Finite Group Databasebeta

← #11258841

Subgroups — #11258841

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×#5833C211yesmaximal, characteristic, complemented
2C2×#5515C211yesmaximal, characteristic, complemented
3C3×#2406C211yesmaximal, characteristic, complemented
4#84092C211yesmaximal, characteristic, complemented
5#82899C212yesmaximal, complemented
6#82853C212yesmaximal, complemented
7#82182C211yesmaximal, characteristic, complemented
8#77214C212yesmaximal, complemented
9#77176C212yesmaximal, complemented
10#77133C212yesmaximal, complemented
11#76934C212yesmaximal, complemented
12#74815C212yesmaximal, complemented
13#74814C212yesmaximal, complemented
14#74641C212yesmaximal, complemented
15#74530C212yesmaximal, complemented
16#74454C212yesmaximal, complemented
17#74404C212yesmaximal, complemented
18#74144C211yesmaximal, characteristic, complemented
19#74057C211yesmaximal, characteristic, complemented
20#46360—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic
22C22×#235C2211yescharacteristic
23C2×C3×#123C2211yescharacteristic
24C2×C3×#123C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26#5833—28no—
27C2×#947C2211yescharacteristic
28C2×#946C2212yes—
29C2×#940C2211yescharacteristic
30C2×#939C2212yes—
31C2×#939C2212yes—
32C2×#938C2212yes—
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×#930C2211yescharacteristic
36C2×#929C2212yes—
37C2×C4×#67C2212yes—
38C22×C4⋊Dic3C2211yescharacteristic
39C2×#924C2211yescharacteristic
40C2×#924C2211yescharacteristic
41#5515—28no—
42C2×#898C2212yes—
43C2×#896C2212yes—
44C2×#894C2212yes—
45C2×#893C2212yes—
46C2×#889C2212yes—
47C2×#884C2212yes—
48C3×#395C2212yes—
49C3×#394C2212yes—
50C3×#386C2211yescharacteristic
51C3×#386C2211yescharacteristic
52C3×#385C2212yes—
53C3×#385C2212yes—
54C3×#381C2211yescharacteristic
55#5229C2211yescharacteristic
56#5223C2212yes—
57#5223C2212yes—
58#5221C2211yescharacteristic
59#5213C2212yes—
60#5213C2212yes—
61#5213C2212yes—
62#5213C2212yes—
63C4×#217C2211yescharacteristic
64#4994C2212yes—
65#4991C2212yes—
66#4990C2212yes—
67#4990C2212yes—
68#4990C2212yes—
69#4989C2212yes—
70#4989C2212yes—
71#4988C2212yes—
72#4986C2212yes—
73#4983C2212yes—
74#4980C2212yes—
75#4960C2212yes—
76#4960C2212yes—
77#4960C2212yes—
78#4960C2212yes—
79#4960C2212yes—
80#4959C2212yes—
81#4959C2212yes—
82#4958C2212yes—
83#4958C2212yes—
84#4957C2212yes—
85#4957C2212yes—
86#4957C2212yes—
87#4956C2212yes—
88#4952C2212yes—
89#4945C2212yes—
90#4944C2212yes—
91#4944C2212yes—
92#4942C2212yes—
93Dic3×C22⋊C4C2212yes—
94#4675C2212yes—
95#4674C2212yes—
96#4674C2212yes—
97#4672C2212yes—
98#4671C2212yes—
99#4671C2212yes—
100#4670C2212yes—
101#4669C2212yes—
102#4667C2212yes—
103#4665C2212yes—
104#4660C2212yes—
105#4658C2212yes—
106#4654C2212yes—
107#4652C2212yes—
108#4649C2212yes—
109#4646C2212yes—
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#2406D311yescharacteristic, complemented
128#2332—31no—
129C2×C3×#41—24no—
130C2×C3×#41—42no—
131C2×C3×#41—42no—
132C22×C3×Q8C2311yescharacteristic
133C22×C3×D4C2311yescharacteristic
134C22×C3×D4C2311yescharacteristic
135C22×C3×D4C2311yescharacteristic
136C23×C3×C4C2311yescharacteristic
137C23×C3×C4C2311yescharacteristic
138C23×C3×C4C2311yescharacteristic
