Finite Group Databasebeta

← #11034543

Subgroups — #11034543

Order 768.

1472 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2296C211yesmaximal, characteristic
2#82256C211yesmaximal, characteristic
3#82248C211yesmaximal, characteristic
4#82243C211yesmaximal, characteristic
5#82240C211yesmaximal, characteristic
6#82075C211yesmaximal, characteristic
7#82060C211yesmaximal, characteristic
8#76105C211yesmaximal, characteristic, complemented
9#76103C211yesmaximal, characteristic, complemented
10#76049C211yesmaximal, characteristic, complemented
11#76039C211yesmaximal, characteristic, complemented
12#76035C211yesmaximal, characteristic, complemented
13#76009C211yesmaximal, characteristic, complemented
14#75974C211yesmaximal, characteristic, complemented
15#75970C211yesmaximal, characteristic, complemented
16#74557C212yesmaximal
17#74555C212yesmaximal
18#74546C212yesmaximal
19#74545C212yesmaximal
20#73703C212yesmaximal, complemented
21#73702C212yesmaximal, complemented
22#73700C212yesmaximal, complemented
23#73697C212yesmaximal, complemented
24#38075—31nomaximal, Sylow
25C2×C3×#117C2211yescharacteristic
26C2×C3×#117C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C2×#888C2211yescharacteristic
30C2×#887C2211yescharacteristic
31C3×#389C2211yescharacteristic
32C3×#389C2211yescharacteristic
33C3×#389C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#385C2212yes—
36C3×#385C2212yes—
37C3×C4×C4⋊C4C2212yes—
38C3×C4×C4⋊C4C2212yes—
39#5212C2211yescharacteristic
40#5212C2211yescharacteristic
41#5212C2211yescharacteristic
42#5211C2212yes—
43#5211C2211yescharacteristic
44#5211C2211yescharacteristic
45#5210C2212yes—
46C4×#217C2211yescharacteristic
47C4×#217C2211yescharacteristic
48#4986C2212yes—
49#4986C2212yes—
50#4985C2212yes—
51#4984C2211yescharacteristic
52#4984C2211yescharacteristic
53#4984C2211yescharacteristic
54#4983C2212yes—
55#4982C2212yes—
56#4982C2212yes—
57#4981C2212yes—
58#4981C2212yes—
59#4980C2212yes—
60#4980C2212yes—
61#4978C2212yes—
62#4978C2212yes—
63#4977C2211yescharacteristic
64#4977C2211yescharacteristic
65#4977C2212yes—
66#4975C2211yescharacteristic
67Dic3×C4⋊C4C2211yescharacteristic
68Dic3×C4⋊C4C2211yescharacteristic
69Dic3×C4⋊C4C2211yescharacteristic
70#4973C2211yescharacteristic
71#4973C2211yescharacteristic
72#4973C2212yes—
73#4973C2212yes—
74#4973C2211yescharacteristic
75#4972C2212yes—
76#4972C2211yescharacteristic
77#4972C2211yescharacteristic
78#4952C2212yes—
79#4952C2212yes—
80#4951C2212yes—
81#4951C2212yes—
82#4948C2212yes—
83#4947C2212yes—
84#4945C2212yes—
85#4944C2212yes—
86#4937C2212yes—
87#4937C2211yescharacteristic
88#4937C2211yescharacteristic
89#4936C2211yescharacteristic
90#4936C2211yescharacteristic
91C4×C4⋊Dic3C2211yescharacteristic
92C4×C4⋊Dic3C2211yescharacteristic
93C4×C4⋊Dic3C2212yes—
94#4933C2212yes—
95#4933C2212yes—
96#4933C2212yes—
97#4933C2212yes—
98#4933C2212yes—
99#4933C2212yes—
100#4932C2211yescharacteristic
101#4932C2211yescharacteristic
102C4×Dic3⋊C4C2212yes—
103#4929C2211yescharacteristic
104#4929C2211yescharacteristic
105#4929C2212yes—
106#4928C2211yescharacteristic
107#4928C2211yescharacteristic
108C3⋊#401C2212yes—
109C3⋊#401C2212yes—
110#4661C2212yes—
111#4660C2212yes—
112#4659C2212yes—
