Finite Group Databasebeta

← #11901223

Subgroups — #11901223

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
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3#10596287C211yesmaximal, characteristic, complemented
4C3×#5816C211yesmaximal, characteristic, complemented
5#10595426C212yesmaximal, complemented
6#10595424C214yesmaximal, complemented
7#10595398C214yesmaximal, complemented
8#10595360C212yesmaximal, complemented
9#10595359C212yesmaximal, complemented
10#10595356C212yesmaximal, complemented
11#10595062C214yesmaximal, complemented
12#10595042C211yesmaximal, characteristic, complemented
13#10595040C211yesmaximal, characteristic, complemented
14D3×#926C211yesmaximal, characteristic, complemented
15#10594896C214yesmaximal, complemented
16#87268—31nomaximal
17#86338—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic
20C2×C3×#239—28no—
21C2×C3×#239C2212yes—
22C2×C3×#239C2212yes—
23C2×C3×#239C2212yescomplemented
24C2×C3×#239C2212yescomplemented
25C2×C3×#235C2211yescharacteristic
26C22×C3×D12C2212yes—
27C22×C3×D12C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×C4×D3C2212yescomplemented
30C2×D3×#67C2212yes—
31C2×#3804C2212yes—
32D3×#235—28no—
33C2×D3×D12C2211yescharacteristic, complemented
34C2×C4×D32C2212yescomplemented
35C2×#3799C2211yescharacteristic, complemented
36C2×#3798C2212yescomplemented
37C2×#3795C2211yescharacteristic, complemented
38C2×D3×Dic6C2211yescharacteristic, complemented
39#64156C2212yescomplemented
40#64155C2214yescomplemented
41#64153C2212yescomplemented
42#64138C2214yescomplemented
43#64135C2211yescharacteristic, complemented
44C3×#947C2212yescomplemented
45C3×#946C2214yescomplemented
46C3×#944C2212yescomplemented
47C3×#929C2214yescomplemented
48C3×#926C2211yescharacteristic, complemented
49#63977C2214yescomplemented
50#63976C2214yescomplemented
51D3×#217C2212yes—
52#63955C2212yescomplemented
53#63922C2218yescomplemented
54#63916C2214yescomplemented
55#63914C2212yescomplemented
56#63911C2212yescomplemented
57#63908C2214yescomplemented
58#63906C2218yescomplemented
59#63904C2218yescomplemented
60D3×C4⋊Dic3C2212yescomplemented
61#63886C2218yescomplemented
62#63885C2218yescomplemented
63#63884C2218yescomplemented
64#63879C2218yescomplemented
65C4×D3×Dic3C2212yescomplemented
66#63863C2212yescomplemented
67#63860C2212yescomplemented
68#63855C2212yescomplemented
69#63851C2218yescomplemented
70#63841C2212yescomplemented
71C22×C3×#41—31no—
72C2×D3×#41—31no—
73C22×#239D311yescharacteristic, complemented
74C22×#235—31no—
75C3×#536—31no—
76#5833—34no—
77#5832—32no—
78#5832—32no—
79#5830—31no—
80#5830—32no—
81#5828—34no—
82#5825—32no—
83#5816—31no—
84#5816—31no—
85#5816—61no—
86#5816D311yescharacteristic, complemented
87#5805—31no—
88#5805—31no—
89#5804—34no—
90#5791—34no—
91C2×#926—31no—
92#5725—32no—
93#5724—32no—
94#5674—32no—
95#5668—32no—
96#5656—34no—
97#5653—34no—
98#5629—34no—
99#5627—34no—
100#5525—31no—
101D3×#117—31no—
102C23×C3×D3C2312yes—
103C23×C3×D3C2311yescharacteristic
104C22×D32C2312yes—
105C2×C32×Q8—24no—
106C2×C32×Q8C2312yes—
107C2×C32×Q8C2312yes—
108C22×C32×C4C2312yes—
109C22×C32×C4C2311yescharacteristic
110C2×#638C2312yes—
