Finite Group Databasebeta

← #11258848

Subgroups — #11258848

Order 768.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5629C211yesmaximal, characteristic, complemented
2C2×#5645C211yesmaximal, characteristic, complemented
3C3×#2332C211yesmaximal, characteristic, complemented
4#76654C212yesmaximal, complemented
5#76618C212yesmaximal, complemented
6#75927C212yesmaximal, complemented
7#75927C212yesmaximal, complemented
8#75858C212yesmaximal, complemented
9#75503C212yesmaximal, complemented
10#75393C212yesmaximal, complemented
11#75387C212yesmaximal, complemented
12#75160C212yesmaximal, complemented
13#75020C212yesmaximal, complemented
14#74144C211yesmaximal, characteristic, complemented
15#74063C211yesmaximal, characteristic, complemented
16#73787C212yesmaximal, complemented
17#73782C212yesmaximal, complemented
18#73586C211yesmaximal, characteristic, complemented
19#73550C211yesmaximal, characteristic, complemented
20#46360—31nomaximal, Sylow
21C22×#239C2211yescharacteristic
22C22×#235C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×#946C2212yes—
25C2×#946C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29#5645—28no—
30#5629—28no—
31C2×#898C2212yes—
32C2×#896C2212yes—
33C2×#895C2212yes—
34C2×#895C2211yescharacteristic
35C2×#895C2212yes—
36C2×#894C2212yes—
37C2×D3×C4⋊C4C2211yescharacteristic
38C2×#890C2212yes—
39C2×#886C2212yes—
40C2×#886C2211yescharacteristic
41C2×#886C2211yescharacteristic
42C2×#884C2212yes—
43C2×#884C2212yes—
44C2×#67⋊C4C2212yes—
45C2×#875C2211yescharacteristic
46C2×#874C2211yescharacteristic
47C2×C4×D12C2212yes—
48C3×#391C2212yes—
49C3×#388C2212yes—
50C3×#388C2212yes—
51C3×#387C2212yes—
52C3×#387C2212yes—
53C3×#381C2211yescharacteristic
54C3×C4×C4⋊C4C2212yes—
55C3×C4×C22⋊C4C2211yescharacteristic
56#4994C2212yes—
57#4991C2212yes—
58#4991C2212yes—
59#4988C2212yes—
60#4987C2212yes—
61#4987C2212yes—
62#4981C2212yes—
63#4960C2212yes—
64#4960C2212yes—
65#4960C2212yes—
66#4960C2212yes—
67#4958C2212yes—
68#4958C2212yes—
69#4958C2211yescharacteristic
70#4958C2211yescharacteristic
71#4940C2212yes—
72#4940C2212yes—
73#4940C2212yes—
74#4940C2212yes—
75#4940C2212yes—
76#4939C2212yes—
77#4939C2211yescharacteristic
78#4939C2212yes—
79#4939C2212yes—
80C4×(C2×D3)⋊C4C2212yes—
81#4929C2211yescharacteristic
82#4674C2212yes—
83#4674C2212yes—
84#4674C2212yes—
85#4674C2212yes—
86#4672C2212yes—
87#4672C2212yes—
88#4672C2212yes—
89#4671C2212yes—
90#4671C2212yes—
91#4671C2212yes—
92#4671C2212yes—
93#4671C2212yes—
94#4670C2212yes—
95#4668C2212yes—
96#4668C2212yes—
97#4668C2212yes—
98#4668C2212yes—
99#4665C2212yes—
100#4665C2212yes—
101#4665C2212yes—
102#4665C2212yes—
103#4665C2212yes—
104#4665C2212yes—
