Finite Group Databasebeta

← #11904444

Subgroups — #11904444

Order 1152.

3255 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C3×#5521C211yesmaximal, characteristic, complemented
6#10595023C211yesmaximal, characteristic, complemented
7#10594856C211yesmaximal, characteristic, complemented
8#10594630C214yesmaximal, complemented
9#10594381C214yesmaximal, complemented
10#10594290C214yesmaximal, complemented
11D3×#886C214yesmaximal, complemented
12#10594003C214yesmaximal, complemented
13#10593895C214yesmaximal, complemented
14#86040—31nomaximal
15#85858—31nomaximal
16C2×#3828C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic, complemented
21C2×D3×#67C2214yes—
22C22×#625C2212yescomplemented
23C22×D3×Dic3C2212yescomplemented
24#64307—28no—
25C2×#3802C2212yescomplemented
26C2×D3×D12C2212yescomplemented
27C2×#3796C2212yescomplemented
28C2×#3795—28no—
29C2×#3795C2214yescomplemented
30C2×#3795C2214yescomplemented
31C2×#3795C2212yescomplemented
32C32×#117C2211yescharacteristic, complemented
33#64106C2214yescomplemented
34#64095C2214yescomplemented
35#64084C2212yescomplemented
36#64078C2212yescomplemented
37C3×#926C2211yescharacteristic, complemented
38C3×#897C2212yescomplemented
39C3×#895C2212yescomplemented
40C3×#893C2214yescomplemented
41C3×#886C2212yescomplemented
42C3×#882C2212yescomplemented
43C3×D3×C22⋊C4C2214yescomplemented
44C3×C4×D12C2214yescomplemented
45C3×C4×D12C2214yescomplemented
46#63977C2212yescomplemented
47#63966C2212yescomplemented
48#63962C2214yescomplemented
49#63922C2218yescomplemented
50D3×(C2×D3)⋊C4C2218yescomplemented
51#63909C2212yescomplemented
52#63908C2218yescomplemented
53#63906C2218yescomplemented
54C4×#626C2214yescomplemented
55#63891C2218yescomplemented
56#63891C2218yescomplemented
57#63890C2218yescomplemented
58D3×C4⋊Dic3C2218yescomplemented
59#63866C2212yescomplemented
60#63860C2212yescomplemented
61#63857C2214yescomplemented
62#63857C2212yescomplemented
63C2×#1009—31no—
64C2×#1004—31no—
65C22×#237—31no—
66C22×#235—31no—
67C3×#525—31no—
68C3×#518—31no—
69#5825—31no—
70#5791—31no—
71D3×#123—34no—
72#5631—34no—
73#5612—34no—
74#5589—34no—
75#5555—34no—
76#5555—34no—
77#5554—34no—
78#5554—34no—
79#5551—34no—
80#5550—34no—
81#5526—31no—
82#5526—31no—
83#5526—31no—
84#5526—61no—
85#5524—31no—
86#5524D311yescharacteristic, complemented
87#5521D311yescharacteristic, complemented
88#5493—34no—
89C2×#886—34no—
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32C2314yes—
93C22×C32×C4C2311yescharacteristic
94C2×#638C2312yes—
95C22×C3⋊Dic3C2312yes—
96#3828—24no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2312yes—
99C2×#634—24no—
100C2×#634C2311yescharacteristic
101C2×#634C2312yes—
102C2×#634C2312yes—
103C2×C3×#67C2312yes—
104C22×C3×Dic3C2311yescharacteristic
105C3×#235—24no—
106C2×C3×D12D418yescomplemented
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2314yes—
109C2×C3×D12C2312yes—
110C2×C3×D12C2312yes—
111C2×C3×C4×D3—24no—
112C2×C3×C4×D3C2312yes—
113C2×C3×C4×D3C2312yes—