111#3828—24no—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×C4×C3⋊D3C2312yes—
114C2×#634C2311yescharacteristic
115C2×C3×#67C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C3×#239—28no—
118C3×#239—28no—
119C3×#239—28no—
120C3×#239—28no—
121C3×#235—24no—
122C2×C3×D12—28no—
123C2×C3×D12—24no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×D12C2314yes—
126C2×C3×D12C2314yes—
127C2×C3×D12C2312yes—
128C2×C3×D12C2312yes—
129C2×C3×C4×D3—28no—
130C2×C3×C4×D3D418yescomplemented
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139D3×#67—28no—
140C2×#627C2312yes—
141C2×#626C2312yes—
142C2×#626C2312yes—
143C2×#626C2318yes—
144C2×#625C2312yes—
145C2×#625C2318yes—
146C2×#624C2312yes—
147#3804—28no—
148C2×D3×Dic3C2312yes—
149C2×D3×Dic3C2312yes—
150C2×D3×Dic3C2314yes—
151D3×D12—24no—
152C4×D32—28no—
153#3799—24no—
154#3798—28no—
155#3795—24no—
156D3×Dic6—24no—
157#3757C2312yes—
158#3752C2318yes—
159C4⋊(C3⋊Dic3)C2312yes—
160#3750C2318yes—
161C4×C3⋊Dic3C2312yes—
162C3×#217C2312yes—
163C3×(C2×D3)⋊C4C2318yes—
164C3×C4⋊Dic3C2312yes—
165C3×Dic3⋊C4C2318yes—
166C3×C4×Dic3C2312yes—
167Dic3⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2318yes—
170(C2×D3)⋊Dic3C2318yes—
171Dic32C2314yes—
172#3449—91noSylow
173C2×C3×#41—32no—
174C2×C3×#41—32no—
175C2×C3×#41—32no—
176C2×C3×#41—32no—
177C2×C3×#41—31no—
178C2×C3×#41—68no—
179C22×C3×Q8—21no—
180C22×C3×Q8C2×D311yescharacteristic, complemented
181C22×C3×Q8C2×D311yescharacteristic, complemented
182C22×C3×D4—32no—
183C22×C3×D4—31no—
184C23×C3×C4—31no—
185C23×C3×C4—32no—
186C22×#67—32no—
187D3×#41—68no—
188C2×#239—28no—
189C2×#239—31no—
190C2×#239C2×D312yes—
191C2×#239C2×D312yes—
192C2×#239C2×D312yescomplemented
193C2×#239C2×D312yescomplemented
194C2×D3×Q8—31no—
195C2×#237—32no—
196C2×#237—31no—
197C2×D3×D4—32no—
198C2×D3×D4—31no—
199C2×#235—31no—
200C2×#235—31no—
201C2×#235—32no—
202C2×#235—31no—
203C2×#235—32no—
204C2×#235—32no—
205C2×#235—31no—
206C2×#235—61no—
207C2×#235—68no—
208C2×#235C2×D311yescharacteristic
209C22×D12—31no—
210C22×D12C2×D312yes—
211C22×D12C2×D311yescharacteristic, complemented
212C22×C4×D3—32no—
213C22×C4×D3—32no—
214C22×C4×D3C2×D311yescharacteristic
215C22×C4×D3C2×D312yescomplemented
216C22×Dic6—31no—
217C3×C4⋊Q8—32no—
218C3×#124—32no—
219C3×#123—34no—
220C3×C22⋊Q8—34no—
221C3×#117—31no—
222#953—34no—
223#953—34no—
224C2×#217—32no—
225#947—32no—
226#947—32no—
227#947—32no—
228#947—62no—
229#947C2×D312yescomplemented
230#946—34no—
231#946—34no—
232#946—64no—
233#946C2×D314yescomplemented
234#944—32no—
235#944—32no—
236#944—62no—
237#944C2×D312yescomplemented
238#940—32no—
239#940—32no—
240#940—32no—
241#939—38no—
242#939—38no—
243#938—34no—
244#938—34no—
245#937—34no—
246#937—38no—
247#936—32no—
248#936—32no—
249#935—38no—
250#930—34no—
251#930—38no—
252#929—34no—
253#929—34no—
254#929—64no—
255#929C2×D314yescomplemented
256C4×#67—38no—
257C4×#67—38no—
258#926—31no—
259#926—31no—
260#926—32no—
261#926—32no—
262#926—32no—
263#926—61no—
264#926C2×D311yescharacteristic, complemented
265C2×C4⋊Dic3—32no—
266#924—38no—
267C2×C4×Dic3—32no—
268#896—38no—
269#895—38no—
270#895—34no—
271#894—38no—
272#893—38no—
273#892—32no—
274D3×C4⋊C4—32no—
275#884—38no—
276#884—38no—
277#882—34no—
278#882—38no—
