Finite Group Databasebeta

← #11901220

Subgroups — #11901220

Order 1152.

3279 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3#10595996C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×D3×#117C211yesmaximal, characteristic, complemented
6#10595045C211yesmaximal, characteristic, complemented
7#10594866C211yesmaximal, characteristic, complemented
8#10594627C214yesmaximal, complemented
9#10594523C214yesmaximal, complemented
10#10594291C214yesmaximal, complemented
11#10594079C214yesmaximal, complemented
12#10594001C212yesmaximal, complemented
13#10593970C212yesmaximal, complemented
14#10593969C212yesmaximal, complemented
15#10593893C212yesmaximal, complemented
16#86338—31nomaximal
17#85735—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C2×D3×#67C2212yes—
24C22×#626C2212yes—
25C22×#624C2212yescomplemented
26C2×#3804C2212yes—
27D3×#235—28no—
28C2×D3×D12C2211yescharacteristic, complemented
29C2×C4×D32C2212yescomplemented
30C2×#3799—28no—
31C2×#3799C2212yes—
32C2×#3799C2212yes—
33C2×#3799C2212yescomplemented
34C2×#3799C2212yescomplemented
35C2×#3799C2211yescharacteristic, complemented
36C2×#3798C2212yescomplemented
37C2×#3795C2211yescharacteristic, complemented
38C2×D3×Dic6C2211yescharacteristic, complemented
39C32×#117C2211yescharacteristic, complemented
40#64104C2214yescomplemented
41#64091C2214yescomplemented
42#64084C2212yescomplemented
43#64083C2212yescomplemented
44C3×#926C2211yescharacteristic, complemented
45C3×#897C2214yescomplemented
46C3×#892C2212yescomplemented
47C3×D3×C4⋊C4C2212yescomplemented
48C3×#886C2214yescomplemented
49C3×D3×C22⋊C4C2212yes—
50C3×#877C2212yescomplemented
51C3×#875C2212yescomplemented
52C3×#872C2212yescomplemented
53C3×C42×D3C2212yescomplemented
54C3×#869C2212yescomplemented
55#63981C2214yescomplemented
56#63966C2214yescomplemented
57#63923C2218yescomplemented
58#63911C2212yescomplemented
59#63910C2218yescomplemented
60#63909C2214yescomplemented
61#63909C2218yescomplemented
62#63906C2218yescomplemented
63#63895C2218yescomplemented
64#63894C2218yescomplemented
65#63890C2218yescomplemented
66#63880C2218yescomplemented
67#63871C2214yescomplemented
68#63866C2212yescomplemented
69#63864C2212yescomplemented
70#63864C2212yescomplemented
71C2×D3×#41—31no—
72C22×#239—31no—
73C22×#235—31no—
74C22×#235—31no—
75C3×#536—31no—
76C2×C3×#117—31no—
77#5830—31no—
78#5816—31no—
79#5725—32no—
80#5724—32no—
81#5674—32no—
82#5668—32no—
83#5656—34no—
84#5653—34no—
85#5629—34no—
86#5627—34no—
87#5526—31no—
88#5526—32no—
89#5526D311yescharacteristic, complemented
90#5525—31no—
91#5525—31no—
92#5525—31no—
93#5525—32no—
94#5525—61no—
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—
107#3828—24no—
108C2×C4⋊(C3⋊D3)—24no—
109C2×C4⋊(C3⋊D3)C2312yes—
110C2×C4⋊(C3⋊D3)C2312yes—
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4⋊(C3⋊D3)C2318yes—
113C2×C4×C3⋊D3C2312yes—
114C2×#634C2311yescharacteristic
115C2×C3×#67C2312yes—
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2311yescharacteristic
118C3×#235—24no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3D418yescomplemented
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×Dic6—24no—
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131D3×#67—28no—