105#4659C2212yes—
106#4659C2212yes—
107#4659C2212yes—
108#4656C2212yes—
109#4653C2212yes—
110C2×#539—31no—
111C2×#537—31no—
112#2815—31no—
113#2728—32no—
114#2714—32no—
115#2703—32no—
116#2703—32no—
117#2690—32no—
118#2673—32no—
119#2591—31no—
120#2490—32no—
121#2481—32no—
122#2464—32no—
123#2461—32no—
124#2456—32no—
125#2431—31no—
126#2407—32no—
127#2406—31no—
128#2332D311yescharacteristic, complemented
129C22×C3×Q8C2311yescharacteristic
130C23×C3×C4C2311yescharacteristic
131C22×#67C2311yescharacteristic
132C22×#67C2311yescharacteristic
133C22×#67C2312yes—
134C22×#67C2312yes—
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2311yescharacteristic
137C2×#239—24no—
138C2×#239—42no—
139C2×#239—42no—
140C2×#235—24no—
141C2×#235—42no—
142C2×#235—42no—
143C22×D12C2312yes—
144C22×D12C2311yescharacteristic
145C22×D12C2312yes—
146C22×D12C2311yescharacteristic
147C22×D12C2312yes—
148C22×D12C2311yescharacteristic
149C22×D12C2312yes—
150C22×D12C2312yes—
151C22×D12C2312yes—
152C22×C4×D3C2311yescharacteristic
153C22×C4×D3C2312yes—
154C22×C4×D3C2311yescharacteristic
155C22×C4×D3C2312yes—
156C22×C4×D3C2312yes—
157C22×Dic6C2311yescharacteristic
158C3×C22⋊Q8D418yescomplemented
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C4⋊C4C2312yes—
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4C2312yes—
164C2×C3×C22⋊C4C2311yescharacteristic
165C2×C3×C22⋊C4C2311yescharacteristic
166C2×C3×C22⋊C4C2312yes—
167C2×C3×C42C2311yescharacteristic
168C2×C3×C42C2312yes—
169C2×C3×C42C2312yes—
170C2×C3×C42C2311yescharacteristic
171#946—28no—
172#946—24no—
173#930—24no—
174#930—24no—
175C2×(C2×D3)⋊C4C2312yes—
176C2×(C2×D3)⋊C4C2312yes—
177C2×(C2×D3)⋊C4C2312yes—
178C2×(C2×D3)⋊C4C2312yes—
179C2×(C2×D3)⋊C4C2312yes—
180C2×(C2×D3)⋊C4C2312yes—
181C2×(C2×D3)⋊C4C2312yes—
182C2×(C2×D3)⋊C4C2312yes—
183C2×(C2×D3)⋊C4C2312yes—
184C2×(C2×D3)⋊C4C2312yes—
185C2×(C2×D3)⋊C4C2312yes—
186C2×(C2×D3)⋊C4C2312yes—
187C2×(C2×D3)⋊C4C2312yes—
188C2×(C2×D3)⋊C4C2312yes—
189C2×(C2×D3)⋊C4C2312yes—
190C2×(C2×D3)⋊C4C2312yes—
191C2×(C2×D3)⋊C4C2312yes—
192C2×(C2×D3)⋊C4C2312yes—
193C2×(C2×D3)⋊C4C2312yes—
194C2×(C2×D3)⋊C4C2312yes—
195C2×(C2×D3)⋊C4C2312yes—
196C2×(C2×D3)⋊C4C2312yes—
197C2×(C2×D3)⋊C4C2312yes—
198C2×C4⋊Dic3C2312yes—
199C2×C4⋊Dic3C2311yescharacteristic
200C2×C4⋊Dic3C2312yes—
201C2×C4⋊Dic3C2312yes—
202C2×C4⋊Dic3C2311yescharacteristic
203C2×C4⋊Dic3C2312yes—
204C2×Dic3⋊C4—24no—
205C2×Dic3⋊C4C2312yes—
206C2×Dic3⋊C4C2312yes—
207C2×Dic3⋊C4C2312yes—
208C2×Dic3⋊C4C2312yes—
209C2×Dic3⋊C4C2312yes—
210C2×C4×Dic3C2312yes—
211#898—28no—
212#896—28no—
213#895—24no—
214#895—28no—
215#895—44no—
216#894—28no—
217D3×C4⋊C4—24no—
218#890—28no—
219#886—28no—
220#886—42no—
