Finite Group Databasebeta

← #11906129

Subgroups — #11906129

Order 1152.

3247 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10595996C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5522C211yesmaximal, characteristic, complemented
6#10595029C211yesmaximal, characteristic, complemented
7C2×#63864C211yesmaximal, characteristic, complemented
8#10594629C214yesmaximal, complemented
9#10594329C214yesmaximal, complemented
10#10594293C218yesmaximal, complemented
11#10594001C212yesmaximal, complemented
12D3×#875C212yesmaximal, complemented
13#10593970C212yesmaximal, complemented
14#10593893C212yesmaximal, complemented
15#86341—31nomaximal
16#85847—31nomaximal
17C2×#3828C2211yescharacteristic, complemented
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×#3811C2214yes—
23C2×#3804C2214yescomplemented
24#64308—28no—
25C2×D3×D12C2212yes—
26C2×D3×D12C2212yes—
27C2×#3799C2212yes—
28C2×#3799C2212yes—
29C2×#3799C2212yescomplemented
30C2×#3797C2212yescomplemented
31#64297—28no—
32C2×#3796C2212yescomplemented
33C2×D3×Dic6C2212yescomplemented
34C32×#117C2211yescharacteristic, complemented
35#64104C2214yescomplemented
36#64091C2214yescomplemented
37#64084C2212yescomplemented
38#64083C2212yescomplemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40C3×#897C2214yescomplemented
41C3×#893C2212yescomplemented
42C3×#887C2212yescomplemented
43C3×#886C2214yescomplemented
44C3×#67⋊C4C2214yescomplemented
45C3×#875C2212yescomplemented
46C3×#872C2212yescomplemented
47C3×C42×D3C2212yescomplemented
48C3×#869C2212yescomplemented
49#63978C2214yescomplemented
50C2×#3722C2214yescomplemented
51#63923C2218yescomplemented
52D3×(C2×D3)⋊C4C2218yescomplemented
53#63911C2211yescharacteristic, complemented
54#63910C2218yescomplemented
55#63909C2218yescomplemented
56C4×#626C2214yescomplemented
57#63895C2218yescomplemented
58#63894C2218yescomplemented
59#63890C2218yescomplemented
60#63866C2211yescharacteristic, complemented
61#63864C2214yescomplemented
62#63864C2212yescomplemented
63#63864C2212yescomplemented
64#63864C2211yescharacteristic, complemented
65#63860C2211yescharacteristic, complemented
66#63852C2218yescomplemented
67C2×#1010—31no—
68C2×#1009—31no—
69C2×#1009—31no—
70C2×#1007—31no—
71C3×#536—31no—
72C3×C4×#41—31no—
73#5832—31no—
74C2×#947—31no—
75#5725—32no—
76#5724—32no—
77#5674—32no—
78D3×#124—32no—
79#5654—38no—
80#5633—34no—
81#5630—34no—
82#5576—34no—
83#5554—34no—
84#5554—38no—
85#5526—32no—
86#5526D311yescharacteristic, complemented
87#5525—31no—
88#5525—31no—
89#5525—32no—
90#5525—61no—
91#5522D311yescharacteristic, complemented
92#5477—31no—
93#5477—32no—
94C2×#875—31no—
95C2×#875—32no—
96C23×C3⋊D3C2312yes—
97C22×D32C2314yes—
98C22×C32×C4C2311yescharacteristic
99C2×#638C2312yes—
100#3828—24no—
101C2×C4⋊(C3⋊D3)—24no—
102C2×C4⋊(C3⋊D3)C2312yes—
103C2×C4⋊(C3⋊D3)C2312yes—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2318yes—
106C2×C4×C3⋊D3C2312yes—
107C2×#634C2311yescharacteristic
108C2×C3×#67C2312yes—
109C2×C3×#67C2312yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2312yes—
112C3×#235—24no—
113C3×#235D418yescomplemented
