Finite Group Databasebeta

← #11232935

Subgroups — #11232935

Order 768.

1442 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2362C211yesmaximal, characteristic
2#82754C211yesmaximal, characteristic
3#82753C211yesmaximal, characteristic
4#82471C211yesmaximal, characteristic, complemented
5#82460C211yesmaximal, characteristic, complemented
6#82249C211yesmaximal, characteristic
7#82239C211yesmaximal, characteristic
8#76489C211yesmaximal, characteristic, complemented
9#76483C211yesmaximal, characteristic, complemented
10#76073C211yesmaximal, characteristic, complemented
11#76034C211yesmaximal, characteristic, complemented
12#75761C212yesmaximal
13#75760C212yesmaximal
14#75758C212yesmaximal
15#75571C212yesmaximal
16#75214C212yesmaximal, complemented
17#75074C212yesmaximal, complemented
18#73706C212yesmaximal, complemented
19#73689C211yesmaximal, characteristic, complemented
20#73686C212yesmaximal, complemented
21#73626C211yesmaximal, characteristic, complemented
22#73511C211yesmaximal, characteristic
23#73482C211yesmaximal, characteristic
24#45317—31nomaximal, Sylow
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×#117C2211yescharacteristic
28C2×Q8×Dic3C2211yescharacteristic
29C2×Q8×Dic3C2211yescharacteristic
30C2×#890C2211yescharacteristic
31C3×#391C2211yescharacteristic
32C3×#389C2211yescharacteristic
33C3×#388C2212yes—
34C3×#388C2212yes—
35C3×#387C2212yes—
36C3×C4×C4⋊C4C2211yescharacteristic
37C3×C4×C4⋊C4C2212yes—
38C3×C4×C22⋊C4C2211yescharacteristic
39#5229C2211yescharacteristic
40#5229C2211yescharacteristic
41#5212C2211yescharacteristic
42#5212C2211yescharacteristic
43C4×#217C2211yescharacteristic
44C4×#217C2211yescharacteristic
45#4986C2212yes—
46#4986C2212yes—
47#4984C2211yescharacteristic
48#4984C2212yes—
49#4984C2211yescharacteristic
50#4984C2212yes—
51#4984C2211yescharacteristic
52#4983C2212yes—
53#4983C2212yes—
54#4982C2212yes—
55#4981C2212yes—
56#4978C2212yes—
57#4978C2212yes—
58#4978C2212yes—
59#4977C2211yescharacteristic
60#4976C2212yes—
61#4975C2211yescharacteristic
62#4975C2211yescharacteristic
63Dic3×C4⋊C4C2211yescharacteristic
64Dic3×C4⋊C4C2211yescharacteristic
65#4972C2211yescharacteristic
66#4972C2211yescharacteristic
67#4972C2211yescharacteristic
68#4953C2211yescharacteristic
69#4953C2212yes—
70#4952C2211yescharacteristic
71#4952C2211yescharacteristic
72#4952C2212yes—
73#4951C2212yes—
74#4951C2212yes—
75#4949C2212yes—
76#4949C2212yes—
77#4948C2211yescharacteristic
78#4948C2212yes—
79#4944C2212yes—
80#4944C2212yes—
81#4944C2212yes—
82#4936C2211yescharacteristic
83#4936C2212yes—
84#4936C2212yes—
85C4×C4⋊Dic3C2211yescharacteristic
86C4×C4⋊Dic3C2212yes—
87C4×C4⋊Dic3C2211yescharacteristic
88#4933C2212yes—
89#4933C2212yes—
90#4933C2212yes—
91#4933C2212yes—
92#4932C2211yescharacteristic
93#4932C2212yes—
94C4×Dic3⋊C4C2211yescharacteristic
95C4×Dic3⋊C4C2211yescharacteristic
96#4928C2211yescharacteristic
97#4928C2211yescharacteristic
98#4928C2212yes—
99#4928C2212yes—
100#4928C2212yes—
101#4928C2212yes—
102C3⋊#401C2211yescharacteristic
103#4660C2211yescharacteristic
104#4660C2212yes—
105#4660C2212yes—
106#4659C2211yescharacteristic
107#4658C2211yescharacteristic
108#4658C2212yes—
109#4658C2212yes—
110#4657C2212yes—
111#4654C2212yes—