221#886—42no—
222#884—28no—
223#884—28no—
224#67⋊C4—28no—
225#875—42no—
226#874—42no—
227C4×D12—44no—
228C3×#95C2312yes—
229C3×#95C2312yes—
230C3×#95C2312yes—
231C3×#95C2312yes—
232C3×#95C2312yes—
233C3×#95C2312yes—
234C3×#95C2312yes—
235C3⋊#95C2312yes—
236C3⋊#95C2312yes—
237C3⋊#95C2312yes—
238C3⋊#95C2312yes—
239C3⋊#95C2312yes—
240C3⋊#95C2312yes—
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C22×#41—31no—
246C22×#41—31no—
247#539—68no—
248#537—68no—
249C2×#127—31no—
250C2×#126—32no—
251C2×#125—32no—
252C2×#124—31no—
253C2×#123—32no—
254C2×#123—32no—
255C2×#123—31no—
256C2×#123—31no—
257C2×C22⋊Q8—32no—
258C2×C22⋊Q8—31no—
259C2×C22⋊Q8—32no—
260C2×C22⋊Q8C2×D311yescharacteristic
261C2×#121—31no—
262C2×#121—31no—
263C2×#121—32no—
264C2×#121—31no—
265C2×#121—32no—
266C2×#121—32no—
267C2×#121—32no—
268C2×C4×D4—32no—
269C2×C4×D4—32no—
270C22×C4⋊C4—31no—
271C22×C4⋊C4—31no—
272#400—32no—
273#400—32no—
274#400—32no—
275#398—32no—
276#397—32no—
277#397—32no—
278#397—32no—
279#397—32no—
280#396—32no—
281#395—32no—
282#394—32no—
283#394—32no—
284#394—32no—
285#394—32no—
286#394—32no—
287#392—32no—
288#392—32no—
289#392—32no—
290#392—32no—
291#392—32no—
292#392—32no—
293#392—32no—
294#392—32no—
295#392—32no—
296#391—31no—
297#391C2×D312yes—
298#390—32no—
299#390—32no—
300#390—31no—
301#390—32no—
302#390—32no—
303#388—32no—
304#388—32no—
305#388—32no—
306#388—32no—
307#388—32no—
308#388—32no—
309#388C2×D312yes—
310#388C2×D312yes—
311#387—32no—
312#387C2×D312yes—
313#387C2×D312yes—
314#386—32no—
315#386—32no—
316#386—31no—
317#386—31no—
318#386—32no—
319#386—32no—
320#386—32no—
321#386—32no—
322#386—32no—
323#386—32no—
324#385—32no—
325#385—32no—
326#385—32no—
327#385—32no—
328#381C2×D311yescharacteristic
329#380—32no—
330#380—32no—
331C4×C4⋊C4C2×D312yes—
332C4×C22⋊C4—32no—
333C4×C22⋊C4C2×D311yescharacteristic
334C24×C3C2411yescharacteristic
335C23×D3C2412yes—
336C23×D3C2411yescharacteristic
337C23×D3C2412yes—
338C23×D3C2411yescharacteristic
339C2×C3×Q8—41no—
340C2×C3×Q8—41no—
341C2×C3×Q8C2×D414yes—
342C22×C3×C4—41no—
343C22×C3×C4—41no—
344C22×C3×C4C2×D414yes—
345C22×C3×C4C2412yes—
346C22×C3×C4C2412yes—
347C22×C3×C4C2412yes—
348C22×C3×C4C2412yes—
349C22×C3×C4C2411yescharacteristic
350C22×C3×C4C2412yes—
351C22×C3×C4C2411yescharacteristic
352C22×C3×C4C2412yes—
353C2×#67—24no—
354C2×#67—22no—
355C2×#67—22no—
356C2×#67—22no—
357C2×#67—24no—
358C2×#67—22no—
359C2×#67—41no—
360C2×#67—41no—
361C2×#67—42no—
362C2×#67—42no—
363C2×#67—42no—
364C2×#67—42no—
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3—42no—
368C22×Dic3—41no—
369C22×Dic3—41no—
370C22×Dic3C2412yes—
371C22×Dic3C2412yes—
372C22×Dic3C2412yes—
373C22×Dic3C2411yescharacteristic
