Finite Group Databasebeta

← #33960810

Subgroups — #33960810

Order 18688.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623842C211yesmaximal, characteristic, complemented
2#22621396C214yesmaximal, complemented
3#22621075C211yesmaximal, characteristic, complemented
4#22621072C211yesmaximal, characteristic, complemented
5#22621059C211yesmaximal, characteristic, complemented
6#22621056C211yesmaximal, characteristic, complemented
7#22620887C211yesmaximal, characteristic, complemented
8#22620883C211yesmaximal, characteristic, complemented
9#22620864C211yesmaximal, characteristic, complemented
10#22620860C211yesmaximal, characteristic, complemented
11#22620837C214yesmaximal, complemented
12#22620672C211yesmaximal, characteristic, complemented
13#22620665C211yesmaximal, characteristic, complemented
14#22620491C211yesmaximal, characteristic, complemented
15#22620486C211yesmaximal, characteristic, complemented
16#22620208C214yesmaximal, complemented
17#22620202C214yesmaximal, complemented
18#22618575C211yesmaximal, characteristic, complemented
19C73×#3511C211yesmaximal, characteristic, complemented
20#17989310—21no—
21#17989302—21no—
22#17989297—21no—
23#17989283—21no—
24#17989283—21no—
25#17989246—21no—
26#17989246—21no—
27#17989242—21no—
28#17989208C2212yes—
29#17989208C2212yes—
30#17989165C2212yes—
31#17989144C2211yescharacteristic
32#17989144C2211yescharacteristic
33#17989137C2211yescharacteristic
34#17989137C2211yescharacteristic
35#17989137C2211yescharacteristic
36C2×#14556591C2211yescharacteristic
37#17989067C2212yes—
38#17988983C2211yescharacteristic
39#17988983C2211yescharacteristic
40#17988983C2211yescharacteristic
41#17988983C2211yescharacteristic
42#17988966C2211yescharacteristic
43#17988963C2211yescharacteristic
44#17988961C2211yescharacteristic
45#17988959C2211yescharacteristic
46#17988939C2211yescharacteristic
47#17988939C2211yescharacteristic
48#17988937C2211yescharacteristic
49#17988937C2211yescharacteristic
50#17988935C2211yescharacteristic
51#17988935C2211yescharacteristic
52#17988933C2211yescharacteristic
53#17988933C2211yescharacteristic
54#17988917C2214yes—
55#17988915C2214yes—
56#17988905C2214yes—
57#17988903C2214yes—
58#17988877C2214yes—
59#17988874C2214yes—
60#17988872C2214yes—
61#17988869C2214yes—
62#17988843C2214yes—
63#17988838C2214yes—
64#17988818C2214yes—
65#17988814C2214yes—
66#17988809C2214yes—
67#17988806C2214yes—
68#17988802C2214yes—
69#17988799C2214yes—
70#17988749C2214yes—
71#17988747C2214yes—
72#17988732C2214yes—
73#17988730C2214yes—
74#17988697C2214yes—
75#17988692C2214yes—
76C4×#11924015C2214yes—
77C4×#11924016C2214yes—
78#17988648C2212yes—
79#17988648C2212yes—
80#17988640C2211yescharacteristic
81#17988640C2211yescharacteristic
82#17988640C2211yescharacteristic
83#17988640C2211yescharacteristic
84#17988614C2212yes—