132C2×#627C2312yes—
133C2×#626—28no—
134C2×#626C2312yes—
135C2×#626C2312yes—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2318yes—
139C2×#625C2312yes—
140C2×#624—28no—
141C2×#624C2314yes—
142C2×#624C2314yes—
143C2×#624C2312yes—
144#3804—28no—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2312yes—
147D3×D12—24no—
148C4×D32—28no—
149#3799—28no—
150#3799—28no—
151#3799—28no—
152#3799—28no—
153#3799—24no—
154#3798—28no—
155#3795—24no—
156D3×Dic6—24no—
157C32×C4⋊C4C2312yes—
158C32×C22⋊C4C2312yes—
159C32×C42C2312yes—
160#3752C2318yes—
161C3×#217C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2318yes—
164C3×C4⋊Dic3C2318yes—
165C3×C4⋊Dic3C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169Dic3⋊Dic3C2318yes—
170#3722C2318yes—
171#3722C2318yes—
172#3449—91noSylow
173C2×C3×#41—31no—
174C22×C3×Q8—31no—
175C23×C3×C4—31no—
176C22×#67—32no—
177C22×#67—32no—
178D3×#41—68no—
179C2×#239—32no—
180C2×#239—32no—
181C2×#239—32no—
182C2×#239—32no—
183C2×#239—31no—
184C2×#239—68no—
185C2×D3×Q8—31no—
186C2×#237—32no—
187C2×#237—31no—
188C2×D3×D4—32no—
189C2×D3×D4—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—32no—
193C2×#235—31no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—32no—
197C2×#235—32no—
198C2×#235—32no—
199C2×#235—31no—
200C2×#235—32no—
201C2×#235—61no—
202C2×#235—68no—
203C2×#235—68no—
204C2×#235C2×D311yescharacteristic
205C22×D12—32no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—61no—
210C22×C4×D3—32no—
211C22×C4×D3—32no—
212C22×C4×D3—32no—
213C22×C4×D3—32no—
214C22×C4×D3C2×D311yescharacteristic
215C22×Dic6—31no—
216C22×Dic6C2×D311yescharacteristic, complemented
217C3×C4⋊Q8—32no—
218C3×#124—32no—
219C3×#123—34no—
220C3×C22⋊Q8—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#947—32no—
232#947—32no—
233#946—34no—
234#944—32no—
235#940—32no—
236#937—34no—
237#930—38no—
238#930—38no—
239#930—34no—
240#929—34no—
241#926C2×D311yescharacteristic, complemented
242#897—34no—
243#897—38no—
244#897C2×D314yescomplemented
245#896—38no—
246#895—38no—
247#895—34no—
248#895—34no—
249#895—34no—
250#895—38no—
251#895—64no—
252#894—38no—
253#893—38no—
254#892C2×D312yescomplemented
255D3×C4⋊C4C2×D312yescomplemented
256#886—34no—
257#886—38no—
258#886C2×D314yescomplemented
259#884—38no—
260#884—38no—
261#882—34no—
262#882—34no—
263#882—34no—
264#882—38no—
265#882—38no—
266#882—64no—
267#67⋊C4—38no—
268D3×C22⋊C4C2×D312yes—
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#874—32no—
278#874—32no—
279#874—62no—
280C4×D12—38no—
281C4×D12—38no—
282#872C2×D312yescomplemented
283C42×D3C2×D312yescomplemented
284#869—32no—
285#869C2×D312yescomplemented
286C23×C32C2411yescharacteristic
287C22×C3⋊D3—24no—
288C22×C3⋊D3—44no—
289C22×C3⋊D3C2412yes—
290C22×C3⋊D3C2414yes—
291C22×C3×D3—42no—
292C22×C3×D3C2×D414yes—
293C22×C3×D3C2412yes—
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⋊Dic3C2412yes—
304C4⋊(C3⋊D3)—24no—
305C4⋊(C3⋊D3)—24no—
306C4⋊(C3⋊D3)—22no—
307C4⋊(C3⋊D3)—48no—
308C4×C3⋊D3—24no—
309#634—22no—
310C3×#67—24no—
311C2×C3×Dic3—24no—
312C2×C3×Dic3C2×D414yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2411yescharacteristic
317C2×C3×Dic3C2411yescharacteristic