374C22×Dic3C2412yes—
375C22×Dic3C2411yescharacteristic
376#239—416no—
377#235—416no—
378C2×D12—22no—
379C2×D12—24no—
380C2×D12—24no—
381C2×D12—22no—
382C2×D12—22no—
383C2×D12—24no—
384C2×D12—24no—
385C2×D12—22no—
386C2×D12—42no—
387C2×D12—42no—
388C2×D12—42no—
389C2×D12—41no—
390C2×D12—42no—
391C2×D12—41no—
392C2×D12—41no—
393C2×D12—41no—
394C2×D12—42no—
395C2×D12—41no—
396C2×D12—42no—
397C2×D12—42no—
398C2×D12—42no—
399C2×D12—42no—
400C2×D12—42no—
401C2×D12—42no—
402C2×D12—42no—
403C2×D12—42no—
404C2×D12—42no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—24no—
409C2×C4×D3—22no—
410C2×C4×D3—24no—
411C2×C4×D3—24no—
412C2×C4×D3—24no—
413C2×C4×D3—41no—
414C2×C4×D3—41no—
415C2×C4×D3—42no—
416C2×C4×D3—42no—
417C2×C4×D3—42no—
418C2×C4×D3—42no—
419C2×C4×D3—42no—
420C2×Dic6—22no—
421C2×Dic6—22no—
422C2×Dic6—41no—
423C3×C4⋊C4—42no—
424C3×C4⋊C4—42no—
425C3×C4⋊C4C2×D418yes—
426C3×C4⋊C4C2×D414yes—
427C3×C22⋊C4—41no—
428C3×C22⋊C4—41no—
429C3×C22⋊C4—42no—
430C3×C22⋊C4C2×D418yes—
431C3×C42—42no—
432C3×C42—41no—
433C3×C42—41no—
434C3×C42—42no—
435(C2×D3)⋊C4—24no—
436(C2×D3)⋊C4—24no—
437(C2×D3)⋊C4—24no—
438(C2×D3)⋊C4—24no—
439(C2×D3)⋊C4—24no—
440(C2×D3)⋊C4—24no—
441(C2×D3)⋊C4—24no—
442(C2×D3)⋊C4—24no—
443(C2×D3)⋊C4—24no—
444(C2×D3)⋊C4—42no—
445(C2×D3)⋊C4—42no—
446(C2×D3)⋊C4—42no—
447(C2×D3)⋊C4—42no—
448(C2×D3)⋊C4—42no—
449(C2×D3)⋊C4—42no—
450(C2×D3)⋊C4—42no—
451(C2×D3)⋊C4—42no—
452(C2×D3)⋊C4—42no—
453(C2×D3)⋊C4—42no—
454(C2×D3)⋊C4—42no—
455(C2×D3)⋊C4—42no—
456(C2×D3)⋊C4—42no—
457(C2×D3)⋊C4—42no—
458C4⋊Dic3—24no—
459C4⋊Dic3—24no—
460C4⋊Dic3—22no—
461C4⋊Dic3—22no—
462C4⋊Dic3—24no—
463C4⋊Dic3—42no—
464Dic3⋊C4—24no—
465Dic3⋊C4—24no—
466Dic3⋊C4—24no—
467Dic3⋊C4—24no—
468Dic3⋊C4—24no—
469C4×Dic3—24no—
470C2×#41—64no—
471C2×#41—64no—
472C2×#41—122no—
473C2×#41—122no—
474C2×#41—122no—
475C2×#41—122no—
476C22×Q8—31no—
477C22×Q8C22×D311yescharacteristic
478C22×D4—31no—
479C22×D4—31no—
480C22×D4—32no—
481C22×D4—32no—
482C22×D4—32no—
483C22×D4—31no—
484C22×D4—32no—
485C22×D4—31no—
486C22×D4—31no—
487C22×D4—32no—
488C22×D4—32no—
489C22×D4—32no—
490C22×D4—32no—
491C23×C4—31no—
492C23×C4—31no—
493C23×C4—31no—
494C23×C4—32no—
495C23×C4—32no—
496C23×C4—32no—
497C23×C4—31no—
498C23×C4C22×D311yescharacteristic
499#127—122no—
500#126—68no—
501#125—68no—
502#124—122no—
503#123—68no—
504#123—68no—
505#123—122no—
506#123—122no—
507C22⋊Q8—64no—
508C22⋊Q8—68no—
509C22⋊Q8—68no—
510C22⋊Q8D1218yescomplemented
511#121—64no—
512#121—64no—
513#121—64no—
514#121—68no—
515#121—68no—
516#121—68no—
517#121—124no—
518C4×D4—68no—
519C4×D4—124no—
520C2×C4⋊C4—32no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—32no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—32no—