85#17988554C2212yes—
86C4×#11924012C2211yescharacteristic
87C2×C4×#10596831C2211yescharacteristic
88#556×C73—21no—
89#555×C73—21no—
90#554×C73—21no—
91#553×C73—21no—
92#553×C73—21no—
93#548×C73—21no—
94#548×C73—21no—
95#547×C73—21no—
96#542×C73C2212yes—
97#542×C73C2212yes—
98#537×C73C2212yes—
99#533×C73C2211yescharacteristic
100#533×C73C2211yescharacteristic
101#532×C73C2211yescharacteristic
102#532×C73C2211yescharacteristic
103#532×C73C2211yescharacteristic
104C2×C4⋊Q8×C73C2211yescharacteristic
105#520×C73C2212yes—
106C4×#41×C73C2211yescharacteristic
107C2×#11924028—21no—
108C2×#11924028—21no—
109C2×#11924028C2312yes—
110C22×Dic146—21no—
111C2×#11924018C2314yes—
112C2×#11924016C2314yes—
113C2×#11924015C2314yes—
114C2×#11924013C2314yes—
115C2×#11924012C2312yes—
116C22×#10596831C2312yes—
117#14556591—21no—
118#14556591—21no—
119#14556591C2311yescharacteristic
120#14556591C2312yes—
121#14556591C2311yescharacteristic
122#14556591C2311yescharacteristic
123#14556588C2311yescharacteristic
124#14556586—22no—
125#14556586—22no—
126#14556583—21no—
127#14556583—21no—
128#14556579—21no—
129#14556579—21no—
130#14556579C2312yes—
131#14556577—22no—
132#14556577—22no—
133#14556573—22no—
134#14556573—22no—
135#14556570—21no—
136#14556570—21no—
137#14556570C2312yes—
138#14556570C2312yes—
139#14556569—22no—
140#14556569—22no—
141#14556567—22no—
142#14556565—21no—
143#14556565—21no—
144#14556565—21no—
145#14556565—21no—
146#14556565C2312yes—
147#14556565C2312yes—
148#14556563—22no—
149#14556563—22no—
150#14556562—22no—
151C4×Dic146—21no—
152C4×Dic146—21no—
153C4×Dic146C2312yes—
154C4×Dic146C2312yes—
155C4×D292—21no—
156C4×D292—21no—
157C4×D292—21no—
158C4×D292—21no—
159C4×D292C2312yes—
160C4×D292C2312yes—
161#14556551—22no—
162#14556551—22no—
163#14556550—21no—
164#14556550—21no—
165#14556549—22no—
166C2×C4⋊Dic73—21no—
167C2×C4⋊Dic73C2312yes—
168C4⋊C4×D73—22no—
169#14556522C2314yes—
170#14556522C2314yes—
171#14556522C2314yes—
172#14556522C2314yes—
173C4⋊#10596831C2312yes—
174C4⋊#10596831C2312yes—
175C4⋊#10596831C2312yes—
176C4⋊#10596831C2312yes—
177#14556515C2314yes—
178#14556515C2314yes—
179#14556514C2314yes—
180#14556514C2314yes—
181#14556512C2314yes—
182#14556512C2314yes—
183#14556511C2314yes—
184#14556511C2314yes—
185C22⋊#10596831C2312yes—
186C22⋊#10596831C2312yes—
187C22⋊#10596831C2312yes—
188C22⋊#10596831C2312yes—
189#14556502C2312yes—
190C4×#10596831C2311yescharacteristic
191C4×#10596831C2311yescharacteristic
192C4×#10596831C2311yescharacteristic
193C4×#10596831C2311yescharacteristic
194C4×#10596831C2312yes—
195C2×#41×C73—21no—
196C2×#41×C73—21no—
197C2×#41×C73C2312yes—
198C2×#41×C73C2311yescharacteristic
199C22×Q8×C73—21no—
200C4⋊Q8×C73—21no—
201C4⋊Q8×C73—21no—
202C4⋊Q8×C73C2311yescharacteristic
203C4⋊Q8×C73C2312yes—
204C4⋊Q8×C73C2311yescharacteristic
