2316yes—
379#124×C73C2316yes—
380#123×C73C23112yes—
381#123×C73C2316yes—
382C22⋊Q8×C73C2313yes—
383C22⋊Q8×C73C2313yes—
384C22⋊Q8×C73C2316yes—
385C22⋊Q8×C73C2316yes—
386C22⋊Q8×C73C2316yes—
387C22⋊Q8×C73C2316yes—
388#121×C73C2311yescharacteristic
389#121×C73C2313yes—
390#121×C73C23112yes—
391#121×C73C2316yes—
392#120×C73C2316yes—
393C4×Q8×C73C2312yes—
394C4×D4×C73C2316yes—
395C4×D4×C73C2316yes—
396C4×D4×C73C2316yes—
397#117×C73C2313yes—
398C2×C4⋊C4×C73C2313yes—
399C2×C4⋊C4×C73C2316yes—
400C2×C22⋊C4×C73C2316yes—
401#11924028—212no—
402#11924027—224no—
403#11924027—28no—
404#11924027—412no—
405C2×Dic146—212no—
406C2×Dic146—412no—
407C2×Dic146C2413yes—
408C2×Dic146C2412yes—
409C2×Dic146C2416yes—
410C2×Dic146C2416yes—
411C2×Dic146C24112yes—
412Q8×D73—28no—
413C2×D292C2411yescharacteristic
414C2×C22⋊D73C2412yes—
415C2×C22⋊D73C2412yes—
416C2×C22⋊D73C2416yes—
417C2×C22⋊D73C2412yes—
418C2×C22⋊D73C2416yes—
419C22×Dic73—212no—
420C22×Dic73—46no—
421C22×Dic73C2413yes—
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2412yes—
424C22×Dic73C2413yes—
425C22×Dic73C2413yes—
426C22×Dic73C2413yes—
427C22×Dic73C2413yes—
428C22×Dic73C2413yes—
429C22×Dic73C2413yes—
430C22×Dic73C2416yes—
431C22×Dic73C2413yes—
432C22×Dic73C2413yes—
433C22×Dic73C2413yes—
434C22×Dic73C2416yes—
435C22×Dic73C2416yes—
436C22×Dic73C2411yescharacteristic
437C2×C4×D73C2412yes—
438C2×C4×D73C2416yes—
439C2×C4×D73C2416yes—
440C4⋊Dic73C2413yes—
441C4⋊Dic73C2416yes—
442C4⋊Dic73C2413yes—
443C4⋊Dic73C2416yes—
444C4⋊Dic73C24112yes—
445C4⋊Dic73C2413yes—
446C4⋊Dic73C2413yes—
447C4⋊Dic73C2413yes—
448C4⋊Dic73C2416yes—
449C4⋊Dic73C2416yes—
450C4⋊Dic73C2416yes—
451C4⋊Dic73C2416yes—
452C4⋊Dic73C2411yescharacteristic
453C4⋊Dic73C2416yes—
454#11924007C24112yes—
455#11924007C2416yes—
456#11924007C2416yes—
457#11924007C2416yes—
458#11924007C2416yes—
459#11924007C2416yes—
460#11924007C24112yes—
461#11924007C24112yes—
462#11924007C24112yes—
463#11924007C24112yes—
464#11924007C2412yes—
465#11924007C2416yes—
466#11924007C2416yes—
467#11924007C2416yes—
468#11924007C2416yes—
469C22⋊Dic73C2416yes—
470C22⋊Dic73C2416yes—
471C22⋊Dic73C24112yes—
472C22⋊Dic73C2416yes—
473C22⋊Dic73C2416yes—
474C22⋊Dic73C2416yes—
475C22⋊Dic73C2416yes—
476C22⋊Dic73C2416yes—
477C22⋊Dic73C2416yes—
478C22⋊Dic73C2416yes—
479C22⋊Dic73C2412yes—
480C22⋊Dic73C2416yes—
481#11924005C2412yes—
482#11924005C2416yes—
483#11924005C2412yes—
484#11924005C2416yes—
485#11924005C2416yes—
486#11924005C2416yes—
487C4×Dic73C2413yes—
488C4×Dic73C2416yes—
489C4×Dic73C2416yes—
490C4×Dic73C2411yescharacteristic
491C4×Dic73C2411yescharacteristic
492C4×Dic73C2411yescharacteristic
493C4×Dic73C2411yescharacteristic
494C4×Dic73C2416yes—
495C4×Dic73C2413yes—
496C4×Dic73C2413yes—
497C4×Dic73C2413yes—
