Finite Group Databasebeta

← #11904443

Subgroups — #11904443

Order 1152.

3289 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3#10595992C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595022C211yesmaximal, characteristic, complemented
7#10594855C211yesmaximal, characteristic, complemented
8#10594633C214yesmaximal, complemented
9#10594530C214yesmaximal, complemented
10#10594296C214yesmaximal, complemented
11#10594295C214yesmaximal, complemented
12#10594007C214yesmaximal, complemented
13#10593869C214yesmaximal, complemented
14#86354—31nomaximal
15#86040—31nomaximal
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic, complemented
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×#3811C2214yes—
22C22×#626C2212yescomplemented
23C22×#624C2212yescomplemented
24#64308—28no—
25C2×D3×D12C2212yescomplemented
26C2×D3×D12C2212yescomplemented
27C2×#3799—28no—
28C2×#3799C2214yescomplemented
29C2×#3799C2214yescomplemented
30C2×#3799C2212yescomplemented
31C2×#3799C2212yescomplemented
32C32×#117C2211yescharacteristic, complemented
33#64135C2211yescharacteristic, complemented
34#64102C2214yescomplemented
35C22⋊C4×C3⋊D3C2214yescomplemented
36C4×C4⋊(C3⋊D3)C2214yescomplemented
37C3×#897C2212yescomplemented
38C3×#897C2214yescomplemented
39C3×#895C2212yescomplemented
40C3×#886C2212yescomplemented
41C3×#886C2214yescomplemented
42C3×#882C2212yescomplemented
43C3×#875C2212yescomplemented
44C3×C4×D12C2214yescomplemented
45C3×#869C2212yescomplemented
46#63976C2212yescomplemented
47#63961C2214yescomplemented
48#63961C2212yescomplemented
49#63922C2218yescomplemented
50#63921C2218yescomplemented
51#63916C2218yescomplemented
52#63912C2218yescomplemented
53#63908C2212yescomplemented
54C4×#625C2214yescomplemented
55#63900C2218yescomplemented
56#63873C2212yescomplemented
57#63863C2212yescomplemented
58#63856C2214yescomplemented
59#63856C2212yescomplemented
60#63854C2218yescomplemented
61#63854C2218yescomplemented
62#63854C2218yescomplemented
63C2×#1009—31no—
64C2×#1009—31no—
65C22×#239—31no—
66C22×#235—31no—
67C3×#536—31no—
68C3×#525—31no—
69#5828—31no—
70#5825—31no—
71#5816—31no—
72#5791—31no—
73#5726—34no—
74#5676—34no—
75#5653—34no—
76D3×#123—34no—
77D3×#123—34no—
78#5631—34no—
79#5631—34no—
80#5630—34no—
81#5612—34no—
82#5589—34no—
83#5551—34no—
84#5550—34no—
85#5526D311yescharacteristic, complemented
86#5524D311yescharacteristic, complemented
87#5521—31no—
88#5521—31no—
89#5521—61no—
90C23×C3⋊D3C2312yes—
91C23×C3×D3C2311yescharacteristic
92C22×D32C2314yes—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)D418yescomplemented
95C2×C4⋊(C3⋊D3)C2312yes—
96C2×C4⋊(C3⋊D3)C2312yes—
97C2×C4×C3⋊D3C2318yes—
98C2×C3×#67C2312yes—
99C2×C3×#67C2312yes—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C3×#235—24no—
103C3×#235—24no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2314yes—
107C2×C3×C4×D3—24no—
108C2×C3×C4×D3C2312yes—
109C2×C3×C4×D3C2312yes—
110C2×C3×C4×D3C2312yes—