205C4⋊Q8×C73C2311yescharacteristic
206#127×C73C2311yescharacteristic
207#126×C73—22no—
208#126×C73—22no—
209#125×C73—21no—
210#125×C73—21no—
211#124×C73—22no—
212#124×C73—22no—
213#124×C73—21no—
214#124×C73—21no—
215#124×C73C2312yes—
216#123×C73—22no—
217#123×C73—22no—
218C22⋊Q8×C73—22no—
219C22⋊Q8×C73—21no—
220C22⋊Q8×C73—21no—
221C22⋊Q8×C73—22no—
222C22⋊Q8×C73—22no—
223C22⋊Q8×C73C2312yes—
224C22⋊Q8×C73C2312yes—
225#121×C73—22no—
226#121×C73—22no—
227#121×C73—22no—
228#121×C73—21no—
229#121×C73—21no—
230#121×C73—21no—
231#121×C73—21no—
232#121×C73C2312yes—
233#121×C73C2312yes—
234C4×Q8×C73—21no—
235C4×Q8×C73—21no—
236C4×Q8×C73D411yescharacteristic
237C4×Q8×C73D411yescharacteristic
238C4×Q8×C73C2312yes—
239C4×Q8×C73C2312yes—
240C4×D4×C73—22no—
241C4×D4×C73—22no—
242C4×D4×C73—21no—
243C4×D4×C73—21no—
244C4×D4×C73—21no—
245C4×D4×C73—21no—
246C4×D4×C73D411yescharacteristic
247C4×D4×C73D411yescharacteristic
248C4×D4×C73D411yescharacteristic
249C4×D4×C73D411yescharacteristic
250C4×D4×C73D411yescharacteristic
251C4×D4×C73D411yescharacteristic
252C4×D4×C73C2312yes—
253C4×D4×C73C2312yes—
254#117×C73—21no—
255#117×C73—21no—
256#117×C73—22no—
257#117×C73C2311yescharacteristic
258#117×C73C2311yescharacteristic
259#117×C73C2311yescharacteristic
260C2×C4⋊C4×C73—21no—
261C2×C4⋊C4×C73—22no—
262C2×C4⋊C4×C73C2312yes—
263C2×C42×C73C2311yescharacteristic
264C2×C42×C73C2311yescharacteristic
265C2×C42×C73C2311yescharacteristic
266#11924028—44no—
267#11924028—82no—
268#11924028—82no—
269C2×Dic146—21no—
270C2×Dic146—21no—
271C2×Dic146—22no—
272C2×Dic146—82no—
273C2×Dic146C2412yes—
274C2×D292—21no—
275C2×D292—21no—
276C2×D292C2412yes—
277C2×C22⋊D73—22no—
278C2×C22⋊D73—22no—
279C2×C22⋊D73—22no—
280C22×Dic73—22no—
281C2×C4×D73—22no—
282C2×C4×D73—22no—
283C2×C4×D73—22no—
284#11924018—44no—
285#11924016—44no—
286#11924015—44no—
287#11924013—44no—
288#11924012—42no—
289C2×#10596831—42no—
290C2×#10596831C2412yes—
291C2×#10596831C2412yes—
292C2×#10596831C2412yes—
293C2×#10596831C2412yes—
294C4⋊Dic73—22no—
295C4⋊Dic73—21no—
296C4⋊Dic73—21no—
297C4⋊Dic73—22no—
298C4⋊Dic73—21no—
299C4⋊Dic73—21no—
300C4⋊Dic73C2412yes—
301C4⋊Dic73C2412yes—
302#11924007—22no—
303#11924007—22no—
304#11924007—22no—
305#11924007—22no—
306C22⋊Dic73—22no—
307C22⋊Dic73—22no—
308#11924005—22no—
309#11924005—22no—
310#11924005—22no—
311#11924005—22no—
312#11924005—22no—
313#11924005—22no—
314C4×Dic73—22no—
315C4×Dic73—22no—
316#41×C73—42no—
317#41×C73—44no—
318#41×C73—82no—
319#41×C73—82no—
320C2×Q8×C73—21no—
321C2×Q8×C73—21no—
322C2×Q8×C73—22no—
323C2×Q8×C73—82no—
324C2×Q8×C73C2×D411yescharacteristic
325C2×Q8×C73C2412yes—
326C2×D4×C73—22no—
327C2×D4×C73—22no—
328C2×D4×C73—22no—
329C2×D4×C73—21no—
330C2×D4×C73—21no—
331C2×D4×C73C2×D411yescharacteristic
332C2×D4×C73C2×D411yescharacteristic
