Finite Group Databasebeta

← #11904543

Subgroups — #11904543

Order 1152.

3237 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64309C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10596077C211yesmaximal, characteristic, complemented
4C3×#5599C212yesmaximal, complemented
5#10595309C211yesmaximal, characteristic, complemented
6#10595299C214yesmaximal, complemented
7#10595158C212yesmaximal, complemented
8#10595144C212yesmaximal, complemented
9#10595142C212yesmaximal, complemented
10#10595016C211yesmaximal, characteristic, complemented
11#10594899C212yesmaximal, complemented
12#10594634C211yesmaximal, characteristic, complemented
13#10594382C212yesmaximal, complemented
14#10594347C211yesmaximal, characteristic, complemented
15#10594286C214yesmaximal, complemented
16#10594190C212yesmaximal, complemented
17#10594189C212yesmaximal, complemented
18#86783—32nomaximal
19C2×#3830C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2212yes—
23C2×#3811C2212yes—
24C22×#627C2212yescomplemented
25C2×#3805C2212yes—
26C2×#3805C2212yescomplemented
27C2×#3804C2214yes—
28#64309—28no—
29#64306—28no—
30C2×#3802C2211yescharacteristic
31C2×C4×D32C2212yes—
32C2×#3798C2212yes—
33C2×#3798C2211yescharacteristic
34C2×#3797C2211yescharacteristic
35C2×#3796C2212yes—
36C2×D3×Dic6C2212yescomplemented
37C32×#121C2211yescharacteristic, complemented
38#64147C2211yescharacteristic, complemented
39#64146C2212yes—
40D4×C3⋊Dic3C2212yescomplemented
41#64133C2211yescharacteristic, complemented
42#64106C2211yescharacteristic, complemented
43#64101C2211yescharacteristic
44#64092C2212yes—
45#64090C2212yescomplemented
46C3×#940C2214yescomplemented
47C3×#940C2212yescomplemented
48C3×#939C2214yescomplemented
49C3×C4×#67C2212yescomplemented
50C3×#895C2212yescomplemented
51C3×#887C2212yescomplemented
52C3×#884C2214yescomplemented
53C3×#67⋊C4C2214yescomplemented
54#63983C2214yes—
55#63982C2211yescharacteristic, complemented
56#63981C2212yes—
57#63980C2212yescomplemented
58#63980C2211yescharacteristic, complemented
59#63980C2212yescomplemented
60#63979C2214yescomplemented
61#63978C2214yescomplemented
62Dic3×#67C2214yescomplemented
63#63970C2214yescomplemented
64#63970C2214yescomplemented
65#63959C2214yescomplemented
66#63922C2214yes—
67C4×#627C2212yescomplemented
68#63915C2212yescomplemented
69#63914C2212yescomplemented
70#63912C2211yescharacteristic, complemented
71#63908C2212yescomplemented
72C4×#626C2212yescomplemented
73#63893C2214yescomplemented
74Dic3×D12C2214yescomplemented
75#63886C2214yescomplemented
76#63879C2214yescomplemented
77#63874C2211yescharacteristic
78#63865C2211yescharacteristic, complemented
79#63860C2212yescomplemented
80#63853C2212yes—
81#63852C2214yescomplemented
82#63851C2214yescomplemented
83Dic3×Dic6C2212yescomplemented
84#63838C2212yescomplemented
85#63836C2214yes—
86C2×#1010—32no—
87C2×D3×#41—32no—
88C3×#550—32no—
89#5834—32no—
90#5831—32no—