113#4658C2212yes—
114#4658C2212yes—
115#4656C2212yes—
116#4655C2212yes—
117#4654C2212yes—
118#4653C2212yes—
119#4652C2212yes—
120#4651C2212yes—
121#4651C2212yes—
122#4650C2212yes—
123#4646C2212yes—
124#2855—31no—
125#2765—32no—
126#2764—32no—
127#2745—32no—
128#2744—32no—
129#2647—31no—
130#2645—31no—
131#2524—32no—
132#2524—32no—
133#2520—32no—
134#2514—31no—
135#2514—32no—
136#2508—31no—
137#2507—31no—
138#2499—31no—
139#2451—31no—
140#2439—31no—
141#2362—31no—
142#2347—31no—
143#2331—31no—
144#2320—31no—
145#2296D311yescharacteristic
146#2283—31no—
147C23×C3×C4C2311yescharacteristic
148C23×C3×C4C2311yescharacteristic
149C23×C3×C4C2311yescharacteristic
150C22×Dic6C2311yescharacteristic
151C22×Dic6C2312yes—
152C3×#117—24no—
153C3×#117—24no—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C4⋊C4C2312yes—
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C22⋊C4C2312yes—
163C2×C3×C22⋊C4C2312yes—
164C2×C3×C42—24no—
165C2×C3×C42C2311yescharacteristic
166C2×C3×C42C2311yescharacteristic
167C2×C3×C42C2312yes—
168C2×C3×C42C2312yes—
169C2×C3×C42C2311yescharacteristic
170C2×C3×C42C2311yescharacteristic
171C2×#217C2312yes—
172C2×#217C2311yescharacteristic
173C2×#217C2311yescharacteristic
174C2×#217C2311yescharacteristic
175C2×#217C2312yes—
176C2×#217C2311yescharacteristic
177C2×C4⋊Dic3C2311yescharacteristic
178C2×C4⋊Dic3C2311yescharacteristic
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2311yescharacteristic
182C2×C4⋊Dic3C2312yes—
183C2×C4⋊Dic3C2311yescharacteristic
184C2×C4⋊Dic3C2312yes—
185C2×C4⋊Dic3C2312yes—
186C2×C4⋊Dic3C2311yescharacteristic
187#924—24no—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2312yes—
197C2×C4×Dic3C2312yes—
198C2×C4×Dic3C2311yescharacteristic
199C2×C4×Dic3C2311yescharacteristic
200C2×C4×Dic3C2311yescharacteristic
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2312yes—
203C2×C4×Dic3C2312yes—
204C2×C4×Dic3C2312yes—
205#888—24no—
206#887—24no—
207C3×#95C2312yes—
208C3×#95C2312yes—
209C3×#95C2312yes—
210C3×#95C2312yes—
211C3⋊#95C2311yescharacteristic
212C3⋊#95C2312yes—
213C3⋊#95C2312yes—
214C3⋊#95C2311yescharacteristic
215C3⋊#95C2312yes—
216C3⋊#95C2312yes—
217C3⋊#95C2311yescharacteristic
218C3⋊#95C2312yes—
219C3⋊#95C2311yescharacteristic
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C3⋊#95C2312yes—
226C3⋊#95C2311yescharacteristic
227C3⋊#95C2312yes—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2312yes—
231C3⋊#95C2312yes—
232C3⋊#95C2312yes—
233C3⋊#95C2311yescharacteristic
234C3⋊#95C2312yes—
235C3⋊#95C2312yes—
236C3⋊#95C2311yescharacteristic
237C3⋊#95C2311yescharacteristic
238C3⋊#95C2312yes—
239C3⋊#95C2312yes—
240C3⋊#95C2312yes—
241C3⋊#95C2311yescharacteristic
242C3⋊#95C2311yescharacteristic
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C3⋊#95C2311yescharacteristic
246C3⋊#95C2311yescharacteristic
247C3⋊#95C2311yescharacteristic
248C3⋊#95C2312yes—
249C3⋊#95C2311yescharacteristic
250C3⋊#95C2311yescharacteristic
251C3⋊#95C2311yescharacteristic
252C2×C4⋊Q8—31no—
253C2×C22⋊Q8—31no—
254C2×C4×Q8—31no—
255C2×#117C2×D311yescharacteristic
256C2×#117C2×D311yescharacteristic
257C22×C42C2×D311yescharacteristic
258#401—32no—
259#401—32no—
260#400—32no—
261#400—32no—
262#400—32no—
263#400—32no—
264#400—32no—
