Finite Group Databasebeta

← #11034484

Subgroups — #11034484

Order 768.

1464 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2346C211yesmaximal, characteristic
2#82256C211yesmaximal, characteristic
3#82226C211yesmaximal, characteristic
4#76105C211yesmaximal, characteristic, complemented
5#76103C211yesmaximal, characteristic, complemented
6#76042C211yesmaximal, characteristic, complemented
7#76012C211yesmaximal, characteristic, complemented
8#75756C212yesmaximal
9#75750C212yesmaximal
10#75717C212yesmaximal
11#75715C212yesmaximal
12#74177C212yesmaximal, complemented
13#74170C212yesmaximal, complemented
14#74000C211yesmaximal, characteristic
15#73900C211yesmaximal, characteristic
16#73691C211yesmaximal, characteristic, complemented
17#73685C211yesmaximal, characteristic, complemented
18#73626C211yesmaximal, characteristic, complemented
19#73625C211yesmaximal, characteristic, complemented
20#73468C211yesmaximal, characteristic
21#73437C211yesmaximal, characteristic
22#73402C212yesmaximal, complemented
23#73399C212yesmaximal, complemented
24#38072—31nomaximal, Sylow
25C2×C3×#117C2211yescharacteristic
26C2×#926C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#890C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C3×#389C2211yescharacteristic
32C3×#389C2211yescharacteristic
33C3×#388C2212yes—
34C3×#388C2212yes—
35C3×#382C2212yes—
36C3×#380C2211yescharacteristic
37C3×C4×C4⋊C4C2211yescharacteristic
38C3×C4×C4⋊C4C2211yescharacteristic
39C3×C4×C22⋊C4C2211yescharacteristic
40C3×#376C2212yes—
41C4×#217C2211yescharacteristic
42#4986C2212yes—
43#4985C2212yes—
44#4984C2211yescharacteristic
45#4984C2211yescharacteristic
46#4984C2211yescharacteristic
47#4983C2212yes—
48#4982C2212yes—
49#4980C2212yes—
50#4980C2212yes—
51#4977C2211yescharacteristic
52#4976C2212yes—
53#4976C2212yes—
54#4975C2211yescharacteristic
55#4975C2211yescharacteristic
56#4973C2211yescharacteristic
57#4973C2211yescharacteristic
58#4973C2211yescharacteristic
59#4973C2211yescharacteristic
60#4972C2211yescharacteristic
61#4972C2211yescharacteristic
62#4972C2211yescharacteristic
63#4972C2211yescharacteristic
64#4972C2211yescharacteristic
65#4952C2212yes—
66#4952C2212yes—
67#4950C2212yes—
68#4949C2212yes—
69#4948C2212yes—
70#4946C2212yes—
71#4946C2212yes—
72#4945C2212yes—
73#4944C2212yes—
74#4943C2212yes—
75#4943C2211yescharacteristic
76#4943C2211yescharacteristic
77#4942C2211yescharacteristic
78#4942C2211yescharacteristic
79C4×C4⋊Dic3C2211yescharacteristic
80#4933C2212yes—
81#4933C2212yes—
82#4933C2212yes—
83#4933C2212yes—
84#4933C2212yes—
85#4933C2212yes—
86#4933C2212yes—
87#4933C2212yes—
88#4932C2211yescharacteristic
89#4932C2211yescharacteristic
90C4×Dic3⋊C4C2211yescharacteristic
91C4×Dic3⋊C4C2212yes—
92C4×Dic3⋊C4C2212yes—
93C4×Dic3⋊C4C2211yescharacteristic
94#4929C2211yescharacteristic
95#4928C2211yescharacteristic
96#4928C2212yes—
97#4928C2212yes—
98C3⋊#401C2212yes—
99#4660C2212yes—
100#4659C2212yes—
101#4659C2212yes—
102#4658C2212yes—
103#4658C2212yes—
104#4658C2212yes—
105#4658C2212yes—
106#4658C2212yes—
107#4657C2212yes—
108#4657C2212yes—
109#4657C2212yes—
110#4655C2212yes—
111#4654C2212yes—
112#4653C2212yes—
113#4653C2212yes—
114#4652C2212yes—
115#4651C2212yes—
116#4651C2211yescharacteristic
117#4651C2211yescharacteristic
118#4650C2212yes—
119#4650C2211yescharacteristic
120#4650C2211yescharacteristic
121#4649C2212yes—
122#4647C2212yes—
123#4647C2212yes—
124#2855—31no—
125#2771—32no—
126#2765—32no—
127#2739—32no—
128#2738—32no—
129#2647—31no—
130#2645—31no—
131#2533—32no—
132#2528—32no—
133#2524—32no—
134#2511—31no—
135#2509—31no—
136#2508—32no—
137#2507—31no—
138#2499—31no—
139#2453—31no—
140#2441—31no—
141#2362—31no—
142#2346D311yescharacteristic
143#2330—31no—
144#2320—31no—
145#2296—31no—
146#2283—31no—
147C23×C3×C4C2311yescharacteristic
148C23×Dic3C2311yescharacteristic
149C23×Dic3C2311yescharacteristic
150C22×Dic6C2311yescharacteristic
