Finite Group Databasebeta

← #11884109

Subgroups — #11884109

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63801C211yesmaximal, characteristic, complemented
5#10592430C211yesmaximal, characteristic, complemented
6C3×#4739C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591187C211yesmaximal, characteristic, complemented
9#10590966C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590850C211yesmaximal, characteristic, complemented
13#10590801C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590760C211yesmaximal, characteristic, complemented
16#80204—31nomaximal
17#79495—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic, complemented
29C2×C3×Dic12C2211yescharacteristic, complemented
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31#63981—21no—
32#63974—21no—
33Dic3×#67—21no—
34#63964—21no—
35#63910—21no—
36#63909C2211yescharacteristic
37#63897—21no—
38#63894C2211yescharacteristic
39#63887—21no—
40#63866C2211yescharacteristic, complemented
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic, complemented
43Dic3×Dic6C2211yescharacteristic, complemented
44#63839—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717—24no—
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51#63801—24no—
52C32×C22⋊C8C2211yescharacteristic
53#63648C2211yescharacteristic
54#63648C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63Q8×#67—31no—
64C22×#215—31no—
65C2×#918—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5630—31no—
69#5550—31no—
70D4×Dic6—31no—
71C3×#451—31no—
72C3×#435—31no—
73#5190—31no—
74#5187—31no—
75#5185—31no—
76#5134—31no—
77#5116—31no—
78#5051—31no—
79#4845—31no—
80#4841—31no—
81#4818—31no—
82#4817—31no—
83#4812—31no—
84#4806—31no—
85#4739D311yescharacteristic, complemented
86#4738—31no—
87#4733—31no—
88#4731—31no—
89#4731—31no—
90#4731—61no—
91#4730D311yescharacteristic, complemented
92#4715—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—22no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—41no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—22no—
118#3799—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3744—22no—
127#3744—41no—
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—22no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×Dic12—22no—
139C3×Dic12—41no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3719—22no—
152#3717—22no—
153#3717—22no—
154#3717—22no—
155#3717D414yescomplemented
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×#235—31no—
161C22×D12—31no—
162C22×D12—31no—
163C22×D12—61no—
164C22×Dic6—31no—
165C22×Dic6C2×D311yescharacteristic
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#947—31no—
173#946—31no—
174#946—61no—
175Q8×Dic3—31no—
176#944—31no—
177#944—61no—
178C2×#216—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—64no—
184#937—61no—
185D4×Dic3—61no—
186#930—31no—
187C4×#67—61no—
188C4×#67C2×D311yescharacteristic
189#924—31no—
190#924—31no—
191#924—31no—
192#924—61no—
193#924—61no—
194#924C2×D311yescharacteristic
195C22×C3⋊C8C2×D311yescharacteristic
196#918—64no—
197#909—64no—
198C2×Dic12—31no—
199C2×Dic12C2×D311yescharacteristic, complemented
200C2×Dic12C2×D311yescharacteristic, complemented
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—61no—
210C2×#204—61no—
211C2×#204—64no—
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
213#895—31no—
214#895—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#888—61no—
219#884—61no—
220#882—61no—
221D3×C22⋊C4—61no—
222D3×C22⋊C4—61no—
223#878—61no—
224#878—61no—
225#875—31no—
226C4×D12—31no—
227#869—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#103—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic
235C3×C22⋊C8C2×D311yescharacteristic
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821—61no—
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#818—31no—
246#816—31no—
247#816—31no—
248#816C2×D311yescharacteristic, complemented
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—42no—
271C4⋊(C3⋊D3)C2×D412yes—
272#634—21no—
273#634—21no—
274C3×#67—22no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#626—42no—
294#626—81no—
295#624—42no—
296#624—81no—
297D3×Dic3—42no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—31no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—31no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—121no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—62no—
324C2×C3×Q8—61no—
325C2×C3×Q8—121no—
326C2×C3×D4—31no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—61no—
333C2×#67—61no—
334C2×#67D1211yescharacteristic
335C22×Dic3—21no—
336C22×Dic3—61no—
337#239—62no—
338#239—121no—
339D3×Q8—62no—
340D3×Q8—121no—
341#235—62no—
342#235—121no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—62no—
350C2×D12—62no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—122no—
356C2×D12—121no—
357C2×D12—121no—
358C2×D12—121no—
359C2×D12—122no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—41no—
371C2×Dic6—61no—
372C2×Dic6—62no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6—121no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—62no—
380C3×Q16—121no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—62no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—121no—
403#217D1211yescharacteristic
404#216—62no—
405#215—34no—
406#215—62no—
407#215—62no—
408#215—62no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4D1211yescharacteristic
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—121no—
435Dic3⋊C4D1211yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439C2×C3⋊C8—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—22no—
443Dic12—41no—
444Dic12—62no—
445#204—34no—
446#204—62no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—62no—
451#204—122no—
452#204—121no—
453#204—121no—
454#204—122no—