333C2×D4×C73C2×D411yescharacteristic
334C2×D4×C73C2412yes—
335C22×C4×C73—22no—
336C22×C4×C73—22no—
337C22×C4×C73—22no—
338C22×C4×C73—22no—
339C22×C4×C73C2×D411yescharacteristic
340C22×C4×C73C2×D411yescharacteristic
341C22×C4×C73C2×D411yescharacteristic
342C22×C4×C73C2×D411yescharacteristic
343C22×C4×C73C2×D411yescharacteristic
344C22×C4×C73C2×D411yescharacteristic
345C22×C4×C73C2411yescharacteristic
346C22×C4×C73C2411yescharacteristic
347C22×C4×C73C2411yescharacteristic
348C4⋊C4×C73—22no—
349C4⋊C4×C73—21no—
350C4⋊C4×C73—21no—
351C4⋊C4×C73—22no—
352C4⋊C4×C73—22no—
353C4⋊C4×C73—22no—
354C4⋊C4×C73—21no—
355C4⋊C4×C73—21no—
356C4⋊C4×C73—22no—
357C4⋊C4×C73—22no—
358C4⋊C4×C73C2×D411yescharacteristic
359C4⋊C4×C73C2×D411yescharacteristic
360C4⋊C4×C73C2×D411yescharacteristic
361C4⋊C4×C73C2×D411yescharacteristic
362C4⋊C4×C73C2×D411yescharacteristic
363C4⋊C4×C73C2×D411yescharacteristic
364C4⋊C4×C73C2412yes—
365C4⋊C4×C73C2412yes—
366C22⋊C4×C73—22no—
367C22⋊C4×C73—22no—
368C22⋊C4×C73—22no—
369C22⋊C4×C73—22no—
370C22⋊C4×C73—22no—
371C22⋊C4×C73—22no—
372C22⋊C4×C73—22no—
373C22⋊C4×C73—22no—
374C22⋊C4×C73C2×D411yescharacteristic
375C22⋊C4×C73C2×D411yescharacteristic
376C22⋊C4×C73C2×D411yescharacteristic
377C22⋊C4×C73C2×D411yescharacteristic
378C22⋊C4×C73C2×D411yescharacteristic
379C22⋊C4×C73C2×D411yescharacteristic
380C42×C73—22no—
381C42×C73—22no—
382C42×C73C2×D411yescharacteristic
383C42×C73C2×D411yescharacteristic
384C42×C73C2×D411yescharacteristic
385C42×C73C2×D411yescharacteristic
386C42×C73C2×D411yescharacteristic
387C42×C73C2×D411yescharacteristic
388C42×C73C2411yescharacteristic
389C42×C73C2411yescharacteristic
390C42×C73C2411yescharacteristic
391C42×C73C2411yescharacteristic
392C23×C73—22no—
393C23×C73C22×D411yescharacteristic
394C23×C73C22×D411yescharacteristic
395C23×C73C22×D411yescharacteristic
396C22×D73—22no—
397Q8×C73—24no—
398Q8×C73—41no—
399Q8×C73—42no—
400Q8×C73—42no—
401Q8×C73—82no—
402D4×C73—24no—
403D4×C73—41no—
404D4×C73—41no—
405D4×C73—41no—
406D4×C73—44no—
407D4×C73—42no—
408D4×C73—42no—
409D4×C73—82no—
410D4×C73—82no—
411C2×C4×C73—22no—
412C2×C4×C73—22no—
413C2×C4×C73—22no—
414C2×C4×C73—22no—
415C2×C4×C73—22no—
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—22no—
419C2×C4×C73—22no—
420C2×C4×C73—22no—
421C2×C4×C73—22no—
422C2×C4×C73—22no—
423C2×C4×C73—44no—
424C2×C4×C73—82no—
425C2×C4×C73—82no—
426C2×C4×C73—82no—
427C2×C4×C73C22×D411yescharacteristic
428C2×C4×C73C22×D411yescharacteristic
429C2×C4×C73C22×D411yescharacteristic
430C2×C4×C73C22×D411yescharacteristic
431C2×C4×C73C22×D411yescharacteristic
432C2×C4×C73C22×D411yescharacteristic
433C2×C4×C73C22×D411yescharacteristic
434C2×C4×C73C22×D411yescharacteristic
435C2×C4×C73C22×D411yescharacteristic
436C2×C4×C73C22×D411yescharacteristic
437C2×C4×C73C22×D411yescharacteristic
438C2×C4×C73C2511yescharacteristic
