Finite Group Databasebeta

← #11904410

Subgroups — #11904410

Order 1152.

3569 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×#64312C211yesmaximal, characteristic, complemented
3C3×#5824C212yesmaximal, complemented
4#10595430C211yesmaximal, characteristic, complemented
5#10595350C211yesmaximal, characteristic, complemented
6#10595341C212yesmaximal, complemented
7#10595308C212yesmaximal, complemented
8#10595254C212yesmaximal, complemented
9#10595223C211yesmaximal, characteristic, complemented
10#10595169C212yesmaximal, complemented
11#10595163C214yesmaximal, complemented
12#10595080C212yesmaximal, complemented
13#10595076C211yesmaximal, characteristic, complemented
14#10595018C212yesmaximal, complemented
15C2×#63897C212yesmaximal, complemented
16#10594917C214yesmaximal, complemented
17#10594805C211yesmaximal, characteristic, complemented
18#86700—32nomaximal
19C2×C32×#41C2211yescharacteristic, complemented
20#64366—28no—
21C2×#3832C2211yescharacteristic
22C2×#3832C2211yescharacteristic, complemented
23C2×D4×C3⋊D3C2212yes—
24C2×D4×C3⋊D3C2211yescharacteristic
25C2×D4×C3⋊D3C2212yescomplemented
26C2×D4×C3⋊D3C2211yescharacteristic, complemented
27C2×#3828C2211yescharacteristic
28C2×#3828C2212yescomplemented
29C22×C4⋊(C3⋊D3)C2212yes—
30C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31C2×C3×#237C2212yescomplemented
32C2×#3811C2212yescomplemented
33C22×#624C2212yescomplemented
34C2×#3804C2214yescomplemented
35#64312—28no—
36C2×C4×D32C2211yescharacteristic, complemented
37C2×#3799C2212yescomplemented
38C2×#3797C2211yescharacteristic, complemented
39C3×#946C2212yescomplemented
40C3×#944C2212yescomplemented
41C3×#939C2214yescomplemented
42C3×#935C2214yescomplemented
43C3×D4×Dic3C2212yescomplemented
44C3×#929C2214yescomplemented
45C3×C4×#67C2212yescomplemented
46C3×#924C2212yescomplemented
47C2×C3×Dic3⋊C4C2214yescomplemented
48#63983C2211yescharacteristic, complemented
49#63981C2214yescomplemented
50#63981C2214yescomplemented
51#63978C2214yescomplemented
52#63975C2211yescharacteristic, complemented
53#63975C2212yescomplemented
54#63974C2212yescomplemented
55#63974C2214yescomplemented
56#63971C2212yescomplemented
57#63966C2214yescomplemented
58C2×#3722C2214yescomplemented
59C2×#3722C2212yescomplemented
60#63953C2212yescomplemented
61#63952C2214yescomplemented
62#63923C2211yescharacteristic, complemented
63#63923C2212yescomplemented
64#63910C2214yescomplemented
65#63910C2214yescomplemented
66#63909C2212yescomplemented
67C4×#626C2212yescomplemented
68#63897C2211yescharacteristic, complemented
69#63897C2212yescomplemented
70#63897C2212yescomplemented
71#63897C2214yescomplemented
72#63897C2212yescomplemented
73#63897C2212yescomplemented
74#63897C2214yescomplemented
75#63896C2212yescomplemented
