Finite Group Databasebeta

← #11901222

Subgroups — #11901222

Order 1152.

3247 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×D3×#117C211yesmaximal, characteristic, complemented
6#10595042C211yesmaximal, characteristic, complemented
7#10594856C211yesmaximal, characteristic, complemented
8#10594626C214yesmaximal, complemented
9#10594522C214yesmaximal, complemented
10#10594290C214yesmaximal, complemented
11#10594078C214yesmaximal, complemented
12#10594000C212yesmaximal, complemented
13#10593969C212yesmaximal, complemented
14#10593897C212yesmaximal, complemented
15#10593894C212yesmaximal, complemented
16#86313—31nomaximal
17#85735—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic
23C2×D3×#67C2212yes—
24C22×#625C2212yes—
25C2×#3804C2212yes—
26C22×D3×Dic3C2212yescomplemented
27D3×#235—28no—
28C2×D3×D12C2211yescharacteristic, complemented
29C2×C4×D32C2212yescomplemented
30C2×#3799C2211yescharacteristic, complemented
31C2×#3798C2212yescomplemented
32C2×#3795—28no—
33C2×#3795C2212yes—
34C2×#3795C2212yes—
35C2×#3795C2212yescomplemented
36C2×#3795C2212yescomplemented
37C2×#3795C2211yescharacteristic, complemented
38C2×D3×Dic6C2211yescharacteristic, complemented
39C32×#117C2211yescharacteristic, complemented
40#64106C2214yescomplemented
41#64095C2214yescomplemented
42#64084C2212yescomplemented
43#64078C2212yescomplemented
44C3×#926C2211yescharacteristic, complemented
45C3×#895C2214yescomplemented
46C3×#892C2212yescomplemented
47C3×D3×C4⋊C4C2212yescomplemented
48C3×#882C2214yescomplemented
49C3×D3×C22⋊C4C2212yes—
50C3×#877C2212yescomplemented
51C3×#875C2212yescomplemented
52C3×#874C2212yescomplemented
53C3×#872C2212yescomplemented
54C3×C42×D3C2212yescomplemented
55#63977C2214yescomplemented
56#63962C2214yescomplemented
57#63922C2218yescomplemented
58#63916C2214yescomplemented
59#63911C2212yescomplemented
60#63908C2218yescomplemented
61#63906C2218yescomplemented
62#63893C2218yescomplemented
63Dic3×D12C2218yescomplemented
64#63891C2218yescomplemented
65#63886C2218yescomplemented
66#63880C2218yescomplemented
67#63866C2212yescomplemented
68#63860C2212yescomplemented
69#63860C2212yescomplemented
70#63857C2214yescomplemented
71C2×D3×#41—31no—
72C22×#237—31no—
73C22×#235—31no—
74C22×#235—31no—
75C3×#535—31no—
76C2×C3×#117—31no—
77#5825—31no—
78#5805—31no—
79#5716—32no—
80#5715—32no—
81#5675—32no—
82#5668—32no—
83#5608—34no—
84#5606—34no—
85#5589—34no—
86#5586—34no—
87#5526—31no—
88#5526—31no—
89#5526—31no—
90#5526—32no—
91#5526—61no—
92#5525—31no—
93#5525—32no—
94#5525D311yescharacteristic, complemented
95#5524—34no—
96#5524—34no—
97D3×#117D311yescharacteristic, complemented
98#5510—34no—
99#5493—34no—
100#5477—32no—
101#5477—32no—
102C23×C3×D3C2312yes—
103C23×C3×D3C2311yescharacteristic
104C22×D32C2312yes—
105C22×C32×C4C2311yescharacteristic
106C2×#638C2312yes—
107C22×C3⋊Dic3C2312yes—