111C2×C3×C4×D3C2312yes—
112C2×C3×Dic6—24no—
113C2×C3×Dic6C2312yes—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2312yes—
116C2×C3×Dic6C2311yescharacteristic
117#3811—216no—
118C2×#626—28no—
119C2×#626C2318yes—
120C2×#626C2314yes—
121C2×#626C2314yes—
122C2×#625C2314yes—
123C2×#624—28no—
124C2×#624C2318yes—
125C2×#624C2314yes—
126D3×D12—28no—
127D3×D12—28no—
128#3799—216no—
129#3799—216no—
130#3799—28no—
131#3799—28no—
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135#3757C2312yes—
136#3752C2318yes—
137C4⋊(C3⋊Dic3)C2312yes—
138C4×C3⋊Dic3C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2318yes—
142C3×C4⋊Dic3C2314yes—
143C3×C4⋊Dic3C2318yes—
144#3724C2318yes—
145#3724C2314yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2318yes—
149#3485—91noSylow
150C2×C3×#41—31no—
151C2×C3×#41—31no—
152C22×C3×Q8—31no—
153C23×C3×C4—31no—
154C22×#67—32no—
155#1009—68no—
156#1009—68no—
157C2×#239—34no—
158C2×#239—34no—
159C2×#239—32no—
160C2×#239—32no—
161C2×#239—68no—
162C2×D3×D4—34no—
163C2×D3×D4—34no—
164C2×D3×D4—32no—
165C2×D3×D4—32no—
166C2×#235—34no—
167C2×#235—34no—
168C2×#235—32no—
169C2×#235—32no—
170C2×#235—68no—
171C2×#235C2×D311yescharacteristic
172C2×#235C2×D311yescharacteristic
173C22×D12—31no—
174C22×D12—31no—
175C22×D12—32no—
176C22×D12—32no—
177C22×D12—32no—
178C22×D12—61no—
179C22×C4×D3—32no—
180C22×C4×D3—32no—
181C22×C4×D3C2×D311yescharacteristic, complemented
182C22×Dic6C2×D311yescharacteristic, complemented
183C3×C4⋊Q8—32no—
184C3×#124—32no—
185C3×#123—32no—
186C3×#123—34no—
187C3×C22⋊Q8—32no—
188C3×C22⋊Q8—34no—
189C3×#121—32no—
190C3×#120—32no—
191C3×C4×D4—34no—
192C3×#117—21no—
193C3×#117C2×D311yescharacteristic, complemented
194C3×#117C2×D311yescharacteristic, complemented
195#953—32no—
196#947—32no—
197#946—34no—
198#946—32no—
199#944—32no—
200#944—32no—
201#938—32no—
202#938—38no—
203#937—32no—
204#937—38no—
205#936—32no—
206#935—32no—
207#935—34no—
208#930—32no—
209#929—32no—
210#929—34no—
211C4×#67—34no—
212C4×#67—34no—
213#926—31no—
214#926—31no—
215#926—61no—
216#924—32no—
217#924—34no—
218#897C2×D312yescomplemented
219#897C2×D314yescomplemented
220#895—38no—
221#895C2×D312yescomplemented
222#894—38no—
223#894—38no—
224#894—38no—
225#893—34no—
226#893—34no—
227#893—64no—
228D3×C4⋊C4—38no—
229D3×C4⋊C4—38no—
230#886C2×D312yescomplemented
231#886C2×D314yescomplemented
232#884—38no—
233#884—38no—
234#883—38no—
235#883—38no—
236#883—38no—
237#882—38no—
238#882C2×D312yescomplemented
239D3×C22⋊C4—34no—
240D3×C22⋊C4—34no—
241D3×C22⋊C4—38no—
242D3×C22⋊C4—38no—
243D3×C22⋊C4—64no—
244#875C2×D312yescomplemented
245C4×D12—34no—
246C4×D12—34no—
247C4×D12—64no—
248C4×D12C2×D314yescomplemented
249#869C2×D312yescomplemented
250C23×C32C2411yescharacteristic
251C22×C3⋊D3—44no—
252C22×C3⋊D3C2×D418yes—
253C22×C3⋊D3C2414yes—
254C22×C3×D3—22no—
255C22×C3×D3—42no—
256C22×C3×D3C2412yes—
257C22×C3×D3C2412yes—
258C22×C3×D3C2412yes—
259C2×D32—28no—
260C2×D32—48no—
261C2×C32×C4C2×D414yes—