76#63894C2212yescomplemented
77#63883C2214yescomplemented
78#63881C2214yescomplemented
79#63874C2211yescharacteristic, complemented
80#63871C2212yescomplemented
81#63865C2214yescomplemented
82#63864C2212yescomplemented
83#63853C2214yescomplemented
84#63849C2211yescharacteristic, complemented
85#63840C2212yescomplemented
86C2×#1009—32no—
87C2×#1009—61no—
88C2×D3×#41—32no—
89C3×#547—32no—
90#5829—32no—
91#5824D312yescomplemented
92#5726—32no—
93#5724—32no—
94#5655—34no—
95#5654—34no—
96#5653—34no—
97D3×#123—34no—
98#5631—32no—
99#5630—32no—
100#5628—32no—
101#5627—32no—
102#5610—34no—
103#5605—34no—
104#5554—32no—
105#5550—32no—
106#5547—32no—
107#5545—32no—
108#5507—34no—
109C2×#894—34no—
110C23×C3⋊D3C2312yes—
111C23×C3⋊D3C2312yes—
112C23×C3⋊D3C2312yes—
113C22×D32C2311yescharacteristic
114C32×#41—24no—
115C2×C32×Q8C2311yescharacteristic
116C2×C32×D4C2312yes—
117C2×C32×D4C2311yescharacteristic
118C22×C32×C4C2312yes—
119C22×C32×C4C2311yescharacteristic
120C2×#638C2311yescharacteristic
121C2×#638C2311yescharacteristic
122C2×#638C2312yes—
123C2×#638C2312yes—
124#3832—24no—
125#3832—24no—
126D4×C3⋊D3—28no—
127D4×C3⋊D3—24no—
128D4×C3⋊D3—28no—
129D4×C3⋊D3D418yescomplemented
130#3828—28no—
131#3828—24no—
132C2×C4⋊(C3⋊D3)—28no—
133C2×C4⋊(C3⋊D3)—24no—
134C2×C4⋊(C3⋊D3)C2311yescharacteristic
135C2×C4⋊(C3⋊D3)C2312yes—
136C2×C4⋊(C3⋊D3)C2312yes—
137C2×C4⋊(C3⋊D3)C2312yes—
138C2×C4⋊(C3⋊D3)C2311yescharacteristic
139C2×C4⋊(C3⋊D3)C2311yescharacteristic
140C2×C4×C3⋊D3C2311yescharacteristic
141C2×C4×C3⋊D3C2312yes—
142C2×C4×C3⋊D3C2312yes—
143C2×C4×C3⋊D3C2311yescharacteristic
144C2×#634C2311yescharacteristic
145C2×C3×#67C2314yes—
146C2×C3×#67C2312yes—
147C22×C3×Dic3C2314yes—
148C22×C3×Dic3C2314yes—
149C3×#237—28no—
150C2×C3×C4×D3C2312yes—
151C2×C3×Dic6C2312yes—
152#3811—28no—
153C2×#627C2312yes—
154C2×#626C2314yes—
155C2×#626C2314yes—
156C2×#626C2312yes—
157C2×#624—28no—
158C2×#624C2312yes—
159C2×#624C2314yes—
160C2×#624C2311yescharacteristic
161C2×#624C2314yes—
162#3804—216no—
163C2×D3×Dic3C2312yes—
164C4×D32—24no—
165#3799—28no—
166#3797—24no—
167C3×#217C2314yes—
168C3×#217C2312yes—
169C3×#217C2314yes—
170C3×(C2×D3)⋊C4C2312yes—
171C3×(C2×D3)⋊C4C2314yes—
172C3×C4⋊Dic3C2312yes—
173C3×Dic3⋊C4C2312yes—
174C3×Dic3⋊C4C2314yes—
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2314yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2312yes—
179#3724C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2312yes—
183#3722C2314yes—
184#3722C2314yes—
185#3722C2314yes—
186#3722C2314yes—
187#3722C2311yescharacteristic
188#3722C2311yescharacteristic
189#3722C2314yes—
190#3722C2312yes—
191(C2×D3)⋊Dic3C2312yes—
192Dic32C2312yes—
193#3485—91noSylow
194C2×C3×#41—21no—
195C2×C3×#41—32no—