318C3×D12—22no—
319C3×C4×D3—24no—
320C3×C4×D3—44no—
321C3×C4×D3C2×D414yes—
322C3×C4×D3C2×D414yes—
323C3×C4×D3C2×D414yes—
324C3×C4×D3C2×D414yes—
325C3×Dic6—22no—
326C3×Dic6—24no—
327C3×Dic6—24no—
328#627—24no—
329#626—24no—
330#626—28no—
331#626—28no—
332#626—24no—
333#626—48no—
334#625—24no—
335#624—28no—
336#624—28no—
337#624—24no—
338D3×Dic3—24no—
339D3×Dic3—24no—
340C22×#41—91no—
341C22×#41—91no—
342#537—94no—
343#536—31no—
344#536—92no—
345#536—91no—
346#535—92no—
347#535—91no—
348#535—91no—
349#534—94no—
350#532—92no—
351#532—92no—
352#525—94no—
353#525—94no—
354C2×#117—31no—
355C24×C3—31no—
356C23×D3—32no—
357C23×D3—32no—
358C23×D3—32no—
359C23×D3—32no—
360C23×D3—62no—
361C23×D3C22×D311yescharacteristic
362C3×#41—64no—
363C2×C3×Q8—32no—
364C2×C3×Q8—32no—
365C2×C3×Q8—31no—
366C2×C3×Q8—64no—
367C2×C3×D4—32no—
368C2×C3×D4—31no—
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—32no—
378C22×C3×C4—34no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C2×#67—32no—
382C2×#67—32no—
383C2×#67—32no—
384C2×#67—32no—
385C2×#67—34no—
386C2×#67—32no—
387C2×#67—34no—
388C2×#67—32no—
389C2×#67—38no—
390C2×#67—62no—
391C2×#67—68no—
392C2×#67—68no—
393C2×#67C22×D312yes—
394C22×Dic3—32no—
395C22×Dic3—32no—
396C22×Dic3C22×D312yes—
397C22×Dic3C22×D311yescharacteristic
398#239—68no—
399#239—68no—
400#239—68no—
401#239—68no—
402#239—64no—
403D3×Q8—64no—
404#237—68no—
405#237—64no—
406D3×D4—68no—
407D3×D4—64no—
408#235—24no—
409#235—68no—
410#235—68no—
411#235—68no—
412#235—68no—
413#235—64no—
414#235—68no—
415#235—64no—
416#235—68no—
417#235—64no—
418#235—64no—
419#235—68no—
420#235—124no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—32no—
424C2×D12—32no—
425C2×D12—32no—
426C2×D12—31no—
427C2×D12—31no—
428C2×D12—32no—
429C2×D12—32no—
430C2×D12—32no—
431C2×D12—38no—
432C2×D12—38no—
433C2×D12—38no—
434C2×D12—61no—
435C2×D12—62no—
436C2×D12—62no—
437C2×D12—68no—
438C2×D12—64no—
439C2×D12—68no—
440C2×D12—64no—
441C2×D12—64no—
442C2×D12—124no—
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—32no—
445C2×C4×D3—32no—
446C2×C4×D3—32no—
447C2×C4×D3—32no—
448C2×C4×D3—34no—
449C2×C4×D3—32no—
450C2×C4×D3—34no—
451C2×C4×D3—34no—
452C2×C4×D3—32no—
453C2×C4×D3—34no—
454C2×C4×D3—62no—
455C2×C4×D3—68no—
456C2×C4×D3—68no—
457C2×C4×D3—68no—
458C2×C4×D3—68no—
459C2×C4×D3D1218yescomplemented
460C2×C4×D3C22×D312yes—
461C2×C4×D3C22×D314yes—
462C2×C4×D3C22×D311yescharacteristic
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—24no—
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6—32no—
470C2×Dic6—32no—
471C2×Dic6—61no—
472C2×Dic6—64no—
473C2×Dic6C22×D312yes—
474C2×Dic6C22×D311yescharacteristic
475C2×Dic6C22×D312yes—
476C3×C4⋊C4—22no—
477C3×C4⋊C4—38no—
478C3×C4⋊C4—34no—
479C3×C4⋊C4—32no—
480C3×C4⋊C4C22×D312yes—
481C3×C4⋊C4C22×D312yes—
482C3×C22⋊C4—22no—
483C3×C22⋊C4—32no—
484C3×C22⋊C4—38no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4C22×D312yes—
487C3×C22⋊C4C22×D312yes—
488C3×C42—22no—
489C3×C42—32no—
490C3×C42—34no—
491C3×C42C22×D312yes—
492C3×C42C22×D312yes—
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—38no—
499(C2×D3)⋊C4—38no—
500(C2×D3)⋊C4—68no—
501(C2×D3)⋊C4C22×D314yes—
502(C2×D3)⋊C4C22×D318yes—