498C4×Dic73C2413yes—
499C4×Dic73C2413yes—
500C4×Dic73C2413yes—
501C4×Dic73C2413yes—
502C4×Dic73C2413yes—
503C4×Dic73C2413yes—
504C4×Dic73C2413yes—
505C4×Dic73C2413yes—
506C4×Dic73C24112yes—
507C4×Dic73C24112yes—
508C4×Dic73C2416yes—
509C4×Dic73C2416yes—
510C24×C73C2413yes—
511#41×C73—24no—
512#41×C73—212no—
513#41×C73—224no—
514#41×C73—212no—
515#41×C73—212no—
516#41×C73#4118yescomplemented
517C2×Q8×C73—24no—
518C2×Q8×C73—28no—
519C2×Q8×C73—212no—
520C2×Q8×C73C2413yes—
521C2×Q8×C73C2416yes—
522C2×Q8×C73C2413yes—
523C2×Q8×C73C2411yescharacteristic
524C2×D4×C73—212no—
525C2×D4×C73C2412yes—
526C2×D4×C73C2416yes—
527C2×D4×C73C2411yescharacteristic
528C2×D4×C73C2416yes—
529C2×D4×C73C2413yes—
530C2×D4×C73C2416yes—
531C2×D4×C73C2413yes—
532C22×C4×C73—212no—
533C22×C4×C73C2416yes—
534C22×C4×C73C2413yes—
535C22×C4×C73C2416yes—
536C22×C4×C73C2413yes—
537C22×C4×C73C2413yes—
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2413yes—
540C22×C4×C73C2416yes—
541C22×C4×C73C2413yes—
542C4⋊C4×C73C2413yes—
543C4⋊C4×C73C2416yes—
544C4⋊C4×C73C2416yes—
545C4⋊C4×C73C24112yes—
546C4⋊C4×C73C2411yescharacteristic
547C4⋊C4×C73C2416yes—
548C22⋊C4×C73C2416yes—
549C22⋊C4×C73C24112yes—
550C22⋊C4×C73C2416yes—
551C22⋊C4×C73C2412yes—
552C22⋊C4×C73C2416yes—
553C22⋊C4×C73C2416yes—
554C42×C73C2416yes—
555C23×C73—26no—
556C23×C73—26no—
557C23×C73—43no—
558C23×C73C2513yes—
559C23×C73C2512yes—
560C23×C73C2513yes—
561C23×C73C2511yescharacteristic
562C22×D73C2512yes—
563Q8×C73—26no—
564Q8×C73—212no—
565Q8×C73—26no—
566Q8×C73C2×#4114yes—
567D4×C73—212no—
568D4×C73—212no—
569D4×C73—24no—
570D4×C73—26no—
571D4×C73—22no—
572D4×C73—46no—
573D4×C73C2×#41112yes—
574C2×C4×C73—26no—
575C2×C4×C73—212no—
576C2×C4×C73—22no—
577C2×C4×C73—26no—
578C2×C4×C73—26no—
579C2×C4×C73—26no—
580C2×C4×C73—212no—
581C2×C4×C73—46no—
582C2×C4×C73C2×#41112yes—
583C2×C4×C73C2512yes—
584C2×C4×C73C2516yes—
585C2×C4×C73C2516yes—
586C2×C4×C73C2511yescharacteristic
587C2×C4×C73C2513yes—
588C2×C4×C73C2513yes—
589C2×C4×C73C2511yescharacteristic
590C22⋊D73—212no—
591C22⋊D73—24no—
592C22⋊D73—24no—
593C22⋊D73—24no—
594C22⋊D73—46no—
595C2×Dic73—212no—
596C2×Dic73—26no—
597C2×Dic73—26no—
598C2×Dic73—26no—
599C2×Dic73—26no—
600C2×Dic73—26no—
601C2×Dic73—24no—
602C2×Dic73—22no—
603C2×Dic73—26no—
604C2×Dic73—26no—
605C2×Dic73—43no—
606C2×Dic73—43no—
607C2×Dic73—43no—
608C2×Dic73—46no—
609C2×Dic73—46no—
610C2×Dic732−1+414yescomplemented
611C2×Dic73C2513yes—
612C2×Dic73C2511yescharacteristic
613C2×Dic73C2513yes—
614C2×Dic73C2512yes—
615C2×Dic73C2513yes—
616C2×Dic73C2513yes—
617C2×Dic73C2516yes—
618C2×Dic73C2516yes—
619C2×Dic73C2511yescharacteristic
620C2×Dic73C2511yescharacteristic
621C2×Dic73C2511yescharacteristic
622D292—22no—
623C4×D73—212no—
624C4×D73—24no—
625C4×D73—46no—