139C23×C3×C4C2311yescharacteristic
140C23×C3×C4C2311yescharacteristic
141C22×#67C2312yes—
142C22×#67C2312yes—
143C22×#67C2312yes—
144C22×#67C2312yes—
145C22×#67C2312yes—
146C22×#67C2312yes—
147C23×Dic3C2312yes—
148C2×#235—24no—
149C2×#235—42no—
150C2×#235—42no—
151C22×D12C2311yescharacteristic
152C22×D12C2311yescharacteristic
153C22×D12C2312yes—
154C22×D12C2312yes—
155C22×C4×D3C2312yes—
156C22×C4×D3C2312yes—
157C22×Dic6C2311yescharacteristic
158C3×#123—42no—
159C3×#123—42no—
160C2×C3×C4⋊C4—24no—
161C2×C3×C4⋊C4C2312yes—
162C2×C3×C4⋊C4C2312yes—
163C2×C3×C4⋊C4C2312yes—
164C2×C3×C4⋊C4C2312yes—
165C2×C3×C22⋊C4C2312yes—
166C2×C3×C22⋊C4C2312yes—
167C2×C3×C22⋊C4C2311yescharacteristic
168C2×C3×C22⋊C4C2312yes—
169C2×C3×C22⋊C4C2311yescharacteristic
170C2×C3×C22⋊C4C2312yes—
171C2×#217C2312yes—
172C2×#217C2312yes—
173C2×#217C2312yes—
174C2×#217C2312yes—
175C2×#217C2312yes—
176#947—42no—
177#946—28no—
178#940—42no—
179#939—28no—
180#939—28no—
181#938—28no—
182#930—24no—
183#930—24no—
184#930—24no—
185#929—28no—
186C4×#67—28no—
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×(C2×D3)⋊C4C2312yes—
199C2×(C2×D3)⋊C4C2312yes—
200C2×(C2×D3)⋊C4C2312yes—
201C2×(C2×D3)⋊C4C2312yes—
202C2×(C2×D3)⋊C4C2312yes—
203C2×C4⋊Dic3—24no—
204C2×C4⋊Dic3C2312yes—
205C2×C4⋊Dic3C2311yescharacteristic
206C2×C4⋊Dic3C2311yescharacteristic
207C2×C4⋊Dic3C2311yescharacteristic
208#924—24no—
209#924D418yescomplemented
210C2×Dic3⋊C4C2312yes—
211C2×Dic3⋊C4C2312yes—
212C2×Dic3⋊C4C2312yes—
213C2×Dic3⋊C4C2312yes—
214C2×Dic3⋊C4C2312yes—
215C2×Dic3⋊C4C2312yes—
216C2×Dic3⋊C4C2312yes—
217C2×C4×Dic3C2312yes—
218C2×C4×Dic3C2312yes—
219C2×C4×Dic3C2311yescharacteristic
220C2×C4×Dic3C2312yes—
221C2×C4×Dic3C2311yescharacteristic
222#898—28no—
223#896—28no—
224#894—28no—
225#893—44no—
226#889—28no—
227#884—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×#41C2×D311yescharacteristic
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×#123C2×D311yescharacteristic
256C2×#123C2×D311yescharacteristic
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—32no—
259C2×C22⋊Q8—31no—
260C2×C22⋊Q8—32no—
261C2×#121—32no—
262C2×#121—32no—
263C2×#121—32no—
264C2×#121—31no—
265C2×#121—31no—
266C2×#121—31no—
267C2×#121—32no—
268C2×C4×D4—32no—
269C2×C4×D4—32no—
270C22×C4⋊C4—31no—
271C22×C4⋊C4C2×D311yescharacteristic
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#395C2×D312yes—
282#394—32no—
283#394—32no—
284#394—32no—
285#394—32no—
286#394C2×D312yes—
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#391—32no—
298#390—31no—
299#390—32no—
300#390—32no—
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#388—32no—
310#388—32no—
311#387—32no—
312#387—32no—
313#387—32no—
314#386—32no—
315#386—32no—
316#386—32no—
317#386—32no—
318#386—32no—
319#386—32no—
320#386—32no—
321#386—32no—
322#386C2×D311yescharacteristic
323#386C2×D311yescharacteristic
324#385—32no—
325#385—32no—
326#385C2×D312yes—
327#385C2×D312yes—
328#381C2×D311yescharacteristic
329#380—32no—
330#380—32no—
331C4×C4⋊C4—32no—
332C4×C22⋊C4—31no—
333C4×C22⋊C4—32no—
334C24×C3C2411yescharacteristic
335C24×C3C2411yescharacteristic
336C24×C3C2411yescharacteristic
337C23×D3C2412yes—
338C23×D3C2412yes—
339C3×#41—416no—
340C2×C3×Q8—22no—
341C2×C3×Q8—22no—
342C2×C3×Q8—41no—