112#4654C2212yes—
113#4654C2212yes—
114#4653C2212yes—
115#4653C2212yes—
116#4653C2212yes—
117#4652C2212yes—
118#4651C2212yes—
119#4651C2212yes—
120#4650C2212yes—
121#4650C2212yes—
122#4649C2212yes—
123#4647C2212yes—
124#2773—32no—
125#2773—32no—
126#2772—32no—
127#2769—32no—
128#2570—31no—
129#2533—32no—
130#2528—32no—
131#2525—32no—
132#2509—31no—
133#2508—32no—
134#2507—31no—
135#2495—31no—
136#2453—31no—
137#2441—31no—
138#2423—31no—
139#2421—31no—
140#2401—31no—
141#2362D311yescharacteristic
142#2355—31no—
143#2351—31no—
144#2346—31no—
145#2330—31no—
146#2320—31no—
147C22×C3×Q8C2311yescharacteristic
148C23×C3×C4C2311yescharacteristic
149C3×C22⋊Q8—24no—
150C3×C4×Q8—24no—
151C3×#117—24no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C22⋊C4C2312yes—
159C2×C3×C22⋊C4C2312yes—
160C2×C3×C22⋊C4C2311yescharacteristic
161C2×C3×C22⋊C4C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2312yes—
165C2×C3×C42C2312yes—
166C2×C3×C42C2312yes—
167C2×#217C2311yescharacteristic
168C2×#217C2312yes—
169C2×#217C2312yes—
170C2×#217C2311yescharacteristic
171C2×#217C2311yescharacteristic
172C2×#217C2311yescharacteristic
173Q8×Dic3—24no—
174Q8×Dic3—24no—
175C2×C4⋊Dic3C2311yescharacteristic
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2312yes—
179C2×C4⋊Dic3C2312yes—
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2311yescharacteristic
182C2×C4⋊Dic3C2311yescharacteristic
183C2×C4⋊Dic3C2311yescharacteristic
184C2×C4⋊Dic3C2312yes—
185C2×C4⋊Dic3C2311yescharacteristic
186C2×C4⋊Dic3C2312yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2311yescharacteristic
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2311yescharacteristic
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2312yes—
197C2×Dic3⋊C4C2312yes—
198C2×Dic3⋊C4C2311yescharacteristic
199C2×Dic3⋊C4C2311yescharacteristic
200C2×Dic3⋊C4C2312yes—
201C2×C4×Dic3C2312yes—
202C2×C4×Dic3C2312yes—
203C2×C4×Dic3C2311yescharacteristic
204C2×C4×Dic3C2311yescharacteristic
205C2×C4×Dic3C2311yescharacteristic
206C2×C4×Dic3C2311yescharacteristic
207C2×C4×Dic3C2312yes—
208C2×C4×Dic3C2312yes—
209C2×C4×Dic3C2312yes—
210#890—24no—
211C3×#95C2312yes—
212C3×#95C2312yes—
213C3×#95C2312yes—
214C3×#95C2311yescharacteristic
215C3×#95C2312yes—
216C3×#95C2311yescharacteristic
217C3⋊#95C2311yescharacteristic
218C3⋊#95C2312yes—
219C3⋊#95C2311yescharacteristic
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C3⋊#95C2312yes—
226C3⋊#95C2312yes—
227C3⋊#95C2312yes—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2312yes—
231C3⋊#95C2312yes—
232C3⋊#95C2311yescharacteristic
233C3⋊#95C2312yes—
234C3⋊#95C2311yescharacteristic
235C3⋊#95C2311yescharacteristic
236C3⋊#95C2312yes—
237C3⋊#95C2312yes—
238C3⋊#95C2311yescharacteristic
239C3⋊#95C2311yescharacteristic
240C3⋊#95C2312yes—
241C3⋊#95C2311yescharacteristic
242C3⋊#95C2311yescharacteristic
243C3⋊#95C2312yes—
244C3⋊#95C2311yescharacteristic
245C3⋊#95C2312yes—
246C3⋊#95C2311yescharacteristic
247C3⋊#95C2311yescharacteristic
248C3⋊#95C2312yes—
249C3⋊#95C2312yes—
250C3⋊#95C2311yescharacteristic
251C3⋊#95C2311yescharacteristic
252C2×#125—31no—
253C2×C22⋊Q8C2×D311yescharacteristic
254C2×C4×Q8—31no—
255C2×C4×Q8—31no—
256C2×C4×Q8C2×D311yescharacteristic