626Dic146—212no—
627Dic146—26no—
628Dic146—24no—
629Dic146—212no—
630Dic146—412no—
631C22×C73—21no—
632C22×C73—23no—
633C22×C73—23no—
634C22×C73—21no—
635C22×C73—22no—
636C22×C73—23no—
637C22×C73—23no—
638C22×C73—22no—
639C22×C73—23no—
640C22×C73—22no—
641C22×C73—412no—
642C22×C73C22×#4116yes—
643C22×C73C2×2−1+412yes—
644C22×C73C2611yescharacteristic
645C2×D73—22no—
646C2×D73—22no—
647C2×D73—22no—
648C4×C73—21no—
649C4×C73—23no—
650C4×C73—26no—
651C4×C73—22no—
652C4×C73—26no—
653C4×C73C22×#4112yes—
654C4×C73C22×#4116yes—
655Dic73—26no—
656Dic73—22no—
657Dic73—23no—
658Dic73—23no—
659Dic73—26no—
660Dic73—23no—
661Dic73—23no—
662Dic73—21no—
663Dic73C2×2−1+412yes—
664Dic73C2×2−1+412yes—
665Dic73#58512yes—
666#62805—731nomaximal, Sylow
667C2×C73—22no—
668C2×C73—26no—
669C2×C73—42no—
670C2×C73—43no—
671C2×C73C23×#4111yescharacteristic
672C2×C73C22×2−1+411yescharacteristic
673C2×C73C2×#58511yescharacteristic
674D73—42no—
675#3523—732no—
676#3520—736no—
677#3518—732no—
678#3515—736no—
679#3511—733no—
680#3509—733no—
681#3503—731no—
682#3499—731no—
683#3495—733no—
684#3495—733no—
685#3489—731no—
686#3489D7311yescharacteristic, complemented
687#3482—732no—
688#3482—736no—
689Q8×#41—732no—
690#3475—736no—
691#3461—733no—
692#3461—733no—
693#3444—733no—
694C2×#533—733no—
695C4×2−1+4—731no—
696C4×2−1+4—731no—
697C2×C4×#41—731no—
698C73#6280511yescharacteristic, complemented, Sylow
699C2×2−1+4—731no—
700C2×2−1+4C2×D7311yescharacteristic
701C22×#41C2×D7311yescharacteristic
702Q82—732no—
703#557—736no—
704#557—736no—
705#557—732no—
706#556—736no—
707#556—736no—
708#556—736no—
709#556—736no—
710#556—736no—
711#555—736no—
712#554—736no—
713#554—736no—
714#554—736no—
715#554—736no—
716#553—7312no—
717#552—7312no—
718#552—7312no—
719#552—7312no—
720#552—736no—
721#552—736no—
722#552—736no—
723#552—736no—
724#552—7312no—
725#551—7312no—
726#551—7312no—
727D4×Q8—732no—
728D4×Q8—732no—
729D4×Q8—732no—
730D4×Q8—736no—
731D4×Q8C2×D7312yes—
732#548—732no—
733#548—7312no—
734#548C2×D7312yes—
735#547—736no—
736#547—736no—
737#547—736no—
738#547—736no—
739#547C2×D7316yes—
740#546—736no—
741#546C2×D7316yes—
742#544—733no—
743#544—733no—
744#542—736no—
745#542—736no—
746#542—736no—
747#542—736no—
748#541—736no—
749#541—736no—
750#541—736no—
751#541—736no—
752#539—7312no—
753#539—7312no—
754#537—733no—
755#537C2×D7313yes—
756#536—733no—
757#536—733no—
758#536—733no—
759#536C2×D7313yes—
760#533—736no—
761#533—733no—
762#533—736no—
763#533—736no—
764#533—736no—
765#533—736no—
766#533—736no—
767#533—736no—
768#533—736no—
769#533—733no—
770#533—736no—
771#533—733no—
772#532—733no—
773#532—731no—
774#532—733no—
775C2×C4⋊Q8—733no—
776C2×C4⋊Q8—733no—
777#529—736no—
778#529—736no—
779#529—736no—
780#529—7312no—
