Finite Group Databasebeta

← #33966018

Subgroups — #33966018

Order 18688.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623817C211yesmaximal, characteristic, complemented
2#22623750C211yesmaximal, characteristic, complemented
3#22622732C212yesmaximal, complemented
4#22622710C212yesmaximal, complemented
5#22622669C212yesmaximal, complemented
6#22622647C212yesmaximal, complemented
7#22622614C212yesmaximal, complemented
8#22622607C212yesmaximal, complemented
9#22622578C212yesmaximal, complemented
10#22622571C212yesmaximal, complemented
11#22620300C212yesmaximal, complemented
12C2×#17988938C211yesmaximal, characteristic, complemented
13#22619776C212yesmaximal, complemented
14#22619746C211yesmaximal, characteristic, complemented
15#22619479C212yesmaximal
16#22619418C211yesmaximal, characteristic, complemented
17#22618865C211yesmaximal, characteristic, complemented
18#22618777C212yesmaximal, complemented
19C4×#135×C73C211yesmaximal, characteristic
20C2×#14556621C2212yes—
21Q8×Dic146C2212yes—
22#17989316C2212yes—
23#17989315C2212yes—
24#17989315C2212yes—
25#17989307C2212yes—
26#17989307C2212yes—
27#17989294—22no—
28#17989294C2212yes—
29#17989277—22no—
30#17989277—22no—
31D4×Dic146—22no—
32D4×Dic146C2212yes—
33#17989215—22no—
34#17989215C2212yes—
35#17989199—22no—
36#17989158C2212yes—
37#17989144—21no—
38#17989144—21no—
39#17989144—21no—
40#17989144C2211yescharacteristic
41C2×#14556591—21no—
42C2×#14556591C2211yescharacteristic
43C2×#14556591C2211yescharacteristic
44#17989070C2212yes—
45#17989064C2212yes—
46#17988954C2214yes—
47#17988945C2214yes—
48#17988940C2214yes—
49#17988938C2212yes—
50#17988938C2212yes—
51#17988938C2212yes—
52#17988938C2212yes—
53#17988936C2214yes—
54#17988897C2214yes—
55#17988893C2214yes—
56#17988882C2212yes—
57#17988881C2214yes—
58#17988877C2212yes—
59#17988872C2212yes—
60#17988871C2214yes—
61#17988867C2212yes—
62#17988807C2214yes—
63#17988800C2214yes—
64#17988797C2212yes—
65#17988797C2212yes—
66#17988795C2214yes—
67#17988792C2212yes—
68#17988792C2212yes—
69#17988790C2214yes—
70#17988717C2212yes—
71#17988717C2212yes—
72C8×Dic146C2212yes—
73C8×Dic146C2212yes—
74#17988691C2214yes—
75#17988684C2214yes—
76#17988679C2214yes—
77#17988678C2214yes—
78#17988630C2212yes—
79#17988613C2212yes—
80#17988611C2211yescharacteristic
81#17988595C2212yes—
82#17988588C2212yes—
83C2×#14556516C2212yes—
84C2×#14556516C2212yes—
85#17988542C2212yes—
86C2×#135×C73C2211yescharacteristic
87C4×#41×C73C2211yescharacteristic
88C4×#41×C73C2211yescharacteristic
89C4×Q16×C73C2211yescharacteristic
90C4×Q16×C73C2211yescharacteristic
91C4×SD16×C73C2211yescharacteristic
92C4×SD16×C73C2211yescharacteristic
93C4×SD16×C73C2211yescharacteristic
94C4×SD16×C73C2211yescharacteristic
95C4×D8×C73C2211yescharacteristic
96C4×D8×C73C2211yescharacteristic
97#427×C73C2211yescharacteristic
98#416×C73C2211yescharacteristic
99#416×C73C2211yescharacteristic
100C2×C4×C8×C73C2211yescharacteristic
101C22×Dic146—22no—
102C22×Dic146—21no—
103C22×Dic146C2312yes—
104#14556621—28no—
105C2×#11924018C2314yes—
106C2×#11924016C2314yes—
107C2×#11924012C2312yes—
108#14556591—22no—
109#14556591—22no—
110#14556591—22no—