343C2×C3×D4—22no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—22no—
347C2×C3×D4—22no—
348C2×C3×D4—22no—
349C2×C3×D4—41no—
350C2×C3×D4—41no—
351C2×C3×D4—41no—
352C22×C3×C4—22no—
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4—22no—
356C22×C3×C4—22no—
357C22×C3×C4—22no—
358C22×C3×C4—42no—
359C22×C3×C4—41no—
360C22×C3×C4—41no—
361C22×C3×C4—41no—
362C22×C3×C4—41no—
363C22×C3×C4—41no—
364C22×C3×C4—41no—
365C22×C3×C4C2×D414yes—
366C22×C3×C4C2412yes—
367C22×C3×C4C2412yes—
368C22×C3×C4C2412yes—
369C22×C3×C4C2411yescharacteristic
370C22×C3×C4C2412yes—
371C22×C3×C4C2411yescharacteristic
372C22×C3×C4C2411yescharacteristic
373C22×C3×C4C2411yescharacteristic
374C2×#67—24no—
375C2×#67—24no—
376C2×#67—24no—
377C2×#67—24no—
378C2×#67—24no—
379C2×#67—24no—
380C2×#67—42no—
381C2×#67—42no—
382C2×#67—42no—
383C2×#67—42no—
384C2×#67—42no—
385C2×#67—42no—
386C2×#67—42no—
387C2×#67—42no—
388C2×#67—42no—
389C2×#67—42no—
390C2×#67—42no—
391C2×#67—42no—
392C22×Dic3—24no—
393C22×Dic3—42no—
394C22×Dic3—42no—
395C22×Dic3C2412yes—
396C22×Dic3C2412yes—
397C22×Dic3C2412yes—
398C22×Dic3C2412yes—
399C22×Dic3C2412yes—
400C22×Dic3C2412yes—
401#235—416no—
402C2×D12—22no—
403C2×D12—22no—
404C2×D12—42no—
405C2×D12—42no—
406C2×D12—42no—
407C2×D12—41no—
408C2×D12—41no—
409C2×D12—42no—
410C2×D12—41no—
411C2×D12—41no—
412C2×D12—42no—
413C2×D12—42no—
414C2×C4×D3—24no—
415C2×C4×D3—24no—
416C2×C4×D3—24no—
417C2×C4×D3—42no—
418C2×C4×D3—42no—
419C2×C4×D3—42no—
420C2×Dic6—41no—
421C2×Dic6—41no—
422C2×Dic6C2×D414yes—
423C3×C4⋊C4—24no—
424C3×C4⋊C4—24no—
425C3×C4⋊C4—24no—
426C3×C4⋊C4—42no—
427C3×C22⋊C4—24no—
428C3×C22⋊C4—42no—
429C3×C22⋊C4—42no—
430C3×C22⋊C4—41no—
431C3×C22⋊C4—42no—
432C3×C22⋊C4—41no—
433#217—24no—
434#217—42no—
435#217—42no—
436#217—42no—
437#217C2×D418yes—
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—24no—
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—
454C4⋊Dic3—22no—
455C4⋊Dic3—22no—
456C4⋊Dic3—24no—
457C4⋊Dic3C2×D414yes—
458Dic3⋊C4—24no—
459Dic3⋊C4—24no—
460Dic3⋊C4—24no—
461Dic3⋊C4—24no—
462Dic3⋊C4—42no—
463Dic3⋊C4—42no—
464Dic3⋊C4C2×D418yes—
465C4×Dic3—24no—
466C4×Dic3—42no—
467C4×Dic3—42no—
468C4×Dic3—41no—
469C4×Dic3—41no—
470C2×#41—24no—
471C2×#41—42no—
472C2×#41—42no—
473C2×#41—64no—
474C2×#41—122no—
475C2×#41—122no—
476C22×Q8—31no—
477C22×Q8C22×D311yescharacteristic
478C22×D4—32no—
479C22×D4—32no—
480C22×D4—32no—
481C22×D4—32no—
482C22×D4—32no—
483C22×D4—32no—
484C22×D4—31no—
485C22×D4—31no—
486C22×D4—32no—
487C22×D4—32no—
488C22×D4C22×D311yescharacteristic
489C22×D4C22×D311yescharacteristic
490C22×D4C22×D311yescharacteristic
491C23×C4—32no—
492C23×C4—32no—
493C23×C4—32no—
494C23×C4C22×D311yescharacteristic
495C23×C4C22×D311yescharacteristic
496C23×C4C22×D311yescharacteristic
497C23×C4C22×D311yescharacteristic
498C23×C4C22×D311yescharacteristic
499#127—122no—
500#126—68no—
501#125—68no—
502#124—122no—
503#123—42no—
504#123—42no—
505#123—68no—
506#123—68no—
507C22⋊Q8—38no—
508C22⋊Q8—68no—
509C22⋊Q8—68no—
510C22⋊Q8—64no—
511#121—68no—
512#121—68no—
513#121—64no—
514#121—68no—
515#121—64no—
516#121—64no—
517#121—124no—
518C4×D4—68no—
519C4×D4—124no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—31no—
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—32no—
