Finite Group Databasebeta

← #11017242

Subgroups — #11017242

Order 768.

1446 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×#2494C211yesmaximal, characteristic
2#78422C212yesmaximal, complemented
3#78420C212yesmaximal, complemented
4#77592C212yesmaximal
5#77570C212yesmaximal
6#76105C211yesmaximal, characteristic, complemented
7#76033C211yesmaximal, characteristic, complemented
8#76032C211yesmaximal, characteristic, complemented
9#75974C211yesmaximal, characteristic, complemented
10#75730C212yesmaximal
11#75678C212yesmaximal
12#75214C212yesmaximal, complemented
13#75188C212yesmaximal, complemented
14#74196C211yesmaximal, characteristic, complemented
15#74171C211yesmaximal, characteristic, complemented
16#74001C211yesmaximal, characteristic
17#73998C211yesmaximal, characteristic
18#73923C211yesmaximal, characteristic
19#73920C211yesmaximal, characteristic
20#73687C211yesmaximal, characteristic, complemented
21#73626C211yesmaximal, characteristic, complemented
22#73512C211yesmaximal, characteristic
23#73437C211yesmaximal, characteristic
24#37295—31nomaximal, Sylow
25C22×C4×Dic3C2211yescharacteristic
26C2×#890C2211yescharacteristic
27C2×#888C2211yescharacteristic
28C2×#879C2212yes—
29C2×#879C2212yes—
30C2×#878C2212yes—
31C3×#401C2212yes—
32C3×#397C2212yes—
33C3×#389C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#388C2212yes—
36C3×#387C2212yes—
37C3×#382C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C3×C4×C4⋊C4C2211yescharacteristic
41C3×C4×C22⋊C4C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C4×#217C2211yescharacteristic
45#4984C2211yescharacteristic
46#4984C2212yes—
47#4984C2211yescharacteristic
48#4984C2211yescharacteristic
49#4984C2211yescharacteristic
50#4983C2212yes—
51#4983C2212yes—
52#4982C2212yes—
53#4982C2212yes—
54#4981C2212yes—
55#4978C2212yes—
56#4977C2211yescharacteristic
57#4977C2211yescharacteristic
58#4975C2211yescharacteristic
59#4975C2211yescharacteristic
60Dic3×C4⋊C4C2211yescharacteristic
61Dic3×C4⋊C4C2211yescharacteristic
62#4973C2212yes—
63#4972C2211yescharacteristic
64#4972C2211yescharacteristic
65#4972C2211yescharacteristic
66#4972C2211yescharacteristic
67#4953C2212yes—
68#4953C2212yes—
69#4952C2212yes—
70#4950C2212yes—
71#4946C2212yes—
72#4945C2212yes—
73#4943C2211yescharacteristic
74#4943C2211yescharacteristic
75#4942C2212yes—
76#4942C2211yescharacteristic
77#4942C2211yescharacteristic
78#4936C2212yes—
79#4935C2211yescharacteristic
80C4×C4⋊Dic3C2211yescharacteristic
81#4933C2212yes—
82#4933C2212yes—
83#4932C2211yescharacteristic
84#4932C2211yescharacteristic
85C4×Dic3⋊C4C2211yescharacteristic
86C4×Dic3⋊C4C2211yescharacteristic
87#4928C2211yescharacteristic
88#4928C2211yescharacteristic
89#4928C2212yes—
90#4661C2212yes—
91#4660C2212yes—
92#4660C2212yes—
93#4660C2212yes—
94#4659C2212yes—
95#4659C2212yes—
96#4658C2212yes—
97#4658C2212yes—
98#4658C2212yes—
99#4657C2212yes—
100#4657C2212yes—
101#4657C2212yes—
102#4656C2212yes—
103#4656C2212yes—
104#4655C2212yes—
105#4655C2212yes—
106#4654C2212yes—
107#4654C2212yes—
108#4653C2212yes—
109#4653C2212yes—
110#4652C2212yes—
111#4652C2212yes—
112#4652C2212yes—
113#4651C2212yes—
114#4651C2211yescharacteristic
115#4651C2211yescharacteristic
116#4650C2211yescharacteristic
117#4650C2211yescharacteristic
118#4647C2212yes—
119#4647C2212yes—
120#4647C2212yes—
121#4647C2212yes—
122#4646C2212yes—
123#4646C2212yes—
124#2857—31no—
125#2851—31no—
126#2776—32no—
127#2769—32no—
128#2762—32no—
129#2755—32no—
130#2747—32no—
131#2722—32no—
132#2698—32no—
133#2689—32no—
134#2660—31no—
135#2647—31no—
136#2509—31no—
137#2508—31no—
138#2507—31no—
139#2507—31no—
140#2496—31no—
141#2496—31no—
142#2495—31no—
143#2494D311yescharacteristic
144#2331—31no—
145#2330—31no—
146#2283—31no—
147C23×C3×C4C2311yescharacteristic
148C23×Dic3C2311yescharacteristic
149C23×Dic3C2311yescharacteristic
150C22×Dic6C2312yes—
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C22⋊C4C2311yescharacteristic