529C2×C4⋊C4—32no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—64no—
532C2×C4⋊C4—64no—
533C2×C4⋊C4C22×D312yes—
534C2×C4⋊C4C22×D312yes—
535C2×C4⋊C4C22×D311yescharacteristic
536C2×C4⋊C4C22×D312yes—
537C2×C22⋊C4—32no—
538C2×C22⋊C4—32no—
539C2×C22⋊C4—32no—
540C2×C22⋊C4—32no—
541C2×C22⋊C4—32no—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—32no—
544C2×C22⋊C4—32no—
545C2×C22⋊C4—32no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—32no—
548C2×C22⋊C4—32no—
549C2×C22⋊C4—32no—
550C2×C22⋊C4—32no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—32no—
554C2×C22⋊C4—32no—
555C2×C22⋊C4—32no—
556C2×C22⋊C4—32no—
557C2×C22⋊C4—32no—
558C2×C22⋊C4—32no—
559C2×C22⋊C4—32no—
560C2×C22⋊C4C22×D311yescharacteristic
561C2×C22⋊C4C22×D311yescharacteristic
562C2×C22⋊C4C22×D312yes—
563C2×C22⋊C4C22×D312yes—
564C2×C42—32no—
565C2×C42C22×D312yes—
566C2×C42C22×D311yescharacteristic
567C2×C42C22×D311yescharacteristic
568C2×C42C22×D312yes—
569#95—32no—
570#95—32no—
571#95—32no—
572#95—32no—
573#95—32no—
574#95—32no—
575#95—32no—
576#95—32no—
577#95—32no—
578#95—32no—
579#95C22×D312yes—
580#95C22×D312yes—
581#95C22×D312yes—
582#95C22×D312yes—
583#95C22×D312yes—
584#95C22×D312yes—
585#95C22×D312yes—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3C22×D412yes—
591C23×C3C2511yescharacteristic
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—21no—
599C22×D3—22no—
600C22×D3—21no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—21no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3H(5,𝔽2)12yes—
616C3×Q8—44no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—44no—
638C2×C3×C4C22×D414yes—
639C2×C3×C4C22×D414yes—
640C2×C3×C4C22×D412yes—
641C2×C3×C4C22×D412yes—
642#67—44no—
643#67—44no—
644#67—48no—
645#67—84no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—21no—
653C2×Dic3—22no—
654C2×Dic3—21no—
655C2×Dic3—22no—
656C2×Dic3—21no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—44no—
664C2×Dic3—82no—
665C2×Dic3H(5,𝔽2)12yes—
666D12—44no—
667D12—48no—
668D12—44no—
669D12—48no—
670D12—82no—
671D12—84no—
672D12—84no—
673D12—84no—
674D12—84no—
675C4×D3—28no—
676C4×D3—48no—
677C4×D3—44no—
678C4×D3—84no—
679C4×D3—84no—
680Dic6—44no—
681C24—31no—
682C24—32no—
683C24—31no—
684C24—32no—
685C24C23×D311yescharacteristic
686#41—1216no—
687#41—1216no—
688C2×Q8—41no—
689C2×Q8—41no—
690C2×Q8—62no—
691C2×Q8—62no—
692C2×Q8—121no—
693C2×Q8C2×D1214yes—
694C2×D4—64no—
695C2×D4—62no—
696C2×D4—64no—
697C2×D4—62no—
698C2×D4—62no—
699C2×D4—64no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—62no—
705C2×D4—62no—
706C2×D4—64no—
707C2×D4—62no—
708C2×D4—122no—
709C2×D4—121no—
710C2×D4—122no—