108#3828—24no—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4×C3⋊D3C2312yes—
111C2×#634—24no—
112C2×#634C2311yescharacteristic
113C2×#634C2312yes—
114C2×#634C2312yes—
115C2×C3×#67C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C3×#235—24no—
118C2×C3×D12—24no—
119C2×C3×D12C2312yes—
120C2×C3×D12C2312yes—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2318yes—
123C2×C3×C4×D3D418yescomplemented
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131D3×#67—28no—
132C2×#627C2312yes—
133C2×#626C2312yes—
134C2×#626C2312yes—
135C2×#626C2318yes—
136C2×#625—28no—
137C2×#625C2314yes—
138C2×#625C2314yes—
139C2×#625C2312yes—
140C2×#624C2312yes—
141#3804—28no—
142C2×D3×Dic3—28no—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2312yes—
147D3×D12—24no—
148C4×D32—28no—
149#3799—24no—
150#3798—28no—
151#3795—28no—
152#3795—28no—
153#3795—28no—
154#3795—28no—
155#3795—24no—
156D3×Dic6—24no—
157C32×C4⋊C4C2312yes—
158C32×C22⋊C4C2312yes—
159C32×C42C2312yes—
160#3752C2318yes—
161C4⋊(C3⋊Dic3)C2318yes—
162C3×#217C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2318yes—
165C3×C4⋊Dic3C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169Dic3⋊Dic3C2318yes—
170(C2×D3)⋊Dic3C2318yes—
171(C2×D3)⋊Dic3C2318yes—
172#3449—91noSylow
173C2×C3×#41—31no—
174C22×C3×D4—31no—
175C23×C3×C4—31no—
176C22×#67—32no—
177C22×#67—32no—
178C22×#67—32no—
179C23×Dic3—32no—
180D3×#41—68no—
181C2×#239—31no—
182C2×D3×Q8—31no—
183C2×#237—32no—
184C2×#237—32no—
185C2×#237—32no—
186C2×#237—32no—
187C2×#237—32no—
188C2×#237—31no—
189C2×#237—68no—
190C2×D3×D4—32no—
191C2×D3×D4—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—32no—
197C2×#235—32no—
198C2×#235—31no—
199C2×#235—32no—
200C2×#235—32no—
201C2×#235—32no—
202C2×#235—31no—
203C2×#235—61no—
204C2×#235—68no—
205C2×#235—68no—
206C2×#235C2×D311yescharacteristic
207C22×D12—31no—
208C22×D12C2×D311yescharacteristic, complemented
209C22×C4×D3—32no—
210C22×C4×D3—32no—
211C22×C4×D3—32no—
212C22×C4×D3C2×D311yescharacteristic
213C22×Dic6—31no—
214C22×Dic6—31no—
215C22×Dic6—31no—
216C22×Dic6—61no—
217C3×#127—32no—
218C3×#124—32no—
219C3×#121—34no—
220C3×#120—34no—
221C3×#117—21no—
222C3×#117—31no—
223C3×#117—32no—
224C3×#117—32no—
225C3×#117—32no—
226C3×#117C2×D311yescharacteristic, complemented
227C3×#117C2×D311yescharacteristic, complemented
228C2×C3×C4⋊C4—32no—
229C2×C3×C22⋊C4—32no—
230C2×C3×C42—32no—
231#953—34no—
232#944—32no—
233#940—32no—
234#939—38no—
235#938—38no—
236#938—34no—
237#937—38no—
238#936—32no—
239#936—32no—
240#935—34no—
241D4×Dic3—38no—
242#930—38no—
243#930—38no—
244#926C2×D311yescharacteristic, complemented
245#924—34no—
246#897—34no—
247#897—34no—
248#897—34no—
249#897—38no—
250#897—64no—
251#895—38no—
252#895—34no—
253#895C2×D314yescomplemented
254#892C2×D312yescomplemented
255D3×C4⋊C4C2×D312yescomplemented
256#886—34no—
257#886—34no—
258#886—34no—
259#886—38no—
260#886—64no—
261#884—38no—
262#883—38no—