503C4⋊Dic3—38no—
504C4⋊Dic3C22×D318yes—
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—24no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—28no—
516C2×C3⋊D3—24no—
517C2×C3⋊D3—48no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—24no—
522C2×C3×D3—44no—
523C2×C3×D3C22×D412yes—
524C2×C3×D3C22×D412yes—
525D32—48no—
526C32×C4—24no—
527C32×C4C22×D412yes—
528C32×C4C22×D412yes—
529C3⋊Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—24no—
532C3×Dic3—24no—
533C3×Dic3C22×D412yes—
534C3×Dic3C22×D412yes—
535C2×#41—31no—
536C2×#41—92no—
537C2×#41—92no—
538C2×#41—91no—
539C2×#41—92no—
540C2×#41—92no—
541C2×#41—91no—
542C2×#41—92no—
543C2×#41—92no—
544C2×#41—91no—
545C2×#41—188no—
546C2×#41—188no—
547C22×Q8—31no—
548C22×Q8—91no—
549C22×D4—91no—
550C22×D4—92no—
551C22×D4—92no—
552C22×D4—91no—
553C23×C4—31no—
554C23×C4—92no—
555C23×C4—92no—
556C4⋊Q8—32no—
557C4⋊Q8—92no—
558#127—92no—
559#127—92no—
560#124—32no—
561#124—92no—
562#124—92no—
563#124—92no—
564#123—34no—
565#123—98no—
566#123—94no—
567C22⋊Q8—34no—
568C22⋊Q8—98no—
569C22⋊Q8—94no—
570#121—98no—
571#121—98no—
572#121—94no—
573#121—98no—
574#121—94no—
575#120—98no—
576#120—94no—
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—122no—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—34no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—34no—
600C22×D3—42no—
601C22×D3—64no—
602C22×D3—62no—
603C22×D3—64no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—244no—
613C22×D3C2×D1214yes—
614C22×D3C23×D312yes—
615C22×D3C23×D311yescharacteristic
616C22×D3C23×D311yescharacteristic
617C3×Q8—62no—
618C3×Q8—64no—
619C3×Q8—64no—
620C3×D4—64no—
621C3×D4—62no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—24no—
625C2×C3×C4—24no—
626C2×C3×C4—34no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—34no—
630C2×C3×C4—34no—
631C2×C3×C4—34no—
632C2×C3×C4—34no—
633C2×C3×C4—34no—
634C2×C3×C4—34no—
635C2×C3×C4—32no—
636C2×C3×C4—64no—
637C2×C3×C4—64no—
638C2×C3×C4—124no—
639C2×C3×C4C2×D1214yes—
640C2×C3×C4D3×D414yes—
641C2×C3×C4C23×D314yes—
642C2×C3×C4C23×D314yes—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—24no—
648#67—68no—
649#67—68no—
650#67—64no—
651#67—64no—
652#67—64no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—124no—
657#67—128no—
658C2×Dic3—24no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—62no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3C2×D1214yes—
665C2×Dic3C23×D314yes—
666C2×Dic3C23×D314yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D311yescharacteristic
669C2×Dic3C23×D311yescharacteristic
670D12—22no—
671D12—64no—
672D12—68no—
673D12—68no—
674D12—64no—
675D12—64no—
676D12—64no—
677D12—62no—
678D12—64no—
679D12—62no—
680D12—64no—
681D12—124no—
682D12—124no—
683D12—122no—
684D12—128no—
685D12—128no—
686D12—128no—
687D12—248no—
688C4×D3—24no—
689C4×D3—44no—
690C4×D3—68no—
691C4×D3—68no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—68no—
699C4×D3—68no—
700C4×D3—124no—
701C4×D3C2×D1214yes—
702C4×D3C2×D1214yes—
703C4×D3C2×D1214yes—
704C4×D3C2×D1214yes—
705Dic6—24no—
706Dic6—24no—
707Dic6—22no—
708Dic6—64no—
709Dic6—62no—
710Dic6—62no—
711Dic6—64no—
712Dic6—122no—
713C2×C32—22no—