265#400—32no—
266#400—32no—
267#398—32no—
268#398—32no—
269#398—32no—
270#398—32no—
271#398—32no—
272#398—32no—
273#397—32no—
274#397—32no—
275#396—32no—
276#395—32no—
277#393—32no—
278#391—31no—
279#391—32no—
280#391—31no—
281#391—31no—
282#391—32no—
283#391—31no—
284#391—31no—
285#391—32no—
286#391—32no—
287#389—31no—
288#389—31no—
289#389—31no—
290#389—31no—
291#389—31no—
292#389—32no—
293#389—31no—
294#389—31no—
295#389C2×D311yescharacteristic
296#389C2×D311yescharacteristic
297#389C2×D311yescharacteristic
298#389C2×D311yescharacteristic
299#388—32no—
300#388—32no—
301#388—32no—
302#388—32no—
303#387—32no—
304#387—32no—
305#387—32no—
306#387—32no—
307#387—32no—
308#387—32no—
309#387—32no—
310#387—32no—
311#387—32no—
312#387—32no—
313#387—32no—
314#387—32no—
315#387—32no—
316#387—32no—
317#385—32no—
318#385C2×D312yes—
319#385C2×D312yes—
320#384—31no—
321#383—32no—
322#383—31no—
323#383—31no—
324#383—32no—
325#383—32no—
326#382—32no—
327#382—31no—
328#382—31no—
329#382—31no—
330#382—31no—
331#382—32no—
332#381—32no—
333#381—31no—
334#381—31no—
335#380—31no—
336#380—31no—
337#380—31no—
338C4×C4⋊C4—31no—
339C4×C4⋊C4—31no—
340C4×C4⋊C4—31no—
341C4×C4⋊C4—32no—
342C4×C4⋊C4—32no—
343C4×C4⋊C4—31no—
344C4×C4⋊C4—31no—
345C4×C4⋊C4C2×D312yes—
346C4×C4⋊C4C2×D312yes—
347C4×C22⋊C4—31no—
348C4×C22⋊C4—31no—
349#376—31no—
350#376—31no—
351C24×C3C2411yescharacteristic
352C22×C3×C4—22no—
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4—22no—
356C22×C3×C4—22no—
357C22×C3×C4—41no—
358C22×C3×C4—41no—
359C22×C3×C4—41no—
360C22×C3×C4#4114yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2412yes—
363C22×C3×C4C2411yescharacteristic
364C22×C3×C4C2411yescharacteristic
365C22×C3×C4C2412yes—
366C22×C3×C4C2412yes—
367C22×C3×C4C2411yescharacteristic
368C22×C3×C4C2412yes—
369C22×C3×C4C2411yescharacteristic
370C22×C3×C4C2411yescharacteristic
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2411yescharacteristic
373C22×Dic3C2412yes—
374C22×Dic3C2411yescharacteristic
375C22×Dic3C2411yescharacteristic
376C22×Dic3C2411yescharacteristic
377C22×Dic3C2411yescharacteristic
378C22×Dic3C2411yescharacteristic
379C22×Dic3C2412yes—
380C22×Dic3C2412yes—
381C22×Dic3C2411yescharacteristic
382C22×Dic3C2412yes—
383C2×Dic6—22no—
384C2×Dic6—22no—
385C2×Dic6—22no—
386C2×Dic6—24no—
387C2×Dic6—42no—
388C2×Dic6—42no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—24no—
393C3×C4⋊C4—42no—
394C3×C4⋊C4—42no—
395C3×C4⋊C4—42no—
396C3×C4⋊C4#4114yes—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C42—22no—
400C3×C42—22no—
401C3×C42—22no—
402C3×C42—22no—
403C3×C42—24no—
404C3×C42—24no—
405#217—24no—
406#217—41no—
407#217—42no—
408#217—41no—
409#217—41no—
410#217—41no—
411C4⋊Dic3—22no—
412C4⋊Dic3—22no—
413C4⋊Dic3—22no—
414C4⋊Dic3—22no—
415C4⋊Dic3—22no—
416C4⋊Dic3—41no—
417C4⋊Dic3—41no—
418C4⋊Dic3—42no—
419C4⋊Dic3—42no—
420C4⋊Dic3—42no—
421Dic3⋊C4—24no—
422Dic3⋊C4—24no—
423Dic3⋊C4—24no—
424Dic3⋊C4—42no—
425Dic3⋊C4—42no—
426Dic3⋊C4—42no—
427Dic3⋊C4—42no—
428Dic3⋊C4—42no—
429Dic3⋊C4—42no—
430C4×Dic3—22no—
431C4×Dic3—24no—
432C4×Dic3—22no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—42no—
436C4×Dic3—42no—
437C4×Dic3—42no—
438C22×Q8—31no—
439C22×Q8—32no—