439C22⋊D73—44no—
440C22⋊D73—82no—
441C22⋊D73—82no—
442C2×Dic73—22no—
443C2×Dic73—22no—
444C2×Dic73—22no—
445C2×Dic73—82no—
446D292—24no—
447D292—42no—
448D292—42no—
449C4×D73—44no—
450C4×D73—82no—
451C4×D73—82no—
452Dic146—24no—
453Dic146—42no—
454Dic146—42no—
455Dic146—82no—
456#10596831—22no—
457#10596831—22no—
458#10596831—22no—
459#10596831—22no—
460C22×C73—21no—
461C22×C73—21no—
462C22×C73—21no—
463C22×C73—21no—
464C22×C73—21no—
465C22×C73—21no—
466C22×C73—21no—
467C22×C73—21no—
468C22×C73—21no—
469C22×C73—42no—
470C22×C73—42no—
471C22×C73—42no—
472C22×C73C23×D411yescharacteristic
473C2×D73—42no—
474C2×D73—42no—
475C2×D73—42no—
476C4×C73—21no—
477C4×C73—21no—
478C4×C73—21no—
479C4×C73—21no—
480C4×C73—21no—
481C4×C73—21no—
482C4×C73—21no—
483C4×C73—21no—
484C4×C73—21no—
485C4×C73—42no—
486C4×C73—42no—
487C4×C73—42no—
488C4×C73#57712yes—
489C4×C73#57712yes—
490C4×C73#58512yes—
491Dic73—42no—
492Dic73—42no—
493Dic73—42no—
494#61015—731nomaximal, Sylow
495C2×C73—41no—
496C2×C73—41no—
497C2×C73—41no—
498C2×C73—82no—
499C2×C73#344911yescharacteristic
500C2×C73C2×#57711yescharacteristic
501C2×C73C2×#57711yescharacteristic
502D73—82no—
503#3511—731no—
504#3511D7311yescharacteristic, complemented
505#3263—734no—
506#3229—731no—
507#3229—731no—
508#3227—731no—
509#3227—731no—
510#3210—731no—
511#3210—731no—
512#3207—731no—
513#3207—731no—
514#3204—734no—
515#3185—731no—
516#3184—731no—
517#3167—731no—
518#3167—731no—
519#3125—734no—
520#3125—734no—
521#2922—731no—
522C73#6101511yescharacteristic, complemented, Sylow
523#556—21no—
524#556—1461no—
525#555—21no—
526#555—1461no—
527#554—21no—
528#554—1461no—
529#553—21no—
530#553—21no—
531#553—1461no—
532#553—1461no—
533#548—21no—
534#548—21no—
535#548—1461no—
536#548—1461no—
537#547—21no—
538#547—1461no—
539#542—732no—
540#542—732no—
541#542C2×D7312yes—
542#542C2×D7312yes—
543#537—732no—
544#537C2×D7312yes—
545#533—731no—
546#533—731no—
547#533C2×D7311yescharacteristic
548#533C2×D7311yescharacteristic
549#532—731no—
550#532—731no—
551#532—731no—
552#532C2×D7311yescharacteristic
553#532C2×D7311yescharacteristic
554#532C2×D7311yescharacteristic
555C2×C4⋊Q8—731no—
556C2×C4⋊Q8C2×D7311yescharacteristic
557#520—732no—
558#520C2×D7312yes—
559C4×#41C2×D7311yescharacteristic
560#498—731no—
561#498—731no—
562#498—731no—
563#498—731no—
564#494—731no—
565#493—731no—
566#492—731no—
567#492—731no—
568#487—731no—
569#487—731no—
570#487—731no—
571#487—731no—
572#486—731no—
573#486—731no—
574#486—731no—
575#486—731no—
576#483—734no—
577#483—734no—
578#481—734no—
579#481—734no—
580#476—734no—
581#476—734no—
582#475—734no—
583#475—734no—
584#470—734no—
585#469—734no—
586#465—734no—
587#465—734no—
588#464—734no—
589#464—734no—
590#463—734no—
591#463—734no—
592#452—734no—
593#452—734no—
594#449—734no—
595#449—734no—