196C2×C3×#41C2×D312yescomplemented
197#1009—616no—
198#1009—616no—
199D3×#41—616no—
200C2×#239—32no—
201C2×#239—32no—
202C2×#239—32no—
203C2×#239—61no—
204C2×#239—61no—
205C2×D3×Q8—32no—
206C2×#237—34no—
207C2×#237C2×D312yescomplemented
208C2×D3×D4—32no—
209C2×D3×D4—34no—
210C2×D3×D4—34no—
211C2×D3×D4—32no—
212C2×D3×D4—34no—
213C2×D3×D4—61no—
214C2×D3×D4—62no—
215C2×D3×D4—62no—
216C2×D3×D4—61no—
217C2×#235—34no—
218C2×#235—32no—
219C2×#235—34no—
220C2×#235—32no—
221C2×#235—61no—
222C2×#235—62no—
223C22×D12—34no—
224C22×D12—32no—
225C22×D12—62no—
226C22×D12—61no—
227C22×C4×D3—34no—
228C22×C4×D3—32no—
229C3×C4⋊Q8—32no—
230C3×#123—34no—
231C3×#123—34no—
232C3×C22⋊Q8—32no—
233C3×C22⋊Q8—32no—
234C3×#121—34no—
235C3×C4×D4—32no—
236C3×C4×D4—32no—
237C2×C3×C4⋊C4—34no—
238#947—32no—
239#946—32no—
240#946C2×D312yescomplemented
241#944C2×D312yescomplemented
242#939—34no—
243#939—32no—
244#939C2×D314yescomplemented
245#937—32no—
246#937—34no—
247#937—34no—
248#935C2×D314yescomplemented
249D4×Dic3C2×D312yescomplemented
250#930—34no—
251#930—32no—
252#929—34no—
253#929C2×D314yescomplemented
254C4×#67—34no—
255C4×#67—32no—
256C4×#67C2×D312yescomplemented
257C2×(C2×D3)⋊C4—34no—
258C2×(C2×D3)⋊C4—34no—
259C2×(C2×D3)⋊C4—34no—
260#924C2×D312yescomplemented
261C2×Dic3⋊C4C2×D314yescomplemented
262#897—32no—
263#896—32no—
264#896—34no—
265#896—34no—
266#895—32no—
267#895—34no—
268#895—34no—
269#894—34no—
270#894—34no—
271#894—34no—
272#894—34no—
273#894—34no—
274#894—34no—
275#894—34no—
276#894—34no—
277#894—32no—
278#894—34no—
279#893—34no—
280#893—32no—
281#892—32no—
282D3×C4⋊C4—34no—
283D3×C4⋊C4—34no—
284#888—34no—
285#886—34no—
286#885—34no—
287#884—32no—
288#884—34no—
289#884—34no—
290#883—32no—
291#883—34no—
292#883—34no—
293#882—34no—
294#882—34no—
295#882—32no—
296#882—34no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299D3×C22⋊C4—34no—
300D3×C22⋊C4—34no—
301D3×C22⋊C4—34no—
302#878—32no—
303#875—32no—
304C4×D12—32no—
305C4×D12—32no—
306#872—32no—
307C23×C32C2411yescharacteristic
308C23×C32C2412yes—
309C22×C3⋊D3—24no—
310C22×C3⋊D3—24no—
311C22×C3⋊D3—44no—
312C22×C3⋊D3—44no—
313C22×C3⋊D3—44no—
314C22×C3⋊D3C2×D418yes—
315C22×C3⋊D3C2411yescharacteristic
316C22×C3⋊D3C2412yes—
317C22×C3⋊D3C2411yescharacteristic
318C22×C3⋊D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—22no—
321C2×D32—42no—
322C32×Q8—22no—
323C32×D4—24no—
324C32×D4C2×D414yes—
325C2×C32×C4—24no—
326C2×C32×C4—22no—
327C2×C32×C4C2411yescharacteristic
328C2×C32×C4C2412yes—
329C2×C32×C4C2411yescharacteristic
330#638—24no—
331#638—22no—
332#638—22no—
333#638C2×D418yes—
334C2×C3⋊Dic3C2411yescharacteristic
335C2×C3⋊Dic3C2411yescharacteristic
336C4⋊(C3⋊D3)—22no—
337C4⋊(C3⋊D3)—24no—
338C4⋊(C3⋊D3)—24no—
339C4⋊(C3⋊D3)—24no—
340C4⋊(C3⋊D3)—22no—