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C23×C4C22×D311yescharacteristic
443C4⋊Q8—64no—
444C22⋊Q8—64no—
445C4×Q8—64no—
446#117—24no—
447#117—24no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—32no—
461C2×C4⋊C4—32no—
462C2×C4⋊C4—32no—
463C2×C4⋊C4—32no—
464C2×C4⋊C4—32no—
465C2×C4⋊C4—32no—
466C2×C4⋊C4—32no—
467C2×C4⋊C4C22×D311yescharacteristic
468C2×C4⋊C4C22×D311yescharacteristic
469C2×C4⋊C4C22×D311yescharacteristic
470C2×C4⋊C4C22×D312yes—
471C2×C4⋊C4C22×D312yes—
472C2×C4⋊C4C22×D312yes—
473C2×C4⋊C4C22×D312yes—
474C2×C4⋊C4C22×D311yescharacteristic
475C2×C22⋊C4—32no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—32no—
481C2×C22⋊C4C22×D312yes—
482C2×C22⋊C4C22×D312yes—
483C2×C42—24no—
484C2×C42—31no—
485C2×C42—32no—
486C2×C42—31no—
487C2×C42—31no—
488C2×C42—31no—
489C2×C42—32no—
490C2×C42—32no—
491C2×C42—32no—
492C2×C42C22×D312yes—
493C2×C42C22×D312yes—
494C2×C42C22×D311yescharacteristic
495C2×C42C22×D311yescharacteristic
496C2×C42C22×D311yescharacteristic
497C2×C42C22×D311yescharacteristic
498#95—31no—
499#95—31no—
500#95—31no—
501#95—31no—
502#95—31no—
503#95—31no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—32no—
511#95—31no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—32no—
516#95—32no—
517#95—32no—
518#95—32no—
519#95—32no—
520#95—32no—
521#95—32no—
522#95—32no—
523#95—32no—
524#95—32no—
525#95—32no—
526#95—32no—
527#95—32no—
528#95—32no—
529#95—32no—
530#95—32no—
531#95—32no—
532#95—32no—
533#95—32no—
534#95—32no—
535#95—32no—
536#95—32no—
537#95—32no—
538#95—32no—
539#95C22×D312yes—
540#95C22×D312yes—
541#95C22×D312yes—
542#95C22×D312yes—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3C2×#4112yes—
550C23×C3C2511yescharacteristic
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—28no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—21no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—44no—
577C2×C3×C4—44no—
578C2×C3×C4C2×#4114yes—
579C2×C3×C4C2×#4112yes—
580C2×C3×C4C2×#4112yes—
581C2×C3×C4C2×#4112yes—
582C2×C3×C42−1+412yes—
583C2×C3×C42−1+412yes—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—22no—
588C2×Dic3—21no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—22no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—22no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620Dic6—44no—
621Dic6—84no—
622C24C23×D311yescharacteristic
623C2×Q8—62no—
624C2×Q8—64no—
625C2×Q8—62no—
626C2×Q8—62no—
627C2×Q8—122no—
628C2×Q8—122no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—31no—
645C22×C4—32no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4#23714yes—
650C22×C4C23×D311yescharacteristic
651C22×C4C23×D312yes—
652C22×C4C23×D311yescharacteristic
653C22×C4C23×D311yescharacteristic
654C22×C4C23×D312yes—
655C22×C4C23×D312yes—
656C22×C4C23×D312yes—
657C22×C4C23×D311yescharacteristic
658C22×C4C23×D311yescharacteristic
659C22×C4C23×D311yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—24no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—64no—
668C4⋊C4—64no—
669C4⋊C4—62no—
670C4⋊C4—64no—
671C4⋊C4—62no—
672C4⋊C4—62no—
673C4⋊C4—62no—
674C4⋊C4—62no—
675C4⋊C4—122no—
676C4⋊C4—122no—
677C4⋊C4—122no—
678C4⋊C4—122no—
679C4⋊C4—122no—
680C4⋊C4—122no—
681C4⋊C4—122no—
682C4⋊C4—121no—
683C4⋊C4—121no—