91#5718—32no—
92#5718—34no—
93#5715—32no—
94#5715—34no—
95#5607—34no—
96#5607—32no—
97#5606—32no—
98#5606—34no—
99#5606—61no—
100#5599—34no—
101#5599D312yescomplemented
102#5598—34no—
103#5598—32no—
104#5576—32no—
105#5572—32no—
106#5552—32no—
107#5552—34no—
108#5547—32no—
109#5547—34no—
110C23×C3⋊D3C2311yescharacteristic
111C22×D32C2312yes—
112C2×C32×D4C2311yescharacteristic
113C2×C32×D4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638C2312yes—
116C2×#638C2312yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2312yes—
119#3830—24no—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2311yescharacteristic
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2312yes—
131C22×C3×Dic3C2314yes—
132C3×#237—28no—
133C3×#235—28no—
134C2×C3×D12C2312yes—
135C2×C3×D12C2314yes—
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2312yes—
138C2×C3×Dic6C2312yes—
139#3811—28no—
140C2×#627—28no—
141C2×#627C2314yes—
142C2×#627C2311yescharacteristic
143C2×#627C2312yes—
144C2×#626C2314yes—
145C2×#626C2312yes—
146C2×#626C2312yes—
147C2×#625C2312yes—
148C2×#625C2311yescharacteristic
149C2×#625C2314yes—
150C2×#624C2312yes—
151#3805—28no—
152#3805—28no—
153#3804—216no—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156#3802—24no—
157C4×D32—28no—
158#3798—24no—
159#3798—28no—
160#3797D418yescomplemented
161#3796—28no—
162D3×Dic6—28no—
163C32×C4⋊C4C2311yescharacteristic
164C32×C22⋊C4C2312yes—
165#3757C2312yes—
166#3757C2312yes—
167#3752C2312yes—
168#3752C2312yes—
169C4⋊(C3⋊Dic3)C2312yes—
170C4⋊(C3⋊Dic3)C2311yescharacteristic
171#3750C2312yes—
172C4×C3⋊Dic3C2312yes—
173C3×#217C2312yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×(C2×D3)⋊C4C2312yes—
176C3×Dic3⋊C4C2312yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2314yes—
179C3×C4×Dic3C2312yes—
180#3724C2311yescharacteristic
181#3724C2311yescharacteristic
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2312yes—
184#3722C2312yes—
185#3722C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2314yes—
190Dic32C2314yes—
191#3487—91noSylow
192C2×C3×#41—32no—
193C2×C3×#41—32no—
194#1010—616no—
195D3×#41—616no—
196C2×#239—32no—
197C2×D3×Q8—32no—
198C2×D3×Q8—32no—
199C2×#237—32no—
200C2×#237—34no—
201C2×#237—34no—
202C2×#237—34no—
203C2×#237—32no—
204C2×#237—61no—
205C2×#237C2×D312yescomplemented
206C2×D3×D4—34no—
207C2×D3×D4—32no—
208C2×#235—34no—
209C2×#235—34no—
210C2×#235—32no—
211C2×#235C2×D312yes—
212C22×C4×D3—32no—
213C22×C4×D3—34no—
214C22×C4×D3—61no—
215C22×Dic6—34no—
216C22×Dic6—32no—
217C3×#127—34no—
218C3×#127—32no—
219C3×#121—21no—
220C3×#121—34no—
221C3×#121—32no—
222C3×#121—34no—
223C3×#121C2×D312yescomplemented
224C3×C4×Q8—32no—
225C3×C4×D4—32no—
226C3×C4×D4—34no—
227Q8×Dic3—32no—
228#940—34no—
229#940—34no—
230#940—34no—
231#940C2×D312yescomplemented
232#940C2×D314yescomplemented
233#939—34no—
234#939—34no—
235#939—34no—
236#939—34no—
237#939—32no—
238#939—34no—