151C3×#117—24no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C4⋊C4C2312yes—
158C2×C3×C22⋊C4C2312yes—
159C2×C3×C22⋊C4C2311yescharacteristic
160C2×C3×C22⋊C4C2311yescharacteristic
161C2×C3×C22⋊C4C2312yes—
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2312yes—
165C2×C3×C42C2312yes—
166C2×C3×C42C2312yes—
167C2×#217C2312yes—
168C2×#217C2312yes—
169C2×#217C2311yescharacteristic
170C2×#217C2311yescharacteristic
171#926—24no—
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2311yescharacteristic
174C2×C4⋊Dic3C2311yescharacteristic
175C2×C4⋊Dic3C2312yes—
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2311yescharacteristic
179#924—24no—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2311yescharacteristic
183C2×Dic3⋊C4C2311yescharacteristic
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2311yescharacteristic
192C2×Dic3⋊C4C2311yescharacteristic
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2312yes—
197C2×C4×Dic3—24no—
198C2×C4×Dic3C2312yes—
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2311yescharacteristic
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2311yescharacteristic
203C2×C4×Dic3C2311yescharacteristic
204C2×C4×Dic3C2311yescharacteristic
205C2×C4×Dic3C2311yescharacteristic
206C2×C4×Dic3C2312yes—
207#890—24no—
208C4×Dic6—24no—
209C3×#95C2312yes—
210C3×#95C2312yes—
211C3×#95C2311yescharacteristic
212C3×#95C2311yescharacteristic
213C3×#95C2312yes—
214C3×#95C2312yes—
215C3×#95C2312yes—
216C3⋊#95C2311yescharacteristic
217C3⋊#95C2311yescharacteristic
218C3⋊#95C2312yes—
219C3⋊#95C2311yescharacteristic
220C3⋊#95C2311yescharacteristic
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2311yescharacteristic
224C3⋊#95C2311yescharacteristic
225C3⋊#95C2311yescharacteristic
226C3⋊#95C2312yes—
227C3⋊#95C2311yescharacteristic
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2311yescharacteristic
231C3⋊#95C2311yescharacteristic
232C3⋊#95C2311yescharacteristic
233C3⋊#95C2311yescharacteristic
234C3⋊#95C2312yes—
235C3⋊#95C2311yescharacteristic
236C3⋊#95C2311yescharacteristic
237C3⋊#95C2312yes—
238C3⋊#95C2312yes—
239C3⋊#95C2312yes—
240C3⋊#95C2312yes—
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C3⋊#95C2312yes—
246C3⋊#95C2312yes—
247C3⋊#95C2312yes—
248C3⋊#95C2312yes—
249C3⋊#95C2312yes—
250C3⋊#95C2312yes—
251C3⋊#95C2312yes—
252C2×#125—31no—
253C2×C22⋊Q8—31no—
254C2×C4×Q8—31no—
255C2×#117—31no—
256C2×#117C2×D311yescharacteristic
257C22×C42—31no—
258#401—32no—
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#400—32no—
268#400—32no—
269#399—32no—
270#398—32no—
271#398—32no—
272#398—32no—
273#398—32no—
274#398—32no—
275#397—32no—
276#397—32no—
277#396—32no—
278#391—31no—
279#391—31no—
280#391—31no—
281#391—31no—
282#391—31no—
283#389—31no—
284#389—31no—
285#389—31no—
286#389—31no—
287#389—31no—
288#389—31no—
289#389—31no—
290#389—31no—
291#389—32no—
292#389—32no—
293#389—32no—
294#389—31no—
295#389—32no—
296#389—32no—
297#389—32no—
298#389C2×D311yescharacteristic
299#389C2×D311yescharacteristic
300#388—32no—
301#388—32no—
302#388C2×D312yes—
303#388C2×D312yes—
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#387—32no—
318#387—32no—
319#385—32no—
320#385—32no—
321#385—32no—
322#384—31no—
323#384—31no—
324#383—32no—
325#383—31no—
326#383—31no—
327#382—31no—
328#382—32no—
329#382—31no—
330#382—31no—
331#382C2×D312yes—
332#381—32no—
333#381—31no—
334#381—31no—
335#380—31no—
336#380—31no—
337#380C2×D311yescharacteristic
338C4×C4⋊C4—31no—
339C4×C4⋊C4—31no—
340C4×C4⋊C4—32no—
341C4×C4⋊C4—31no—
342C4×C4⋊C4—32no—
343C4×C4⋊C4—32no—
344C4×C4⋊C4C2×D311yescharacteristic
345C4×C4⋊C4C2×D311yescharacteristic
346C4×C22⋊C4—31no—
347C4×C22⋊C4C2×D311yescharacteristic
348#376—31no—
349#376—31no—
350#376C2×D312yes—
351C24×C3C2411yescharacteristic
352C22×C3×C4—22no—
353C22×C3×C4—22no—
354C22×C3×C4#4114yes—
355C22×C3×C4C2411yescharacteristic
356C22×C3×C4C2412yes—