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×Dic6—24no—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124#3811—216no—
125C2×#627C2314yes—
126C2×#626C2314yes—
127C2×#626C2314yes—
128C2×#626C2314yes—
129C2×#626C2314yes—
130C2×#624C2314yes—
131C2×#624C2314yes—
132#3804—216no—
133C2×D3×Dic3C2314yes—
134D3×D12—28no—
135D3×D12—28no—
136#3799—28no—
137#3799—28no—
138#3799—28no—
139#3797—28no—
140#3796—28no—
141D3×Dic6—28no—
142C32×C4⋊C4C2312yes—
143C32×C22⋊C4C2312yes—
144C32×C42C2312yes—
145#3752C2318yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2318yes—
148C3×C4⋊Dic3C2318yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154Dic3⋊Dic3C2314yes—
155#3722C2318yes—
156#3722C2318yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159#3500—91noSylow
160C2×C3×#41—31no—
161C2×C3×#41—31no—
162C22×C3×Q8—31no—
163#1010—68no—
164#1009—68no—
165#1009—68no—
166#1007—68no—
167C2×#239—32no—
168C2×#239—32no—
169C2×#239—32no—
170C2×#239—32no—
171C2×D3×Q8—32no—
172C2×D3×Q8—32no—
173C2×D3×Q8—32no—
174C2×#237—34no—
175C2×#237—32no—
176C2×D3×D4—34no—
177C2×D3×D4—34no—
178C2×D3×D4—32no—
179C2×D3×D4—32no—
180C2×#235—31no—
181C2×#235—31no—
182C2×#235—34no—
183C2×#235—32no—
184C2×#235—32no—
185C2×#235—32no—
186C2×#235—61no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—32no—
192C22×D12—32no—
193C22×D12—61no—
194C22×Dic6—32no—
195C22×Dic6C2×D311yescharacteristic, complemented
196C3×C4⋊Q8—32no—
197C3×#124—32no—
198C3×#123—34no—
199C3×C22⋊Q8—34no—
200C3×C4×Q8—32no—
201C3×C4×D4—32no—
202C3×C4×D4—34no—
203C3×#117—21no—
204C3×#117—32no—
205C3×#117C2×D311yescharacteristic, complemented
206C3×#117C2×D311yescharacteristic, complemented
207C2×C3×C42—31no—
208C2×C3×C42—32no—
209#947—34no—
210#947—32no—
211#947—32no—
212#947—31no—
213#944—31no—
214#940—31no—
215#939—34no—
216#936—31no—
217#930—34no—
218#930—38no—
219C4×#67—34no—
220C2×(C2×D3)⋊C4—34no—
221C2×(C2×D3)⋊C4—34no—
222C2×(C2×D3)⋊C4—38no—
223C2×C4×Dic3C2×D311yescharacteristic, complemented
224#897—38no—
225#897C2×D314yescomplemented
226#896—38no—
227#895—38no—
228#895—34no—
229#895—34no—
230#895—38no—
231#895—64no—
232#894—38no—
233#893—38no—
234#893C2×D312yescomplemented
235#887C2×D312yescomplemented
236#886—38no—
237#886C2×D314yescomplemented
238#885—38no—
239#884—38no—
240#882—34no—
241#882—34no—
242#882—38no—
243#882—38no—
244#882—64no—
245#67⋊C4C2×D314yescomplemented
246D3×C22⋊C4—38no—
247#875—31no—
248#875—32no—
249#875—32no—
250#875—34no—
251#875—31no—
252#875—32no—
253#875—32no—
254#875—38no—
255#875—62no—
256#875C2×D312yescomplemented
257#874—31no—
258#874—32no—
259#874—32no—
260#874—62no—
261C4×D12—34no—
262C4×D12—38no—
263#872C2×D312yescomplemented
264C42×D3C2×D312yescomplemented
265#869—31no—
266#869C2×D312yescomplemented
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—24no—
269C22×C3⋊D3—44no—
270C22×C3⋊D3C2414yes—
271C22×C3⋊D3C2412yes—
272C22×C3×D3C2412yes—
273C22×C3×D3C2412yes—
274C2×D32—28no—
275C2×D32—48no—
276C2×C32×C4C2×D414yes—
277C2×C32×C4C2414yes—
278C2×C32×C4C2411yescharacteristic
279C2×C32×C4C2411yescharacteristic
280#638—24no—
281C2×C3⋊Dic3C2412yes—