239#939—34no—
240#939C2×D314yescomplemented
241#938—32no—
242#938—34no—
243#938—34no—
244#938—32no—
245#938—61no—
246#937—34no—
247#937—34no—
248#937—34no—
249#937—32no—
250#937—34no—
251#937—62no—
252#936—34no—
253#936—32no—
254D4×Dic3—34no—
255D4×Dic3—34no—
256D4×Dic3—34no—
257D4×Dic3—62no—
258#930—34no—
259#930—32no—
260C4×#67—34no—
261C4×#67—34no—
262C4×#67—32no—
263C4×#67C2×D312yescomplemented
264#924—32no—
265#924—34no—
266#924—61no—
267#897—32no—
268#897—34no—
269#897—61no—
270#896—34no—
271#896—32no—
272#895—34no—
273#895C2×D312yescomplemented
274#894—32no—
275#892—32no—
276#892—34no—
277#892—61no—
278#887—34no—
279#887C2×D312yescomplemented
280#885—34no—
281#885—34no—
282#885—34no—
283#884—32no—
284#884C2×D314yescomplemented
285#883—34no—
286#883—32no—
287#883—62no—
288#882—32no—
289#882—34no—
290#67⋊C4—34no—
291#67⋊C4—34no—
292#67⋊C4—62no—
293#67⋊C4C2×D314yescomplemented
294#878—32no—
295#878—34no—
296#875—32no—
297#875—34no—
298C4×D12—34no—
299C4×D12—32no—
300#872—34no—
301#872—32no—
302C4×Dic6—32no—
303C4×Dic6—34no—
304C23×C32C2411yescharacteristic
305C23×C32C2412yes—
306C22×C3⋊D3—22no—
307C22×C3⋊D3—41no—
308C22×C3⋊D3—41no—
309C22×C3⋊D3C2411yescharacteristic
310C22×C3⋊D3C2411yescharacteristic
311C22×C3×D3C2414yes—
312C22×C3×D3C2412yes—
313C2×D32—24no—
314C2×D32—42no—
315C2×D32—42no—
316C32×D4—22no—
317C32×D4—42no—
318C2×C32×C4—22no—
319C2×C32×C4C2412yes—
320C2×C32×C4C2411yescharacteristic
321C2×C32×C4C2411yescharacteristic
322#638—24no—
323#638—42no—
324C2×C3⋊Dic3—22no—
325C2×C3⋊Dic3—24no—
326C2×C3⋊Dic3C2412yes—
327C2×C3⋊Dic3C2412yes—
328C2×C3⋊Dic3C2411yescharacteristic
329C2×C3⋊Dic3C2411yescharacteristic
330C4×C3⋊D3—22no—
331C4×C3⋊D3—22no—
332C4×C3⋊D3—22no—
333C4×C3⋊D3C2×D414yes—
334#634—22no—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—44no—
338C3×#67—42no—
339C3×#67—44no—
340C2×C3×Dic3—28no—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C3×D12—24no—
346C3×D12—44no—
347C3×C4×D3—24no—
348C3×C4×D3—28no—
349C3×Dic6C2×D418yes—
350#627—22no—
351#627—28no—
352#627C2×D418yes—
353#626—24no—
354#626—28no—
355#626—42no—
356#625—24no—
357#625—22no—
358#625—44no—
359#624C2×D418yes—
360D3×Dic3—28no—
361D3×Dic3—28no—
362C2×2−1+4—91no—
363C22×#41—91no—
364#550—32no—
365#550—92no—
366#550—92no—
367#550—92no—
368#548—92no—
369#548—92no—
370#548—92no—
371#548—92no—
372#535—91no—
373#535—94no—
374#535—91no—
375#525—91no—
376#525—94no—
377#525—91no—
378#519—91no—
379C23×D3—32no—
380C23×D3—34no—
381C23×D3—61no—
382C3×#41—68no—
383C3×#41—68no—
384C2×C3×Q8—32no—
385C2×C3×D4—22no—
386C2×C3×D4—21no—
387C2×C3×D4—34no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—32no—
392C2×C3×D4—32no—
393C2×C3×D4—34no—
394C2×C3×D4C22×D312yes—
395C2×C3×D4C22×D314yes—
396C22×C3×C4—21no—
397C22×C3×C4—34no—
398C22×C3×C4—34no—
399C22×C3×C4—32no—
400C22×C3×C4C22×D312yes—
401C2×#67—34no—
402C2×#67—32no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—32no—