341C4⋊(C3⋊D3)C2×D414yes—
342C4×C3⋊D3—24no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—24no—
345C4×C3⋊D3C2×D414yes—
346#634—22no—
347C3×#67—28no—
348C3×#67—42no—
349C2×C3×Dic3—28no—
350C2×C3×Dic3—44no—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2414yes—
356C3×C4×D3—24no—
357C3×Dic6—24no—
358#627—24no—
359#626—28no—
360#626—42no—
361#626—44no—
362#624—24no—
363#624—28no—
364#624—22no—
365#624—44no—
366D3×Dic3—24no—
367C2×H(5,𝔽2)—91no—
368C22×#41—91no—
369#547—32no—
370#547—94no—
371#547—92no—
372#546—92no—
373#546—92no—
374#546—94no—
375#536—91no—
376#536—91no—
377#534—92no—
378#534—92no—
379#525—91no—
380#525—91no—
381C2×#123—92no—
382C2×#123—92no—
383#518—91no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—32no—
388C23×D3—62no—
389C23×D3—62no—
390C23×D3—62no—
391C3×#41—28no—
392C3×#41—28no—
393C3×#41—68no—
394C2×C3×Q8—21no—
395C2×C3×Q8—32no—
396C2×C3×Q8C22×D312yes—
397C2×C3×D4—22no—
398C2×C3×D4—21no—
399C2×C3×D4—34no—
400C2×C3×D4—32no—
401C2×C3×D4C22×D314yes—
402C2×C3×D4C22×D312yes—
403C22×C3×C4—22no—
404C22×C3×C4—21no—
405C22×C3×C4—34no—
406C22×C3×C4—34no—
407C22×C3×C4—32no—
408C22×C3×C4C22×D314yes—
409C22×C3×C4C22×D312yes—
410C2×#67—34no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—32no—
417C2×#67—62no—
418C2×#67—61no—
419C2×#67—62no—
420C2×#67—61no—
421C2×#67C22×D314yes—
422C2×#67C22×D312yes—
423C22×Dic3—32no—
424C22×Dic3C22×D314yes—
425C22×Dic3C22×D314yes—
426#239—68no—
427#239—68no—
428#239—68no—
429#239—68no—
430#239—68no—
431D3×Q8—68no—
432#237—28no—
433#237—616no—
434D3×D4—316no—
435D3×D4—68no—
436D3×D4—616no—
437D3×D4—616no—
438D3×D4—616no—
439D3×D4—616no—
440D3×D4—616no—
441D3×D4—68no—
442D3×D4—68no—
443#235—68no—
444#235—68no—
445#235—616no—
446#235—616no—
447#235—68no—
448#235—616no—
449C2×D12—32no—
450C2×D12—34no—
451C2×D12—32no—
452C2×D12—32no—
453C2×D12—34no—
454C2×D12—34no—
455C2×D12—34no—
456C2×D12—32no—
457C2×D12—34no—
458C2×D12—61no—
459C2×D12—62no—
460C2×D12—61no—
461C2×D12—62no—
462C2×D12—62no—
463C2×D12—61no—
464C2×D12—68no—
465C2×D12—616no—
466C2×D12—68no—
467C2×D12—616no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—32no—
476C2×C4×D3—34no—
477C2×C4×D3—34no—
478C2×C4×D3—34no—
479C2×C4×D3—61no—
480C2×C4×D3—62no—
481C2×C4×D3—61no—
482C2×C4×D3—62no—
483C2×C4×D3—68no—
484C2×C4×D3—616no—
485C2×C4×D3C22×D312yes—
486C2×Dic6—32no—
487C2×Dic6—34no—
488C2×Dic6—61no—
489C2×Dic6C22×D312yes—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—34no—
492C3×C4⋊C4—34no—
493C3×C4⋊C4—32no—
494C3×C4⋊C4—32no—
495C3×C4⋊C4—34no—
496C3×C22⋊C4—32no—
497C3×C22⋊C4—34no—
498C3×C22⋊C4—34no—
499C3×C22⋊C4—32no—
500C3×C22⋊C4—34no—
501C3×C42—32no—
502#217—32no—
503#217C22×D312yes—
504#217C22×D314yes—
505#217C22×D314yes—
506(C2×D3)⋊C4—32no—