532C2×C4⋊C4—64no—
533C2×C4⋊C4C22×D312yes—
534C2×C4⋊C4C22×D312yes—
535C2×C4⋊C4C22×D312yes—
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⋊C4C22×D312yes—
559C2×C22⋊C4C22×D311yescharacteristic
560C2×C22⋊C4C22×D311yescharacteristic
561C2×C22⋊C4C22×D312yes—
562C2×C22⋊C4C22×D312yes—
563C2×C22⋊C4C22×D312yes—
564C2×C42—32no—
565C2×C42—32no—
566C2×C42—31no—
567C2×C42—31no—
568C2×C42—32no—
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#95—32no—
580#95—32no—
581#95—32no—
582#95C22×D312yes—
583#95C22×D312yes—
584#95C22×D312yes—
585#95C22×D312yes—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3C22×D412yes—
600C23×C3H(5,𝔽2)12yes—
601C23×C3C2511yescharacteristic
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
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×D3—22no—
616C3×Q8—44no—
617C3×D4—44no—
618C3×D4—44no—
619C3×D4—44no—
620C2×C3×C4—28no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—21no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—21no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—44no—
643C2×C3×C4—44no—
644C2×C3×C4—44no—
645C2×C3×C4—82no—
646C2×C3×C4C22×D412yes—
647C2×C3×C4C22×D412yes—
648C2×C3×C4H(5,𝔽2)12yes—
649#67—48no—
650#67—48no—
651#67—84no—
652#67—84no—
653#67—84no—
654#67—84no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—84no—
672C2×Dic3C22×D414yes—
673C2×Dic3C22×D414yes—
674D12—44no—
675D12—48no—
676D12—82no—
677D12—84no—
678C4×D3—48no—
679C4×D3—84no—
680Dic6—44no—
681C24—32no—
682C24—32no—
683C24C23×D311yescharacteristic
684C24C23×D311yescharacteristic
685C24C23×D311yescharacteristic
686#41—416no—
687#41—1216no—
688C2×Q8—22no—
689C2×Q8—22no—
690C2×Q8—34no—
691C2×Q8—41no—
692C2×Q8—121no—
693C2×Q8—121no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—64no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—64no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—62no—
710C2×D4—62no—
711C2×D4—122no—
712C2×D4—121no—
713C2×D4—121no—
714C2×D4—122no—
715C2×D4—122no—
716C2×D4—122no—
717C2×D4—121no—
718C2×D4—121no—
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—122no—
728C2×D4—122no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—42no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—64no—
753C22×C4—64no—
754C22×C4—64no—
755C22×C4—64no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4—122no—
759C22×C4—122no—
760C22×C4—122no—
761C22×C4D3×D414yes—
762C22×C4C23×D312yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D311yescharacteristic
766C22×C4C23×D312yes—
767C22×C4C23×D311yescharacteristic
768C22×C4C23×D311yescharacteristic
769C22×C4C23×D311yescharacteristic
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—34no—
774C4⋊C4—38no—
775C4⋊C4—42no—
776C4⋊C4—64no—
777C4⋊C4—64no—
778C4⋊C4—64no—
779C4⋊C4—64no—
780C4⋊C4—64no—
781C4⋊C4—62no—
782C4⋊C4—62no—
783C4⋊C4—122no—
784C4⋊C4—122no—
785C22⋊C4—24no—
786C22⋊C4—38no—
787C22⋊C4—41no—
788C22⋊C4—42no—
789C22⋊C4—41no—
790C22⋊C4—42no—
791C22⋊C4—42no—
792C22⋊C4—64no—
793C22⋊C4—64no—
794C22⋊C4—64no—
795C22⋊C4—64no—
796C22⋊C4—64no—
797C22⋊C4—64no—
798C22⋊C4—64no—
799C22⋊C4—64no—
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⋊C4—122no—
812C42—64no—
813C42—122no—
814C42—121no—
815C42—121no—