408C2×#67—34no—
409C2×#67—32no—
410C2×#67—62no—
411C2×#67—62no—
412C2×#67C22×D314yes—
413C2×#67C22×D314yes—
414C2×#67C22×D314yes—
415C2×#67C22×D312yes—
416C2×#67C22×D314yes—
417C22×Dic3—32no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—34no—
421C22×Dic3—62no—
422C22×Dic3—61no—
423C22×Dic3C22×D314yes—
424#239—68no—
425D3×Q8—316no—
426D3×Q8—68no—
427#237—28no—
428#237—616no—
429#237—616no—
430#237—616no—
431#237—68no—
432#237—68no—
433#237—124no—
434D3×D4—68no—
435D3×D4—616no—
436#235—28no—
437#235—616no—
438#235—68no—
439#235—616no—
440C2×D12—34no—
441C2×D12—32no—
442C2×D12—32no—
443C2×D12C22×D312yes—
444C2×D12C22×D314yes—
445C2×C4×D3—32no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—34no—
449C2×C4×D3—32no—
450C2×C4×D3—32no—
451C2×C4×D3—32no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—616no—
457C2×C4×D3—68no—
458C2×C4×D3—124no—
459C2×C4×D3C22×D312yes—
460C2×C4×D3C22×D314yes—
461C2×Dic6—34no—
462C2×Dic6—32no—
463C2×Dic6—34no—
464C2×Dic6—32no—
465C2×Dic6—34no—
466C2×Dic6—61no—
467C2×Dic6—616no—
468C2×Dic6—68no—
469C2×Dic6C22×D312yes—
470C3×C4⋊C4—21no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—32no—
473C3×C4⋊C4C22×D312yes—
474C3×C22⋊C4—22no—
475C3×C22⋊C4—32no—
476C3×C22⋊C4—34no—
477C3×C22⋊C4—32no—
478C3×C22⋊C4C22×D314yes—
479C3×C42—34no—
480C3×C42—32no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—32no—
485#217—34no—
486#217—34no—
487#217—62no—
488#217—62no—
489#217C22×D312yes—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4—62no—
502(C2×D3)⋊C4C22×D314yes—
503(C2×D3)⋊C4C22×D312yes—
504C4⋊Dic3—32no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—32no—
508C4⋊Dic3—62no—
509C4⋊Dic3—61no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—62no—
516Dic3⋊C4C22×D314yes—
517Dic3⋊C4C22×D312yes—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—62no—
522C4×Dic3C22×D314yes—
523C4×Dic3C22×D312yes—
524C22×C32—21no—
525C22×C32—22no—
526C22×C32—21no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—21no—
530C22×C32C2511yescharacteristic
531C2×C3⋊D3—21no—
532C2×C3⋊D3—21no—
533C2×C3⋊D3—21no—
534C2×C3⋊D3—21no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—44no—
537C2×C3⋊D3C22×D412yes—
538C2×C3×D3—22no—
539C2×C3×D3—24no—
540C2×C3×D3—22no—
541C2×C3×D3—24no—
542C2×C3×D3—22no—
543C2×C3×D3—24no—
544D32—48no—
545C32×C4—21no—
546C32×C4—22no—
547C32×C4C22×D412yes—
548C3⋊Dic3—21no—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D412yes—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D418yes—
5562−1+4—188no—
557C2×#41—32no—
558C2×#41—32no—
559C2×#41—91no—
560C2×#41—92no—
561C2×#41—94no—
562C2×#41—92no—
563C2×#41—92no—
564C2×#41—92no—
565C2×#41—91no—
566C2×#41—188no—
567C22×Q8—92no—
568C22×Q8—92no—
569C22×Q8—91no—
570C22×D4—92no—
571C22×D4—91no—
572C23×C4—92no—
573C23×C4—91no—
574#127—34no—
575#127—32no—
576#127—94no—
577#127—92no—
578#124—94no—
579#124—92no—
580#124—92no—
581#124—94no—