279#67⋊C4—38no—
280D3×C22⋊C4—32no—
281#877—32no—
282#875—32no—
283#874—32no—
284#872—32no—
285C42×D3—32no—
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—
298C32×Q8—24no—
299C32×Q8—24no—
300C2×C32×C4—24no—
301C2×C32×C4C2×D414yes—
302C2×C32×C4C2414yes—
303C2×C32×C4C2411yescharacteristic
304C2×C32×C4C2411yescharacteristic
305#638—24no—
306C2×C3⋊Dic3C2414yes—
307C2×C3⋊Dic3C2412yes—
308C4⋊(C3⋊D3)—22no—
309C4×C3⋊D3—24no—
310#634—22no—
311C3×#67—24no—
312C2×C3×Dic3C2×D414yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2411yescharacteristic
316C2×C3×Dic3C2411yescharacteristic
317C3×D12—28no—
318C3×D12—28no—
319C3×D12—22no—
320C3×D12—24no—
321C3×D12—24no—
322C3×C4×D3—24no—
323C3×C4×D3—28no—
324C3×C4×D3—28no—
325C3×C4×D3C2×D414yes—
326C3×C4×D3C2×D414yes—
327C3×C4×D3C2×D414yes—
328C3×C4×D3C2×D414yes—
329C3×Dic6—22no—
330#627—24no—
331#626—24no—
332#626—24no—
333#626—48no—
334#625—24no—
335#625—48no—
336#624—24no—
337D3×Dic3—24no—
338D3×Dic3—24no—
339D3×Dic3—44no—
340C22×#41—31no—
341C22×#41—91no—
342#537—94no—
343#536—31no—
344#536—92no—
345#536—91no—
346#535—91no—
347#535—92no—
348#535—91no—
349#534—94no—
350#532—92no—
351#532—92no—
352#525—94no—
353#525—94no—
354C2×#117—91no—
355C24×C3—31no—
356C24×C3—32no—
357C23×D3—32no—
358C23×D3—32no—
359C23×D3C22×D312yes—
360C23×D3C22×D311yescharacteristic
361C3×#41—68no—
362C3×#41—68no—
363C3×#41—68no—
364C3×#41—68no—
365C3×#41—64no—
366C2×C3×Q8—24no—
367C2×C3×Q8—24no—
368C2×C3×Q8—22no—
369C2×C3×Q8—22no—
370C2×C3×Q8—31no—
371C2×C3×Q8—44no—
372C2×C3×Q8C22×D312yes—
373C2×C3×Q8C22×D312yes—
374C2×C3×Q8C22×D312yes—
375C2×C3×Q8C22×D312yes—
376C2×C3×D4—32no—
377C2×C3×D4—34no—
378C2×C3×D4—32no—
379C2×C3×D4—32no—
380C2×C3×D4—34no—
381C2×C3×D4—31no—
382C2×C3×D4—68no—
383C2×C3×D4—64no—
384C22×C3×C4—21no—
385C22×C3×C4—22no—
386C22×C3×C4—31no—
387C22×C3×C4—38no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C22×C3×C4—34no—
394C22×C3×C4—32no—
395C22×C3×C4—68no—
396C22×C3×C4C22×D312yes—
397C22×C3×C4C22×D312yes—
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C2×#67—32no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—32no—
404C2×#67—38no—
405C2×#67—38no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—38no—
409C2×#67—62no—
410C2×#67—68no—
411C2×#67C22×D312yes—
412C22×Dic3—32no—
413C22×Dic3—32no—
414C22×Dic3—34no—
415C22×Dic3C22×D311yescharacteristic
416#239—28no—
417#239—28no—
418#239—28no—
419#239—28no—
420#239—64no—
421D3×Q8—64no—
422#237—68no—
423#237—64no—
424D3×D4—68no—
425D3×D4—64no—
426#235—24no—
427#235—64no—
428#235—68no—
429#235—64no—
430#235—68no—
431#235—64no—
432#235—64no—
433#235—68no—
434#235—124no—
435C2×D12—28no—
436C2×D12—24no—
437C2×D12—32no—
438C2×D12—32no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—38no—
442C2×D12—61no—
443C2×D12—64no—
444C2×D12C22×D312yes—
445C2×D12C22×D314yes—
446C2×D12C22×D314yes—
447C2×D12C22×D312yes—
448C2×D12C22×D311yescharacteristic
449C2×C4×D3—28no—
450C2×C4×D3—32no—
451C2×C4×D3—32no—
452C2×C4×D3—32no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—32no—
456C2×C4×D3—34no—
457C2×C4×D3—62no—
458C2×C4×D3—68no—
459C2×C4×D3—68no—
460C2×C4×D3#6718yescomplemented
461C2×C4×D3C22×D314yes—
462C2×C4×D3C22×D314yes—