282C4⋊(C3⋊D3)—22no—
283C4⋊(C3⋊D3)—24no—
284C4⋊(C3⋊D3)—24no—
285C4⋊(C3⋊D3)—48no—
286C4×C3⋊D3—24no—
287#634—22no—
288C3×#67—24no—
289C3×#67C2×D418yes—
290C2×C3×Dic3—24no—
291C2×C3×Dic3—42no—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2414yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C3×D12—22no—
298C3×D12C2×D414yes—
299C3×C4×D3—24no—
300C3×C4×D3—44no—
301C3×C4×D3C2×D418yes—
302C3×Dic6—24no—
303C3×Dic6—24no—
304C3×Dic6—22no—
305C3×Dic6C2×D414yes—
306#627—28no—
307#626—28no—
308#626—28no—
309#626—28no—
310#626—44no—
311#624—28no—
312#624—28no—
313D3×Dic3—28no—
314C2×2−1+4—91no—
315C2×H(5,𝔽2)—91no—
316#548—94no—
317#546—94no—
318#546—98no—
319#536—31no—
320#536—92no—
321#535—92no—
322#535—91no—
323#532—92no—
324#532—91no—
325C2×#124—92no—
326C2×#124—91no—
327C4×#41—31no—
328C23×D3—32no—
329C23×D3—32no—
330C23×D3—34no—
331C23×D3—34no—
332C23×D3—62no—
333C3×#41—38no—
334C3×#41—64no—
335C2×C3×Q8—31no—
336C2×C3×Q8—31no—
337C2×C3×Q8—32no—
338C2×C3×Q8—32no—
339C2×C3×Q8—64no—
340C2×C3×D4—32no—
341C2×C3×D4—32no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C22×C3×C4—21no—
345C22×C3×C4—32no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4—34no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—32no—
353C2×#67—32no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—62no—
359C2×#67C22×D312yes—
360C2×#67C22×D312yes—
361C22×Dic3—34no—
362C22×Dic3C22×D312yes—
363C22×Dic3C22×D312yes—
364#239—68no—
365#239—68no—
366#239—68no—
367#239—68no—
368D3×Q8—68no—
369D3×Q8—68no—
370D3×Q8—68no—
371#237—68no—
372#237—616no—
373D3×D4—68no—
374D3×D4—616no—
375D3×D4—616no—
376D3×D4—68no—
377#235—24no—
378#235—68no—
379#235—68no—
380#235—64no—
381#235—64no—
382#235—616no—
383#235—68no—
384#235—124no—
385#235D1218yescomplemented
386C2×D12—34no—
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—32no—
392C2×D12—32no—
393C2×D12—32no—
394C2×D12—32no—
395C2×D12—34no—
396C2×D12—38no—
397C2×D12—38no—
398C2×D12—61no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—68no—
402C2×D12—68no—
403C2×D12—64no—
404C2×D12—64no—
405C2×D12—68no—
406C2×D12—124no—
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D311yescharacteristic
409C2×C4×D3—34no—
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—62no—
417C2×C4×D3C22×D312yes—
418C2×C4×D3C22×D314yes—
419C2×C4×D3C22×D312yes—
420C2×Dic6—24no—
421C2×Dic6—31no—
422C2×Dic6—31no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—61no—
426C2×Dic6—68no—
427C2×Dic6C22×D311yescharacteristic
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D311yescharacteristic
431C3×C4⋊C4—22no—
432C3×C4⋊C4—38no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4C22×D312yes—
435C3×C4⋊C4C22×D312yes—
436C3×C22⋊C4—22no—
437C3×C22⋊C4—38no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4C22×D312yes—
440C3×C22⋊C4C22×D312yes—
441C3×C42—22no—
442C3×C42—31no—
443C3×C42—34no—
444C3×C42—32no—
445C3×C42—31no—
446C3×C42C22×D312yes—
447C3×C42C22×D312yes—
448#217—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—38no—
451(C2×D3)⋊C4—38no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—38no—