114C2×C3×C4×D3C2312yes—
115C2×C3×C4×D3C2318yes—
116C2×C3×Dic6C2311yescharacteristic
117D3×#67—216no—
118C2×#626C2314yes—
119C2×#626C2314yes—
120C2×#625—28no—
121C2×#625C2318yes—
122C2×#625C2314yes—
123C2×D3×Dic3—28no—
124C2×D3×Dic3C2318yes—
125C2×D3×Dic3C2314yes—
126#3802—28no—
127D3×D12—28no—
128#3796—28no—
129#3795—216no—
130#3795—216no—
131#3795—28no—
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135#3752C2318yes—
136C4⋊(C3⋊Dic3)C2318yes—
137C3×#217C2312yes—
138C3×(C2×D3)⋊C4C2318yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×C4⋊Dic3C2312yes—
143C3×C4×Dic3C2312yes—
144Dic3⋊Dic3C2318yes—
145Dic3⋊Dic3C2314yes—
146#3722C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2314yes—
149#3485—91noSylow
150C2×C3×#41—31no—
151C22×C3×D4—31no—
152C23×C3×C4—31no—
153C22×#67—32no—
154C22×#67—32no—
155C22×#67—34no—
156C23×Dic3—32no—
157#1009—68no—
158C2×#239—32no—
159#1004—68no—
160C2×#237—34no—
161C2×#237—34no—
162C2×#237—32no—
163C2×#237—32no—
164C2×#237—68no—
165C2×D3×D4—34no—
166C2×D3×D4—32no—
167C2×D3×D4—32no—
168C2×D3×D4—32no—
169C2×#235—31no—
170C2×#235—31no—
171C2×#235—34no—
172C2×#235—34no—
173C2×#235—32no—
174C2×#235—61no—
175C2×#235—68no—
176C2×#235C2×D311yescharacteristic
177C22×D12—32no—
178C22×D12C2×D311yescharacteristic
179C22×C4×D3—32no—
180C22×C4×D3C2×D311yescharacteristic, complemented
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6—61no—
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×D4—34no—
189C3×C4×D4—34no—
190C3×C4×D4—34no—
191C3×#117—21no—
192C3×#117—31no—
193C3×#117C2×D311yescharacteristic, complemented
194C3×#117C2×D311yescharacteristic, complemented
195C2×C3×C22⋊C4—34no—
196#953—32no—
197#944—32no—
198#938—38no—
199#937—38no—
200#936—32no—
201#935—34no—
202#930—38no—
203#930—38no—
204#930—32no—
205#929—32no—
206C4×#67—34no—
207C2×(C2×D3)⋊C4—38no—
208#926C2×D311yescharacteristic, complemented
209C2×C4⋊Dic3—38no—
210#924—32no—
211#924—34no—
212#897—32no—
213#897—34no—
214#897—34no—
215#897—34no—
216#897—64no—
217#897C2×D312yescomplemented
218#895—32no—
219#895C2×D312yescomplemented
220#894—38no—
221#893C2×D314yescomplemented
222D3×C4⋊C4—38no—
223#886—34no—
224#886—32no—
225#886—34no—
226#886—34no—
227#886—38no—
228#886—38no—
229#886—38no—
230#886—64no—
231#886C2×D312yescomplemented
232#884—38no—
233#883—38no—
234#883—38no—
235#882—32no—
236#882—38no—
237#882C2×D312yescomplemented
238D3×C22⋊C4—38no—
239D3×C22⋊C4C2×D314yescomplemented
240#875—32no—
241#875—32no—
242#875—32no—
243#875—62no—
244C4×D12—34no—
245C4×D12C2×D314yescomplemented
246C4×D12C2×D314yescomplemented
247#869—32no—
248#869—32no—
249#869—32no—
250#869—62no—
251C23×C32C2411yescharacteristic
252C22×C3⋊D3C2412yes—
253C22×C3×D3—22no—
254C22×C3×D3—44no—
255C22×C3×D3—42no—
256C22×C3×D3C2×D418yes—
257C22×C3×D3C2412yes—
258C22×C3×D3C2412yes—
259C22×C3×D3C2414yes—
260C2×D32—28no—
261C2×D32—48no—
262C2×C32×C4C2×D414yes—
263C2×C32×C4C2414yes—
264C2×C32×C4C2411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—24no—