158C2×C3×C22⋊C4C2312yes—
159C2×C3×C22⋊C4C2311yescharacteristic
160C2×C3×C22⋊C4C2312yes—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2312yes—
164C2×#217C2311yescharacteristic
165C2×#217C2312yes—
166C2×#217C2312yes—
167C2×#217C2311yescharacteristic
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2312yes—
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2312yes—
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2311yescharacteristic
183C2×Dic3⋊C4C2311yescharacteristic
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2311yescharacteristic
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2311yescharacteristic
194C2×Dic3⋊C4C2312yes—
195C2×C4×Dic3—24no—
196C2×C4×Dic3C2311yescharacteristic
197C2×C4×Dic3C2311yescharacteristic
198C2×C4×Dic3C2311yescharacteristic
199C2×C4×Dic3C2311yescharacteristic
200C2×C4×Dic3C2311yescharacteristic
201C2×C4×Dic3C2312yes—
202C2×C4×Dic3C2312yes—
203C2×C4×Dic3C2312yes—
204C2×C4×Dic3C2311yescharacteristic
205#890—24no—
206#888—24no—
207#879—44no—
208#879—44no—
209#878—44no—
210C3×#95C2312yes—
211C3×#95C2312yes—
212C3×#95C2312yes—
213C3×#95C2312yes—
214C3×#95C2311yescharacteristic
215C3×#95C2311yescharacteristic
216C3×#95C2312yes—
217C3×#95C2312yes—
218C3×#95C2312yes—
219C3⋊#95C2311yescharacteristic
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C3⋊#95C2311yescharacteristic
226C3⋊#95C2311yescharacteristic
227C3⋊#95C2311yescharacteristic
228C3⋊#95C2311yescharacteristic
229C3⋊#95C2311yescharacteristic
230C3⋊#95C2311yescharacteristic
231C3⋊#95C2311yescharacteristic
232C3⋊#95C2312yes—
233C3⋊#95C2311yescharacteristic
234C3⋊#95C2312yes—
235C3⋊#95C2312yes—
236C3⋊#95C2311yescharacteristic
237C3⋊#95C2311yescharacteristic
238C3⋊#95C2311yescharacteristic
239C3⋊#95C2311yescharacteristic
240C3⋊#95C2311yescharacteristic
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C3⋊#95C2312yes—
246C3⋊#95C2312yes—
247C3⋊#95C2312yes—
248C3⋊#95C2312yes—
249C3⋊#95C2312yes—
250C3⋊#95C2312yes—
251C3⋊#95C2312yes—
252C2×C4⋊Q8—31no—
253C2×#126—32no—
254C2×#126—32no—
255C2×#125—31no—
256C2×C22⋊Q8—32no—
257C22×C42—31no—
258#401C2×D312yes—
259#400—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#398—32no—
274#398—32no—
275#398—32no—
276#397—32no—
277#397—32no—
278#397—32no—
279#397C2×D312yes—
280#395—32no—
281#395—32no—
282#391—32no—
283#391—32no—
284#391—32no—
285#389—31no—
286#389—31no—
287#389—31no—
288#389—31no—
289#389—31no—
290#389—31no—
291#389—31no—
292#389—31no—
293#389—32no—
294#389—32no—
295#389—31no—
296#389—31no—
297#389—32no—
298#389—32no—
299#389—32no—
300#389—32no—
301#389C2×D311yescharacteristic
302#389C2×D311yescharacteristic
303#388—32no—
304#388C2×D312yes—
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#387C2×D312yes—
318#385—32no—
319#385—32no—
320#384—31no—
321#384—31no—
322#384—31no—
323#383—32no—
324#383—31no—
325#383—31no—
326#382—31no—
327#382—31no—
328#382—32no—
329#382—31no—
330#382—31no—
331#382C2×D311yescharacteristic
332#381—31no—
333#381—31no—
334#380—31no—
335#380—31no—
336#380—32no—
337#380—31no—
338#380—31no—
339#380C2×D311yescharacteristic
340#380C2×D311yescharacteristic
341C4×C4⋊C4—31no—
342C4×C4⋊C4—31no—
343C4×C4⋊C4—31no—
344C4×C4⋊C4—31no—
345C4×C4⋊C4—31no—
346C4×C4⋊C4C2×D311yescharacteristic
347C4×C22⋊C4—31no—
348C4×C22⋊C4C2×D311yescharacteristic
349#376—31no—
350#376—31no—
351C24×C3C2411yescharacteristic
352C22×C3×C4—22no—
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4C2411yescharacteristic
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2412yes—
359C22×C3×C4C2412yes—
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2412yes—
363C22×C3×C4C2412yes—
364C22×C3×C4C2411yescharacteristic
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3—22no—
368C22×Dic3—22no—
369C22×Dic3—41no—
370C22×Dic3—41no—
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2411yescharacteristic
373C22×Dic3C2412yes—