463C2×C4×D3C22×D312yes—
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×C4×D3C22×D311yescharacteristic
467C2×C4×D3C22×D311yescharacteristic
468C2×Dic6—31no—
469C2×Dic6—31no—
470C2×Dic6—32no—
471C2×Dic6—32no—
472C2×Dic6—61no—
473C2×Dic6—64no—
474C2×Dic6C22×D311yescharacteristic
475C3×C4⋊C4—32no—
476C3×C4⋊C4—38no—
477C3×C22⋊C4—32no—
478C3×C22⋊C4—38no—
479C3×C42—32no—
480#217—32no—
481#217—32no—
482#217—38no—
483#217—38no—
484#217—34no—
485#217—62no—
486#217C22×D312yes—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—38no—
489(C2×D3)⋊C4—38no—
490(C2×D3)⋊C4—38no—
491(C2×D3)⋊C4—38no—
492(C2×D3)⋊C4—68no—
493(C2×D3)⋊C4C22×D318yes—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—34no—
497C4⋊Dic3—62no—
498C4⋊Dic3C22×D312yes—
499Dic3⋊C4—38no—
500Dic3⋊C4—38no—
501Dic3⋊C4—34no—
502Dic3⋊C4—68no—
503Dic3⋊C4C22×D318yes—
504C4×Dic3—32no—
505C4×Dic3—32no—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C4×Dic3—62no—
509C4×Dic3C22×D312yes—
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—22no—
518C2×C3×D3—24no—
519C2×C3×D3—24no—
520C2×C3×D3—28no—
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—22no—
530C3⋊Dic3—24no—
531C3×Dic3—22no—
532C3×Dic3—24no—
533C3×Dic3C22×D412yes—
534C3×Dic3C22×D412yes—
535C2×#41—32no—
536C2×#41—32no—
537C2×#41—32no—
538C2×#41—32no—
539C2×#41—31no—
540C2×#41—68no—
541C2×#41—92no—
542C2×#41—92no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—188no—
547C22×Q8—91no—
548C22×Q8D3211yescharacteristic, complemented
549C22×D4—32no—
550C22×D4—31no—
551C22×D4—91no—
552C22×D4—92no—
553C23×C4—31no—
554C23×C4—32no—
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—92no—
582#117—92no—
583#117—92no—
584#117—91no—
585C2×C4⋊C4—92no—
586C2×C22⋊C4—92no—
587C2×C42—92no—
588C23×C3—21no—
589C23×C3—31no—
590C23×C3—31no—
591C23×C3—34no—
592C23×C3—34no—
593C23×C3—32no—
594C23×C3—64no—
595C23×C3—122no—
596C23×C3—124no—
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×#6714yes—
610C22×D3C23×D314yes—
611C22×D3C23×D312yes—
612C22×D3C23×D311yescharacteristic
613C22×D3C23×D311yescharacteristic
614C3×Q8—24no—
615C3×Q8—24no—
616C3×Q8—24no—
617C3×Q8—24no—
618C3×Q8—44no—
619C3×Q8—44no—
620C3×Q8—62no—
621C3×D4—68no—
622C3×D4—68no—
623C3×D4—64no—
624C3×D4—64no—
625C3×D4—64no—
626C3×D4—62no—
627C2×C3×C4—24no—
628C2×C3×C4—24no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—24no—
632C2×C3×C4—24no—
633C2×C3×C4—34no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—34no—
637C2×C3×C4—34no—
638C2×C3×C4—34no—
639C2×C3×C4—34no—
640C2×C3×C4—34no—
641C2×C3×C4—32no—
642C2×C3×C4—44no—
643C2×C3×C4—68no—
644C2×C3×C4—68no—
645C2×C3×C4—64no—
646C2×C3×C4D3×D414yes—
647C2×C3×C4C2×#6714yes—
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654#67—24no—
655#67—64no—
656#67—64no—
657#67—64no—
658#67—64no—
659#67—64no—
660#67—64no—
661#67—124no—
662#67—128no—
663#67—128no—
664#67—128no—
665C2×Dic3—34no—
666C2×Dic3—34no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—64no—
670C2×Dic3—62no—
671C2×Dic3—64no—
672C2×Dic3—64no—
673C2×Dic3—124no—
674C2×Dic3C2×#6714yes—
675C2×Dic3C23×D314yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D311yescharacteristic
678C2×Dic3C23×D311yescharacteristic
679D12—28no—