111#14556591—21no—
112#14556591—21no—
113#14556591—21no—
114#14556591—21no—
115#14556591D411yescharacteristic
116#14556591D411yescharacteristic
117#14556591C2312yes—
118#14556591C2312yes—
119#14556591C2312yes—
120#14556591C2312yes—
121#14556590—24no—
122#14556590C2314yes—
123#14556589C2314yes—
124#14556584—24no—
125#14556584—24no—
126#14556583—22no—
127#14556583—22no—
128#14556583—22no—
129#14556583D412yes—
130#14556582—24no—
131#14556582C2314yes—
132#14556581—24no—
133#14556581—24no—
134#14556578C2314yes—
135#14556572—24no—
136#14556570—22no—
137#14556570—22no—
138#14556570—22no—
139#14556570—22no—
140#14556570—22no—
141#14556570—22no—
142#14556570D412yes—
143#14556570D412yes—
144#14556568—24no—
145#14556568—24no—
146#14556568—24no—
147Q8×Dic73C2314yes—
148C4×Dic146—22no—
149C4×Dic146—22no—
150C4×Dic146—22no—
151C4×Dic146—22no—
152C4×Dic146—22no—
153C4×Dic146—22no—
154C4×Dic146C2312yes—
155C4×Dic146C2312yes—
156#14556556C2314yes—
157#14556556C2314yes—
158D4×Dic73—24no—
159D4×Dic73C2314yes—
160#14556550—22no—
161#14556550—22no—
162#14556550—22no—
163#14556550C2312yes—
164#14556547—24no—
165C2×C4⋊Dic73—22no—
166C2×C4⋊Dic73—22no—
167C2×C4⋊Dic73—21no—
168C2×C4⋊Dic73—21no—
169C2×C4⋊Dic73—21no—
170C2×C4⋊Dic73C2312yes—
171#14556524C2314yes—
172#14556522C2314yes—
173C4⋊#10596831C2312yes—
174C4⋊#10596831C2312yes—
175#14556520C2314yes—
176#14556520C2314yes—
177#14556516C2314yes—
178#14556516C2314yes—
179#14556516C2314yes—
180#14556516C2314yes—
181#14556515C2314yes—
182#14556514C2314yes—
183#14556514C2314yes—
184#14556512C2314yes—
185#14556501C2314yes—
186C8×Dic73C2314yes—
187C2×#41×C73C2311yescharacteristic
188C2×#41×C73C2311yescharacteristic
189#135×C73—24no—
190C2×Q16×C73C2311yescharacteristic
191C2×SD16×C73C2311yescharacteristic
192C2×SD16×C73C2311yescharacteristic
193C2×D8×C73C2311yescharacteristic
194C22×C8×C73C2311yescharacteristic
195C22×C8×C73C2311yescharacteristic
196C4×Q8×C73C2311yescharacteristic
197C4×Q8×C73C2311yescharacteristic
198C4×Q8×C73C2311yescharacteristic
199C4×Q8×C73C2311yescharacteristic
200C4×D4×C73—21no—
201C4×D4×C73—21no—
202C4×D4×C73—21no—
203C4×D4×C73—21no—
204C4×D4×C73C2311yescharacteristic
205C4×D4×C73C2311yescharacteristic
206C4×D4×C73C2311yescharacteristic
207C4×D4×C73C2311yescharacteristic
208#117×C73—21no—
209#117×C73—21no—
210#117×C73C2311yescharacteristic
211#117×C73C2311yescharacteristic
212C2×C42×C73—21no—
213C2×C42×C73—21no—
214C2×C42×C73C2311yescharacteristic
215#107×C73C2311yescharacteristic
216#107×C73C2311yescharacteristic
217#106×C73C2311yescharacteristic
218#106×C73C2311yescharacteristic
219#103×C73C2311yescharacteristic
220#103×C73C2311yescharacteristic
221#103×C73C2311yescharacteristic
222#103×C73C2311yescharacteristic
223#102×C73C2311yescharacteristic
224#102×C73C2311yescharacteristic
225#102×C73C2311yescharacteristic
226#102×C73C2311yescharacteristic
227C4×C8×C73C2311yescharacteristic
228C4×C8×C73C2311yescharacteristic
229C4×C8×C73C2311yescharacteristic
230C4×C8×C73C2311yescharacteristic
231C2×Dic146—24no—
232C2×Dic146—24no—
233C2×Dic146—22no—
234C2×Dic146—22no—
235C2×Dic146—22no—
236C2×Dic146—24no—
237C2×Dic146—84no—
238C2×Dic146—82no—
239C2×Dic146C2×D412yes—