582#123—92no—
583#123—92no—
584C22⋊Q8—91no—
585C22⋊Q8—94no—
586C22⋊Q8—91no—
587C22⋊Q8—94no—
588C22⋊Q8—91no—
589C22⋊Q8—91no—
590#121—34no—
591#121—32no—
592#121—34no—
593#121—91no—
594#121—94no—
595#121—92no—
596#121—94no—
597#121—94no—
598#121—91no—
599#121—94no—
600#121—92no—
601#121—92no—
602#121—91no—
603#121D3211yescharacteristic, complemented
604#120—92no—
605#120—94no—
606#120—94no—
607#120—92no—
608C4×Q8—32no—
609C4×Q8—92no—
610C4×Q8—92no—
611C4×Q8—92no—
612C4×D4—32no—
613C4×D4—34no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620#117—91no—
621#117—94no—
622#117—91no—
623C23×C3—21no—
624C23×C3—22no—
625C23×C3—34no—
626C23×C3—32no—
627C23×C3C23×D312yes—
628C23×C3C23×D314yes—
629C22×D3—32no—
630C22×D3—32no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—68no—
634C22×D3—64no—
635C22×D3—122no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3C23×D314yes—
643C22×D3C23×D312yes—
644C3×Q8—38no—
645C3×D4—24no—
646C3×D4—42no—
647C3×D4—44no—
648C3×D4—44no—
649C3×D4—68no—
650C3×D4—68no—
651C3×D4—64no—
652C3×D4—124no—
653C3×D4—124no—
654C3×D4—122no—
655C3×D4—124no—
656C2×C3×C4—24no—
657C2×C3×C4—21no—
658C2×C3×C4—22no—
659C2×C3×C4—21no—
660C2×C3×C4—34no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—42no—
665C2×C3×C4—68no—
666C2×C3×C4—68no—
667C2×C3×C4—64no—
668C2×C3×C4C23×D314yes—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D312yes—
671#67—28no—
672#67—28no—
673#67—42no—
674#67—44no—
675#67—44no—
676#67—64no—
677#67—68no—
678#67—64no—
679#67—68no—
680#67—68no—
681#67—124no—
682#67—122no—
683#67—124no—
684#67—124no—
685#67—124no—
686#67—124no—
687C2×Dic3—28no—
688C2×Dic3—32no—
689C2×Dic3—34no—
690C2×Dic3—32no—
691C2×Dic3—34no—
692C2×Dic3—61no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—61no—
696C2×Dic3—68no—
697C2×Dic3—64no—
698C2×Dic3—68no—
699C2×Dic3—68no—
700C2×Dic3—122no—
701C2×Dic3—124no—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D314yes—
706D12—24no—
707D12—44no—
708D12—68no—
709D12—64no—
710D12—122no—
711C4×D3—24no—
712C4×D3—28no—
713C4×D3—38no—
714C4×D3—316no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—68no—
719C4×D3—68no—
720C4×D3—64no—
721C4×D3—122no—
722C4×D3—122no—
723C4×D3—122no—
724Dic6—316no—
725Dic6—64no—
726Dic6—68no—
727Dic6—64no—
728Dic6—68no—
729Dic6—122no—
730Dic6D3×D418yes—
731C2×C32—41no—
732C2×C32—42no—
733C2×C32C23×D411yescharacteristic
734C2×C32#58511yescharacteristic
735C2×C32#58511yescharacteristic
736C3⋊D3—22no—
737C3⋊D3—41no—
738C3×D3—44no—
739C3×D3—42no—
740C24—92no—
741C24—91no—
742#41—68no—
743#41—68no—
744#41—184no—
745#41—188no—
746#41—1816no—
747#41—184no—
748#41—188no—
749#41—188no—
750#41—188no—
751C2×Q8—32no—
752C2×Q8—92no—
753C2×Q8—94no—
754C2×Q8—91no—
755C2×Q8—98no—
756C2×Q8—91no—
757C2×Q8—188no—
758C2×Q8—188no—
759C2×D4—34no—
760C2×D4—34no—
761C2×D4—34no—
762C2×D4—32no—
763C2×D4—34no—
764C2×D4—32no—
765C2×D4—34no—
766C2×D4—92no—
767C2×D4—94no—