781#529—733no—
782#529—733no—
783#529—733no—
784#529—733no—
785#529—7312no—
786#529—736no—
787#529—736no—
788#529—736no—
789C2×#125—736no—
790#525—733no—
791#525—736no—
792#525—736no—
793#525C2×D7313yes—
794C2×C22⋊Q8—733no—
795C2×C22⋊Q8—736no—
796C2×C22⋊Q8C2×D7313yes—
797#520—731no—
798#520—733no—
799#520—736no—
800#520—736no—
801#520—733no—
802#520C2×D7311yescharacteristic
803#519—733no—
804#519—732no—
805#519—732no—
806#519—733no—
807C4×#41—731no—
808C4×#41—733no—
809C4×#41—733no—
810C4×#41—731no—
811C4×#41—731no—
812C4×#41—733no—
813C4×#41—733no—
814C4×#41—731no—
815C4×#41—733no—
816C4×#41—736no—
817C4×#41—736no—
818C4×#41—736no—
819C4×#41—736no—
820C4×#41—733no—
821C2×C4×Q8—731no—
822C2×C4×Q8—731no—
823C2×C4×Q8—733no—
824C2×C4×Q8—732no—
825C2×C4×Q8—732no—
826C2×C4×Q8—733no—
827C2×C4×Q8—736no—
828C2×C4×D4—733no—
829C2×C4×D4—733no—
830C2×#117—733no—
831C2×#117—736no—
832C22×C42—733no—
8332−1+4—28no—
8342−1+4—1468no—
835C2×#41—28no—
836C2×#41—736no—
837C2×#41—732no—
838C2×#41—736no—
839C2×#41—733no—
840C2×#41C22×D7313yes—
841C2×#41C22×D7313yes—
842C2×#41C22×D7311yescharacteristic
843C2×#41C22×D7313yes—
844C2×#41C22×D7316yes—
845C2×#41C22×D7311yescharacteristic
846C22×Q8—732no—
847C22×Q8—736no—
848C22×Q8—733no—
849C22×Q8C22×D7311yescharacteristic
850C22×Q8C22×D7313yes—
851C22×Q8C22×D7312yes—
852C22×D4C22×D7313yes—
853C23×C4—733no—
854C23×C4—733no—
855C23×C4C22×D7313yes—
856C4⋊Q8—733no—
857C4⋊Q8—736no—
858C4⋊Q8—736no—
859C4⋊Q8—736no—
860C4⋊Q8—736no—
861C4⋊Q8—733no—
862C4⋊Q8—736no—
863C4⋊Q8—736no—
864C4⋊Q8—736no—
865C4⋊Q8—731no—
866C4⋊Q8—736no—
867C4⋊Q8—736no—
868C4⋊Q8C22×D7316yes—
869#127—731no—
870#126—736no—
871#126—736no—
872#126—7312no—
873#126—736no—
874#126—736no—
875#126—7312no—
876#126—7312no—
877#126—7312no—
878#126—7312no—
879#126—7312no—
880#125—736no—
881#125—7312no—
882#125—7312no—
883#125—7312no—
884#125—733no—
885#125—733no—
886#125—736no—
887#125—7312no—
888#125—7312no—
889#125—736no—
890#125—7312no—
891#125—7312no—
892#125—736no—
893#124—733no—
894#124—733no—
895#124—736no—
896#124—7312no—
897#124—732no—
898#124—736no—
899#124—7312no—
900#124C22×D7316yes—
901#123—736no—
902#123—736no—
903#123—7312no—
904#123—7312no—
905#123—7312no—
906#123—736no—
907#123—7312no—
908#123—736no—
909#123—736no—
910#123—7312no—
911#123C22×D7316yes—
912#123C22×D73112yes—
913C22⋊Q8—736no—
914C22⋊Q8—736no—
915C22⋊Q8—736no—
916C22⋊Q8—733no—
917C22⋊Q8—736no—
918C22⋊Q8—736no—
919C22⋊Q8—736no—
920C22⋊Q8—733no—
921C22⋊Q8—736no—
922C22⋊Q8—7312no—
923C22⋊Q8—736no—
924C22⋊Q8—7312no—
925C22⋊Q8—736no—
926C22⋊Q8—7312no—
927C22⋊Q8—7312no—
928C22⋊Q8—7312no—
929C22⋊Q8—736no—
930C22⋊Q8—736no—
931C22⋊Q8—736no—
932C22⋊Q8—7312no—
933C22⋊Q8—7312no—
934C22⋊Q8C22×D7313yes—
935C22⋊Q8C22×D7316yes—
936C22⋊Q8C22×D7316yes—