263#882—34no—
264#882—38no—
265#882C2×D314yescomplemented
266#67⋊C4—38no—
267D3×C22⋊C4C2×D312yes—
268#878—38no—
269#877C2×D312yescomplemented
270#875—32no—
271#875—32no—
272#875—32no—
273#875—32no—
274#875—62no—
275#875C2×D312yescomplemented
276#874—32no—
277#874C2×D312yescomplemented
278C4×D12—38no—
279C4×D12—38no—
280#872C2×D312yescomplemented
281C42×D3C2×D312yescomplemented
282#869—32no—
283#869—32no—
284#869—32no—
285#869—62no—
286C23×C32C2411yescharacteristic
287C22×C3⋊D3C2412yes—
288C22×C3×D3—24no—
289C22×C3×D3—42no—
290C22×C3×D3—44no—
291C22×C3×D3C2×D414yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2414yes—
294C22×C3×D3C2411yescharacteristic
295C22×C3×D3C2411yescharacteristic
296C2×D32—24no—
297C2×D32—44no—
298C2×C32×C4C2×D414yes—
299C2×C32×C4C2414yes—
300C2×C32×C4C2411yescharacteristic
301C2×C32×C4C2411yescharacteristic
302#638—24no—
303C2×C3⋊Dic3—24no—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2414yes—
306C4⋊(C3⋊D3)—22no—
307C4×C3⋊D3—24no—
308#634—22no—
309#634—24no—
310#634—24no—
311C3×#67—24no—
312C2×C3×Dic3C2×D414yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2411yescharacteristic
316C2×C3×Dic3C2411yescharacteristic
317C3×D12—24no—
318C3×D12—24no—
319C3×D12—22no—
320C3×D12—48no—
321C3×C4×D3—24no—
322C3×C4×D3—44no—
323C3×C4×D3C2×D414yes—
324C3×C4×D3C2×D414yes—
325C3×C4×D3C2×D414yes—
326C3×C4×D3C2×D414yes—
327C3×Dic6—22no—
328#627—24no—
329#626—24no—
330#626—24no—
331#626—48no—
332#625—28no—
333#625—28no—
334#625—24no—
335#624—24no—
336D3×Dic3—24no—
337D3×Dic3—28no—
338D3×Dic3—28no—
339D3×Dic3—24no—
340C22×#41—91no—
341C22×#41—91no—
342#537—94no—
343#536—92no—
344#536—91no—
345#536—91no—
346#535—31no—
347#535—92no—
348#535—91no—
349#534—94no—
350#532—92no—
351#532—92no—
352#525—94no—
353#525—94no—
354C2×#117—31no—
355C24×C3—31no—
356C24×C3—32no—
357C23×D3—32no—
358C23×D3—32no—
359C23×D3C22×D312yes—
360C23×D3C22×D311yescharacteristic
361C3×#41—64no—
362C2×C3×Q8—31no—
363C2×C3×D4—32no—
364C2×C3×D4—31no—
365C2×C3×D4—32no—
366C2×C3×D4—32no—
367C2×C3×D4—38no—
368C2×C3×D4—64no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—38no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—32no—
377C22×C3×C4—34no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C2×#67—32no—
381C2×#67—32no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—32no—
386C2×#67—34no—
387C2×#67—32no—
388C2×#67—32no—
389C2×#67—32no—
390C2×#67—38no—
391C2×#67—62no—
392C2×#67—68no—
393C2×#67—68no—
394C2×#67—68no—
395C2×#67C22×D312yes—
396C22×Dic3—32no—
397C22×Dic3—32no—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—62no—
403C22×Dic3—68no—
404C22×Dic3C22×D311yescharacteristic
405#239—64no—
406D3×Q8—64no—
407#237—68no—
408#237—68no—
409#237—68no—
410#237—68no—
411#237—68no—
412#237—64no—
413D3×D4—68no—
414D3×D4—64no—
415#235—24no—
416#235—64no—
417#235—68no—
418#235—68no—
419#235—68no—
420#235—68no—