507(C2×D3)⋊C4—32no—
508(C2×D3)⋊C4—32no—
509(C2×D3)⋊C4—32no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—32no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4C22×D314yes—
523(C2×D3)⋊C4C22×D312yes—
524C4⋊Dic3—32no—
525C4⋊Dic3—34no—
526C4⋊Dic3C22×D312yes—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—32no—
531Dic3⋊C4C22×D312yes—
532Dic3⋊C4C22×D314yes—
533Dic3⋊C4C22×D314yes—
534Dic3⋊C4C22×D314yes—
535Dic3⋊C4C22×D314yes—
536C4×Dic3—34no—
537C4×Dic3C22×D312yes—
538C22×C32—21no—
539C22×C32—24no—
540C22×C32—22no—
541C22×C32C22×D414yes—
542C22×C32C2511yescharacteristic
543C2×C3⋊D3—21no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3—24no—
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—24no—
549C2×C3⋊D3—48no—
550C2×C3⋊D3—84no—
551C2×C3⋊D3—84no—
552C2×C3⋊D3C22×D412yes—
553C2×C3⋊D3C22×D414yes—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557D32—44no—
558C32×C4—21no—
559C32×C4—22no—
560C32×C4C22×D412yes—
561C3⋊Dic3—21no—
562C3⋊Dic3C22×D412yes—
563C3×Dic3—22no—
564C3×Dic3—24no—
565C3×Dic3—22no—
566C3×Dic3—24no—
567C3×Dic3—22no—
568H(5,𝔽2)—188no—
569C2×#41—32no—
570C2×#41—94no—
571C2×#41—92no—
572C2×#41—91no—
573C2×#41—91no—
574C2×#41—91no—
575C2×#41—92no—
576C2×#41—188no—
577C2×#41D3211yescharacteristic, complemented
578C22×Q8—91no—
579C22×D4—92no—
580C22×D4—91no—
581C22×D4—92no—
582C22×D4—92no—
583C22×D4—91no—
584C22×D4—92no—
585C22×D4—91no—
586C23×C4—92no—
587C23×C4—91no—
588C4⋊Q8—32no—
589C4⋊Q8—92no—
590#124—92no—
591#124—92no—
592#123—34no—
593#123—34no—
594#123—91no—
595#123—92no—
596#123—94no—
597#123—94no—
598#123—91no—
599#123—92no—
600#123—92no—
601#123—92no—
602#123—92no—
603#123—94no—
604#123—94no—
605C22⋊Q8—32no—
606C22⋊Q8—32no—
607C22⋊Q8—92no—
608C22⋊Q8—94no—
609C22⋊Q8—92no—
610#121—34no—
611#121—94no—
612#121—94no—
613#121—92no—
614#121—92no—
615#121—94no—
616#120—91no—
617#120—92no—
618#120—94no—
619#120—94no—
620#120—91no—
621C4×D4—32no—
622C4×D4—32no—
623C4×D4—92no—
624C4×D4—92no—
625C4×D4—94no—
626C4×D4—94no—
627#117—91no—
628#117—91no—
629C2×C4⋊C4—34no—
630C2×C4⋊C4—94no—
631C2×C22⋊C4—92no—
632C2×C22⋊C4—94no—
633C2×C22⋊C4—92no—
634C2×C22⋊C4—94no—
635C23×C3—21no—
636C23×C3—22no—
637C23×C3—32no—
638C23×C3C23×D312yes—
639C23×C3C23×D314yes—
640C22×D3—32no—
641C22×D3—34no—
642C22×D3—316no—
643C22×D3—32no—
644C22×D3—34no—
645C22×D3—61no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—61no—
649C22×D3—68no—
650C22×D3—64no—
651C22×D3—68no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—68no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—244no—
664C22×D3—244no—
665C22×D3—244no—
666C22×D3C23×D312yes—
667C3×Q8—24no—
668C3×Q8—24no—
669C3×Q8—64no—
670C3×D4—28no—
671C3×D4—28no—
672C3×D4—24no—
673C3×D4—68no—
674C3×D4—122no—
675C3×D4D3×D418yes—