937C22⋊Q8C22×D7316yes—
938C22⋊Q8C22×D7313yes—
939C22⋊Q8C22×D7316yes—
940#121—732no—
941#121—736no—
942#121—736no—
943#121—736no—
944#121—7312no—
945#121—736no—
946#121—731no—
947#121—733no—
948#121C22×D7311yescharacteristic
949#121C22×D7313yes—
950#121C22×D73112yes—
951#121C22×D7316yes—
952#120—736no—
953#120C22×D7316yes—
954C4×Q8—731no—
955C4×Q8—736no—
956C4×Q8—733no—
957C4×Q8—731no—
958C4×Q8—733no—
959C4×Q8—733no—
960C4×Q8—731no—
961C4×Q8—731no—
962C4×Q8—733no—
963C4×Q8—733no—
964C4×Q8—736no—
965C4×Q8—736no—
966C4×Q8—732no—
967C4×Q8—736no—
968C4×Q8—733no—
969C4×Q8—736no—
970C4×Q8—736no—
971C4×Q8—736no—
972C4×Q8—733no—
973C4×Q8—736no—
974C4×Q8—736no—
975C4×Q8—7312no—
976C4×Q8—7312no—
977C4×Q8—7312no—
978C4×Q8—733no—
979C4×Q8—736no—
980C4×Q8—736no—
981C4×Q8—736no—
982C4×Q8—736no—
983C4×Q8—736no—
984C4×Q8C22×D7312yes—
985C4×D4—733no—
986C4×D4—733no—
987C4×D4—733no—
988C4×D4—736no—
989C4×D4—736no—
990C4×D4—733no—
991C4×D4—733no—
992C4×D4—733no—
993C4×D4—733no—
994C4×D4—736no—
995C4×D4—736no—
996C4×D4—733no—
997C4×D4—736no—
998C4×D4—731no—
999C4×D4—736no—
1000C4×D4—733no—
1001C4×D4—736no—
1002C4×D4—7312no—
1003C4×D4—736no—
1004C4×D4—736no—
1005C4×D4—7312no—
1006C4×D4—736no—
1007C4×D4—736no—
1008C4×D4—736no—
1009C4×D4—736no—
1010C4×D4—731no—
1011C4×D4—733no—
1012C4×D4—736no—
1013C4×D4—732no—
1014C4×D4—736no—
1015C4×D4—736no—
1016C4×D4—736no—
1017C4×D4—736no—
1018C4×D4C22×D7316yes—
1019C4×D4C22×D7316yes—
1020C4×D4C22×D7316yes—
1021#117—733no—
1022#117—733no—
1023#117—736no—
1024#117—733no—
1025#117—736no—
1026#117—733no—
1027#117—733no—
1028#117—736no—
1029#117—7312no—
1030#117—736no—
1031#117—736no—
1032#117—736no—
1033#117—736no—
1034#117—736no—
1035#117—7312no—
1036#117—7312no—
1037#117—7312no—
1038#117—7312no—
1039#117—736no—
1040#117—736no—
1041#117—736no—
1042#117—736no—
1043#117C22×D7313yes—
1044C2×C4⋊C4—733no—
1045C2×C4⋊C4—733no—
1046C2×C4⋊C4—736no—
1047C2×C4⋊C4—736no—
1048C2×C4⋊C4—736no—
1049C2×C4⋊C4—736no—
1050C2×C4⋊C4—733no—
1051C2×C4⋊C4—736no—
1052C2×C4⋊C4—736no—
1053C2×C4⋊C4—736no—
1054C2×C4⋊C4—736no—
1055C2×C4⋊C4C22×D7313yes—
1056C2×C4⋊C4C22×D7316yes—
1057C2×C22⋊C4—736no—
1058C2×C22⋊C4—736no—
1059C2×C22⋊C4C22×D7316yes—
1060C2×C42—733no—
1061C2×C42—736no—
1062C2×C42—736no—
1063C2×C42—733no—
1064C2×C42—733no—
1065C2×C42—733no—
1066C2×C42—733no—
1067C2×C42—736no—
1068C2×C42—733no—
1069C2×C42—733no—
1070C2×C42—733no—
1071C2×C42—733no—
1072C2×C42—733no—
1073C2×C42—733no—
1074C2×C42—731no—
1075C2×C42—736no—
1076C24C23×D7313yes—
1077#41—24no—
1078#41—212no—
1079#41—224no—
1080#41—212no—
1081#41—212no—
1082#41—29212no—
1083#41—1468no—
1084#41—14624no—
1085#41—14612no—
1086#41#1192402718yescomplemented
1087C2×Q8—24no—
1088C2×Q8—28no—
1089C2×Q8—212no—
1090C2×Q8—29212no—