240C2×Dic146C2×D412yes—
241C2×Dic146C2414yes—
242C22×Dic73—22no—
243C22×Dic73—22no—
244C22×Dic73—24no—
245#11924018—28no—
246#11924016—28no—
247#11924012—24no—
248C2×#10596831C2414yes—
249C4⋊Dic73—22no—
250C4⋊Dic73—22no—
251C4⋊Dic73—22no—
252C4⋊Dic73—22no—
253C4⋊Dic73—22no—
254C4⋊Dic73—22no—
255C4⋊Dic73—22no—
256C4⋊Dic73—24no—
257C4⋊Dic73—24no—
258C4⋊Dic73C2×D412yes—
259C4⋊Dic73C2×D412yes—
260C4⋊Dic73C2×D412yes—
261C4⋊Dic73C2×D412yes—
262C4⋊Dic73C2414yes—
263#11924007—24no—
264#11924007—24no—
265#11924007—24no—
266#11924007—24no—
267#11924007—24no—
268#11924007—24no—
269#11924007C2×D414yes—
270#11924007C2×D414yes—
271C22⋊Dic73—24no—
272C22⋊Dic73—24no—
273C22⋊Dic73—24no—
274C22⋊Dic73C2×D414yes—
275C4×Dic73—24no—
276C4×Dic73—24no—
277C4×Dic73—24no—
278C4×Dic73C2414yes—
279#41×C73—22no—
280#41×C73—22no—
281#41×C73—22no—
282#41×C73#4114yes—
283C2×Q8×C73C2411yescharacteristic
284C2×Q8×C73C2411yescharacteristic
285C2×D4×C73—21no—
286C2×D4×C73—21no—
287C2×D4×C73C2411yescharacteristic
288C2×D4×C73C2411yescharacteristic
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73C2×D411yescharacteristic
296C22×C4×C73C2×D411yescharacteristic
297C22×C4×C73C2411yescharacteristic
298Q16×C73—22no—
299SD16×C73—22no—
300SD16×C73—22no—
301D8×C73—22no—
302C2×C8×C73—22no—
303C2×C8×C73—22no—
304C2×C8×C73C2411yescharacteristic
305C2×C8×C73C2411yescharacteristic
306C2×C8×C73C2411yescharacteristic
307C2×C8×C73C2411yescharacteristic
308C4⋊C4×C73—21no—
309C4⋊C4×C73—21no—
310C4⋊C4×C73—21no—
311C4⋊C4×C73—21no—
312C4⋊C4×C73C2411yescharacteristic
313C4⋊C4×C73C2411yescharacteristic
314C4⋊C4×C73C2411yescharacteristic
315C4⋊C4×C73C2411yescharacteristic
316C22⋊C4×C73—21no—
317C22⋊C4×C73—21no—
318C22⋊C4×C73—21no—
319C22⋊C4×C73—21no—
320C22⋊C4×C73—21no—
321C22⋊C4×C73—21no—
322C42×C73—21no—
323C42×C73—21no—
324C42×C73—21no—
325C42×C73—21no—
326C42×C73—21no—
327C42×C73—21no—
328C42×C73C2×D411yescharacteristic
329C42×C73C2×D411yescharacteristic
330C42×C73C2411yescharacteristic
331C42×C73C2411yescharacteristic
332C23×C73—21no—
333C23×C73—21no—
334C23×C73C22×D411yescharacteristic
335Q8×C73—21no—
336Q8×C73—21no—
337Q8×C73—21no—
338Q8×C73C2×#4112yes—
339D4×C73—24no—
340D4×C73—21no—
341D4×C73—21no—
342D4×C73—21no—
343D4×C73—42no—
344D4×C73C2×#4112yes—
345C2×C4×C73—21no—
346C2×C4×C73—24no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
351C2×C4×C73—21no—
352C2×C4×C73—21no—
353C2×C4×C73—21no—
354C2×C4×C73—42no—
355C2×C4×C73—42no—
356C2×C4×C73—42no—
357C2×C4×C73—42no—
358C2×C4×C73—42no—
359C2×C4×C73C22×D411yescharacteristic
360C2×C4×C73C22×D411yescharacteristic
361C2×C4×C73C22×D411yescharacteristic
362C2×C4×C73C22×D411yescharacteristic
363C2×C4×C73C22×D411yescharacteristic
364C2×C4×C73C2×#4112yes—
365C2×C4×C732−1+412yes—
366C2×C4×C73C2511yescharacteristic
367C2×Dic73—24no—
368C2×Dic73—24no—
369C2×Dic73—44no—
370C2×Dic73—84no—
371C2×Dic73—82no—
372C2×Dic73C22×D414yes—
373C2×Dic73C22×D414yes—
374Dic146—24no—
375Dic146—24no—
376Dic146—24no—
377Dic146—24no—
378Dic146—44no—
379Dic146—44no—
380Dic146—84no—
381Dic146—82no—
382C8×C73—21no—
383C8×C73—21no—
384C8×C73—21no—
385C8×C73—21no—