680D12—28no—
681D12—22no—
682D12—24no—
683D12—24no—
684D12—64no—
685D12—64no—
686D12—62no—
687D12—62no—
688D12—122no—
689D12—128no—
690C4×D3—24no—
691C4×D3—28no—
692C4×D3—28no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—124no—
700C4×D3—124no—
701C4×D3C2×#6714yes—
702C4×D3C2×#6714yes—
703C4×D3C2×#6714yes—
704C4×D3C2×#6714yes—
705Dic6—22no—
706Dic6—64no—
707Dic6—62no—
708Dic6—62no—
709Dic6—64no—
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—68no—
723#41—68no—
724#41—68no—
725#41—68no—
726#41—64no—
727#41—188no—
728#41—188no—
729#41—184no—
730#41—184no—
731#41—184no—
732C2×Q8—24no—
733C2×Q8—31no—
734C2×Q8—92no—
735C2×Q8—91no—
736C2×Q8—184no—
737C2×Q8C2×D3212yes—
738C2×Q8C2×D3212yes—
739C2×D4—32no—
740C2×D4—34no—
741C2×D4—34no—
742C2×D4—32no—
743C2×D4—31no—
744C2×D4—32no—
745C2×D4—68no—
746C2×D4—64no—
747C2×D4—92no—
748C2×D4—92no—
749C2×D4—98no—
750C2×D4—92no—
751C2×D4—92no—
752C2×D4—98no—
753C2×D4—91no—
754C2×D4—184no—
755C2×D4—188no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—38no—
762C22×C4—34no—
763C22×C4—32no—
764C22×C4—34no—
765C22×C4—68no—
766C22×C4—92no—
767C22×C4—92no—
768C22×C4—92no—
769C22×C4—94no—
770C22×C4—92no—
771C22×C4—188no—
772C22×C4C2×D3212yes—
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—32no—
775C4⋊C4—38no—
776C4⋊C4—94no—
777C4⋊C4—92no—
778C4⋊C4—98no—
779C22⋊C4—32no—
780C22⋊C4—38no—
781C22⋊C4—94no—
782C22⋊C4—98no—
783C22⋊C4—98no—
784C22⋊C4—92no—
785C22⋊C4—98no—
786C42—32no—
787C42—94no—
788C42—92no—
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—64no—
800C22×C3—68no—
801C22×C3—62no—
802C22×C3—124no—
803C22×C3—128no—
804C22×C3C2×D3×D412yes—
805C22×C3C22×#6712yes—
806C22×C3C24×D311yescharacteristic
807C22×C3C24×D311yescharacteristic
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—28no—
812C2×D3—24no—
813C2×D3—24no—
814C2×D3—44no—
815C2×D3—48no—
816C2×D3—62no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—62no—
820C2×D3—122no—
821C2×D3—124no—
822C2×D3—128no—
823C2×D3—128no—
824C2×D3C22×#6712yes—
825C2×D3C22×#6712yes—
826C3×C4—24no—
827C3×C4—24no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—44no—
833C3×C4—64no—
834C3×C4—62no—
835C3×C4C2×D3×D412yes—
836C3×C4C2×D3×D412yes—
837C3×C4C22×#6712yes—
838C3×C4C22×#6712yes—
839Dic3—22no—
840Dic3—24no—
841Dic3—62no—
842Dic3—64no—
843Dic3—64no—
844Dic3—62no—
845Dic3—122no—
846Dic3—124no—
847Dic3C22×#6712yes—
848Dic3C22×#6712yes—
849C32#344911yescharacteristic, complemented, Sylow
850C23—31no—
851C23—31no—
852C23—34no—
853C23—32no—
854C23—34no—
855C23—64no—
856C23—92no—
857C23—122no—
858C23—124no—
859C23—184no—
860C23—364no—
861C23C22×D3211yescharacteristic
862Q8—24no—
863Q8—24no—
864Q8—62no—
865Q8—184no—
866Q8—182no—
867D4—68no—
868D4—68no—
869D4—64no—
870D4—64no—
871D4—64no—
872D4—62no—
873D4—184no—
874D4—184no—
875D4—184no—
876D4—184no—
877D4—182no—
878D4—368no—
879D4—368no—
880C2×C4—24no—
881C2×C4—34no—
882C2×C4—31no—
883C2×C4—31no—
884C2×C4—34no—
885C2×C4—34no—
886C2×C4—34no—
887C2×C4—34no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—68no—
891C2×C4—68no—
892C2×C4—64no—
893C2×C4—94no—
894C2×C4—92no—
895C2×C4—184no—
896C2×C4—184no—
897C2×C4—184no—
898C2×C4—184no—
899C2×C4—364no—
900C2×C4D3×#6714yes—