267C2×C3⋊Dic3—24no—
268C2×C3⋊Dic3C2412yes—
269C2×C3⋊Dic3C2414yes—
270C4⋊(C3⋊D3)—22no—
271C4×C3⋊D3—24no—
272#634—24no—
273#634—24no—
274#634—22no—
275C3×#67—24no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3C2414yes—
278C2×C3×Dic3C2412yes—
279C2×C3×Dic3C2412yes—
280C3×D12—22no—
281C3×D12—44no—
282C3×D12C2×D418yes—
283C3×D12C2×D418yes—
284C3×C4×D3—24no—
285C3×C4×D3—24no—
286C3×C4×D3—24no—
287C3×C4×D3—48no—
288C3×Dic6—22no—
289#626—28no—
290#626—44no—
291#625—216no—
292#625—28no—
293D3×Dic3—216no—
294D3×Dic3—28no—
295C2×H(5,𝔽2)—91no—
296C22×#41—91no—
297#547—94no—
298#547—94no—
299#546—94no—
300#546—94no—
301#536—91no—
302#536—91no—
303#534—94no—
304#525—31no—
305#525—91no—
306C2×#123—94no—
307#518—31no—
308C24×C3—32no—
309C24×C3—31no—
310C23×D3—34no—
311C23×D3—34no—
312C23×D3C22×D311yescharacteristic
313C23×D3C22×D312yes—
314C3×#41—64no—
315C2×C3×Q8—31no—
316C2×C3×D4—32no—
317C2×C3×D4—38no—
318C2×C3×D4—32no—
319C2×C3×D4—32no—
320C2×C3×D4—31no—
321C2×C3×D4—34no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—32no—
325C22×C3×C4—32no—
326C22×C3×C4—32no—
327C22×C3×C4—38no—
328C22×C3×C4—64no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—32no—
332C2×#67—32no—
333C2×#67—38no—
334C2×#67—34no—
335C2×#67—38no—
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—62no—
340C2×#67—616no—
341C2×#67—68no—
342C2×#67—68no—
343C2×#67C22×D312yes—
344C22×Dic3—32no—
345C22×Dic3—32no—
346C22×Dic3—34no—
347C22×Dic3—38no—
348C22×Dic3—62no—
349C22×Dic3—68no—
350C22×Dic3C22×D311yescharacteristic
351#239—68no—
352#237—68no—
353#237—616no—
354#237—616no—
355#237—68no—
356D3×D4—68no—
357D3×D4—68no—
358D3×D4—616no—
359D3×D4—68no—
360#235—24no—
361#235—64no—
362#235—64no—
363#235—616no—
364#235—616no—
365#235—68no—
366#235—124no—
367C2×D12—34no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—34no—
371C2×D12—61no—
372C2×D12—68no—
373C2×D12D1218yescomplemented
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D314yes—
376C2×D12C22×D312yes—
377C2×D12C22×D312yes—
378C2×C4×D3—24no—
379C2×C4×D3—38no—
380C2×C4×D3—34no—
381C2×C4×D3—32no—
382C2×C4×D3—32no—
383C2×C4×D3—62no—
384C2×C4×D3—68no—
385C2×C4×D3C22×D312yes—
386C2×C4×D3C22×D312yes—
387C2×C4×D3C22×D312yes—
388C2×C4×D3C22×D318yes—
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—32no—
392C2×Dic6—32no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—61no—
396C2×Dic6—62no—
397C2×Dic6—62no—
398C2×Dic6—64no—
399C2×Dic6—64no—
400C2×Dic6—124no—
401C2×Dic6C22×D311yescharacteristic
402C3×C4⋊C4—22no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4—32no—
405C3×C4⋊C4C22×D312yes—
406C3×C4⋊C4C22×D312yes—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—32no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—38no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4C22×D312yes—
413C3×C22⋊C4C22×D312yes—
414C3×C42—22no—
415C3×C42—32no—
416C3×C42C22×D312yes—
417C3×C42C22×D312yes—
418#217—38no—
419#217—34no—
420#217C22×D312yes—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—38no—