684C4⋊C4—122no—
685C4⋊C4—122no—
686C4⋊C4#23514yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—64no—
690C22⋊C4—121no—
691C22⋊C4—122no—
692C22⋊C4—121no—
693C22⋊C4—121no—
694C22⋊C4—121no—
695C42—24no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—24no—
701C42—62no—
702C42—64no—
703C42—62no—
704C42—62no—
705C42—62no—
706C42—122no—
707C42—122no—
708C42—122no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3C22×#4111yescharacteristic
717C22×C3C22×#4111yescharacteristic
718C22×C3C2×2−1+411yescharacteristic
719C22×C3C2×2−1+411yescharacteristic
720C22×C3#58511yescharacteristic
721C22×C3#58511yescharacteristic
722C22×C3#58511yescharacteristic
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—24no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—42no—
730C3×C4—41no—
731C3×C4—42no—
732C3×C4#55214yes—
733Dic3—42no—
734Dic3—42no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—42no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—42no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23C2×#23712yes—
752C23C24×D311yescharacteristic
753Q8—124no—
754Q8—244no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—61no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—61no—
816C2×C4—62no—
817C2×C4—61no—
818C2×C4C2×#23514yes—
819C2×C4C2×#23512yes—
820C2×C4C2×#23712yes—
821C2×C4C2×#23712yes—
822C2×C4#100712yes—
823C2×C4#101012yes—
824C2×C3—42no—
825C2×C3#345511yescharacteristic
826C2×C3C2×#55211yescharacteristic
827C2×C3#349511yescharacteristic
828C2×C3#351811yescharacteristic
829C2×C3#352111yescharacteristic
830C2×C3#355511yescharacteristic
831C2×C3#356511yescharacteristic
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22C22×#23511yescharacteristic
840C22C22×#23711yescharacteristic
841C22C2×#100711yescharacteristic
842C22C2×#101011yescharacteristic
843C22#596411yescharacteristic
844C22#596411yescharacteristic
845C22#596411yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—122no—
856C4—121no—
857C4—121no—
858C4—122no—
859C4—121no—
860C4—121no—
861C4—121no—
862C4—122no—
863C4—121no—
864C4—122no—
865C4—121no—
866C4—121no—
867C4#551314yes—
868C3#3807511yescharacteristic, complemented, Sylow
869C2—42no—
870C2C2×#551311yescharacteristic
871C2#8583211yescharacteristic
872C2#8585411yescharacteristic
873C2#8601911yescharacteristic
874C2#8602811yescharacteristic
875C2#8626911yescharacteristic
876C2#8629311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2296C2
prime radicalC24×C3C24
hypercenter#2296D3
hypocenterC3#38075
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2296

Complements

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

NH ≅ G/Ntype
8. #76105C2semidirect
9. #76103C2semidirect
10. #76049C2semidirect
11. #76039C2semidirect
12. #76035C2semidirect
13. #76009C2semidirect
14. #75974C2semidirect
15. #75970C2semidirect
20. #73703C2semidirect
21. #73702C2semidirect
22. #73700C2semidirect
23. #73697C2semidirect
868. C3#38075semidirect

Maximal subgroups

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

subgroupindex
C3×#22962
#822562
#822482
#822432
#822402
#820752
#820602
#761052
#761032
#760492
#760392
#760352
#760092
#759742
#759702
#745572
#745552
#745462
#745452
#737032
#737022
#737002
#736972
#380753