596#442—734no—
597#441—734no—
598C4×SD16—734no—
599C4×SD16—734no—
600#433—732no—
601#433—732no—
602#431—731no—
603#431—731no—
604#431—731no—
605#431—731no—
606#424—732no—
607#408—732no—
608C4×M16—731no—
609C2×C4×C8—731no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—732no—
613C2×#41—1461no—
614C2×#41—1461no—
615C2×#41C22×D7312yes—
616C2×#41C22×D7311yescharacteristic
617C22×Q8—21no—
618C22×Q8—1461no—
619C2×Q16—734no—
620C2×SD16—734no—
621C2×SD16—734no—
622C2×D8—734no—
623C2×M16—732no—
624C22×C8—732no—
625C4⋊Q8—21no—
626C4⋊Q8—21no—
627C4⋊Q8—731no—
628C4⋊Q8—731no—
629C4⋊Q8—732no—
630C4⋊Q8—731no—
631C4⋊Q8—1461no—
632C4⋊Q8—1461no—
633C4⋊Q8C22×D7311yescharacteristic
634C4⋊Q8C22×D7311yescharacteristic
635C4⋊Q8C22×D7311yescharacteristic
636C4⋊Q8C22×D7312yes—
637#127—731no—
638#127C22×D7311yescharacteristic
639#126—22no—
640#126—22no—
641#126—1462no—
642#126—1462no—
643#125—21no—
644#125—21no—
645#125—1461no—
646#125—1461no—
647#124—22no—
648#124—22no—
649#124—21no—
650#124—21no—
651#124—732no—
652#124—1462no—
653#124—1462no—
654#124—1461no—
655#124—1461no—
656#124C22×D7312yes—
657#123—22no—
658#123—22no—
659#123—1462no—
660#123—1462no—
661C22⋊Q8—22no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—22no—
665C22⋊Q8—22no—
666C22⋊Q8—732no—
667C22⋊Q8—732no—
668C22⋊Q8—1462no—
669C22⋊Q8—1461no—
670C22⋊Q8—1461no—
671C22⋊Q8—1462no—
672C22⋊Q8—1462no—
673C22⋊Q8C22×D7312yes—
674C22⋊Q8C22×D7312yes—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—732no—
683#121—732no—
684#121—1462no—
685#121—1462no—
686#121—1462no—
687#121—1461no—
688#121—1461no—
689#121—1461no—
690#121—1461no—
691#121C22×D7312yes—
692#121C22×D7312yes—
693C4×Q8—21no—
694C4×Q8—21no—
695C4×Q8—732no—
696C4×Q8—732no—
697C4×Q8—1461no—
698C4×Q8—1461no—
699C4×Q8C22⋊D7311yescharacteristic
700C4×Q8C22⋊D7311yescharacteristic
701C4×Q8C22×D7312yes—
702C4×Q8C22×D7312yes—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—21no—
706C4×D4—21no—
707C4×D4—21no—
708C4×D4—21no—
709C4×D4—732no—
710C4×D4—732no—
711C4×D4—1462no—
712C4×D4—1462no—
713C4×D4—1461no—
714C4×D4—1461no—
715C4×D4—1461no—
716C4×D4—1461no—
717C4×D4C22⋊D7311yescharacteristic
718C4×D4C22⋊D7311yescharacteristic
719C4×D4C22⋊D7311yescharacteristic
720C4×D4C22⋊D7311yescharacteristic
721C4×D4C22⋊D7311yescharacteristic
722C4×D4C22⋊D7311yescharacteristic
723C4×D4C22×D7312yes—
724C4×D4C22×D7312yes—
725#117—21no—
726#117—21no—
727#117—22no—
728#117—1461no—
729#117—1461no—
730#117—1462no—
731#117C22×D7311yescharacteristic
732#117C22×D7311yescharacteristic
733#117C22×D7311yescharacteristic
734C2×C4⋊C4—21no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—732no—
737C2×C4⋊C4—1461no—
738C2×C4⋊C4—1462no—
739C2×C4⋊C4C22×D7312yes—
740C2×C42C22×D7311yescharacteristic
741C2×C42C22×D7311yescharacteristic
742C2×C42C22×D7311yescharacteristic
743#106—734no—