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2411yescharacteristic
359C22×C3×C4C2412yes—
360C22×C3×C4C2412yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2412yes—
363C22×C3×C4C2411yescharacteristic
364C22×C3×C4C2411yescharacteristic
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3—22no—
368C22×Dic3—41no—
369C22×Dic3—41no—
370C22×Dic3—41no—
371C22×Dic3C2411yescharacteristic
372C22×Dic3C2411yescharacteristic
373C22×Dic3C2412yes—
374C22×Dic3C2411yescharacteristic
375C22×Dic3C2411yescharacteristic
376C22×Dic3C2411yescharacteristic
377C22×Dic3C2411yescharacteristic
378C22×Dic3C2411yescharacteristic
379C22×Dic3C2412yes—
380C22×Dic3C2412yes—
381C22×Dic3C2412yes—
382C22×Dic3C2411yescharacteristic
383C2×Dic6—22no—
384C2×Dic6—22no—
385C2×Dic6—22no—
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—41no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—42no—
396C3×C42—22no—
397C3×C42—24no—
398C3×C42—22no—
399C3×C42—42no—
400C3×C42—42no—
401#217—24no—
402#217—24no—
403#217—41no—
404#217—41no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—24no—
408C4⋊Dic3—42no—
409C4⋊Dic3—42no—
410C4⋊Dic3—42no—
411C4⋊Dic3#4114yes—
412Dic3⋊C4—24no—
413Dic3⋊C4—24no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—42no—
419Dic3⋊C4—42no—
420Dic3⋊C4—41no—
421Dic3⋊C4—41no—
422Dic3⋊C4—42no—
423Dic3⋊C4—42no—
424Dic3⋊C4—42no—
425Dic3⋊C4—42no—
426Dic3⋊C4—42no—
427Dic3⋊C4—42no—
428Dic3⋊C4—42no—
429C4×Dic3—22no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—24no—
436C4×Dic3—24no—
437C4×Dic3—42no—
438C22×Q8—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4C22×D311yescharacteristic
442#125—64no—
443C22⋊Q8—64no—
444C4×Q8—64no—
445#117—24no—
446#117—64no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4—32no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—32no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—31no—
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—32no—
468C2×C4⋊C4—32no—
469C2×C4⋊C4—32no—
470C2×C4⋊C4—32no—
471C2×C4⋊C4C22×D311yescharacteristic
472C2×C4⋊C4C22×D311yescharacteristic
473C2×C4⋊C4C22×D311yescharacteristic
474C2×C4⋊C4C22×D311yescharacteristic
475C2×C4⋊C4C22×D312yes—
476C2×C4⋊C4C22×D312yes—
477C2×C22⋊C4—32no—
478C2×C22⋊C4—32no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4C22×D312yes—
482C2×C22⋊C4C22×D311yescharacteristic
483C2×C22⋊C4C22×D311yescharacteristic
484C2×C22⋊C4C22×D312yes—
485C2×C42—32no—
486C2×C42—32no—
487C2×C42—31no—
488C2×C42—31no—
489C2×C42—31no—
490C2×C42—31no—
491C2×C42—31no—
492C2×C42—31no—
493C2×C42—32no—
494C2×C42—64no—
495C2×C42C22×D312yes—
496C2×C42C22×D311yescharacteristic
497C2×C42C22×D311yescharacteristic
498C2×C42C22×D312yes—
499C2×C42C22×D312yes—
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—31no—
511#95—31no—
512#95—31no—
513#95—31no—
514#95—32no—
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#95C22×D311yescharacteristic
537#95C22×D312yes—
538#95C22×D312yes—
539#95C22×D312yes—
540#95C22×D311yescharacteristic
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—28no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4C2×#4112yes—
579C2×C3×C4C2×#4112yes—
580C2×C3×C4C2×#4112yes—
581C2×C3×C42−1+412yes—
582C2×Dic3—21no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—22no—
591C2×Dic3—21no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—22no—
600C2×Dic3—21no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—21no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—44no—
617C2×Dic3—44no—
618C2×Dic3C2×#4114yes—
619C2×Dic32−1+412yes—
620Dic6—44no—
621C24C23×D311yescharacteristic
622C2×Q8—62no—
623C2×Q8—62no—
624C2×Q8—62no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—31no—
628C22×C4—32no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—32no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—31no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—121no—
643C22×C4—121no—
644C22×C4—121no—