1091C2×Q8—7312no—
1092C2×Q8—732no—
1093C2×Q8—736no—
1094C2×Q8—733no—
1095C2×Q8—736no—
1096C2×Q8—1468no—
1097C2×Q8—14612no—
1098C2×Q8C23×D7316yes—
1099C2×Q8C23×D7313yes—
1100C2×Q8C23×D7313yes—
1101C2×Q8C23×D7311yescharacteristic
1102C2×D4—212no—
1103C2×D4—736no—
1104C2×D4—732no—
1105C2×D4—732no—
1106C2×D4—736no—
1107C2×D4—732no—
1108C2×D4—731no—
1109C2×D4C23×D7316yes—
1110C2×D4C23×D7316yes—
1111C2×D4C23×D7313yes—
1112C2×D4C23×D7311yescharacteristic
1113C2×D4C23×D7312yes—
1114C2×D4C23×D7316yes—
1115C2×D4C23×D7313yes—
1116C22×C4—212no—
1117C22×C4—2926no—
1118C22×C4—733no—
1119C22×C4—733no—
1120C22×C4—733no—
1121C22×C4—736no—
1122C22×C4—736no—
1123C22×C4—736no—
1124C22×C4—731no—
1125C22×C4—733no—
1126C22×C4—731no—
1127C22×C4—732no—
1128C22×C4—733no—
1129C22×C4—733no—
1130C22×C4—733no—
1131C22×C4—733no—
1132C22×C4—733no—
1133C22×C4—733no—
1134C22×C4—736no—
1135C22×C4—732no—
1136C22×C4—736no—
1137C22×C4—14612no—
1138C22×C4C23×D7311yescharacteristic
1139C22×C4C23×D7313yes—
1140C22×C4C23×D7313yes—
1141C22×C4C23×D7313yes—
1142C22×C4C23×D7313yes—
1143C22×C4C23×D7316yes—
1144C22×C4C23×D7316yes—
1145C22×C4C23×D7316yes—
1146C22×C4C23×D7313yes—
1147C4⋊C4—736no—
1148C4⋊C4—736no—
1149C4⋊C4—736no—
1150C4⋊C4—7312no—
1151C4⋊C4—736no—
1152C4⋊C4—736no—
1153C4⋊C4—7312no—
1154C4⋊C4—7312no—
1155C4⋊C4—7312no—
1156C4⋊C4—7312no—
1157C4⋊C4—732no—
1158C4⋊C4—736no—
1159C4⋊C4—736no—
1160C4⋊C4—736no—
1161C4⋊C4—736no—
1162C4⋊C4—733no—
1163C4⋊C4—733no—
1164C4⋊C4—736no—
1165C4⋊C4—736no—
1166C4⋊C4—7312no—
1167C4⋊C4—733no—
1168C4⋊C4—736no—
1169C4⋊C4—733no—
1170C4⋊C4—733no—
1171C4⋊C4—736no—
1172C4⋊C4—731no—
1173C4⋊C4—736no—
1174C4⋊C4—736no—
1175C4⋊C4—736no—
1176C4⋊C4C23×D7316yes—
1177C4⋊C4C23×D7316yes—
1178C4⋊C4C23×D7313yes—
1179C4⋊C4C23×D73112yes—
1180C4⋊C4C23×D7316yes—
1181C4⋊C4C23×D7311yescharacteristic
1182C22⋊C4—736no—
1183C22⋊C4—736no—
1184C22⋊C4—736no—
1185C22⋊C4—736no—
1186C22⋊C4—736no—
1187C22⋊C4—7312no—
1188C22⋊C4—736no—
1189C22⋊C4—732no—
1190C22⋊C4—736no—
1191C22⋊C4—736no—
1192C22⋊C4—736no—
1193C22⋊C4—736no—
1194C22⋊C4—732no—
1195C22⋊C4—732no—
1196C22⋊C4—736no—
1197C22⋊C4—736no—
1198C22⋊C4—736no—
1199C22⋊C4—736no—
1200C22⋊C4C23×D7316yes—
1201C22⋊C4C23×D73112yes—
1202C22⋊C4C23×D7312yes—
1203C22⋊C4C23×D7316yes—
1204C22⋊C4C23×D7316yes—
1205C22⋊C4C23×D7316yes—
1206C42—731no—
1207C42—731no—
1208C42—733no—
1209C42—731no—
1210C42—731no—
1211C42—733no—
1212C42—733no—
1213C42—736no—
1214C42—736no—
1215C42—733no—
1216C42—733no—
1217C42—733no—
1218C42—733no—
1219C42—733no—
1220C42—733no—
1221C42—733no—
1222C42—733no—
1223C42—733no—
1224C42—736no—
1225C42—736no—
1226C42—7312no—
1227C42—7312no—
1228C42—736no—
1229C42C23×D7316yes—
1230C23—26no—
1231C23—26no—
1232C23—43no—
1233C23—732no—
1234C23C24×D7313yes—
1235C23C24×D7312yes—