714C2×C32C23×D411yescharacteristic
715C2×C32#58512yes—
716C3⋊D3—42no—
717C3⋊D3—44no—
718C3×D3—22no—
719C3×D3—22no—
720C3×D3—42no—
721C24—31no—
722C24—92no—
723C24—92no—
724#41—64no—
725#41—188no—
726#41—188no—
727#41—184no—
728#41—188no—
729#41—188no—
730#41—188no—
731#41—188no—
732#41—184no—
733#41—184no—
734C2×Q8—32no—
735C2×Q8—32no—
736C2×Q8—31no—
737C2×Q8—64no—
738C2×Q8—92no—
739C2×Q8—91no—
740C2×Q8—184no—
741C2×D4—32no—
742C2×D4—31no—
743C2×D4—94no—
744C2×D4—92no—
745C2×D4—94no—
746C2×D4—92no—
747C2×D4—98no—
748C2×D4—92no—
749C2×D4—92no—
750C2×D4—92no—
751C2×D4—91no—
752C2×D4—92no—
753C2×D4—98no—
754C2×D4—184no—
755C2×D4—188no—
756C2×D4—188no—
757C2×D4—184no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—38no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—34no—
767C22×C4—94no—
768C22×C4—92no—
769C22×C4—94no—
770C22×C4—92no—
771C22×C4—92no—
772C22×C4—92no—
773C22×C4—188no—
774C22×C4—188no—
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—34no—
777C4⋊C4—32no—
778C4⋊C4—38no—
779C4⋊C4—98no—
780C4⋊C4C2×D3212yes—
781C22⋊C4—32no—
782C22⋊C4—34no—
783C22⋊C4—38no—
784C22⋊C4—98no—
785C22⋊C4—98no—
786C22⋊C4—98no—
787C22⋊C4C2×D3212yes—
788C42—34no—
789C42—32no—
790C42C2×D3212yes—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—32no—
796C22×C3—32no—
797C22×C3—42no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—64no—
802C22×C3—124no—
803C22×C3C22×D1212yes—
804C22×C3C2×D3×D412yes—
805C22×C3C24×D311yescharacteristic
806C22×C3C24×D311yescharacteristic
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—24no—
811C2×D3—44no—
812C2×D3—64no—
813C2×D3—62no—
814C2×D3—64no—
815C2×D3—62no—
816C2×D3—64no—
817C2×D3—68no—
818C2×D3—64no—
819C2×D3—68no—
820C2×D3—122no—
821C2×D3—124no—
822C2×D3—124no—
823C2×D3—128no—
824C2×D3—128no—
825C2×D3—128no—
826C2×D3—128no—
827C2×D3—128no—
828C2×D3—248no—
829C2×D3C22×D1212yes—
830C2×D3C22×D1212yes—
831C3×C4—24no—
832C3×C4—24no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—32no—
836C3×C4—32no—
837C3×C4—44no—
838C3×C4—62no—
839C3×C4—64no—
840C3×C4—64no—
841C3×C4C22×D1212yes—
842C3×C4C22×D1212yes—
843C3×C4C2×D3×D412yes—
844C3×C4C2×D3×D412yes—
845Dic3—24no—
846Dic3—22no—
847Dic3—24no—
848Dic3—62no—
849Dic3—62no—
850Dic3—122no—
851Dic3C22×D1212yes—
852Dic3C22×D1212yes—
853C32#344911yescharacteristic, complemented, Sylow
854C23—31no—
855C23—31no—
856C23—34no—
857C23—32no—
858C23—92no—
859C23—94no—
860C23—122no—
861C23—184no—
862C23—184no—
863C23—364no—
864C23—364no—
865C23C22×D3211yescharacteristic
866Q8—64no—
867Q8—64no—
868Q8—62no—
869Q8—184no—
870Q8—182no—
871D4—64no—
872D4—62no—
873D4—184no—
874D4—184no—
875D4—188no—
876D4—188no—
877D4—184no—
878D4—184no—
879D4—184no—
880D4—182no—
881D4—184no—
882D4—368no—
883D4—368no—
884C2×C4—34no—
885C2×C4—31no—
886C2×C4—31no—
887C2×C4—34no—
888C2×C4—34no—
889C2×C4—34no—
890C2×C4—34no—
891C2×C4—34no—
892C2×C4—34no—
893C2×C4—32no—
894C2×C4—64no—
895C2×C4—64no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—184no—
899C2×C4—188no—
900C2×C4—188no—
901C2×C4—184no—
902C2×C4—184no—
903C2×C4—184no—
904C2×C4D3×D1214yes—
905C2×C4C22×D3214yes—
906C2×C4C22×D3211yescharacteristic
907C2×C4C22×D3211yescharacteristic
908C2×C3—22no—