386#10596831—24no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—22no—
390C22×C73—41no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73#54812yes—
396C22×C73C23×D411yescharacteristic
397C4×C73—22no—
398C4×C73—21no—
399C4×C73—21no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73—41no—
404C4×C73—41no—
405C4×C73#54812yes—
406C4×C73#57712yes—
407C4×C73#57812yes—
408C4×C73C22×#4111yescharacteristic
409C4×C73C2×2−1+411yescharacteristic
410Dic73—24no—
411Dic73—24no—
412Dic73—44no—
413Dic73—44no—
414#61330—731nomaximal, Sylow
415C2×C73—22no—
416C2×C73—42no—
417C2×C73—81no—
418C2×C73C2×#54811yescharacteristic
419C2×C73C2×#57711yescharacteristic
420C2×C73C2×#57811yescharacteristic
421#3509—731no—
422#3503—731no—
423#3374—732no—
424#3372—732no—
425#3369—732no—
426#3367—732no—
427#3364—732no—
428#3363—732no—
429#3360—732no—
430#3359—732no—
431#3137—732no—
432C2×#487—731no—
433#3082—732no—
434#3079—731no—
435#3046—732no—
436#3039—731no—
437#2960—731no—
438#2947—732no—
439C4×#135D7311yescharacteristic
440C73#6133011yescharacteristic, complemented, Sylow
441C2×#137—732no—
442C2×#135C2×D7311yescharacteristic
443Q82—732no—
444#557—732no—
445#557—732no—
446#557—732no—
447#556—732no—
448#556—732no—
449#554—732no—
450#554—1462no—
451#552—1462no—
452#552—1462no—
453D4×Q8—732no—
454D4×Q8—1462no—
455#544—732no—
456#544—1462no—
457#541—1462no—
458#536—732no—
459#533—731no—
460#533—1461no—
461#533—1461no—
462#533—1461no—
463C2×C4⋊Q8—731no—
464C2×C4⋊Q8—731no—
465C2×C4⋊Q8—1461no—
466#520—732no—
467#519—732no—
468C4×#41C2×D7311yescharacteristic
469C4×#41C2×D7311yescharacteristic
470#491—734no—
471#489—734no—
472#488—734no—
473#487—734no—
474#487—732no—
475#487—732no—
476#487—732no—
477#487—732no—
478#479—734no—
479#479—734no—
480#477—732no—
481#477—734no—
482#476—732no—
483#475—732no—
484#475—734no—
485#474—732no—
486#464—734no—
487#463—734no—
488#462—734no—
489#462—732no—
490#462—732no—
491#461—734no—
492#461—732no—
493#461—732no—
494#446—732no—
495#446—732no—
496C8×Q8—732no—
497C8×Q8—732no—
498#441—734no—
499#440—734no—
500C4×Q16—734no—
501C4×Q16C2×D7311yescharacteristic
502C4×Q16C2×D7311yescharacteristic
503C4×SD16—734no—
504C4×SD16C2×D7311yescharacteristic
505C4×SD16C2×D7311yescharacteristic
506C4×SD16C2×D7311yescharacteristic
507C4×SD16C2×D7311yescharacteristic
508C4×D8C2×D7311yescharacteristic
509C4×D8C2×D7311yescharacteristic
510#428—732no—
511#427C2×D7311yescharacteristic
512#424—732no—
513#423—731no—
514#419—732no—
515#417—732no—
516#416C2×D7311yescharacteristic
517#416C2×D7311yescharacteristic
518C2×#103—732no—
519C2×#103—732no—
520#405—732no—
521C2×C4×C8C2×D7311yescharacteristic
522C2×#41C22×D7311yescharacteristic
523C2×#41C22×D7311yescharacteristic
524C22×Q8—732no—
525C22×Q8—1462no—
526C22×Q8—1461no—
527#137—1468no—
528#135—24no—
529C2×Q16—734no—
530C2×Q16C22×D7311yescharacteristic
531C2×SD16—734no—
532C2×SD16C22×D7311yescharacteristic
533C2×SD16C22×D7311yescharacteristic
534C2×D8C22×D7311yescharacteristic
535C2×M16—732no—
536C22×C8C22×D7311yescharacteristic
537C22×C8C22×D7311yescharacteristic
538C4⋊Q8—734no—
539C4⋊Q8—734no—
540C4⋊Q8—731no—
541C4⋊Q8—731no—
542C4⋊Q8—732no—
543C4⋊Q8—732no—
544C4⋊Q8—732no—
545C4⋊Q8—732no—