1236C23C24×D7313yes—
1237C23C24×D7311yescharacteristic
1238Q8—212no—
1239Q8—26no—
1240Q8—26no—
1241Q8—29212no—
1242Q8—14612no—
1243Q8—1464no—
1244Q8—14612no—
1245Q8—1466no—
1246Q8C2×#1192402714yes—
1247D4—212no—
1248D4—212no—
1249D4—24no—
1250D4—26no—
1251D4—22no—
1252D4—46no—
1253D4—2926no—
1254D4—1464no—
1255D4—1464no—
1256D4—14612no—
1257D4—1464no—
1258D4—1462no—
1259D4C2×#11924027112yes—
1260C2×C4—26no—
1261C2×C4—212no—
1262C2×C4—22no—
1263C2×C4—26no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—212no—
1267C2×C4—46no—
1268C2×C4—2926no—
1269C2×C4—2923no—
1270C2×C4—2923no—
1271C2×C4—2923no—
1272C2×C4—2926no—
1273C2×C4—2926no—
1274C2×C4—734no—
1275C2×C4—731no—
1276C2×C4—731no—
1277C2×C4—731no—
1278C2×C4—733no—
1279C2×C4—731no—
1280C2×C4—733no—
1281C2×C4—732no—
1282C2×C4—733no—
1283C2×C4—733no—
1284C2×C4—736no—
1285C2×C4—736no—
1286C2×C4—1464no—
1287C2×C4—1462no—
1288C2×C4—1466no—
1289C2×C4—1466no—
1290C2×C4—1466no—
1291C2×C4—1466no—
1292C2×C4—1466no—
1293C2×C4—1466no—
1294C2×C4—1464no—
1295C2×C4—14612no—
1296C2×C4—1466no—
1297C2×C4—14612no—
1298C2×C4C2×#11924027112yes—
1299C2×C4C24×D7311yescharacteristic
1300C2×C4C24×D7316yes—
1301C2×C4C24×D7313yes—
1302C2×C4C24×D7312yes—
1303C2×C4C24×D7316yes—
1304C2×C4C24×D7311yescharacteristic
1305C2×C4C24×D7313yes—
1306C22—21no—
1307C22—23no—
1308C22—23no—
1309C22—21no—
1310C22—22no—
1311C22—23no—
1312C22—23no—
1313C22—22no—
1314C22—22no—
1315C22—23no—
1316C22—412no—
1317C22—1462no—
1318C22—1462no—
1319C22—1462no—
1320C22C22×#1192402716yes—
1321C222−1+4×D7312yes—
1322C22C25×D7311yescharacteristic
1323C4—21no—
1324C4—23no—
1325C4—26no—
1326C4—22no—
1327C4—26no—
1328C4—732no—
1329C4—732no—
1330C4—732no—
1331C4—1466no—
1332C4—1463no—
1333C4—1463no—
1334C4—1462no—
1335C4—1463no—
1336C4—1461no—
1337C4—1466no—
1338C4—1463no—
1339C4C22×#1192402716yes—
1340C4C22×#1192402712yes—
1341C2—22no—
1342C2—26no—
1343C2—43no—
1344C2—42no—
1345C2—2922no—
1346C2C23×#1192402711yescharacteristic
1347C2C2×2−1+4×D7311yescharacteristic
1348C2#585×D7311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3489C2
hypercenter#3489D73
hypocenterC73#62805
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #22624018C2semidirect
2. #22623967C2semidirect
3. #22623939C2semidirect
4. #22623896C2semidirect
5. #22623840C2semidirect
6. #22623816C2semidirect
7. #22623744C2semidirect
8. #22623712C2semidirect
9. #22623685C2semidirect
10. #22623677C2semidirect
11. #22623611C2semidirect
12. #22623547C2semidirect
13. #22623543C2semidirect
14. Q8×#11924027C2semidirect
15. #22623482C2semidirect
16. #22623359C2semidirect
17. #22623355C2semidirect
18. #22623223C2semidirect
19. C2×#17989139C2semidirect
20. 2−1+4×Dic73C2semidirect
21. #22623142C2semidirect
22. C2×#41×Dic73C2semidirect