423(C2×D3)⋊C4—38no—
424(C2×D3)⋊C4—38no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—68no—
428(C2×D3)⋊C4C22×D318yes—
429(C2×D3)⋊C4C22×D314yes—
430(C2×D3)⋊C4C22×D314yes—
431C4⋊Dic3—38no—
432C4⋊Dic3—38no—
433C4⋊Dic3—38no—
434C4⋊Dic3—34no—
435C4⋊Dic3—68no—
436C4⋊Dic3C22×D312yes—
437C4⋊Dic3C22×D314yes—
438Dic3⋊C4—34no—
439Dic3⋊C4—38no—
440C4×Dic3C22×D312yes—
441C22×C32—22no—
442C22×C32C22×D412yes—
443C22×C32C2511yescharacteristic
444C2×C3⋊D3—22no—
445C2×C3⋊D3—24no—
446C2×C3×D3—28no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—24no—
452C2×C3×D3—48no—
453C2×C3×D3—44no—
454C2×C3×D3C22×D418yes—
455D32—88no—
456C32×C4—24no—
457C32×C4C22×D412yes—
458C32×C4C22×D412yes—
459C3⋊Dic3—24no—
460C3⋊Dic3—22no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—24no—
464H(5,𝔽2)—188no—
465C2×#41—31no—
466C2×#41—94no—
467C2×#41—94no—
468C2×#41—92no—
469C2×#41—92no—
470C2×#41—91no—
471C2×#41—188no—
472C22×Q8—91no—
473C22×D4—31no—
474C22×D4—92no—
475C22×D4—92no—
476C22×D4—94no—
477C22×D4—92no—
478C23×C4—31no—
479C23×C4—92no—
480C4⋊Q8—92no—
481C4⋊Q8—92no—
482#124—92no—
483#124—92no—
484#123—32no—
485#123—98no—
486#123—98no—
487#123—98no—
488#123—92no—
489#123—94no—
490#123—94no—
491C22⋊Q8—32no—
492C22⋊Q8—92no—
493C22⋊Q8—94no—
494C22⋊Q8—94no—
495#121—32no—
496#121—98no—
497#121—92no—
498#121—98no—
499#120—32no—
500#120—98no—
501#120—92no—
502C4×D4—34no—
503C4×D4—34no—
504C4×D4—34no—
505C4×D4—94no—
506#117—31no—
507#117D3211yescharacteristic, complemented
508C2×C4⋊C4—98no—
509C2×C22⋊C4—34no—
510C2×C22⋊C4—98no—
511C23×C3—21no—
512C23×C3—34no—
513C23×C3—38no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—62no—
517C23×C3—124no—
518C23×C3—122no—
519C23×C3C23×D311yescharacteristic
520C23×C3C23×D311yescharacteristic
521C22×D3—22no—
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—44no—
525C22×D3—42no—
526C22×D3—62no—
527C22×D3—68no—
528C22×D3—68no—
529C22×D3—128no—
530C22×D3—128no—
531C22×D3C2×D1218yes—
532C22×D3C23×D312yes—
533C22×D3C23×D312yes—
534C22×D3C23×D314yes—
535C3×Q8—62no—
536C3×D4—38no—
537C3×D4—38no—
538C3×D4—64no—
539C3×D4—62no—
540C3×D4—124no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—24no—
544C2×C3×C4—24no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—34no—
548C2×C3×C4—62no—
549C2×C3×C4—64no—
550C2×C3×C4—64no—
551C2×C3×C4—64no—
552C2×C3×C4—128no—
553C2×C3×C4C2×D1214yes—
554C2×C3×C4D3×D414yes—
555C2×C3×C4C23×D314yes—
556C2×C3×C4C23×D314yes—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561#67—24no—
562#67—68no—
563#67—68no—
564#67—616no—
565#67—64no—
566#67—64no—
567#67—616no—
568#67—68no—
569#67—124no—
570#67—124no—
571C2×Dic3—22no—
572C2×Dic3—32no—
573C2×Dic3—34no—
574C2×Dic3—32no—
575C2×Dic3—34no—
576C2×Dic3—62no—
577C2×Dic3—64no—
578C2×Dic3—616no—
579C2×Dic3—68no—
580C2×Dic3—64no—
581C2×Dic3—64no—
582C2×Dic3—124no—
583C2×Dic3C23×D314yes—
584C2×Dic3C23×D312yes—
585C2×Dic3C23×D312yes—
586D12—22no—
587D12—44no—
588D12—68no—
589D12—62no—
590D12—62no—
591D12—122no—