744#106—734no—
745#106—734no—
746#106—734no—
747C4⋊C8—732no—
748C4⋊C8—732no—
749C4⋊C8—732no—
750C4⋊C8—732no—
751#103—734no—
752#103—734no—
753#103—734no—
754#103—734no—
755#102—734no—
756#102—734no—
757#102—734no—
758#102—734no—
759C22⋊C8—732no—
760C22⋊C8—732no—
761C22⋊C8—732no—
762C22⋊C8—732no—
763#97—732no—
764C4×C8—731no—
765C4×C8—731no—
766C4×C8—732no—
767C4×C8—731no—
768C4×C8—731no—
769#41—42no—
770#41—44no—
771#41—82no—
772#41—82no—
773#41—2924no—
774#41—5842no—
775#41—5842no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—22no—
779C2×Q8—82no—
780C2×Q8—5842no—
781C2×Q8—732no—
782C2×Q8—1461no—
783C2×Q8—1461no—
784C2×Q8—1462no—
785C2×Q8C2×C22⋊D7311yescharacteristic
786C2×Q8C23×D7312yes—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—732no—
793C2×D4—1462no—
794C2×D4—1462no—
795C2×D4—1462no—
796C2×D4—1461no—
797C2×D4—1461no—
798C2×D4C2×C22⋊D7311yescharacteristic
799C2×D4C2×C22⋊D7311yescharacteristic
800C2×D4C2×C22⋊D7311yescharacteristic
801C2×D4C23×D7312yes—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—1462no—
807C22×C4—1462no—
808C22×C4—1462no—
809C22×C4—1462no—
810C22×C4C2×C22⋊D7311yescharacteristic
811C22×C4C2×C22⋊D7311yescharacteristic
812C22×C4C2×C22⋊D7311yescharacteristic
813C22×C4C2×C22⋊D7311yescharacteristic
814C22×C4C2×C22⋊D7311yescharacteristic
815C22×C4C2×C22⋊D7311yescharacteristic
816C22×C4C23×D7311yescharacteristic
817C22×C4C23×D7311yescharacteristic
818C22×C4C23×D7311yescharacteristic
819Q16—2924no—
820SD16—2924no—
821SD16—2924no—
822D8—2924no—
823M16—2922no—
824C2×C8—2922no—
825C2×C8—732no—
826C2×C8—732no—
827C2×C8—732no—
828C2×C8—732no—
829C4⋊C4—22no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—732no—
840C4⋊C4—732no—
841C4⋊C4—1462no—
842C4⋊C4—1462no—
843C4⋊C4—1462no—
844C4⋊C4—1462no—
845C4⋊C4—1462no—
846C4⋊C4—1461no—
847C4⋊C4—1461no—
848C4⋊C4—1462no—
849C4⋊C4—1461no—
850C4⋊C4—1461no—
851C4⋊C4C2×C22⋊D7311yescharacteristic
852C4⋊C4C2×C22⋊D7311yescharacteristic
853C4⋊C4C2×C22⋊D7311yescharacteristic
854C4⋊C4C2×C22⋊D7311yescharacteristic
855C4⋊C4C2×C22⋊D7311yescharacteristic
856C4⋊C4C2×C22⋊D7311yescharacteristic
857C4⋊C4C23×D7312yes—
858C4⋊C4C23×D7312yes—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—1462no—
868C22⋊C4—1462no—
869C22⋊C4—1462no—
870C22⋊C4—1462no—
871C22⋊C4—1462no—
872C22⋊C4—1462no—
873C22⋊C4—1462no—
874C22⋊C4—1462no—
875C22⋊C4C2×C22⋊D7311yescharacteristic
876C22⋊C4C2×C22⋊D7311yescharacteristic
877C22⋊C4C2×C22⋊D7311yescharacteristic
878C22⋊C4C2×C22⋊D7311yescharacteristic
879C22⋊C4C2×C22⋊D7311yescharacteristic
880C22⋊C4C2×C22⋊D7311yescharacteristic
881C42—22no—
882C42—22no—
883C42—1462no—
884C42—1462no—
885C42C2×C22⋊D7311yescharacteristic
886C42C2×C22⋊D7311yescharacteristic
887C42C2×C22⋊D7311yescharacteristic
888C42C2×C22⋊D7311yescharacteristic
889C42C2×C22⋊D7311yescharacteristic