262C2×C32×C4C2414yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3C2414yes—
266C4⋊(C3⋊D3)C2×D418yes—
267C4⋊(C3⋊D3)C2×D418yes—
268C4×C3⋊D3—48no—
269C3×#67—24no—
270C3×#67—24no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—24no—
273C2×C3×Dic3C2412yes—
274C2×C3×Dic3C2412yes—
275C2×C3×Dic3C2414yes—
276C2×C3×Dic3C2412yes—
277C3×D12—22no—
278C3×D12—22no—
279C3×D12—44no—
280C3×C4×D3—24no—
281C3×C4×D3—24no—
282C3×C4×D3—24no—
283C3×C4×D3—24no—
284C3×Dic6—24no—
285C3×Dic6—24no—
286C3×Dic6—22no—
287C3×Dic6—22no—
288#626—216no—
289#626—28no—
290#626—28no—
291#625—44no—
292#624—216no—
293#624—28no—
294C2×H(5,𝔽2)—91no—
295C22×#41—91no—
296#547—94no—
297#547—94no—
298#546—94no—
299#546—94no—
300#536—31no—
301#536—91no—
302#534—94no—
303#525—31no—
304#525—91no—
305C2×#123—94no—
306#518—91no—
307C24×C3—31no—
308C23×D3—32no—
309C23×D3—32no—
310C23×D3—34no—
311C23×D3—34no—
312C23×D3—62no—
313C23×D3C22×D311yescharacteristic
314C3×#41—64no—
315C3×#41—64no—
316C2×C3×Q8—31no—
317C2×C3×Q8—32no—
318C2×C3×Q8—32no—
319C2×C3×Q8—31no—
320C2×C3×Q8—64no—
321C2×C3×D4—32no—
322C2×C3×D4—32no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—34no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—32no—
329C22×C3×C4—32no—
330C22×C3×C4—32no—
331C22×C3×C4—32no—
332C22×C3×C4—32no—
333C22×C3×C4—64no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—38no—
341C2×#67—68no—
342C2×#67C22×D312yes—
343C2×#67C22×D312yes—
344C22×Dic3C22×D312yes—
345C22×Dic3C22×D311yescharacteristic
346#239—616no—
347#239—616no—
348#239—68no—
349#239—68no—
350D3×D4—68no—
351D3×D4—68no—
352D3×D4—616no—
353D3×D4—616no—
354#235—24no—
355#235—24no—
356#235—616no—
357#235—616no—
358#235—68no—
359#235—68no—
360C2×D12—38no—
361C2×D12—38no—
362C2×D12—32no—
363C2×D12—32no—
364C2×D12—32no—
365C2×D12—32no—
366C2×D12—38no—
367C2×D12—34no—
368C2×D12—34no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—68no—
372C2×D12—68no—
373C2×D12—68no—
374C2×D12—68no—
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D314yes—
378C2×C4×D3—24no—
379C2×C4×D3—38no—
380C2×C4×D3—38no—
381C2×C4×D3—34no—
382C2×C4×D3—34no—
383C2×C4×D3—38no—
384C2×C4×D3—38no—
385C2×C4×D3—68no—
386C2×C4×D3—68no—
387C2×C4×D3—68no—
388C2×C4×D3C22×D312yes—
389C2×C4×D3C22×D312yes—
390C2×C4×D3C22×D312yes—
391C2×C4×D3C22×D312yes—
392C2×Dic6—24no—
393C2×Dic6C22×D311yescharacteristic
394C2×Dic6C22×D312yes—
395C2×Dic6C22×D312yes—
396C2×Dic6C22×D311yescharacteristic
397C3×C4⋊C4—22no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—38no—
400C3×C4⋊C4C22×D312yes—
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—38no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4C22×D312yes—
407C3×C22⋊C4C22×D312yes—
408C3×C42—22no—
409C3×C42C22×D312yes—
410C3×C42C22×D312yes—
411#217—32no—
412#217—32no—
413#217—34no—
414#217—38no—
415#217—34no—
416#217—62no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—38no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—38no—