592D12—124no—
593D12C2×D1218yes—
594D12C2×D1218yes—
595C4×D3—24no—
596C4×D3—24no—
597C4×D3—24no—
598C4×D3—48no—
599C4×D3—616no—
600C4×D3—68no—
601C4×D3—64no—
602C4×D3—64no—
603C4×D3—124no—
604Dic6—22no—
605Dic6—64no—
606Dic6—64no—
607Dic6—62no—
608Dic6—64no—
609Dic6—64no—
610Dic6—62no—
611Dic6—124no—
612Dic6—124no—
613Dic6—122no—
614C2×C32—22no—
615C2×C32C23×D411yescharacteristic
616C2×C32#58512yes—
617C3⋊D3—42no—
618C3×D3—28no—
619C3×D3—42no—
620C3×D3—42no—
621C24—32no—
622C24—31no—
623C24—94no—
624#41—64no—
625#41—1816no—
626#41—1816no—
627#41—188no—
628#41—188no—
629#41—184no—
630C2×Q8—31no—
631C2×Q8—92no—
632C2×Q8—92no—
633C2×Q8—91no—
634C2×Q8—184no—
635C2×D4—32no—
636C2×D4—32no—
637C2×D4—32no—
638C2×D4—31no—
639C2×D4—34no—
640C2×D4—38no—
641C2×D4—94no—
642C2×D4—94no—
643C2×D4—98no—
644C2×D4—94no—
645C2×D4—92no—
646C2×D4—91no—
647C2×D4—188no—
648C2×D4—188no—
649C2×D4—1816no—
650C2×D4—188no—
651C22×C4—31no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—38no—
656C22×C4—64no—
657C22×C4—98no—
658C22×C4—94no—
659C22×C4—92no—
660C22×C4—92no—
661C22×C4—188no—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—32no—
665C4⋊C4—94no—
666C4⋊C4—98no—
667C4⋊C4—98no—
668C4⋊C4C2×D3212yes—
669C22⋊C4—32no—
670C22⋊C4—38no—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—94no—
674C22⋊C4—98no—
675C22⋊C4—94no—
676C22⋊C4—98no—
677C22⋊C4C2×D3212yes—
678C42—32no—
679C42C2×D3212yes—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—38no—
685C22×C3—42no—
686C22×C3—68no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—64no—
692C22×C3—128no—
693C22×C3—124no—
694C22×C3C22×D1212yes—
695C22×C3C2×D3×D412yes—
696C22×C3C24×D311yescharacteristic
697C22×C3C24×D311yescharacteristic
698C2×D3—28no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—24no—
703C2×D3—22no—
704C2×D3—48no—
705C2×D3—44no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—122no—
711C2×D3—124no—
712C2×D3—248no—
713C2×D3—248no—
714C2×D3C22×D1218yes—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—44no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—64no—
723C3×C4C22×D1212yes—
724C3×C4C22×D1212yes—
725C3×C4C2×D3×D412yes—
726C3×C4C2×D3×D412yes—
727Dic3—22no—
728Dic3—22no—
729Dic3—24no—
730Dic3—64no—
731Dic3—62no—
732Dic3—64no—
733Dic3—62no—
734Dic3—124no—
735Dic3—122no—
736C32#348511yescharacteristic, complemented, Sylow
737C23—34no—
738C23—38no—
739C23—32no—
740C23—32no—
741C23—62no—
742C23—92no—
743C23—124no—
744C23—122no—
745C23—188no—
746C23—368no—
747C23C22×D3211yescharacteristic
748Q8—62no—
749Q8—184no—
750Q8—184no—
751Q8—182no—
752D4—38no—
753D4—38no—
754D4—64no—
755D4—62no—
756D4—124no—
757D4—188no—
758D4—188no—
759D4—1816no—
760D4—184no—
761D4—182no—
762D4—364no—
763C2×C4—34no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—62no—
767C2×C4—64no—
768C2×C4—64no—
769C2×C4—64no—
770C2×C4—94no—
771C2×C4—92no—
772C2×C4—128no—
773C2×C4—1816no—
774C2×C4—188no—
775C2×C4—184no—
776C2×C4—184no—
777C2×C4D3×D1214yes—