909C2×C3—22no—
910C2×C3—21no—
911C2×C3—22no—
912C2×C3—42no—
913C2×C3—62no—
914C2×C3—62no—
915C2×C3—122no—
916C2×C3C23×D1211yescharacteristic
917C2×C3C22×D3×D411yescharacteristic
918C2×C3#596412yes—
919C2×C3#596812yes—
920D3—22no—
921D3—22no—
922D3—42no—
923D3—122no—
924D3—124no—
925D3—124no—
926D3—122no—
927D3—244no—
928D3—242no—
929C22—22no—
930C22—32no—
931C22—32no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—64no—
936C22—124no—
937C22—184no—
938C22—182no—
939C22—184no—
940C22—188no—
941C22—368no—
942C22—368no—
943C22C2×D3×D1212yes—
944C22C23×D3211yescharacteristic
945C4—24no—
946C4—32no—
947C4—32no—
948C4—62no—
949C4—64no—
950C4—64no—
951C4—182no—
952C4C2×D3×D1212yes—
953C4C2×D3×D1212yes—
954C3—21no—
955C3#8573511yescharacteristic, complemented
956C3#8633811yescharacteristic, complemented
957C2—22no—
958C2—62no—
959C2—62no—
960C2—122no—
961C2—364no—
962C2—362no—
963C2C22×D3×D1211yescharacteristic
964C2#1059669712yes—
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×#3799C2semidirect
3. #10595996C2semidirect
4. C3×#5526C2semidirect
5. C3×D3×#117C2semidirect
6. #10595045C2semidirect
7. #10594866C2semidirect
8. #10594627C2semidirect
9. #10594523C2semidirect
10. #10594291C2semidirect
11. #10594079C2semidirect
12. #10594001C2semidirect
13. #10593970C2semidirect
14. #10593969C2semidirect
15. #10593893C2semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
22. C22×C3×Dic6C22semidirect
25. C22×#624C22semidirect
28. C2×D3×D12C22semidirect
29. C2×C4×D32C22semidirect
33. C2×#3799C22semidirect
34. C2×#3799C22semidirect
35. C2×#3799C22semidirect
36. C2×#3798C22semidirect
37. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. C32×#117C22semidirect
40. #64104C22semidirect
41. #64091C22semidirect
42. #64084C22semidirect
43. #64083C22semidirect
44. C3×#926C22semidirect
45. C3×#897C22semidirect
46. C3×#892C22semidirect
47. C3×D3×C4⋊C4C22semidirect
48. C3×#886C22semidirect
50. C3×#877C22semidirect
51. C3×#875C22semidirect
52. C3×#872C22semidirect
53. C3×C42×D3C22semidirect
54. C3×#869C22semidirect
55. #63981C22semidirect
56. #63966C22semidirect
57. #63923C22semidirect
58. #63911C22semidirect
59. #63910C22semidirect
60. #63909C22semidirect
61. #63909C22semidirect
62. #63906C22semidirect
63. #63895C22semidirect
64. #63894C22semidirect
65. #63890C22semidirect
66. #63880C22semidirect
67. #63871C22semidirect
68. #63866C22semidirect
69. #63864C22semidirect
70. #63864C22semidirect
89. #5526D3semidirect
97. D3×#117D3semidirect
120. C2×C3×C4×D3D4semidirect
216. C22×Dic6C2×D3semidirect
226. C3×#117C2×D3semidirect
227. C3×#117C2×D3semidirect
241. #926C2×D3semidirect
244. #897C2×D3semidirect
254. #892C2×D3semidirect
255. D3×C4⋊C4C2×D3semidirect
258. #886C2×D3semidirect
269. #877C2×D3semidirect
275. #875C2×D3semidirect
282. #872C2×D3semidirect
283. C42×D3C2×D3semidirect
285. #869C2×D3semidirect
459. C2×C4×D3D12semidirect
584. #117D32semidirect
853. C32#3449semidirect
955. C3#85735semidirect
956. C3#86338semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×#37992
#105959962
C3×#55262
C3×D3×#1172
#105950452
#105948662
#105946272
#105945232
#105942912
#105940792
#105940012
#105939702
#105939692
#105938932
#863383
#857353