454(C2×D3)⋊C4—38no—
455(C2×D3)⋊C4—38no—
456(C2×D3)⋊C4—38no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—68no—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D318yes—
461C4⋊Dic3—34no—
462C4⋊Dic3C22×D318yes—
463Dic3⋊C4—34no—
464Dic3⋊C4C22×D314yes—
465C4×Dic3C22×D311yescharacteristic
466C4×Dic3C22×D314yes—
467C4×Dic3C22×D311yescharacteristic
468C4×Dic3C22×D312yes—
469C22×C32—22no—
470C22×C32C22×D412yes—
471C22×C32C2511yescharacteristic
472C2×C3⋊D3—22no—
473C2×C3⋊D3—24no—
474C2×C3⋊D3—24no—
475C2×C3⋊D3—28no—
476C2×C3⋊D3—84no—
477C2×C3×D3—24no—
478C2×C3×D3—22no—
479C2×C3×D3—24no—
480C2×C3×D3C22×D414yes—
481D32—88no—
482C32×C4—24no—
483C32×C4C22×D412yes—
484C32×C4C22×D412yes—
485C3⋊Dic3—22no—
486C3×Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3C22×D414yes—
4912−1+4—188no—
492H(5,𝔽2)—188no—
493C2×#41—31no—
494C2×#41—31no—
495C2×#41—94no—
496C2×#41—92no—
497C2×#41—92no—
498C2×#41—92no—
499C2×#41—92no—
500C2×#41—91no—
501C22×Q8—31no—
502C22×Q8—92no—
503C22×Q8—92no—
504C22×D4—92no—
505C22×D4—92no—
506C22×D4—94no—
507C22×D4—91no—
508C4⋊Q8—32no—
509C4⋊Q8—91no—
510#127—91no—
511#127—92no—
512#124—32no—
513#124—98no—
514#124—91no—
515#124—92no—
516#124—92no—
517#124—94no—
518#124—91no—
519#124—92no—
520#123—34no—
521#123—98no—
522C22⋊Q8—34no—
523C22⋊Q8—98no—
524#121—98no—
525#121—98no—
526#121—94no—
527#121—94no—
528#120—98no—
529#120—94no—
530C4×Q8—32no—
531C4×D4—32no—
532C4×D4—34no—
533C4×D4—98no—
534C4×D4—94no—
535#117—32no—
536#117D3211yescharacteristic, complemented
537C2×C22⋊C4—98no—
538C2×C22⋊C4—94no—
539C2×C42—31no—
540C2×C42—32no—
541C23×C3—21no—
542C23×C3—32no—
543C23×C3—32no—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—34no—
547C22×D3—34no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—64no—
551C22×D3—62no—
552C22×D3—68no—
553C22×D3—64no—
554C22×D3—64no—
555C22×D3—68no—
556C22×D3—124no—
557C22×D3—128no—
558C22×D3—128no—
559C22×D3—124no—
560C22×D3—124no—
561C22×D3—244no—
562C22×D3C23×D312yes—
563C22×D3C23×D312yes—
564C3×Q8—34no—
565C3×Q8—64no—
566C3×Q8—64no—
567C3×Q8—62no—
568C3×D4—38no—
569C3×D4—34no—
570C3×D4—64no—
571C3×D4—62no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—24no—
575C2×C3×C4—24no—
576C2×C3×C4—32no—
577C2×C3×C4—38no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—34no—
582C2×C3×C4—64no—
583C2×C3×C4—64no—
584C2×C3×C4—124no—
585C2×C3×C4—122no—
586C2×C3×C4C2×D1214yes—
587C2×C3×C4D3×D414yes—
588C2×C3×C4C23×D314yes—
589C2×C3×C4C23×D314yes—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594#67—24no—
595#67—68no—
596#67—68no—
597#67—64no—
598#67—64no—
599#67—68no—
600#67—124no—
601#67—124no—
602#67C2×D1218yes—
603C2×Dic3—24no—
604C2×Dic3—32no—
605C2×Dic3—32no—
606C2×Dic3—42no—
607C2×Dic3—62no—
608C2×Dic3—68no—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D314yes—
613C2×Dic3C23×D312yes—
614D12—22no—
615D12—68no—
616D12—68no—
617D12—68no—
618D12—64no—
619D12—64no—
620D12—62no—
621D12—64no—
622D12—64no—
623D12—62no—
624D12—124no—
625D12—124no—
626D12—122no—
627D12—128no—
628D12—128no—
629D12—124no—
630D12—248no—
631D12C2×D1214yes—
632C4×D3—24no—
633C4×D3—44no—