374C22×Dic3C2411yescharacteristic
375C22×Dic3C2411yescharacteristic
376C22×Dic3C2411yescharacteristic
377C22×Dic3C2412yes—
378C22×Dic3C2412yes—
379C22×Dic3C2412yes—
380C22×Dic3C2411yescharacteristic
381C22×Dic3C2411yescharacteristic
382C22×Dic3C2411yescharacteristic
383C2×Dic6—24no—
384C2×Dic6—42no—
385C2×Dic6—42no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—42no—
391C3×C4⋊C4—42no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—42no—
395C3×C22⋊C4—41no—
396C3×C42—22no—
397C3×C42—22no—
398C3×C42—42no—
399#217—24no—
400#217—22no—
401#217—24no—
402#217—41no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—24no—
408C4⋊Dic3—42no—
409C4⋊Dic3—42no—
410C4⋊Dic3—42no—
411C4⋊Dic3—42no—
412C4⋊Dic3—42no—
413C4⋊Dic3—42no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4—24no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—42no—
420Dic3⋊C4—42no—
421Dic3⋊C4—42no—
422Dic3⋊C4—42no—
423Dic3⋊C4—42no—
424Dic3⋊C4—42no—
425Dic3⋊C4—41no—
426Dic3⋊C4—42no—
427Dic3⋊C4—41no—
428Dic3⋊C4—42no—
429Dic3⋊C4—42no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—42no—
436C4×Dic3—42no—
437C4×Dic3—42no—
438C4×Dic3#4114yes—
439C22×Q8—32no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4C22×D311yescharacteristic
443C4⋊Q8—64no—
444#126—124no—
445#126—124no—
446#125—64no—
447C22⋊Q8—124no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—32no—
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—32no—
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⋊C4—31no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—32no—
470C2×C4⋊C4—32no—
471C2×C4⋊C4—32no—
472C2×C4⋊C4—32no—
473C2×C4⋊C4—32no—
474C2×C4⋊C4—32no—
475C2×C4⋊C4C22×D311yescharacteristic
476C2×C4⋊C4C22×D311yescharacteristic
477C2×C4⋊C4C22×D311yescharacteristic
478C2×C4⋊C4C22×D311yescharacteristic
479C2×C4⋊C4C22×D312yes—
480C2×C4⋊C4C22×D312yes—
481C2×C22⋊C4—32no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—32no—
484C2×C22⋊C4—31no—
485C2×C22⋊C4C22×D312yes—
486C2×C22⋊C4C22×D311yescharacteristic
487C2×C22⋊C4C22×D311yescharacteristic
488C2×C22⋊C4C22×D312yes—
489C2×C42—31no—
490C2×C42—31no—
491C2×C42—31no—
492C2×C42—31no—
493C2×C42—31no—
494C2×C42—31no—
495C2×C42—32no—
496C2×C42—32no—
497C2×C42—32no—
498C2×C42—64no—
499C2×C42C22×D311yescharacteristic
500C2×C42C22×D311yescharacteristic
501C2×C42C22×D312yes—
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—31no—
511#95—31no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—31no—
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#95C22×D311yescharacteristic
536#95C22×D311yescharacteristic
537#95C22×D312yes—
538#95C22×D312yes—
539#95C22×D312yes—
540#95C22×D312yes—
541#95C22×D312yes—
542#95C22×D312yes—
543#95C22×D312yes—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3H(5,𝔽2)12yes—
551C23×C3C2511yescharacteristic
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
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—21no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—21no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—22no—
578C2×C3×C4—21no—
579C2×C3×C4—44no—
580C2×C3×C4C2×#4112yes—
581C2×C3×C42−1+412yes—
582C2×C3×C42−1+412yes—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—22no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—22no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—21no—
609C2×Dic3—22no—
610C2×Dic3—21no—
611C2×Dic3—22no—
612C2×Dic3—21no—
613C2×Dic3—22no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—44no—
617C2×Dic3—44no—
618C2×Dic3C2×#4112yes—
619C2×Dic3C2×#4112yes—
620C2×Dic32−1+412yes—
621Dic6—84no—
622C24C23×D311yescharacteristic
623C2×Q8—64no—
624C2×Q8—122no—
625C2×Q8—122no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—32no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—121no—
646C22×C4—121no—
647C22×C4C23×D311yescharacteristic
648C22×C4C23×D311yescharacteristic
649C22×C4C23×D311yescharacteristic
650C22×C4C23×D312yes—