421(C2×D3)⋊C4—38no—
422(C2×D3)⋊C4—68no—
423(C2×D3)⋊C4C22×D314yes—
424(C2×D3)⋊C4C22×D314yes—
425(C2×D3)⋊C4C22×D318yes—
426C4⋊Dic3—32no—
427C4⋊Dic3—32no—
428C4⋊Dic3—62no—
429C4⋊Dic3C22×D318yes—
430C4⋊Dic3C22×D314yes—
431Dic3⋊C4—34no—
432Dic3⋊C4—38no—
433Dic3⋊C4—38no—
434Dic3⋊C4—34no—
435C4×Dic3—32no—
436C4×Dic3—32no—
437C4×Dic3—62no—
438C22×C32—22no—
439C22×C32C22×D412yes—
440C22×C32C2511yescharacteristic
441C2×C3⋊D3—28no—
442C2×C3⋊D3—48no—
443C2×C3⋊D3C22×D418yes—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—24no—
449C2×C3×D3—22no—
450C2×C3×D3—24no—
451C2×C3×D3—44no—
452D32—88no—
453C32×C4—24no—
454C32×C4C22×D412yes—
455C32×C4C22×D412yes—
456C3⋊Dic3—24no—
457C3×Dic3—22no—
458C3×Dic3—24no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461H(5,𝔽2)—188no—
462C2×#41—31no—
463C2×#41—31no—
464C2×#41—94no—
465C2×#41—94no—
466C2×#41—92no—
467C2×#41—92no—
468C2×#41—188no—
469C22×Q8—31no—
470C22×D4—92no—
471C22×D4—92no—
472C22×D4—92no—
473C22×D4—94no—
474C22×D4—91no—
475C23×C4—31no—
476C23×C4—92no—
477C4⋊Q8—32no—
478C4⋊Q8—92no—
479#124—32no—
480#124—92no—
481#123—32no—
482#123—34no—
483#123—98no—
484#123—98no—
485#123—98no—
486#123—92no—
487#123—94no—
488C22⋊Q8—32no—
489C22⋊Q8—34no—
490C22⋊Q8—92no—
491C22⋊Q8—94no—
492#121—32no—
493#121—98no—
494#121—98no—
495#121—92no—
496#120—32no—
497#120—98no—
498#120—92no—
499C4×D4—34no—
500C4×D4—94no—
501C4×D4—94no—
502C4×D4—94no—
503#117—91no—
504#117D3211yescharacteristic, complemented
505C2×C4⋊C4—98no—
506C2×C22⋊C4—98no—
507C2×C22⋊C4—94no—
508C23×C3—21no—
509C23×C3—32no—
510C23×C3—32no—
511C23×C3—32no—
512C23×C3—62no—
513C23×C3—122no—
514C23×C3C23×D311yescharacteristic
515C23×C3C23×D311yescharacteristic
516C22×D3—22no—
517C22×D3—34no—
518C22×D3—34no—
519C22×D3—38no—
520C22×D3—38no—
521C22×D3—42no—
522C22×D3—64no—
523C22×D3—68no—
524C22×D3—68no—
525C22×D3—68no—
526C22×D3—128no—
527C22×D3—128no—
528C22×D3—124no—
529C22×D3—124no—
530C22×D3—244no—
531C22×D3C23×D312yes—
532C22×D3C23×D312yes—
533C22×D3C23×D312yes—
534C3×Q8—64no—
535C3×Q8—64no—
536C3×Q8—62no—
537C3×Q8—62no—
538C3×D4—64no—
539C3×D4—64no—
540C3×D4—62no—
541C3×D4—62no—
542C3×D4—124no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—24no—
546C2×C3×C4—24no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—34no—
550C2×C3×C4—32no—
551C2×C3×C4—62no—
552C2×C3×C4—64no—
553C2×C3×C4—64no—
554C2×C3×C4—64no—
555C2×C3×C4—64no—
556C2×C3×C4—64no—
557C2×C3×C4D3×D414yes—
558C2×C3×C4D3×D414yes—
559C2×C3×C4C23×D314yes—
560C2×C3×C4C23×D314yes—
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—24no—
566#67—24no—
567#67—616no—
568#67—68no—
569#67—68no—
570#67—124no—
571#67—124no—
572C2×Dic3—24no—
573C2×Dic3—22no—
574C2×Dic3—34no—
575C2×Dic3—34no—
576C2×Dic3—64no—
577C2×Dic3C23×D312yes—
578C2×Dic3C23×D312yes—
579C2×Dic3C23×D314yes—
580C2×Dic3C23×D312yes—
581D12—22no—
582D12—22no—
583D12—38no—
584D12—38no—
585D12—38no—
586D12—38no—
587D12—44no—
588D12—68no—
589D12—68no—
590D12—68no—