634C4×D3—68no—
635C4×D3—68no—
636C4×D3—68no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—124no—
642C4×D3C2×D1218yes—
643Dic6—24no—
644Dic6—24no—
645Dic6—22no—
646Dic6—68no—
647Dic6—62no—
648Dic6—62no—
649Dic6—68no—
650Dic6—122no—
651Dic6C2×D1214yes—
652C2×C32—22no—
653C2×C32C23×D411yescharacteristic
654C2×C32#58512yes—
655C3⋊D3—44no—
656C3⋊D3—42no—
657C3×D3—24no—
658C3×D3—42no—
659C24—94no—
660C24—92no—
661#41—38no—
662#41—64no—
663#41—188no—
664#41—188no—
665#41—1816no—
666#41—188no—
667#41—188no—
668#41—184no—
669C2×Q8—31no—
670C2×Q8—32no—
671C2×Q8—32no—
672C2×Q8—31no—
673C2×Q8—64no—
674C2×Q8—94no—
675C2×Q8—91no—
676C2×Q8—188no—
677C2×Q8—188no—
678C2×D4—32no—
679C2×D4—32no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—94no—
683C2×D4—94no—
684C2×D4—94no—
685C2×D4—94no—
686C2×D4—92no—
687C2×D4—92no—
688C2×D4—92no—
689C2×D4—91no—
690C2×D4—98no—
691C2×D4—188no—
692C2×D4—188no—
693C2×D4—1816no—
694C2×D4—184no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—34no—
700C22×C4—94no—
701C22×C4—94no—
702C22×C4—94no—
703C22×C4—92no—
704C22×C4C2×D3211yescharacteristic
705C4⋊C4—34no—
706C4⋊C4—38no—
707C4⋊C4—94no—
708C4⋊C4C2×D3212yes—
709C22⋊C4—38no—
710C22⋊C4—34no—
711C22⋊C4—98no—
712C22⋊C4—98no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—98no—
716C22⋊C4C2×D3212yes—
717C42—31no—
718C42—31no—
719C42—34no—
720C42—32no—
721C42C2×D3212yes—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—34no—
727C22×C3—42no—
728C22×C3—64no—
729C22×C3—62no—
730C22×C3—64no—
731C22×C3C22×D1212yes—
732C22×C3C2×D3×D412yes—
733C22×C3C24×D311yescharacteristic
734C22×C3C24×D311yescharacteristic
735C2×D3—24no—
736C2×D3—22no—
737C2×D3—24no—
738C2×D3—62no—
739C2×D3—64no—
740C2×D3—62no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—68no—
744C2×D3—64no—
745C2×D3—68no—
746C2×D3—122no—
747C2×D3—124no—
748C2×D3—124no—
749C2×D3—128no—
750C2×D3—248no—
751C2×D3—248no—
752C2×D3—244no—
753C2×D3—244no—
754C2×D3—248no—
755C2×D3C22×D1214yes—
756C3×C4—24no—
757C3×C4—24no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—34no—
761C3×C4—44no—
762C3×C4—64no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4C22×D1212yes—
767C3×C4C22×D1212yes—
768C3×C4C2×D3×D412yes—
769C3×C4C2×D3×D412yes—
770Dic3—24no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—62no—
775Dic3—62no—
776Dic3—122no—
777Dic3C22×D1214yes—
778C32#350011yescharacteristic, complemented, Sylow
779C23—32no—
780C23—32no—
781C23—94no—
782C23—92no—
783C23—188no—
784C23—184no—
785C23—364no—
786C23—368no—
787C23C22×D3211yescharacteristic
788Q8—34no—
789Q8—64no—
790Q8—64no—
791Q8—62no—
792Q8—188no—
793Q8—182no—
794D4—38no—
795D4—34no—
796D4—64no—
797D4—62no—
798D4—188no—
799D4—188no—
800D4—188no—
801D4—184no—
802D4—184no—
803D4—184no—
804D4—182no—
805D4—368no—
806D4—364no—
807C2×C4—32no—
808C2×C4—38no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—34no—
812C2×C4—32no—
813C2×C4—64no—
814C2×C4—64no—
815C2×C4—92no—
816C2×C4—124no—
817C2×C4—122no—
818C2×C4—188no—
819C2×C4—188no—
820C2×C4—188no—
821C2×C4—184no—
822C2×C4D3×D1214yes—
823C2×C4C22×D3214yes—