676C2×C3×C4—28no—
677C2×C3×C4—24no—
678C2×C3×C4—28no—
679C2×C3×C4—24no—
680C2×C3×C4—21no—
681C2×C3×C4—22no—
682C2×C3×C4—21no—
683C2×C3×C4—34no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—34no—
687C2×C3×C4—32no—
688C2×C3×C4—68no—
689C2×C3×C4—64no—
690C2×C3×C4—124no—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D314yes—
693C2×C3×C4C23×D312yes—
694#67—28no—
695#67—316no—
696#67—42no—
697#67—68no—
698#67—68no—
699#67—64no—
700#67—64no—
701#67—64no—
702#67—64no—
703#67—68no—
704#67—68no—
705#67—124no—
706#67—122no—
707C2×Dic3—28no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—44no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—64no—
714C2×Dic3C23×D314yes—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D314yes—
718C2×Dic3C23×D312yes—
719D12—38no—
720D12—64no—
721D12—64no—
722D12—68no—
723D12—68no—
724D12—68no—
725D12—64no—
726D12—68no—
727D12—68no—
728D12—68no—
729D12—64no—
730D12—68no—
731D12—64no—
732D12—122no—
733D12—124no—
734C4×D3—24no—
735C4×D3—38no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—68no—
741C4×D3—68no—
742C4×D3—64no—
743C4×D3—68no—
744C4×D3—68no—
745C4×D3—68no—
746C4×D3—64no—
747C4×D3—64no—
748C4×D3—124no—
749C4×D3—124no—
750Dic6—24no—
751Dic6—68no—
752Dic6—64no—
753Dic6—64no—
754C2×C32—24no—
755C2×C32—41no—
756C2×C32C23×D411yescharacteristic
757C2×C32#58512yes—
758C3⋊D3—22no—
759C3⋊D3—24no—
760C3⋊D3—42no—
761C3⋊D3—41no—
762C3×D3—42no—
763C24—91no—
764C24—92no—
765C24—92no—
766C24—92no—
767#41—24no—
768#41—68no—
769#41—184no—
770#41—188no—
771#41—1816no—
772#41—188no—
773#41—184no—
774#41—184no—
775C2×Q8—32no—
776C2×Q8—92no—
777C2×Q8—91no—
778C2×Q8—184no—
779C2×Q8C2×D3211yescharacteristic
780C2×D4—34no—
781C2×D4—32no—
782C2×D4—94no—
783C2×D4—92no—
784C2×D4—94no—
785C2×D4—92no—
786C2×D4—98no—
787C2×D4—91no—
788C2×D4—92no—
789C2×D4—91no—
790C2×D4—91no—
791C2×D4—92no—
792C2×D4—91no—
793C2×D4—92no—
794C2×D4—92no—
795C2×D4—91no—
796C2×D4—184no—
797C2×D4—188no—
798C2×D4—188no—
799C2×D4—188no—
800C2×D4—188no—
801C2×D4—184no—
802C2×D4C2×D3212yes—
803C2×D4C2×D3211yescharacteristic
804C22×C4—34no—
805C22×C4—34no—
806C22×C4—32no—
807C22×C4—94no—
808C22×C4—91no—
809C22×C4—92no—
810C22×C4—94no—
811C22×C4—92no—
812C22×C4—91no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—91no—
816C22×C4—184no—
817C22×C4—188no—
818C22×C4C2×D3212yes—
819C22×C4C2×D3211yescharacteristic
820C4⋊C4—32no—
821C4⋊C4—34no—
822C4⋊C4—34no—
823C4⋊C4—34no—
824C4⋊C4—34no—
825C4⋊C4—32no—
826C4⋊C4—92no—
827C4⋊C4—94no—
828C4⋊C4—92no—
829C22⋊C4—32no—
830C22⋊C4—34no—
831C22⋊C4—34no—
832C22⋊C4—32no—
833C22⋊C4—34no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—92no—
837C22⋊C4—92no—
838C22⋊C4—94no—
839C22⋊C4—94no—
840C22⋊C4—94no—
841C22⋊C4—94no—
842C22⋊C4—94no—