257C2×#117C2×D311yescharacteristic
258#401—31no—
259#400—32no—
260#400—32no—
261#400—32no—
262#400—31no—
263#400—32no—
264#400—31no—
265#400—31no—
266#400—32no—
267#400—32no—
268#399—32no—
269#399—32no—
270#398—32no—
271#398—32no—
272#398—32no—
273#398—32no—
274#398—32no—
275#397—31no—
276#397—31no—
277#397—32no—
278#397—31no—
279#397—32no—
280#396—31no—
281#396—32no—
282#391—31no—
283#391—31no—
284#391C2×D311yescharacteristic
285#389—31no—
286#389—31no—
287#389—31no—
288#389—31no—
289#389—31no—
290#389—32no—
291#389—32no—
292#389—31no—
293#389—32no—
294#389—31no—
295#389—32no—
296#389—32no—
297#389—31no—
298#389—32no—
299#389—32no—
300#389—32no—
301#389C2×D311yescharacteristic
302#388—32no—
303#388—32no—
304#388—32no—
305#388—32no—
306#388—32no—
307#388C2×D312yes—
308#388C2×D312yes—
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#387—32no—
318#387—32no—
319#387—32no—
320#387—32no—
321#387—32no—
322#387—32no—
323#387C2×D312yes—
324#384—31no—
325#384—31no—
326#383—32no—
327#383—32no—
328#382—31no—
329#382—31no—
330#382—32no—
331#382—32no—
332#382—32no—
333#382—32no—
334#380—31no—
335#380—31no—
336C4×C4⋊C4—31no—
337C4×C4⋊C4—31no—
338C4×C4⋊C4—31no—
339C4×C4⋊C4—31no—
340C4×C4⋊C4—31no—
341C4×C4⋊C4—32no—
342C4×C4⋊C4—31no—
343C4×C4⋊C4—32no—
344C4×C4⋊C4C2×D311yescharacteristic
345C4×C4⋊C4C2×D312yes—
346C4×C22⋊C4—31no—
347C4×C22⋊C4—31no—
348C4×C22⋊C4C2×D311yescharacteristic
349#376—31no—
350#376—32no—
351C24×C3C2411yescharacteristic
352C2×C3×Q8—22no—
353C2×C3×Q8—22no—
354C2×C3×Q8#4114yes—
355C22×C3×C4—22no—
356C22×C3×C4—22no—
357C22×C3×C4—22no—
358C22×C3×C4C2411yescharacteristic
359C22×C3×C4C2411yescharacteristic
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2412yes—
364C22×C3×C4C2412yes—
365C22×C3×C4C2412yes—
366C22×C3×C4C2412yes—
367C22×C3×C4C2411yescharacteristic
368C22×Dic3C2411yescharacteristic
369C22×Dic3C2411yescharacteristic
370C22×Dic3C2411yescharacteristic
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2412yes—
373C22×Dic3C2412yes—
374C22×Dic3C2411yescharacteristic
375C22×Dic3C2412yes—
376C22×Dic3C2411yescharacteristic
377C22×Dic3C2412yes—
378C22×Dic3C2411yescharacteristic
379C22×Dic3C2411yescharacteristic
380C3×C4⋊C4—22no—
381C3×C4⋊C4—24no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—24no—
384C3×C4⋊C4—42no—
385C3×C4⋊C4#4114yes—
386C3×C22⋊C4—24no—
387C3×C22⋊C4—24no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—41no—
390C3×C42—24no—
391C3×C42—24no—
392C3×C42—22no—
393C3×C42—22no—
394C3×C42—42no—
395#217—22no—
396#217—41no—
397#217—41no—
398#217—42no—
399#217—41no—
400#217—42no—
401C4⋊Dic3—24no—
402C4⋊Dic3—22no—
403C4⋊Dic3—24no—
404C4⋊Dic3—24no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—22no—
408C4⋊Dic3—24no—
409C4⋊Dic3—22no—
410C4⋊Dic3—41no—
411C4⋊Dic3—42no—
412C4⋊Dic3—42no—
413Dic3⋊C4—24no—
414Dic3⋊C4—22no—
415Dic3⋊C4—42no—
416Dic3⋊C4—41no—
417Dic3⋊C4—42no—
418Dic3⋊C4—42no—
419Dic3⋊C4—42no—
420Dic3⋊C4—42no—
421Dic3⋊C4—42no—
422Dic3⋊C4—42no—
423Dic3⋊C4—41no—
424Dic3⋊C4—41no—
425Dic3⋊C4—42no—
426Dic3⋊C4—42no—
427C4×Dic3—22no—
428C4×Dic3—24no—
429C4×Dic3—22no—
430C4×Dic3—24no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3—42no—
434C4×Dic3—42no—
435C4×Dic3—42no—
436C22×Q8C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438#125—64no—