824C2×C4C22×D3211yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C2×C3—22no—
827C2×C3—22no—
828C2×C3—21no—
829C2×C3—22no—
830C2×C3—42no—
831C2×C3—64no—
832C2×C3—122no—
833C2×C3C23×D1211yescharacteristic
834C2×C3C22×D3×D411yescharacteristic
835C2×C3#596412yes—
836C2×C3#596812yes—
837D3—24no—
838D3—42no—
839D3—124no—
840D3—122no—
841D3—124no—
842D3—122no—
843D3—244no—
844D3—242no—
845C22—22no—
846C22—34no—
847C22—64no—
848C22—62no—
849C22—64no—
850C22—182no—
851C22—184no—
852C22—184no—
853C22—188no—
854C22—724no—
855C22—728no—
856C22C2×D3×D1212yes—
857C22C23×D3211yescharacteristic
858C4—24no—
859C4—34no—
860C4—62no—
861C4—64no—
862C4—62no—
863C4—62no—
864C4—182no—
865C4C2×D3×D1212yes—
866C4C2×D3×D1212yes—
867C3—21no—
868C3#8584711yescharacteristic, complemented
869C3#8634111yescharacteristic, complemented
870C2—22no—
871C2—64no—
872C2—122no—
873C2—364no—
874C2—362no—
875C2C22×D3×D1211yescharacteristic
876C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3500
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C2×#64297C2semidirect
3. #10595996C2semidirect
4. C3×#5526C2semidirect
5. C3×#5522C2semidirect
6. #10595029C2semidirect
7. C2×#63864C2semidirect
8. #10594629C2semidirect
9. #10594329C2semidirect
10. #10594293C2semidirect
11. #10594001C2semidirect
12. D3×#875C2semidirect
13. #10593970C2semidirect
14. #10593893C2semidirect
17. C2×#3828C22semidirect
21. C22×C3×Dic6C22semidirect
23. C2×#3804C22semidirect
29. C2×#3799C22semidirect
30. C2×#3797C22semidirect
32. C2×#3796C22semidirect
33. C2×D3×Dic6C22semidirect
34. C32×#117C22semidirect
35. #64104C22semidirect
36. #64091C22semidirect
37. #64084C22semidirect
38. #64083C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#897C22semidirect
41. C3×#893C22semidirect
42. C3×#887C22semidirect
43. C3×#886C22semidirect
44. C3×#67⋊C4C22semidirect
45. C3×#875C22semidirect
46. C3×#872C22semidirect
47. C3×C42×D3C22semidirect
48. C3×#869C22semidirect
49. #63978C22semidirect
50. C2×#3722C22semidirect
51. #63923C22semidirect
52. D3×(C2×D3)⋊C4C22semidirect
53. #63911C22semidirect
54. #63910C22semidirect
55. #63909C22semidirect
56. C4×#626C22semidirect
57. #63895C22semidirect
58. #63894C22semidirect
59. #63890C22semidirect
60. #63866C22semidirect
61. #63864C22semidirect
62. #63864C22semidirect
63. #63864C22semidirect
64. #63864C22semidirect
65. #63860C22semidirect
66. #63852C22semidirect
86. #5526D3semidirect
91. #5522D3semidirect
113. C3×#235D4semidirect
195. C22×Dic6C2×D3semidirect
205. C3×#117C2×D3semidirect
206. C3×#117C2×D3semidirect
223. C2×C4×Dic3C2×D3semidirect
225. #897C2×D3semidirect
234. #893C2×D3semidirect
235. #887C2×D3semidirect
237. #886C2×D3semidirect
245. #67⋊C4C2×D3semidirect
256. #875C2×D3semidirect
263. #872C2×D3semidirect
264. C42×D3C2×D3semidirect
266. #869C2×D3semidirect
385. #235D12semidirect
536. #117D32semidirect
778. C32#3500semidirect
868. C3#85847semidirect
869. C3#86341semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C2×#642972
#105959962
C3×#55262
C3×#55222
#105950292
C2×#638642
#105946292
#105943292
#105942932
#105940012
D3×#8752
#105939702
#105938932
#863413
#858473