546C4⋊Q8—1462no—
547C4⋊Q8—1462no—
548C4⋊Q8—1462no—
549C4⋊Q8—1464no—
550C4⋊Q8—1461no—
551C4⋊Q8—1461no—
552C4⋊Q8—1461no—
553C4⋊Q8—1461no—
554#126—1464no—
555#126—1464no—
556#125—734no—
557#125—732no—
558#125—1462no—
559#125—1462no—
560#125—1462no—
561#125—1464no—
562#125—1464no—
563#125—1464no—
564#124—734no—
565#123—1464no—
566C22⋊Q8—732no—
567C22⋊Q8—732no—
568C22⋊Q8—1464no—
569C22⋊Q8—1464no—
570C22⋊Q8—1464no—
571C22⋊Q8—1462no—
572C22⋊Q8—1462no—
573C22⋊Q8—1462no—
574C22⋊Q8—1462no—
575C22⋊Q8—1462no—
576C22⋊Q8—1462no—
577C4×Q8—732no—
578C4×Q8—732no—
579C4×Q8—734no—
580C4×Q8—734no—
581C4×Q8—734no—
582C4×Q8—1462no—
583C4×Q8—1462no—
584C4×Q8—1462no—
585C4×Q8—1462no—
586C4×Q8—1462no—
587C4×Q8—1462no—
588C4×Q8C22×D7311yescharacteristic
589C4×Q8C22×D7311yescharacteristic
590C4×Q8C22×D7311yescharacteristic
591C4×Q8C22×D7311yescharacteristic
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—734no—
597C4×D4—1464no—
598C4×D4C22×D7311yescharacteristic
599C4×D4C22×D7311yescharacteristic
600C4×D4C22×D7311yescharacteristic
601C4×D4C22×D7311yescharacteristic
602#117—21no—
603#117—21no—
604#117—732no—
605#117—1464no—
606#117—1462no—
607#117—1462no—
608#117—1462no—
609#117C22×D7311yescharacteristic
610#117C22×D7311yescharacteristic
611C2×C4⋊C4—732no—
612C2×C4⋊C4—1462no—
613C2×C4⋊C4—1462no—
614C2×C4⋊C4—1461no—
615C2×C4⋊C4—1461no—
616C2×C4⋊C4—1461no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C22×D7311yescharacteristic
620#107—734no—
621#107C22×D7311yescharacteristic
622#107C22×D7311yescharacteristic
623#106—734no—
624#106C22×D7311yescharacteristic
625#106C22×D7311yescharacteristic
626C4⋊C8—734no—
627C4⋊C8—734no—
628C4⋊C8—732no—
629C4⋊C8—732no—
630#103—734no—
631#103—734no—
632#103—734no—
633#103—734no—
634#103—734no—
635#103—734no—
636#103—734no—
637#103C22×D7311yescharacteristic
638#103C22×D7311yescharacteristic
639#103C22×D7311yescharacteristic
640#103C22×D7311yescharacteristic
641#102—734no—
642#102C22×D7311yescharacteristic
643#102C22×D7311yescharacteristic
644#102C22×D7311yescharacteristic
645#102C22×D7311yescharacteristic
646#97—734no—
647C4×C8—734no—
648C4×C8C22×D7311yescharacteristic
649C4×C8C22×D7311yescharacteristic
650C4×C8C22×D7311yescharacteristic
651C4×C8C22×D7311yescharacteristic
652#41—22no—
653#41—22no—
654#41—22no—
655#41#1192402814yes—
656C2×Q8—5842no—
657C2×Q8—5844no—
658C2×Q8—732no—
659C2×Q8—732no—
660C2×Q8—734no—
661C2×Q8—1464no—
662C2×Q8—1464no—
663C2×Q8—1464no—
664C2×Q8—1462no—
665C2×Q8—1462no—
666C2×Q8—1462no—
667C2×Q8C23×D7311yescharacteristic
668C2×Q8C23×D7311yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4C23×D7311yescharacteristic
672C2×D4C23×D7311yescharacteristic
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—1462no—
680C22×C4—1464no—
681C22×C4—1462no—
682C22×C4D4×D7311yescharacteristic
683C22×C4D4×D7311yescharacteristic
684C22×C4C23×D7311yescharacteristic
685Q16—22no—
686Q16—1468no—
687SD16—22no—
688SD16—22no—
689SD16—1468no—
690D8—22no—
691M16—1464no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—734no—
695C2×C8C23×D7311yescharacteristic
696C2×C8C23×D7311yescharacteristic
697C2×C8C23×D7311yescharacteristic