421#235—68no—
422#235—64no—
423#235—68no—
424#235—64no—
425#235—64no—
426#235—68no—
427#235—124no—
428C2×D12—24no—
429C2×D12—32no—
430C2×D12—32no—
431C2×D12—31no—
432C2×D12—31no—
433C2×D12—38no—
434C2×D12—61no—
435C2×D12—64no—
436C2×D12C22×D312yes—
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D312yes—
439C2×D12C22×D318yes—
440C2×C4×D3—32no—
441C2×C4×D3—34no—
442C2×C4×D3—32no—
443C2×C4×D3—34no—
444C2×C4×D3—32no—
445C2×C4×D3—32no—
446C2×C4×D3—32no—
447C2×C4×D3—32no—
448C2×C4×D3—62no—
449C2×C4×D3—68no—
450C2×C4×D3—68no—
451C2×C4×D3—68no—
452C2×C4×D3D1218yescomplemented
453C2×C4×D3C22×D312yes—
454C2×C4×D3C22×D314yes—
455C2×C4×D3C22×D311yescharacteristic
456C2×C4×D3C22×D311yescharacteristic
457C2×C4×D3C22×D311yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×Dic6—32no—
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—32no—
463C2×Dic6—32no—
464C2×Dic6—32no—
465C2×Dic6—32no—
466C2×Dic6—32no—
467C2×Dic6—61no—
468C2×Dic6—62no—
469C2×Dic6—62no—
470C2×Dic6—64no—
471C2×Dic6—64no—
472C2×Dic6—64no—
473C2×Dic6—124no—
474C2×Dic6C22×D311yescharacteristic
475C3×C4⋊C4—22no—
476C3×C4⋊C4—34no—
477C3×C4⋊C4—32no—
478C3×C4⋊C4C22×D312yes—
479C3×C4⋊C4C22×D312yes—
480C3×C22⋊C4—22no—
481C3×C22⋊C4—32no—
482C3×C22⋊C4—38no—
483C3×C22⋊C4—34no—
484C3×C22⋊C4C22×D312yes—
485C3×C22⋊C4C22×D312yes—
486C3×C42—22no—
487C3×C42—32no—
488C3×C42—34no—
489C3×C42C22×D312yes—
490C3×C42C22×D312yes—
491#217—38no—
492#217—38no—
493#217C22×D312yes—
494(C2×D3)⋊C4—38no—
495(C2×D3)⋊C4—38no—
496(C2×D3)⋊C4—38no—
497(C2×D3)⋊C4—38no—
498(C2×D3)⋊C4—68no—
499(C2×D3)⋊C4C22×D314yes—
500(C2×D3)⋊C4C22×D318yes—
501C4⋊Dic3—38no—
502C4⋊Dic3—38no—
503C4⋊Dic3—38no—
504C4⋊Dic3—68no—
505C4⋊Dic3C22×D312yes—
506Dic3⋊C4—38no—
507Dic3⋊C4C22×D314yes—
508C4×Dic3C22×D312yes—
509C4×Dic3C22×D314yes—
510C22×C32—22no—
511C22×C32C22×D412yes—
512C22×C32C2511yescharacteristic
513C2×C3⋊D3—22no—
514C2×C3⋊D3—24no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—24no—
518C2×C3×D3—22no—
519C2×C3×D3—28no—
520C2×C3×D3—24no—
521C2×C3×D3—44no—
522C2×C3×D3—48no—
523C2×C3×D3C22×D412yes—
524C2×C3×D3C22×D412yes—
525D32—48no—
526C32×C4—24no—
527C32×C4C22×D412yes—
528C32×C4C22×D412yes—
529C3⋊Dic3—24no—
530C3⋊Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—24no—
533C3×Dic3C22×D412yes—
534C3×Dic3C22×D412yes—
535C2×#41—31no—
536C2×#41—92no—
537C2×#41—92no—
538C2×#41—92no—
539C2×#41—92no—
540C2×#41—91no—
541C2×#41—92no—
542C2×#41—92no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—188no—
546C2×#41—188no—
547C22×Q8—91no—
548C22×Q8—91no—
549C22×D4—31no—
550C22×D4—91no—
551C22×D4—92no—
552C22×D4—92no—
553C23×C4—31no—
554C23×C4—92no—
555C23×C4—92no—
556C4⋊Q8—92no—
557C4⋊Q8—92no—
558#127—32no—
559#127—92no—
560#124—32no—
561#124—92no—
562#124—92no—
563#124—92no—
564#123—98no—
565#123—94no—
566#123—94no—
567C22⋊Q8—98no—
568C22⋊Q8—94no—
569C22⋊Q8—94no—
570#121—34no—
571#121—98no—
572#121—94no—