439C22⋊Q8—24no—
440C4×Q8—24no—
441C4×Q8—64no—
442C4×Q8—64no—
443#117—24no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—32no—
447C2×C4⋊C4—32no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—32no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—32no—
457C2×C4⋊C4—32no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—31no—
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⋊C4—32no—
468C2×C4⋊C4—32no—
469C2×C4⋊C4—32no—
470C2×C4⋊C4C22×D311yescharacteristic
471C2×C4⋊C4C22×D312yes—
472C2×C4⋊C4C22×D311yescharacteristic
473C2×C4⋊C4C22×D312yes—
474C2×C4⋊C4C22×D312yes—
475C2×C4⋊C4C22×D311yescharacteristic
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—32no—
481C2×C22⋊C4—32no—
482C2×C22⋊C4C22×D312yes—
483C2×C22⋊C4C22×D312yes—
484C2×C22⋊C4C22×D311yescharacteristic
485C2×C22⋊C4C22×D311yescharacteristic
486C2×C42—31no—
487C2×C42—31no—
488C2×C42—32no—
489C2×C42—32no—
490C2×C42—31no—
491C2×C42—31no—
492C2×C42—32no—
493C2×C42—32no—
494C2×C42—32no—
495C2×C42C22×D312yes—
496C2×C42C22×D311yescharacteristic
497C2×C42C22×D312yes—
498C2×C42C22×D311yescharacteristic
499C2×C42C22×D312yes—
500#95—31no—
501#95—32no—
502#95—31no—
503#95—32no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95—32no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—32no—
513#95—32no—
514#95—32no—
515#95—31no—
516#95—32no—
517#95—31no—
518#95—31no—
519#95—32no—
520#95—31no—
521#95—31no—
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#95C22×D311yescharacteristic
536#95C22×D311yescharacteristic
537#95C22×D312yes—
538#95C22×D312yes—
539#95C22×D312yes—
540#95C22×D312yes—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3C2511yescharacteristic
549C3×Q8—28no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—44no—
576C2×C3×C4C2×#4114yes—
577C2×C3×C4C2×#4112yes—
578C2×C3×C4C2×#4114yes—
579C2×C3×C4C2×#4112yes—
580C2×C3×C42−1+412yes—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—22no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—22no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—21no—
598C2×Dic3—22no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—21no—
616C2×Dic32−1+412yes—
617C24C23×D311yescharacteristic
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8#23514yes—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—32no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—32no—
631C22×C4—31no—
632C22×C4—32no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—32no—
636C22×C4C23×D311yescharacteristic
637C22×C4C23×D311yescharacteristic
638C22×C4C23×D311yescharacteristic
639C22×C4C23×D311yescharacteristic
640C22×C4C23×D311yescharacteristic
641C22×C4C23×D312yes—
642C22×C4C23×D312yes—
643C22×C4C23×D312yes—
644C22×C4C23×D312yes—
645C22×C4C23×D311yescharacteristic
646C4⋊C4—22no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—42no—
651C4⋊C4—62no—
652C4⋊C4—64no—
653C4⋊C4—62no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—62no—
657C4⋊C4—62no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—122no—
663C4⋊C4—122no—
664C4⋊C4—122no—
665C4⋊C4—121no—
666C4⋊C4—122no—
667C4⋊C4—122no—
668C4⋊C4—122no—
669C4⋊C4—122no—
670C4⋊C4—121no—
671C4⋊C4—122no—
672C4⋊C4—122no—