698C2×C8C23×D7311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—734no—
704C4⋊C4—734no—
705C4⋊C4—732no—
706C4⋊C4—732no—
707C4⋊C4—732no—
708C4⋊C4—732no—
709C4⋊C4—734no—
710C4⋊C4—1464no—
711C4⋊C4—1464no—
712C4⋊C4—1464no—
713C4⋊C4—1464no—
714C4⋊C4—1464no—
715C4⋊C4—1464no—
716C4⋊C4—1464no—
717C4⋊C4—1464no—
718C4⋊C4—1462no—
719C4⋊C4—1462no—
720C4⋊C4—1462no—
721C4⋊C4—1462no—
722C4⋊C4—1462no—
723C4⋊C4—1462no—
724C4⋊C4—1462no—
725C4⋊C4C23×D7311yescharacteristic
726C4⋊C4C23×D7311yescharacteristic
727C4⋊C4C23×D7311yescharacteristic
728C4⋊C4C23×D7311yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—734no—
736C22⋊C4—1464no—
737C22⋊C4—1464no—
738C22⋊C4—1464no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—734no—
746C42—1464no—
747C42—1464no—
748C42—1464no—
749C42D4×D7311yescharacteristic
750C42D4×D7311yescharacteristic
751C42C23×D7311yescharacteristic
752C42C23×D7311yescharacteristic
753C23—21no—
754C23—21no—
755C23C2×D4×D7311yescharacteristic
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—2924no—
760Q8—2924no—
761Q8—5842no—
762Q8—5844no—
763Q8—1464no—
764Q8—1464no—
765Q8—1464no—
766Q8—1464no—
767Q8C2×#1192402812yes—
768D4—24no—
769D4—21no—
770D4—21no—
771D4—21no—
772D4—42no—
773D4C2×#1192402812yes—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—2924no—
789C2×C4—5842no—
790C2×C4—5844no—
791C2×C4—734no—
792C2×C4—734no—
793C2×C4—1464no—
794C2×C4—1464no—
795C2×C4C2×D4×D7311yescharacteristic
796C2×C4C2×D4×D7311yescharacteristic
797C2×C4C2×D4×D7311yescharacteristic
798C2×C4C2×D4×D7311yescharacteristic
799C2×C4C2×D4×D7311yescharacteristic
800C2×C4C2×#1192402812yes—
801C2×C4#1455663812yes—
802C2×C4C24×D7311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—1464no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1798924612yes—
817C22C22×D4×D7311yescharacteristic
818C4—22no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—2924no—
827C4—2924no—
828C4—1464no—
829C4—1464no—
830C4#1798924612yes—
831C4#1798939412yes—
832C4#1798940112yes—
833C4C22×#1192402811yescharacteristic
834C4C2×#1455663811yescharacteristic
835C2—22no—
836C2—42no—
837C2—81no—
838C2C2×#1798924611yescharacteristic
839C2C2×#1798939411yescharacteristic
840C2C2×#1798940111yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC4×#135×C73C2
socleC22×C73C23×D4
prime radicalC2×#135×C73C22
hypercenterC4×#135D73
hypocenterC73#61330
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #22623817C2semidirect
2. #22623750C2semidirect
3. #22622732C2semidirect
4. #22622710C2semidirect
5. #22622669C2semidirect
6. #22622647C2semidirect
7. #22622614C2semidirect
8. #22622607C2semidirect
9. #22622578C2semidirect
10. #22622571C2semidirect
11. #22620300C2semidirect
12. C2×#17988938C2semidirect
13. #22619776C2semidirect
14. #22619746C2semidirect
16. #22619418C2semidirect
17. #22618865C2semidirect
18. #22618777C2semidirect
440. C73#61330semidirect

Maximal subgroups

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

subgroupindex
#226238172
#226237502
#226227322
#226227102
#226226692
#226226472
#226226142
#226226072
#226225782
#226225712
#226203002
C2×#179889382
#226197762
#226197462
#226194792
#226194182
#226188652
#226187772
C4×#135×C732
#6133073