778C2×C4C22×D3214yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—21no—
784C2×C3—22no—
785C2×C3—42no—
786C2×C3—68no—
787C2×C3—122no—
788C2×C3—122no—
789C2×C3C23×D1211yescharacteristic
790C2×C3C22×D3×D411yescharacteristic
791C2×C3#596412yes—
792C2×C3#596612yes—
793D3—28no—
794D3—42no—
795D3—42no—
796D3—122no—
797D3—122no—
798D3—242no—
799C22—22no—
800C22—38no—
801C22—68no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22—64no—
806C22—62no—
807C22—128no—
808C22—124no—
809C22—182no—
810C22—184no—
811C22—728no—
812C22C2×D3×D1212yes—
813C22C23×D3211yescharacteristic
814C4—24no—
815C4—62no—
816C4—62no—
817C4—64no—
818C4—182no—
819C4—184no—
820C4C2×D3×D1212yes—
821C4C2×D3×D1212yes—
822C3—21no—
823C3#8585811yescharacteristic, complemented
824C3#8604011yescharacteristic, complemented
825C2—22no—
826C2—68no—
827C2—122no—
828C2—122no—
829C2—362no—
830C2C22×D3×D1211yescharacteristic
831C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C22×#3795C2semidirect
3. #10595997C2semidirect
4. C3×#5524C2semidirect
5. C3×#5521C2semidirect
6. #10595023C2semidirect
7. #10594856C2semidirect
8. #10594630C2semidirect
9. #10594381C2semidirect
10. #10594290C2semidirect
11. D3×#886C2semidirect
12. #10594003C2semidirect
13. #10593895C2semidirect
17. C22×#634C22semidirect
20. C22×C3×C4×D3C22semidirect
22. C22×#625C22semidirect
23. C22×D3×Dic3C22semidirect
25. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
27. C2×#3796C22semidirect
29. C2×#3795C22semidirect
30. C2×#3795C22semidirect
31. C2×#3795C22semidirect
32. C32×#117C22semidirect
33. #64106C22semidirect
34. #64095C22semidirect
35. #64084C22semidirect
36. #64078C22semidirect
37. C3×#926C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
40. C3×#893C22semidirect
41. C3×#886C22semidirect
42. C3×#882C22semidirect
43. C3×D3×C22⋊C4C22semidirect
44. C3×C4×D12C22semidirect
45. C3×C4×D12C22semidirect
46. #63977C22semidirect
47. #63966C22semidirect
48. #63962C22semidirect
49. #63922C22semidirect
50. D3×(C2×D3)⋊C4C22semidirect
51. #63909C22semidirect
52. #63908C22semidirect
53. #63906C22semidirect
54. C4×#626C22semidirect
55. #63891C22semidirect
56. #63891C22semidirect
57. #63890C22semidirect
58. D3×C4⋊Dic3C22semidirect
59. #63866C22semidirect
60. #63860C22semidirect
61. #63857C22semidirect
62. #63857C22semidirect
86. #5524D3semidirect
87. #5521D3semidirect
106. C2×C3×D12D4semidirect
180. C22×C4×D3C2×D3semidirect
193. C3×#117C2×D3semidirect
194. C3×#117C2×D3semidirect
208. #926C2×D3semidirect
217. #897C2×D3semidirect
219. #895C2×D3semidirect
221. #893C2×D3semidirect
231. #886C2×D3semidirect
237. #882C2×D3semidirect
239. D3×C22⋊C4C2×D3semidirect
245. C4×D12C2×D3semidirect
246. C4×D12C2×D3semidirect
373. C2×D12D12semidirect
507. #117D32semidirect
736. C32#3485semidirect
823. C3#85858semidirect
824. C3#86040semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C22×#37952
#105959972
C3×#55242
C3×#55212
#105950232
#105948562
#105946302
#105943812
#105942902
D3×#8862
#105940032
#105938952
#860403
#858583