673C4⋊C4—121no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C4⋊C4—121no—
677C4⋊C4#23714yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—62no—
683C22⋊C4—121no—
684C22⋊C4—121no—
685C22⋊C4—122no—
686C22⋊C4—121no—
687C22⋊C4—122no—
688C42—24no—
689C42—24no—
690C42—22no—
691C42—22no—
692C42—42no—
693C42—64no—
694C42—62no—
695C42—64no—
696C42—62no—
697C42—62no—
698C42—62no—
699C42—122no—
700C42—122no—
701C42—122no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3C22×#4111yescharacteristic
710C22×C3C22×#4111yescharacteristic
711C22×C3C2×2−1+411yescharacteristic
712C22×C3C2×2−1+411yescharacteristic
713C22×C3#58511yescharacteristic
714C22×C3#58511yescharacteristic
715C22×C3#58511yescharacteristic
716C3×C4—24no—
717C3×C4—24no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4#55214yes—
726Dic3—22no—
727Dic3—41no—
728Dic3—41no—
729Dic3—42no—
730Dic3—41no—
731Dic3—42no—
732Dic3—41no—
733Dic3—41no—
734Dic3—42no—
735Dic3—41no—
736Dic3—41no—
737Dic3—42no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23C24×D311yescharacteristic
746Q8—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—32no—
773C2×C4—44no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—62no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—61no—
809C2×C4C2×#23514yes—
810C2×C4C2×#23512yes—
811C2×C4C2×#23714yes—
812C2×C4C2×#23712yes—
813C2×C4#101012yes—
814C2×C3—81no—
815C2×C3C2×#55211yescharacteristic
816C2×C3#351511yescharacteristic
817C2×C3#351611yescharacteristic
818C2×C3#352411yescharacteristic
819C2×C3#352411yescharacteristic
820C2×C3#355511yescharacteristic
821C2×C3#356511yescharacteristic
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22C22×#23511yescharacteristic
830C22C22×#23711yescharacteristic
831C22C2×#101011yescharacteristic
832C22#596411yescharacteristic
833C22#596411yescharacteristic
834C22D3×2−1+411yescharacteristic
835C22#596811yescharacteristic
836C4—24no—
837C4—24no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—41no—
845C4—62no—
846C4—121no—
847C4—122no—
848C4—121no—
849C4—122no—
850C4—121no—
851C4—121no—
852C4—122no—
853C4—121no—
854C4—121no—
855C4—122no—
856C4—121no—
857C4#554114yes—
858C3#4531711yescharacteristic, complemented, Sylow
859C2—81no—
860C2C2×#554111yescharacteristic
861C2#8585511yescharacteristic
862C2#8588311yescharacteristic
863C2#8668211yescharacteristic
864C2#8672311yescharacteristic
865C2#8685511yescharacteristic
866C2#8699611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2362C2
prime radicalC24×C3C24
hypercenter#2362D3
hypocenterC3#45317
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2362

Complements

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

NH ≅ G/Ntype
4. #82471C2semidirect
5. #82460C2semidirect
8. #76489C2semidirect
9. #76483C2semidirect
10. #76073C2semidirect
11. #76034C2semidirect
16. #75214C2semidirect
17. #75074C2semidirect
18. #73706C2semidirect
19. #73689C2semidirect
20. #73686C2semidirect
21. #73626C2semidirect
858. C3#45317semidirect

Maximal subgroups

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

subgroupindex
C3×#23622
#827542
#827532
#824712
#824602
#822492
#822392
#764892
#764832
#760732
#760342
#757612
#757602
#757582
#755712
#752142
#750742
#737062
#736892
#736862
#736262
#735112
#734822
#453173