901C2×C4C22×D3214yes—
902C2×C4C22×D3211yescharacteristic
903C2×C4C22×D3211yescharacteristic
904C2×C3—22no—
905C2×C3—22no—
906C2×C3—22no—
907C2×C3—21no—
908C2×C3—42no—
909C2×C3—62no—
910C2×C3—62no—
911C2×C3—124no—
912C2×C3—122no—
913C2×C3C22×D3×D411yescharacteristic
914C2×C3#596412yes—
915C2×C3#596812yes—
916C2×C3C23×#6711yescharacteristic
917D3—22no—
918D3—22no—
919D3—42no—
920D3—44no—
921D3—122no—
922D3—122no—
923D3—242no—
924C22—22no—
925C22—32no—
926C22—32no—
927C22—62no—
928C22—62no—
929C22—68no—
930C22—64no—
931C22—64no—
932C22—62no—
933C22—124no—
934C22—128no—
935C22—184no—
936C22—182no—
937C22—368no—
938C22C2×D3×#6712yes—
939C22C23×D3211yescharacteristic
940C4—24no—
941C4—32no—
942C4—32no—
943C4—64no—
944C4—62no—
945C4—184no—
946C4—182no—
947C4C2×D3×#6712yes—
948C4C2×D3×#6712yes—
949C3—21no—
950C3#8633811yescharacteristic, complemented
951C3#8726811yescharacteristic, complemented
952C2—22no—
953C2—62no—
954C2—62no—
955C2—124no—
956C2—122no—
957C2—362no—
958C2#1059668812yes—
959C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×D3×#235C2semidirect
3. #10596287C2semidirect
4. C3×#5816C2semidirect
5. #10595426C2semidirect
6. #10595424C2semidirect
7. #10595398C2semidirect
8. #10595360C2semidirect
9. #10595359C2semidirect
10. #10595356C2semidirect
11. #10595062C2semidirect
12. #10595042C2semidirect
13. #10595040C2semidirect
14. D3×#926C2semidirect
15. #10594896C2semidirect
18. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×#239C22semidirect
27. C22×C3×D12C22semidirect
29. C22×C3×C4×D3C22semidirect
33. C2×D3×D12C22semidirect
34. C2×C4×D32C22semidirect
35. C2×#3799C22semidirect
36. C2×#3798C22semidirect
37. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. #64156C22semidirect
40. #64155C22semidirect
41. #64153C22semidirect
42. #64138C22semidirect
43. #64135C22semidirect
44. C3×#947C22semidirect
45. C3×#946C22semidirect
46. C3×#944C22semidirect
47. C3×#929C22semidirect
48. C3×#926C22semidirect
49. #63977C22semidirect
50. #63976C22semidirect
52. #63955C22semidirect
53. #63922C22semidirect
54. #63916C22semidirect
55. #63914C22semidirect
56. #63911C22semidirect
57. #63908C22semidirect
58. #63906C22semidirect
59. #63904C22semidirect
60. D3×C4⋊Dic3C22semidirect
61. #63886C22semidirect
62. #63885C22semidirect
63. #63884C22semidirect
64. #63879C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63863C22semidirect
67. #63860C22semidirect
68. #63855C22semidirect
69. #63851C22semidirect
70. #63841C22semidirect
73. C22×#239D3semidirect
86. #5816D3semidirect
130. C2×C3×C4×D3D4semidirect
180. C22×C3×Q8C2×D3semidirect
181. C22×C3×Q8C2×D3semidirect
192. C2×#239C2×D3semidirect
193. C2×#239C2×D3semidirect
211. C22×D12C2×D3semidirect
215. C22×C4×D3C2×D3semidirect
229. #947C2×D3semidirect
233. #946C2×D3semidirect
237. #944C2×D3semidirect
255. #929C2×D3semidirect
264. #926C2×D3semidirect
460. C2×C4×D3#67semidirect
548. C22×Q8D32semidirect
849. C32#3449semidirect
950. C3#86338semidirect
951. C3#87268semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×D3×#2352
#105962872
C3×#58162
#105954262
#105954242
#105953982
#105953602
#105953592
#105953562
#105950622
#105950422
#105950402
D3×#9262
#105948962
#872683
#863383