768C2×D4—92no—
769C2×D4—92no—
770C2×D4—91no—
771C2×D4—92no—
772C2×D4—94no—
773C2×D4—92no—
774C2×D4—188no—
775C2×D4—184no—
776C2×D4C2×D3211yescharacteristic
777C2×D4C2×D3212yes—
778C22×C4—34no—
779C22×C4—32no—
780C22×C4—34no—
781C22×C4—92no—
782C22×C4—94no—
783C22×C4—94no—
784C22×C4—91no—
785C22×C4—92no—
786C22×C4—91no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—184no—
791C22×C4—188no—
792C22×C4C2×D3211yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—32no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—94no—
798C4⋊C4—92no—
799C4⋊C4—91no—
800C4⋊C4—92no—
801C4⋊C4—92no—
802C4⋊C4C2×D3211yescharacteristic
803C22⋊C4—32no—
804C22⋊C4—32no—
805C22⋊C4—34no—
806C22⋊C4—92no—
807C22⋊C4—92no—
808C22⋊C4—92no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C22⋊C4—94no—
812C22⋊C4—92no—
813C22⋊C4—92no—
814C22⋊C4—92no—
815C22⋊C4—92no—
816C22⋊C4C2×D3212yes—
817C42—34no—
818C42—32no—
819C42—94no—
820C42—92no—
821C22×C3—22no—
822C22×C3—24no—
823C22×C3—22no—
824C22×C3—24no—
825C22×C3—22no—
826C22×C3—24no—
827C22×C3—22no—
828C22×C3—21no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—62no—
835C22×C3—64no—
836C22×C3—62no—
837C22×C3—64no—
838C22×C3—62no—
839C22×C3—64no—
840C22×C3C24×D312yes—
841C2×D3—22no—
842C2×D3—24no—
843C2×D3—22no—
844C2×D3—24no—
845C2×D3—22no—
846C2×D3—24no—
847C2×D3—34no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—1216no—
860C2×D3—128no—
861C2×D3—128no—
862C3×C4—22no—
863C3×C4—24no—
864C3×C4—22no—
865C3×C4—38no—
866C3×C4—41no—
867C3×C4—42no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4C2×D3×D414yes—
872Dic3—22no—
873Dic3—22no—
874Dic3—22no—
875Dic3—34no—
876Dic3—62no—
877Dic3—64no—
878Dic3—62no—
879Dic3—64no—
880Dic3—122no—
881Dic3—121no—
882Dic3—122no—
883Dic3C2×D3×D418yes—
884C32#348711yescharacteristic, complemented, Sylow
885C23—34no—
886C23—32no—
887C23—91no—
888C23—91no—
889C23—182no—
890C23—184no—
891C23—361no—
892C23—361no—
893C23—362no—
894C23—362no—
895C23C22×D3211yescharacteristic
896C23C22×D3212yes—
897Q8—38no—
898Q8—98no—
899Q8—188no—
900Q8—182no—
901Q8—182no—
902D4—22no—
903D4—42no—
904D4—68no—
905D4—68no—
906D4—64no—
907D4—124no—
908D4—124no—
909D4—124no—
910D4—122no—
911D4—188no—
912D4—184no—
913D4—184no—
914D4—182no—
915D4—184no—
916D4—362no—
917D4—362no—
918D4—364no—
919C2×C4—22no—
920C2×C4—34no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—68no—
925C2×C4—68no—
926C2×C4—64no—
927C2×C4—98no—
928C2×C4—91no—
929C2×C4—94no—
930C2×C4—92no—
931C2×C4—92no—
932C2×C4—91no—
933C2×C4—182no—
934C2×C4—182no—
935C2×C4—188no—
936C2×C4—188no—
937C2×C4—182no—
938C2×C4—184no—
939C2×C4—182no—
940C2×C4C22×D3212yes—
941C2×C4C22×D3211yescharacteristic
942C2×C4C22×D3211yescharacteristic
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—42no—
947C2×C3—42no—
948C2×C3—44no—
949C2×C3—82no—
950C2×C3—124no—
951C2×C3—122no—
952C2×C3C22×D3×D412yes—
953C2×C3#596412yes—
954C2×C3#596612yes—