645C22×C4#23514yes—
646C22×C4C23×D311yescharacteristic
647C22×C4C23×D312yes—
648C22×C4C23×D311yescharacteristic
649C22×C4C23×D311yescharacteristic
650C22×C4C23×D312yes—
651C22×C4C23×D312yes—
652C22×C4C23×D311yescharacteristic
653C22×C4C23×D312yes—
654C22×C4C23×D311yescharacteristic
655C22×C4C23×D311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—34no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—64no—
666C4⋊C4—64no—
667C4⋊C4—62no—
668C4⋊C4—62no—
669C4⋊C4—64no—
670C4⋊C4—62no—
671C4⋊C4—62no—
672C4⋊C4—122no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C4⋊C4—122no—
677C4⋊C4—122no—
678C4⋊C4—122no—
679C4⋊C4—122no—
680C4⋊C4—121no—
681C4⋊C4—121no—
682C4⋊C4—122no—
683C4⋊C4—122no—
684C4⋊C4—122no—
685C4⋊C4—122no—
686C22⋊C4—24no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—42no—
690C22⋊C4—64no—
691C22⋊C4—64no—
692C22⋊C4—121no—
693C22⋊C4—121no—
694C42—24no—
695C42—22no—
696C42—22no—
697C42—42no—
698C42—42no—
699C42—64no—
700C42—64no—
701C42—62no—
702C42—62no—
703C42—62no—
704C42—62no—
705C42—62no—
706C42—62no—
707C42—122no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3C22×#4111yescharacteristic
716C22×C3C22×#4111yescharacteristic
717C22×C3C2×2−1+411yescharacteristic
718C22×C3C2×2−1+411yescharacteristic
719C22×C3#58511yescharacteristic
720C22×C3#58511yescharacteristic
721C22×C3#58511yescharacteristic
722C3×C4—22no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4#55214yes—
732Dic3—22no—
733Dic3—24no—
734Dic3—42no—
735Dic3—41no—
736Dic3—41no—
737Dic3—42no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741Dic3—42no—
742Dic3—41no—
743Dic3—41no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23C2×#23512yes—
751C23C24×D311yescharacteristic
752Q8—124no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—34no—
781C2×C4—32no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—62no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—124no—
817C2×C4—124no—
818C2×C4C2×#23512yes—
819C2×C4C2×#23512yes—
820C2×C4D3×#4112yes—
821C2×C4#101012yes—
822C2×C3—42no—
823C2×C3#345511yescharacteristic
824C2×C3C2×#55211yescharacteristic
825C2×C3#349511yescharacteristic
826C2×C3#351511yescharacteristic
827C2×C3#352411yescharacteristic
828C2×C3#355511yescharacteristic
829C2×C3#356511yescharacteristic
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22C22×#23511yescharacteristic
838C22C2×D3×#4111yescharacteristic
839C22C2×#101011yescharacteristic
840C22#596411yescharacteristic
841C22#596411yescharacteristic
842C22#596611yescharacteristic
843C22D3×2−1+411yescharacteristic
844C4—22no—
845C4—41no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—64no—
854C4—62no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—122no—
860C4—121no—
861C4—122no—
862C4—121no—
863C4—121no—
864C4—122no—
865C4#553114yes—
866C3#3807211yescharacteristic, complemented, Sylow
867C2—42no—
868C2C2×#553111yescharacteristic
869C2#8583711yescharacteristic
870C2#8590411yescharacteristic
871C2#8683711yescharacteristic
872C2#8684911yescharacteristic
873C2#8696511yescharacteristic
874C2#8697011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2346C2
prime radicalC24×C3C24
hypercenter#2346D3
hypocenterC3#38072
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2346

Complements

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

NH ≅ G/Ntype
4. #76105C2semidirect
5. #76103C2semidirect
6. #76042C2semidirect
7. #76012C2semidirect
12. #74177C2semidirect
13. #74170C2semidirect
16. #73691C2semidirect
17. #73685C2semidirect
18. #73626C2semidirect
19. #73625C2semidirect
22. #73402C2semidirect
23. #73399C2semidirect
866. C3#38072semidirect

Maximal subgroups

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

subgroupindex
C3×#23462
#822562
#822262
#761052
#761032
#760422
#760122
#757562
#757502
#757172
#757152
#741772
#741702
#740002
#739002
#736912
#736852
#736262
#736252
#734682
#734372
#734022
#733992
#380723