843C22⋊C4—92no—
844C42—32no—
845C42—92no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—24no—
853C22×C3—21no—
854C22×C3—44no—
855C22×C3—42no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3C2×D3×D418yes—
860C22×C3C24×D312yes—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—34no—
865C2×D3—38no—
866C2×D3—62no—
867C2×D3—64no—
868C2×D3—64no—
869C2×D3—62no—
870C2×D3—64no—
871C2×D3—62no—
872C2×D3—64no—
873C2×D3—62no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—64no—
878C2×D3—64no—
879C2×D3—62no—
880C2×D3—124no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—124no—
884C2×D3—128no—
885C2×D3—1216no—
886C2×D3—248no—
887C2×D3—248no—
888C2×D3—248no—
889C2×D3—248no—
890C2×D3—248no—
891C3×C4—22no—
892C3×C4—24no—
893C3×C4—22no—
894C3×C4—24no—
895C3×C4—22no—
896C3×C4—64no—
897C3×C4—62no—
898C3×C4—62no—
899C3×C4—64no—
900C3×C4—62no—
901C3×C4C2×D3×D414yes—
902Dic3—24no—
903Dic3—22no—
904Dic3—24no—
905Dic3—22no—
906Dic3—22no—
907Dic3—34no—
908Dic3—62no—
909Dic3—62no—
910Dic3—62no—
911C32#348511yescharacteristic, complemented, Sylow
912C23—32no—
913C23—91no—
914C23—92no—
915C23—98no—
916C23—92no—
917C23—91no—
918C23—184no—
919C23—182no—
920C23—184no—
921C23—364no—
922C23—364no—
923C23—364no—
924C23—362no—
925C23C22×D3211yescharacteristic
926C23C22×D3212yes—
927Q8—22no—
928Q8—64no—
929Q8—182no—
930Q8—184no—
931D4—24no—
932D4—68no—
933D4—98no—
934D4—94no—
935D4—122no—
936D4—182no—
937D4—184no—
938D4—184no—
939D4—184no—
940D4—188no—
941D4—182no—
942D4—182no—
943D4—184no—
944D4—182no—
945D4—364no—
946D4—362no—
947D4#381114yes—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—34no—
953C2×C4—32no—
954C2×C4—34no—
955C2×C4—68no—
956C2×C4—64no—
957C2×C4—91no—
958C2×C4—94no—
959C2×C4—91no—
960C2×C4—124no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—182no—
964C2×C4—184no—
965C2×C4—188no—
966C2×C4—184no—
967C2×C4—182no—
968C2×C4—364no—
969C2×C4C22×D3212yes—
970C2×C4C22×D3211yescharacteristic
971C2×C4C22×D3211yescharacteristic
972C2×C3—28no—
973C2×C3—22no—
974C2×C3—21no—
975C2×C3—44no—
976C2×C3—42no—
977C2×C3—42no—
978C2×C3—122no—
979C2×C3C22×D3×D412yes—
980C2×C3#596412yes—
981C2×C3#596812yes—
982D3—42no—
983D3—64no—
984D3—68no—
985D3—122no—
986D3—124no—
987D3—122no—
988D3—124no—
989D3—122no—
990D3—124no—
991C22—24no—
992C22—22no—
993C22—21no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—92no—
998C22—94no—
999C22—184no—
1000C22—182no—
1001C22—182no—
1002C22—184no—
1003C22—182no—
1004C22—181no—
1005C22—368no—
1006C22—364no—
1007C22—724no—
1008C22—724no—
1009C22C2×#381114yes—
1010C22C23×D3211yescharacteristic
1011C4—21no—
1012C4—22no—
1013C4—62no—
1014C4—64no—
1015C4—62no—
1016C4—62no—
1017C4—64no—
1018C4—92no—
1019C4—181no—
1020C4C2×#381112yes—
1021C3—21no—