711C2×D4—121no—
712C2×D4—121no—
713C2×D4—122no—
714C2×D4—122no—
715C2×D4—122no—
716C2×D4—121no—
717C2×D4—121no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—122no—
725C2×D4—122no—
726C2×D4—122no—
727C2×D4—121no—
728C2×D4—121no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C22×C4—31no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—31no—
738C22×C4—32no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—62no—
742C22×C4—64no—
743C22×C4—62no—
744C22×C4—62no—
745C22×C4—62no—
746C22×C4—62no—
747C22×C4—64no—
748C22×C4—62no—
749C22×C4—64no—
750C22×C4—64no—
751C22×C4—122no—
752C22×C4—121no—
753C22×C4—121no—
754C22×C4—122no—
755C22×C4—122no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4—122no—
759C22×C4—121no—
760C22×C4—121no—
761C22×C4C2×D1214yes—
762C22×C4C23×D312yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D312yes—
766C22×C4C23×D311yescharacteristic
767C22×C4C23×D312yes—
768C22×C4C23×D311yescharacteristic
769C22×C4C23×D312yes—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—64no—
773C4⋊C4—64no—
774C4⋊C4—62no—
775C4⋊C4—64no—
776C4⋊C4—64no—
777C4⋊C4—64no—
778C4⋊C4—64no—
779C4⋊C4—62no—
780C4⋊C4—64no—
781C4⋊C4—64no—
782C4⋊C4—122no—
783C4⋊C4C2×D1214yes—
784C4⋊C4C2×D1218yes—
785C22⋊C4—41no—
786C22⋊C4—41no—
787C22⋊C4—42no—
788C22⋊C4—64no—
789C22⋊C4—64no—
790C22⋊C4—64no—
791C22⋊C4—64no—
792C22⋊C4—64no—
793C22⋊C4—64no—
794C22⋊C4—64no—
795C22⋊C4—64no—
796C22⋊C4—64no—
797C22⋊C4—122no—
798C22⋊C4—122no—
799C22⋊C4—122no—
800C22⋊C4—122no—
801C22⋊C4—122no—
802C22⋊C4—122no—
803C22⋊C4—122no—
804C22⋊C4—122no—
805C22⋊C4—122no—
806C22⋊C4—122no—
807C22⋊C4—122no—
808C22⋊C4—122no—
809C22⋊C4—122no—
810C22⋊C4—122no—
811C22⋊C4C2×D1218yes—
812C42—42no—
813C42—41no—
814C42—41no—
815C42—42no—
816C42—64no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3C23×D411yescharacteristic
823C22×C3C2×H(5,𝔽2)11yescharacteristic
824C22×C3C2×H(5,𝔽2)11yescharacteristic
825C22×C3#58512yes—
826C22×C3#58512yes—
827C2×D3—22no—
828C2×D3—24no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—42no—
832C2×D3—42no—
833C2×D3—41no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—24no—
854C3×C4—24no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859Dic3—22no—
860Dic3—41no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865C23—22no—
866C23—21no—
867C23—21no—
868C23—22no—
869C23—32no—
870C23—61no—
871C23—62no—
872C23—61no—
873C23—62no—
874C23—62no—
875C23—61no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—61no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—61no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23C22×D1212yes—
894C23C24×D311yescharacteristic
895Q8—44no—
896Q8—124no—
897D4—124no—
898D4—128no—