816C42—122no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—24no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3C23×D411yescharacteristic
833C22×C3C2×H(5,𝔽2)11yescharacteristic
834C22×C3C2×H(5,𝔽2)11yescharacteristic
835C22×C3#58512yes—
836C22×C3#58512yes—
837C2×D3—42no—
838C2×D3—42no—
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—22no—
854C3×C4—42no—
855C3×C4—41no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859Dic3—24no—
860Dic3—24no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23C2×D3×D412yes—
893C23#100412yes—
894C23C24×D311yescharacteristic
895Q8—44no—
896Q8—124no—
897D4—44no—
898D4—44no—
899D4—44no—
900D4—124no—
901D4—128no—
902D4—128no—
903D4—128no—
904D4—242no—
905D4—244no—
906D4—244no—
907D4—244no—
908D4—244no—
909D4—244no—
910C2×C4—28no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—34no—
933C2×C4—34no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—62no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—82no—
954C2×C4—128no—
955C2×C4—244no—
956C2×C4—244no—
957C2×C4C2×D3×D412yes—
958C2×C4C2×D3×D412yes—
959C2×C4#100412yes—
960C2×C3—42no—
961C2×C3—42no—
962C2×C3—81no—
963C2×C3#348411yescharacteristic
964C2×C3#348711yescharacteristic
965C2×C3#350011yescharacteristic
966C2×C3#353912yes—
967C2×C3#356012yes—
968D3—82no—
969D3—82no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—24no—
975C22—41no—
976C22—41no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—42no—
985C22—122no—
986C22—122no—
987C22—122no—
988C22—122no—
989C22—122no—
990C22—122no—
991C22—122no—
992C22—122no—
993C22—122no—
994C22—122no—
995C22—122no—
996C22—122no—
997C22—122no—
998C22—122no—
999C22C22×D3×D411yescharacteristic
1000C22C2×#100411yescharacteristic
1001C22C2×#100411yescharacteristic
1002C22#596412yes—
1003C22#596812yes—
1004C4—22no—
1005C4—22no—
1006C4—22no—
1007C4—42no—
1008C4—41no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—64no—
1013C4—64no—
1014C4—122no—
1015C4—122no—
1016C4—122no—
1017C4—122no—
1018C3#4636011yescharacteristic, complemented, Sylow
1019C2—42no—
1020C2—42no—
1021C2—81no—
1022C2—242no—
1023C2—242no—
1024C2#8591911yescharacteristic
1025C2#8602311yescharacteristic
1026C2#8634111yescharacteristic
1027C2#8669712yes—
1028C2#8670612yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2406C2
hypercenter#2406D3
hypocenterC3#46360
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2406

Complements

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

NH ≅ G/Ntype
1. C2×#5833C2semidirect
2. C2×#5515C2semidirect
3. C3×#2406C2semidirect
4. #84092C2semidirect
5. #82899C2semidirect
6. #82853C2semidirect
7. #82182C2semidirect
8. #77214C2semidirect
9. #77176C2semidirect
10. #77133C2semidirect
11. #76934C2semidirect
12. #74815C2semidirect
13. #74814C2semidirect
14. #74641C2semidirect
15. #74530C2semidirect
16. #74454C2semidirect
17. #74404C2semidirect
18. #74144C2semidirect
19. #74057C2semidirect
127. #2406D3semidirect
209. #924D4semidirect
1018. C3#46360semidirect

Maximal subgroups

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

subgroupindex
C2×#58332
C2×#55152
C3×#24062
#840922
#828992
#828532
#821822
#772142
#771762
#771332
#769342
#748152
#748142
#746412
#745302
#744542
#744042
#741442
#740572
#463603