890C42C2×C22⋊D7311yescharacteristic
891C42C23×D7311yescharacteristic
892C42C23×D7311yescharacteristic
893C42C23×D7311yescharacteristic
894C42C23×D7311yescharacteristic
895C23—22no—
896C23—1462no—
897C23C22×C22⋊D7311yescharacteristic
898C23C22×C22⋊D7311yescharacteristic
899C23C22×C22⋊D7311yescharacteristic
900Q8—24no—
901Q8—41no—
902Q8—42no—
903Q8—42no—
904Q8—82no—
905Q8—2922no—
906Q8—2922no—
907Q8—5842no—
908Q8—1464no—
909D4—24no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—44no—
914D4—42no—
915D4—42no—
916D4—82no—
917D4—82no—
918D4—2924no—
919D4—2922no—
920D4—2922no—
921D4—5842no—
922D4—5842no—
923D4—1464no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—44no—
937C2×C4—82no—
938C2×C4—82no—
939C2×C4—82no—
940C2×C4—2924no—
941C2×C4—5842no—
942C2×C4—5842no—
943C2×C4—5842no—
944C2×C4—1462no—
945C2×C4—1462no—
946C2×C4—1462no—
947C2×C4C22×C22⋊D7311yescharacteristic
948C2×C4C22×C22⋊D7311yescharacteristic
949C2×C4C22×C22⋊D7311yescharacteristic
950C2×C4C22×C22⋊D7311yescharacteristic
951C2×C4C22×C22⋊D7311yescharacteristic
952C2×C4C22×C22⋊D7311yescharacteristic
953C2×C4C22×C22⋊D7311yescharacteristic
954C2×C4C22×C22⋊D7311yescharacteristic
955C2×C4C22×C22⋊D7311yescharacteristic
956C2×C4C22×C22⋊D7311yescharacteristic
957C2×C4C22×C22⋊D7311yescharacteristic
958C2×C4C24×D7311yescharacteristic
959C8—1462no—
960C8—1462no—
961C8—1462no—
962C8—1462no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—2922no—
976C22—2922no—
977C22—2922no—
978C22C23×C22⋊D7311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—2922no—
992C4—2922no—
993C4—2922no—
994C4#1798939512yes—
995C4#1798939812yes—
996C4#1798942312yes—
997C2—41no—
998C2—41no—
999C2—41no—
1000C2—82no—
1001C2—5842no—
1002C2#2262326011yescharacteristic
1003C2C2×#1798939511yescharacteristic
1004C2C2×#1798939811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3511C2
socleC22×C73C23×D4
hypercenter#3511D73
hypocenterC73#61015
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #22623842C2semidirect
2. #22621396C2semidirect
3. #22621075C2semidirect
4. #22621072C2semidirect
5. #22621059C2semidirect
6. #22621056C2semidirect
7. #22620887C2semidirect
8. #22620883C2semidirect
9. #22620864C2semidirect
10. #22620860C2semidirect
11. #22620837C2semidirect
12. #22620672C2semidirect
13. #22620665C2semidirect
14. #22620491C2semidirect
15. #22620486C2semidirect
16. #22620208C2semidirect
17. #22620202C2semidirect
18. #22618575C2semidirect
19. C73×#3511C2semidirect
504. #3511D73semidirect
522. C73#61015semidirect

Maximal subgroups

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

subgroupindex
#226238422
#226213962
#226210752
#226210722
#226210592
#226210562
#226208872
#226208832
#226208642
#226208602
#226208372
#226206722
#226206652
#226204912
#226204862
#226202082
#226202022
#226185752
C73×#35112
#6101573