591D12—68no—
592D12—616no—
593C4×D3—24no—
594C4×D3—24no—
595C4×D3—24no—
596C4×D3—24no—
597C4×D3—616no—
598C4×D3—616no—
599C4×D3—68no—
600C4×D3—68no—
601C4×D3—128no—
602C4×D3—128no—
603C4×D3—248no—
604Dic6—24no—
605Dic6—24no—
606Dic6—22no—
607Dic6—22no—
608C2×C32—22no—
609C2×C32C23×D411yescharacteristic
610C2×C32#58512yes—
611C3⋊D3—28no—
612C3×D3—42no—
613C3×D3—42no—
614C3×D3—42no—
615C24—31no—
616C24—94no—
617C24—92no—
618#41—64no—
619#41—64no—
620#41—1816no—
621#41—1816no—
622#41—188no—
623#41—188no—
624C2×Q8—32no—
625C2×Q8—31no—
626C2×Q8—32no—
627C2×Q8—31no—
628C2×Q8—64no—
629C2×D4—32no—
630C2×D4—32no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—34no—
634C2×D4—98no—
635C2×D4—94no—
636C2×D4—94no—
637C2×D4—94no—
638C2×D4—92no—
639C2×D4—92no—
640C2×D4—98no—
641C2×D4—188no—
642C2×D4—188no—
643C2×D4—188no—
644C2×D4—1816no—
645C22×C4—31no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—64no—
652C22×C4—98no—
653C22×C4—94no—
654C22×C4—98no—
655C22×C4—188no—
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—34no—
658C4⋊C4—38no—
659C4⋊C4—94no—
660C4⋊C4—98no—
661C4⋊C4—92no—
662C4⋊C4C2×D3212yes—
663C22⋊C4—34no—
664C22⋊C4—38no—
665C22⋊C4—34no—
666C22⋊C4—94no—
667C22⋊C4—98no—
668C22⋊C4—94no—
669C22⋊C4—92no—
670C22⋊C4—98no—
671C22⋊C4C2×D3212yes—
672C42—92no—
673C42C2×D3212yes—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—21no—
678C22×C3—42no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—64no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—64no—
686C22×C3—124no—
687C22×C3C2×D3×D412yes—
688C22×C3C2×D3×D412yes—
689C22×C3C24×D311yescharacteristic
690C22×C3C24×D311yescharacteristic
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—24no—
696C2×D3—22no—
697C2×D3—24no—
698C2×D3—38no—
699C2×D3—38no—
700C2×D3—44no—
701C2×D3—68no—
702C2×D3—68no—
703C2×D3—68no—
704C2×D3—128no—
705C2×D3—128no—
706C2×D3—128no—
707C2×D3—248no—
708C2×D3—248no—
709C2×D3—248no—
710C3×C4—24no—
711C3×C4—24no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—44no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—64no—
719C3×C4C2×D3×D412yes—
720C3×C4C2×D3×D412yes—
721C3×C4C2×D3×D412yes—
722C3×C4C2×D3×D412yes—
723Dic3—24no—
724Dic3—22no—
725Dic3—22no—
726Dic3—22no—
727Dic3—64no—
728Dic3—64no—
729Dic3—124no—
730C32#348511yescharacteristic, complemented, Sylow
731C23—32no—
732C23—32no—
733C23—32no—
734C23—62no—
735C23—94no—
736C23—98no—
737C23—122no—
738C23—188no—
739C23—364no—
740C23—368no—
741C23C22×D3211yescharacteristic
742Q8—64no—
743Q8—64no—
744Q8—62no—
745Q8—62no—
746D4—64no—
747D4—64no—
748D4—62no—
749D4—62no—
750D4—98no—
751D4—98no—
752D4—124no—
753D4—188no—
754D4—188no—
755D4—1816no—
756D4—364no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—62no—
762C2×C4—64no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—94no—
768C2×C4—1816no—
769C2×C4—188no—
770C2×C4—368no—
771C2×C4#380214yes—
772C2×C4C22×D3214yes—
773C2×C4C22×D3211yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—22no—