899D4—124no—
900D4—128no—
901D4—124no—
902D4—124no—
903D4—128no—
904D4—244no—
905D4—242no—
906D4—244no—
907D4—244no—
908D4—244no—
909D4—244no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—32no—
931C2×C4—44no—
932C2×C4—68no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—62no—
938C2×C4—62no—
939C2×C4—61no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—128no—
951C2×C4—124no—
952C2×C4—124no—
953C2×C4—244no—
954C2×C4—244no—
955C2×C4—242no—
956C2×C4C22×D1214yes—
957C2×C4C22×D1214yes—
958C2×C4C22×D1212yes—
959C2×C4C22×D1212yes—
960C2×C3—42no—
961C2×C3#348411yescharacteristic
962C2×C3#348711yescharacteristic
963C2×C3#350011yescharacteristic
964C2×C3#353912yes—
965C2×C3#356012yes—
966D3—42no—
967D3—82no—
968D3—81no—
969D3—82no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—42no—
974C22—42no—
975C22—64no—
976C22—62no—
977C22—121no—
978C22—121no—
979C22—122no—
980C22—122no—
981C22—122no—
982C22—122no—
983C22—122no—
984C22—122no—
985C22—121no—
986C22—122no—
987C22—122no—
988C22—122no—
989C22—121no—
990C22—122no—
991C22—122no—
992C22—122no—
993C22—121no—
994C22—122no—
995C22—122no—
996C22—122no—
997C22—122no—
998C22—122no—
999C22C23×D1211yescharacteristic
1000C22#596412yes—
1001C22D3×H(5,𝔽2)11yescharacteristic
1002C22D3×H(5,𝔽2)11yescharacteristic
1003C22#596812yes—
1004C4—24no—
1005C4—22no—
1006C4—22no—
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—62no—
1013C4—122no—
1014C4—121no—
1015C4—122no—
1016C4—122no—
1017C4—122no—
1018C3#4636011yescharacteristic, complemented, Sylow
1019C2—42no—
1020C2—122no—
1021C2—242no—
1022C2—241no—
1023C2—242no—
1024C2#8584711yescharacteristic
1025C2#8586711yescharacteristic
1026C2#8587411yescharacteristic
1027C2#8643612yes—
1028C2#8656812yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2332C2
hypercenter#2332D3
hypocenterC3#46360
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
1. C2×#5629C2semidirect
2. C2×#5645C2semidirect
3. C3×#2332C2semidirect
4. #76654C2semidirect
5. #76618C2semidirect
6. #75927C2semidirect
7. #75927C2semidirect
8. #75858C2semidirect
9. #75503C2semidirect
10. #75393C2semidirect
11. #75387C2semidirect
12. #75160C2semidirect
13. #75020C2semidirect
14. #74144C2semidirect
15. #74063C2semidirect
16. #73787C2semidirect
17. #73782C2semidirect
18. #73586C2semidirect
19. #73550C2semidirect
128. #2332D3semidirect
158. C3×C22⋊Q8D4semidirect
510. C22⋊Q8D12semidirect
1018. C3#46360semidirect

Maximal subgroups

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

subgroupindex
C2×#56292
C2×#56452
C3×#23322
#766542
#766182
#759272
#758582
#755032
#753932
#753872
#751602
#750202
#741442
#740632
#737872
#737822
#735862
#735502
#463603