573#121—98no—
574#121—98no—
575#120—34no—
576#120—98no—
577#120—94no—
578C4×D4—98no—
579C4×D4—98no—
580#117—31no—
581#117—32no—
582#117—32no—
583#117—32no—
584#117D3211yescharacteristic, complemented
585C2×C4⋊C4—32no—
586C2×C22⋊C4—32no—
587C2×C42—32no—
588C23×C3—21no—
589C23×C3—31no—
590C23×C3—31no—
591C23×C3—34no—
592C23×C3—32no—
593C23×C3—34no—
594C23×C3—64no—
595C23×C3—124no—
596C23×C3—122no—
597C23×C3C23×D311yescharacteristic
598C23×C3C23×D311yescharacteristic
599C22×D3—24no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—42no—
603C22×D3—44no—
604C22×D3—62no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3C2×D1214yes—
610C22×D3C23×D312yes—
611C22×D3C23×D314yes—
612C22×D3C23×D311yescharacteristic
613C22×D3C23×D311yescharacteristic
614C3×Q8—62no—
615C3×D4—64no—
616C3×D4—62no—
617C3×D4—64no—
618C3×D4—64no—
619C3×D4—128no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—24no—
623C2×C3×C4—24no—
624C2×C3×C4—34no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—34no—
628C2×C3×C4—34no—
629C2×C3×C4—34no—
630C2×C3×C4—34no—
631C2×C3×C4—32no—
632C2×C3×C4—34no—
633C2×C3×C4—64no—
634C2×C3×C4—124no—
635C2×C3×C4C2×D1214yes—
636C2×C3×C4D3×D414yes—
637C2×C3×C4C23×D314yes—
638C2×C3×C4C23×D314yes—
639C2×C3×C4C23×D311yescharacteristic
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643#67—24no—
644#67—64no—
645#67—64no—
646#67—68no—
647#67—68no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—68no—
652#67—68no—
653#67—64no—
654#67—124no—
655#67—128no—
656C2×Dic3—34no—
657C2×Dic3—32no—
658C2×Dic3—34no—
659C2×Dic3—32no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3—68no—
667C2×Dic3—68no—
668C2×Dic3—124no—
669C2×Dic3C2×D1214yes—
670C2×Dic3C23×D314yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D311yescharacteristic
673C2×Dic3C23×D311yescharacteristic
674D12—24no—
675D12—24no—
676D12—22no—
677D12—48no—
678D12—64no—
679D12—64no—
680D12—62no—
681D12—62no—
682D12—122no—
683D12—128no—
684C4×D3—24no—
685C4×D3—44no—
686C4×D3—64no—
687C4×D3—68no—
688C4×D3—64no—
689C4×D3—68no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—124no—
695C4×D3C2×D1214yes—
696C4×D3C2×D1214yes—
697C4×D3C2×D1214yes—
698C4×D3C2×D1214yes—
699Dic6—22no—
700Dic6—64no—
701Dic6—64no—
702Dic6—64no—
703Dic6—62no—
704Dic6—62no—
705Dic6—64no—
706Dic6—64no—
707Dic6—64no—
708Dic6—124no—
709Dic6—124no—
710Dic6—122no—
711C2×C32—22no—
712C2×C32C23×D411yescharacteristic
713C2×C32#58512yes—
714C3⋊D3—42no—
715C3×D3—22no—
716C3×D3—22no—
717C3×D3—42no—
718C3×D3—44no—
719C24—31no—
720C24—32no—
721C24—92no—
722#41—64no—
723#41—188no—
724#41—188no—
725#41—188no—
726#41—188no—
727#41—188no—
728#41—188no—
729#41—184no—
730#41—184no—
731#41—184no—
732C2×Q8—31no—
733C2×Q8—92no—
734C2×Q8—92no—
735C2×Q8—91no—
736C2×Q8—92no—
737C2×Q8—184no—
738C2×Q8—184no—
739C2×D4—32no—
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—31no—
743C2×D4—38no—