651C22×C4C23×D312yes—
652C22×C4C23×D311yescharacteristic
653C22×C4C23×D311yescharacteristic
654C22×C4C23×D312yes—
655C22×C4C23×D312yes—
656C22×C4C23×D311yescharacteristic
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—64no—
666C4⋊C4—62no—
667C4⋊C4—62no—
668C4⋊C4—64no—
669C4⋊C4—62no—
670C4⋊C4—62no—
671C4⋊C4—62no—
672C4⋊C4—62no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C4⋊C4—122no—
677C4⋊C4—122no—
678C4⋊C4—122no—
679C4⋊C4—122no—
680C4⋊C4—122no—
681C4⋊C4—122no—
682C4⋊C4—122no—
683C4⋊C4—121no—
684C4⋊C4—122no—
685C4⋊C4—122no—
686C4⋊C4—121no—
687C4⋊C4—122no—
688C4⋊C4—122no—
689C4⋊C4—122no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—41no—
693C22⋊C4—42no—
694C22⋊C4—64no—
695C22⋊C4—62no—
696C22⋊C4—64no—
697C22⋊C4—121no—
698C42—22no—
699C42—22no—
700C42—34no—
701C42—42no—
702C42—62no—
703C42—62no—
704C42—62no—
705C42—62no—
706C42—62no—
707C42—122no—
708C42—122no—
709C42—122no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3C22×#4111yescharacteristic
718C22×C3C2×H(5,𝔽2)11yescharacteristic
719C22×C3C2×2−1+411yescharacteristic
720C22×C3C2×2−1+411yescharacteristic
721C22×C3C2×2−1+411yescharacteristic
722C22×C3#58511yescharacteristic
723C22×C3#58511yescharacteristic
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4—41no—
732C3×C4—42no—
733C3×C4#54114yes—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—42no—
738Dic3—42no—
739Dic3—41no—
740Dic3—42no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—42no—
745Dic3—41no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23#100912yes—
753C23C24×D311yescharacteristic
754Q8—244no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—44no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—61no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—61no—
800C2×C4—62no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—61no—
813C2×C4—62no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—62no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—124no—
820C2×C4—124no—
821C2×C4D3×#4112yes—
822C2×C4#101012yes—
823C2×C4#101012yes—
824C2×C3—42no—
825C2×C3C2×#54111yescharacteristic
826C2×C3#349411yescharacteristic
827C2×C3#349511yescharacteristic
828C2×C3#354411yescharacteristic
829C2×C3#355511yescharacteristic
830C2×C3#355911yescharacteristic
831C2×C3#356511yescharacteristic
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22C2×D3×#4111yescharacteristic
840C22C2×#100911yescharacteristic
841C22C2×#101011yescharacteristic
842C22C2×#101011yescharacteristic
843C22#596411yescharacteristic
844C22#596611yescharacteristic
845C22D3×2−1+411yescharacteristic
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—62no—
856C4—62no—
857C4—62no—
858C4—122no—
859C4—121no—
860C4—121no—
861C4—122no—
862C4—121no—
863C4—121no—
864C4—122no—
865C4—122no—
866C4—121no—
867C4#570114yes—
868C3#3729511yescharacteristic, complemented, Sylow
869C2—42no—
870C2C2×#570111yescharacteristic
871C2#8615611yescharacteristic
872C2#8655111yescharacteristic
873C2#8684711yescharacteristic
874C2#8690011yescharacteristic
875C2#8690311yescharacteristic
876C2#8699611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2494C2
prime radicalC24×C3C24
hypercenter#2494D3
hypocenterC3#37295
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2494

Complements

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

NH ≅ G/Ntype
2. #78422C2semidirect
3. #78420C2semidirect
6. #76105C2semidirect
7. #76033C2semidirect
8. #76032C2semidirect
9. #75974C2semidirect
12. #75214C2semidirect
13. #75188C2semidirect
14. #74196C2semidirect
15. #74171C2semidirect
20. #73687C2semidirect
21. #73626C2semidirect
868. C3#37295semidirect

Maximal subgroups

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

subgroupindex
C3×#24942
#784222
#784202
#775922
#775702
#761052
#760332
#760322
#759742
#757302
#756782
#752142
#751882
#741962
#741712
#740012
#739982
#739232
#739202
#736872
#736262
#735122
#734372
#372953