779C2×C3—42no—
780C2×C3—122no—
781C2×C3—122no—
782C2×C3—122no—
783C2×C3C22×D3×D411yescharacteristic
784C2×C3C22×D3×D411yescharacteristic
785C2×C3#596412yes—
786C2×C3#596812yes—
787D3—42no—
788D3—42no—
789D3—42no—
790D3—68no—
791D3—68no—
792D3—128no—
793C22—22no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—64no—
799C22—62no—
800C22—64no—
801C22—98no—
802C22—124no—
803C22—188no—
804C22—368no—
805C22—728no—
806C22C2×#380212yes—
807C22C23×D3211yescharacteristic
808C4—24no—
809C4—62no—
810C4—62no—
811C4—62no—
812C4—64no—
813C4—184no—
814C4C2×#380212yes—
815C4C2×#380212yes—
816C3—21no—
817C3#8604011yescharacteristic, complemented
818C3#8635411yescharacteristic, complemented
819C2—22no—
820C2—122no—
821C2—122no—
822C2—122no—
823C2—188no—
824C2C22×#380211yescharacteristic
825C2#1059669712yes—
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×#64308C2semidirect
2. C22×#3799C2semidirect
3. #10595992C2semidirect
4. C3×#5526C2semidirect
5. C3×#5524C2semidirect
6. #10595022C2semidirect
7. #10594855C2semidirect
8. #10594633C2semidirect
9. #10594530C2semidirect
10. #10594296C2semidirect
11. #10594295C2semidirect
12. #10594007C2semidirect
13. #10593869C2semidirect
19. C22×C3×C4×D3C22semidirect
20. C22×C3×Dic6C22semidirect
22. C22×#626C22semidirect
23. C22×#624C22semidirect
25. C2×D3×D12C22semidirect
26. C2×D3×D12C22semidirect
28. C2×#3799C22semidirect
29. C2×#3799C22semidirect
30. C2×#3799C22semidirect
31. C2×#3799C22semidirect
32. C32×#117C22semidirect
33. #64135C22semidirect
34. #64102C22semidirect
35. C22⋊C4×C3⋊D3C22semidirect
36. C4×C4⋊(C3⋊D3)C22semidirect
37. C3×#897C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
40. C3×#886C22semidirect
41. C3×#886C22semidirect
42. C3×#882C22semidirect
43. C3×#875C22semidirect
44. C3×C4×D12C22semidirect
45. C3×#869C22semidirect
46. #63976C22semidirect
47. #63961C22semidirect
48. #63961C22semidirect
49. #63922C22semidirect
50. #63921C22semidirect
51. #63916C22semidirect
52. #63912C22semidirect
53. #63908C22semidirect
54. C4×#625C22semidirect
55. #63900C22semidirect
56. #63873C22semidirect
57. #63863C22semidirect
58. #63856C22semidirect
59. #63856C22semidirect
60. #63854C22semidirect
61. #63854C22semidirect
62. #63854C22semidirect
85. #5526D3semidirect
86. #5524D3semidirect
94. C2×C4⋊(C3⋊D3)D4semidirect
181. C22×C4×D3C2×D3semidirect
182. C22×Dic6C2×D3semidirect
193. C3×#117C2×D3semidirect
194. C3×#117C2×D3semidirect
218. #897C2×D3semidirect
219. #897C2×D3semidirect
221. #895C2×D3semidirect
230. #886C2×D3semidirect
231. #886C2×D3semidirect
238. #882C2×D3semidirect
244. #875C2×D3semidirect
248. C4×D12C2×D3semidirect
249. #869C2×D3semidirect
504. #117D32semidirect
730. C32#3485semidirect
817. C3#86040semidirect
818. C3#86354semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C22×#37992
#105959922
C3×#55262
C3×#55242
#105950222
#105948552
#105946332
#105945302
#105942962
#105942952
#105940072
#105938692
#863543
#860403