1022C3#8670012yescomplemented
1023C2—24no—
1024C2—41no—
1025C2—122no—
1026C2—182no—
1027C2—184no—
1028C2—361no—
1029C2—362no—
1030C2#1059669712yes—
1031C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×#64312C2semidirect
3. C3×#5824C2semidirect
4. #10595430C2semidirect
5. #10595350C2semidirect
6. #10595341C2semidirect
7. #10595308C2semidirect
8. #10595254C2semidirect
9. #10595223C2semidirect
10. #10595169C2semidirect
11. #10595163C2semidirect
12. #10595080C2semidirect
13. #10595076C2semidirect
14. #10595018C2semidirect
15. C2×#63897C2semidirect
16. #10594917C2semidirect
17. #10594805C2semidirect
19. C2×C32×#41C22semidirect
22. C2×#3832C22semidirect
25. C2×D4×C3⋊D3C22semidirect
26. C2×D4×C3⋊D3C22semidirect
28. C2×#3828C22semidirect
30. C22×C4⋊(C3⋊D3)C22semidirect
31. C2×C3×#237C22semidirect
32. C2×#3811C22semidirect
33. C22×#624C22semidirect
34. C2×#3804C22semidirect
36. C2×C4×D32C22semidirect
37. C2×#3799C22semidirect
38. C2×#3797C22semidirect
39. C3×#946C22semidirect
40. C3×#944C22semidirect
41. C3×#939C22semidirect
42. C3×#935C22semidirect
43. C3×D4×Dic3C22semidirect
44. C3×#929C22semidirect
45. C3×C4×#67C22semidirect
46. C3×#924C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. #63983C22semidirect
49. #63981C22semidirect
50. #63981C22semidirect
51. #63978C22semidirect
52. #63975C22semidirect
53. #63975C22semidirect
54. #63974C22semidirect
55. #63974C22semidirect
56. #63971C22semidirect
57. #63966C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. #63953C22semidirect
61. #63952C22semidirect
62. #63923C22semidirect
63. #63923C22semidirect
64. #63910C22semidirect
65. #63910C22semidirect
66. #63909C22semidirect
67. C4×#626C22semidirect
68. #63897C22semidirect
69. #63897C22semidirect
70. #63897C22semidirect
71. #63897C22semidirect
72. #63897C22semidirect
73. #63897C22semidirect
74. #63897C22semidirect
75. #63896C22semidirect
76. #63894C22semidirect
77. #63883C22semidirect
78. #63881C22semidirect
79. #63874C22semidirect
80. #63871C22semidirect
81. #63865C22semidirect
82. #63864C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63840C22semidirect
91. #5824D3semidirect
129. D4×C3⋊D3D4semidirect
196. C2×C3×#41C2×D3semidirect
207. C2×#237C2×D3semidirect
240. #946C2×D3semidirect
241. #944C2×D3semidirect
244. #939C2×D3semidirect
248. #935C2×D3semidirect
249. D4×Dic3C2×D3semidirect
253. #929C2×D3semidirect
256. C4×#67C2×D3semidirect
260. #924C2×D3semidirect
261. C2×Dic3⋊C4C2×D3semidirect
577. C2×#41D32semidirect
911. C32#3485semidirect
1022. C3#86700semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#643122
C3×#58242
#105954302
#105953502
#105953412
#105953082
#105952542
#105952232
#105951692
#105951632
#105950802
#105950762
#105950182
C2×#638972
#105949172
#105948052
#867003