744C2×D4—64no—
745C2×D4—92no—
746C2×D4—92no—
747C2×D4—98no—
748C2×D4—94no—
749C2×D4—94no—
750C2×D4—92no—
751C2×D4—92no—
752C2×D4—91no—
753C2×D4—184no—
754C2×D4—188no—
755C2×D4—188no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—38no—
762C22×C4—32no—
763C22×C4—34no—
764C22×C4—92no—
765C22×C4—94no—
766C22×C4—92no—
767C22×C4—94no—
768C22×C4—92no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—188no—
772C22×C4—188no—
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—34no—
775C4⋊C4—32no—
776C4⋊C4—98no—
777C4⋊C4—98no—
778C4⋊C4C2×D3212yes—
779C22⋊C4—32no—
780C22⋊C4—34no—
781C22⋊C4—38no—
782C22⋊C4—98no—
783C22⋊C4—98no—
784C22⋊C4—98no—
785C22⋊C4C2×D3212yes—
786C42—34no—
787C42—32no—
788C42C2×D3212yes—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—32no—
794C22×C3—32no—
795C22×C3—42no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—64no—
799C22×C3—62no—
800C22×C3—68no—
801C22×C3—64no—
802C22×C3—124no—
803C22×C3—128no—
804C22×C3C22×D1212yes—
805C22×C3C2×D3×D412yes—
806C22×C3C24×D311yescharacteristic
807C22×C3C24×D311yescharacteristic
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—28no—
814C2×D3—44no—
815C2×D3—48no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—64no—
819C2×D3—64no—
820C2×D3—122no—
821C2×D3—124no—
822C2×D3—128no—
823C2×D3—128no—
824C2×D3C22×D1212yes—
825C2×D3C22×D1212yes—
826C3×C4—24no—
827C3×C4—24no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—44no—
833C3×C4—62no—
834C3×C4—64no—
835C3×C4C22×D1212yes—
836C3×C4C22×D1212yes—
837C3×C4C2×D3×D412yes—
838C3×C4C2×D3×D412yes—
839Dic3—22no—
840Dic3—24no—
841Dic3—62no—
842Dic3—64no—
843Dic3—62no—
844Dic3—64no—
845Dic3—124no—
846Dic3—122no—
847Dic3C22×D1212yes—
848Dic3C22×D1212yes—
849C32#344911yescharacteristic, complemented, Sylow
850C23—31no—
851C23—31no—
852C23—34no—
853C23—34no—
854C23—32no—
855C23—64no—
856C23—92no—
857C23—122no—
858C23—124no—
859C23—184no—
860C23—364no—
861C23C22×D3211yescharacteristic
862Q8—62no—
863Q8—184no—
864Q8—184no—
865Q8—182no—
866Q8—184no—
867D4—64no—
868D4—64no—
869D4—64no—
870D4—62no—
871D4—128no—
872D4—184no—
873D4—184no—
874D4—188no—
875D4—184no—
876D4—188no—
877D4—184no—
878D4—182no—
879D4—368no—
880C2×C4—34no—
881C2×C4—31no—
882C2×C4—31no—
883C2×C4—34no—
884C2×C4—34no—
885C2×C4—34no—
886C2×C4—34no—
887C2×C4—34no—
888C2×C4—32no—
889C2×C4—64no—
890C2×C4—92no—
891C2×C4—94no—
892C2×C4—124no—
893C2×C4—184no—
894C2×C4—184no—
895C2×C4—188no—
896C2×C4—188no—
897C2×C4—184no—
898C2×C4—184no—
899C2×C4—184no—
900C2×C4D3×D1214yes—
901C2×C4C22×D3214yes—
902C2×C4C22×D3211yescharacteristic
903C2×C4C22×D3211yescharacteristic
904C2×C3—22no—
905C2×C3—22no—
906C2×C3—21no—
907C2×C3—22no—
908C2×C3—42no—
909C2×C3—62no—
910C2×C3—62no—
911C2×C3—122no—
912C2×C3—124no—
913C2×C3C23×D1211yescharacteristic
914C2×C3C22×D3×D411yescharacteristic
915C2×C3#596412yes—
916C2×C3#596612yes—
917D3—22no—
918D3—22no—
919D3—44no—