23. C73×#3489C2semidirect
25. Q8×Dic146C22semidirect
26. #17989313C22semidirect
27. #17989312C22semidirect
28. #17989312C22semidirect
29. #17989308C22semidirect
30. #17989308C22semidirect
31. #17989307C22semidirect
32. #17989306C22semidirect
33. #17989306C22semidirect
34. #17989301C22semidirect
35. #17989296C22semidirect
37. #17989295C22semidirect
39. #17989280C22semidirect
42. #17989277C22semidirect
43. #17989274C22semidirect
44. #17989274C22semidirect
45. #17989274C22semidirect
46. #17989272C22semidirect
47. #17989271C22semidirect
50. D4×Dic146C22semidirect
52. Q8×C22⋊D73C22semidirect
53. Q8×C22⋊D73C22semidirect
55. #17989243C22semidirect
56. #17989237C22semidirect
58. #17989236C22semidirect
59. #17989236C22semidirect
61. #17989218C22semidirect
62. #17989215C22semidirect
63. #17989210C22semidirect
64. #17989206C22semidirect
65. #17989204C22semidirect
66. #17989204C22semidirect
67. #17989198C22semidirect
68. #17989197C22semidirect
69. #17989197C22semidirect
70. #17989197C22semidirect
71. #17989182C22semidirect
72. #17989181C22semidirect
74. #17989161C22semidirect
76. #17989158C22semidirect
77. #17989142C22semidirect
78. #17989140C22semidirect
83. #17989139C22semidirect
84. #17989139C22semidirect
85. #17989139C22semidirect
86. #17989139C22semidirect
87. #17989139C22semidirect
88. #17989139C22semidirect
89. #17989133C22semidirect
91. #17989132C22semidirect
92. C2×#14556590C22semidirect
93. C2×#14556589C22semidirect
95. #17989123C22semidirect
97. #17989118C22semidirect
98. #17989118C22semidirect
99. #17989118C22semidirect
101. #17989117C22semidirect
102. #17989116C22semidirect
103. #17989114C22semidirect
104. #17989114C22semidirect
105. #17989114C22semidirect
106. C2×#14556581C22semidirect
113. #17989070C22semidirect
114. #17989070C22semidirect
115. #17989068C22semidirect
116. #17989066C22semidirect
117. #17989065C22semidirect
118. #17989065C22semidirect
119. #17989064C22semidirect
120. #17989063C22semidirect
129. #41×Dic73C22semidirect
130. #41×Dic73C22semidirect
131. #17989055C22semidirect
133. C4×#11924027C22semidirect
134. C4×#11924027C22semidirect
137. C2×Q8×Dic73C22semidirect
138. C2×Q8×Dic73C22semidirect
139. C2×#14556556C22semidirect
140. C2×#14556556C22semidirect
141. C4×Q8×D73C22semidirect
516. #41×C73#41semidirect
610. C2×Dic732−1+4semidirect
686. #3489D73semidirect
698. C73#62805semidirect
1086. #41#11924027semidirect

Maximal subgroups

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

subgroupindex
#226240182
#226239672
#226239392
#226238962
#226238402
#226238162
#226237442
#226237122
#226236852
#226236772
#226236112
#226235472
#226235432
Q8×#119240272
#226234822
#226233592
#226233552
#226232232
C2×#179891392
2−1+4×Dic732
#226231422
C2×#41×Dic732
C73×#34892
#6280573