955D3—44no—
956D3—42no—
957D3—64no—
958D3—122no—
959D3—122no—
960D3—122no—
961C22—21no—
962C22—22no—
963C22—21no—
964C22—22no—
965C22—22no—
966C22—21no—
967C22—62no—
968C22—64no—
969C22—62no—
970C22—64no—
971C22—62no—
972C22—64no—
973C22—92no—
974C22—181no—
975C22—181no—
976C22—181no—
977C22—181no—
978C22—181no—
979C22—364no—
980C22—368no—
981C22C23×D3211yescharacteristic
982C4—21no—
983C4—22no—
984C4—38no—
985C4—62no—
986C4—62no—
987C4—62no—
988C4—92no—
989C4—181no—
990C4—182no—
991C4—182no—
992C4D32×D412yes—
993C3—21no—
994C3#8678312yescomplemented
995C2—41no—
996C2—42no—
997C2—124no—
998C2—122no—
999C2—182no—
1000C2—361no—
1001C2C2×D32×D411yescharacteristic
1002C2#1059667911yescharacteristic
1003C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64309C2semidirect
2. C2×#64306C2semidirect
3. #10596077C2semidirect
4. C3×#5599C2semidirect
5. #10595309C2semidirect
6. #10595299C2semidirect
7. #10595158C2semidirect
8. #10595144C2semidirect
9. #10595142C2semidirect
10. #10595016C2semidirect
11. #10594899C2semidirect
12. #10594634C2semidirect
13. #10594382C2semidirect
14. #10594347C2semidirect
15. #10594286C2semidirect
16. #10594190C2semidirect
17. #10594189C2semidirect
21. C2×C3×#237C22semidirect
24. C22×#627C22semidirect
26. C2×#3805C22semidirect
36. C2×D3×Dic6C22semidirect
37. C32×#121C22semidirect
38. #64147C22semidirect
40. D4×C3⋊Dic3C22semidirect
41. #64133C22semidirect
42. #64106C22semidirect
45. #64090C22semidirect
46. C3×#940C22semidirect
47. C3×#940C22semidirect
48. C3×#939C22semidirect
49. C3×C4×#67C22semidirect
50. C3×#895C22semidirect
51. C3×#887C22semidirect
52. C3×#884C22semidirect
53. C3×#67⋊C4C22semidirect
55. #63982C22semidirect
57. #63980C22semidirect
58. #63980C22semidirect
59. #63980C22semidirect
60. #63979C22semidirect
61. #63978C22semidirect
62. Dic3×#67C22semidirect
63. #63970C22semidirect
64. #63970C22semidirect
65. #63959C22semidirect
67. C4×#627C22semidirect
68. #63915C22semidirect
69. #63914C22semidirect
70. #63912C22semidirect
71. #63908C22semidirect
72. C4×#626C22semidirect
73. #63893C22semidirect
74. Dic3×D12C22semidirect
75. #63886C22semidirect
76. #63879C22semidirect
78. #63865C22semidirect
79. #63860C22semidirect
81. #63852C22semidirect
82. #63851C22semidirect
83. Dic3×Dic6C22semidirect
84. #63838C22semidirect
101. #5599D3semidirect
160. #3797D4semidirect
205. C2×#237C2×D3semidirect
223. C3×#121C2×D3semidirect
231. #940C2×D3semidirect
232. #940C2×D3semidirect
240. #939C2×D3semidirect
263. C4×#67C2×D3semidirect
273. #895C2×D3semidirect
279. #887C2×D3semidirect
284. #884C2×D3semidirect
293. #67⋊C4C2×D3semidirect
603. #121D32semidirect
884. C32#3487semidirect
994. C3#86783semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
C2×#643062
#105960772
C3×#55992
#105953092
#105952992
#105951582
#105951442
#105951422
#105950162
#105948992
#105946342
#105943822
#105943472
#105942862
#105941902
#105941892
#867833