920D3—42no—
921D3—122no—
922D3—122no—
923D3—242no—
924C22—22no—
925C22—32no—
926C22—32no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—64no—
931C22—64no—
932C22—68no—
933C22—124no—
934C22—128no—
935C22—182no—
936C22—184no—
937C22—368no—
938C22C2×D3×D1212yes—
939C22C23×D3211yescharacteristic
940C4—24no—
941C4—32no—
942C4—32no—
943C4—62no—
944C4—64no—
945C4—184no—
946C4—182no—
947C4C2×D3×D1212yes—
948C4C2×D3×D1212yes—
949C3—21no—
950C3#8573511yescharacteristic, complemented
951C3#8631311yescharacteristic, complemented
952C2—22no—
953C2—62no—
954C2—62no—
955C2—124no—
956C2—122no—
957C2—362no—
958C2C22×D3×D1211yescharacteristic
959C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C22×#3795C2semidirect
3. #10595997C2semidirect
4. C3×#5525C2semidirect
5. C3×D3×#117C2semidirect
6. #10595042C2semidirect
7. #10594856C2semidirect
8. #10594626C2semidirect
9. #10594522C2semidirect
10. #10594290C2semidirect
11. #10594078C2semidirect
12. #10594000C2semidirect
13. #10593969C2semidirect
14. #10593897C2semidirect
15. #10593894C2semidirect
19. C22×#634C22semidirect
21. C22×C3×D12C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×D3×D12C22semidirect
29. C2×C4×D32C22semidirect
30. C2×#3799C22semidirect
31. C2×#3798C22semidirect
35. C2×#3795C22semidirect
36. C2×#3795C22semidirect
37. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. C32×#117C22semidirect
40. #64106C22semidirect
41. #64095C22semidirect
42. #64084C22semidirect
43. #64078C22semidirect
44. C3×#926C22semidirect
45. C3×#895C22semidirect
46. C3×#892C22semidirect
47. C3×D3×C4⋊C4C22semidirect
48. C3×#882C22semidirect
50. C3×#877C22semidirect
51. C3×#875C22semidirect
52. C3×#874C22semidirect
53. C3×#872C22semidirect
54. C3×C42×D3C22semidirect
55. #63977C22semidirect
56. #63962C22semidirect
57. #63922C22semidirect
58. #63916C22semidirect
59. #63911C22semidirect
60. #63908C22semidirect
61. #63906C22semidirect
62. #63893C22semidirect
63. Dic3×D12C22semidirect
64. #63891C22semidirect
65. #63886C22semidirect
66. #63880C22semidirect
67. #63866C22semidirect
68. #63860C22semidirect
69. #63860C22semidirect
70. #63857C22semidirect
94. #5525D3semidirect
97. D3×#117D3semidirect
123. C2×C3×C4×D3D4semidirect
208. C22×D12C2×D3semidirect
226. C3×#117C2×D3semidirect
227. C3×#117C2×D3semidirect
244. #926C2×D3semidirect
253. #895C2×D3semidirect
254. #892C2×D3semidirect
255. D3×C4⋊C4C2×D3semidirect
265. #882C2×D3semidirect
269. #877C2×D3semidirect
275. #875C2×D3semidirect
277. #874C2×D3semidirect
280. #872C2×D3semidirect
281. C42×D3C2×D3semidirect
452. C2×C4×D3D12semidirect
584. #117D32semidirect
849. C32#3449semidirect
950. C3#85735semidirect
951. C3#86313semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×#37952
#105959972
C3×#55252
C3×D3×#1172
#105950422
#105948562
#105946262
#105945222
#105942902
#105940782
#105940002
#105939692
#105938972
#105938942
#863133
#857353