455ΓL(1,𝔽25)—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32#13712yescomplemented
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—84no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—31no—
489C2×Q16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8D3211yescharacteristic
526#97—31no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3C2×D1211yescharacteristic
530C23×C3D3×D411yescharacteristic
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—124no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—242no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—242no—
546C22×D3C2×D1211yescharacteristic
547C3×Q8—32no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8—122no—
554C3×D4—62no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4C2×D1211yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—22no—
578#67—122no—
579#67—241no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—42no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—122no—
592C2×Dic3C2×D1211yescharacteristic
593C2×Dic3C2×D1211yescharacteristic
594C2×Dic3C2×D1211yescharacteristic
595D12—32no—
596D12—32no—
597D12—62no—
598D12—62no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—122no—
608D12—122no—
609D12—124no—
610D12—122no—
611D12—241no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—241no—
618C4×D3—241no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—122no—
632Dic6—122no—
633Dic6D3×D412yes—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—32no—
639C3×C8—41no—
640C3×C8—41no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8D3×D412yes—
644C2×C32—22no—
645C2×C32D4211yescharacteristic
646C2×C32C2×#13711yescharacteristic
647C2×C32#57711yescharacteristic
648C3⋊D3—42no—
649C3⋊D3—81no—
650C3×D3—41no—
651C24—181no—
652#41—182no—
653#41—361no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—62no—
658C2×Q8—61no—
659C2×Q8—91no—
660C2×Q8—121no—
661C2×Q8—181no—
662C2×Q8—182no—
663C2×Q8—361no—
664C2×D4—31no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—361no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—62no—
679Q16—121no—
680Q16—182no—
681SD16—94no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685SD16—182no—
686SD16—361no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C42—181no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—22no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3#90912yescomplemented
725C22×C3#91812yescomplemented
726C22×C3C22×D1211yescharacteristic
727C22×C3C2×D3×D411yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—122no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—122no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C2×D3—248no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—62no—
760C3×C4—61no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4#100411yescharacteristic
767C3×C4#100911yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—22no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781C32#326611yescharacteristic, complemented, Sylow
782C23—31no—
783C23—181no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788C23D3×D1211yescharacteristic
789Q8—32no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—122no—
796Q8—181no—
797Q8—181no—
798Q8—362no—
799D4—62no—
800D4—92no—
801D4—181no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—721no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4D3×D1211yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—21no—
828C8—32no—
829C8—61no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—121no—
837C2×C3D4×D1211yescharacteristic
838C2×C3#559011yescharacteristic
839C2×C3C2×#90911yescharacteristic
840C2×C3#575111yescharacteristic
841C2×C3C2×#91811yescharacteristic
842C2×C3#577811yescharacteristic
843D3—41no—
844D3—122no—
845D3—122no—
846D3—242no—
847D3—242no—
848D3—241no—
849D3—241no—
850C22—21no—
851C22—21no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—182no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—724no—
862C22#6380112yescomplemented
863C22C2×D3×D1211yescharacteristic
864C4—21no—
865C4—61no—
866C4—61no—
867C4—61no—
868C4—62no—
869C4—121no—
870C4—121no—
871C4—121no—
872C4—361no—
873C4—361no—
874C4D32×D411yescharacteristic
875C4#6431411yescharacteristic
876C3—21no—
877C3#7949511yescharacteristic, complemented
878C3#8020411yescharacteristic, complemented
879C2—22no—
880C2—121no—
881C2—362no—
882C2—721no—
883C2#1059427711yescharacteristic
884C2C2×#6380111yescharacteristic
885C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22⋊C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. Dic6×#67C2semidirect
3. C22×#3717C2semidirect
4. C2×#63801C2semidirect
5. #10592430C2semidirect
6. C3×#4739C2semidirect
7. C3×#4730C2semidirect
8. #10591187C2semidirect
9. #10590966C2semidirect
10. #10590951C2semidirect
11. #10590899C2semidirect
12. #10590850C2semidirect
13. #10590801C2semidirect
14. #10590795C2semidirect
15. #10590760C2semidirect
21. C2×D3×Dic6C22semidirect
28. C2×C3×Dic12C22semidirect
29. C2×C3×Dic12C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
40. #63866C22semidirect
42. #63856C22semidirect
43. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
85. #4739D3semidirect
91. #4730D3semidirect
155. #3717D4semidirect
199. C2×Dic12C2×D3semidirect
200. C2×Dic12C2×D3semidirect
212. C2×ΓL(1,𝔽25)C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
248. #816C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
458. C22×C32#137semidirect
724. C22×C3#909semidirect
725. C22×C3#918semidirect
781. C32#3266semidirect
862. C22#63801semidirect
877. C3#79495semidirect
878. C3#80204semidirect

Maximal subgroups

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

subgroupindex
#105950182
Dic6×#672
C22×#37172
C2×#638012
#105924302
C3×#47392
C3×#47302
#105911872
#105909662
#105909512
#105908992
#105908502
#105908012
#105907952
#105907602
#802043
#794953