Finite Group Databasebeta

← #11884123

Subgroups — #11884123

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64124C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3Q8×#626C211yesmaximal, characteristic, complemented
4#10595246C211yesmaximal, characteristic
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591592C211yesmaximal, characteristic, complemented
9#10591489C211yesmaximal, characteristic, complemented
10#10591466C211yesmaximal, characteristic, complemented
11#10591459C211yesmaximal, characteristic, complemented
12#10590897C211yesmaximal, characteristic, complemented
13#10590852C211yesmaximal, characteristic, complemented
14#10590845C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#79795—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic
25#64124—24no—
26C2×#3746C2211yescharacteristic, complemented
27C2×#3743C2211yescharacteristic, complemented
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×D3×SD16—24no—
33C2×C3×#204C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35#63978—21no—
36#63977—21no—
37#63962—21no—
38C2×(C2×D3)⋊Dic3—21no—
39#63916C2211yescharacteristic
40C4×#626—21no—
41C4×#626C2211yescharacteristic
42#63871—21no—
43#63871C2211yescharacteristic, complemented
44#63866—21no—
45#63866C2211yescharacteristic, complemented
46#63860C2211yescharacteristic
47#63857—21no—
48#63857C2211yescharacteristic
49#63857C2211yescharacteristic
50C2×#3719C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C22×C3×SD16—31no—
64Q8×#67—31no—
65#5806—31no—
66C2×#915—31no—
67C2×#915—31no—
68C2×#915—61no—
69C2×D3×SD16D311yescharacteristic, complemented
70Q8×D12—31no—
71#5554—31no—
72C3×#440—31no—
73#5228—31no—
74#5218—31no—
75#5174—31no—
76#5173—31no—
77#5170—31no—
78#5167—31no—
79#5166—31no—
80#5164D311yescharacteristic, complemented
81#5162—31no—
82#5116—31no—
83#5111—31no—
84#5028—31no—
85#5019—31no—
86#4887—31no—
87#4886—31no—
88#4809—31no—
89#4806—31no—
90#4783—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—41no—
101#3830—22no—
102#3830—41no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634—21no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×D3×Q8—22no—
111C3×D3×Q8—41no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626D411yescharacteristic
121C32×SD16D414yescomplemented
122C2×C32×C8C2311yescharacteristic
123#3756—22no—
124#3754—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3746—22no—
127#3743—22no—
128C3×#217—21no—
129C3×#215—22no—
130C3×#214—22no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×D3×C8—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3719—41no—
155#3716—41no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×D4—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—61no—
162C2×D3×Q8C2×D311yescharacteristic
163C2×#237—31no—
164C2×#237—31no—
165C2×#237—61no—
166C2×D3×D4C2×D311yescharacteristic
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—64no—
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×SD16C2×D311yescharacteristic
174C22×C3×C8—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177#953—61no—
178C2×#217—61no—
179#946—31no—
180#946—61no—
181Q8×Dic3C2×D311yescharacteristic, complemented
182#944—31no—
183#944—61no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#215C2×D311yescharacteristic
189#939—61no—
190#938—31no—
191#936—31no—
192#935—61no—
193D4×Dic3C2×D311yescharacteristic
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—61no—
198C2×#214C2×D311yescharacteristic
199#930—61no—
200C4×#67—31no—
201C4×#67—61no—
202C2×(C2×D3)⋊C4—61no—
203#924—31no—
204#924—31no—
205#924—61no—
206#915—68no—
207#915—64no—
208#915—64no—
209D3×SD16—24no—
210C2×Dic12—31no—
211C2×Dic12—31no—
212C2×Dic12—31no—
213C2×Dic12—61no—
214C2×#204—31no—
215C2×#204C2×D311yescharacteristic
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×ΓL(1,𝔽25)—61no—
219C2×D3×C8C2×D311yescharacteristic
220#897—31no—
221#897—31no—
222#897—31no—
223#897—61no—
224#897—61no—
225#895—31no—
226#886—61no—
227#882—61no—
228#875—31no—
229C4×D12—31no—
230C4×D12—61no—
231#869—31no—
232#869—61no—
233C3×#107—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#97—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#832—31no—
240#832C2×D311yescharacteristic
241#830—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#818C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#810—31no—
252#810—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8C2×D412yes—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—42no—
276#634—21no—
277#634—21no—
278#634—21no—
279#634—21no—
280#634—42no—
281C3×#67—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—81no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297#626—22no—
298#626—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—91no—
304C22×SD16—31no—
305D4×Q8—91no—
306#546—91no—
307#497—91no—
308#468—91no—
309#467—91no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—91no—
314#450—91no—
315#448—91no—
316#440—31no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8—62no—
324C2×C3×Q8—121no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C22×Dic3—21no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—121no—
347D3×Q8—22no—
348D3×Q8—41no—
349D3×Q8—64no—
350D3×Q8—62no—
351D3×Q8—62no—
352D3×Q8—121no—
353D3×Q8—121no—
354D3×Q8—122no—
355#237—64no—
356#237—62no—
357#237—62no—
358#237—121no—
359#237—121no—
360#237—122no—
361D3×D4—22no—
362D3×D4—41no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—121no—
373C2×C4×D3C22×D311yescharacteristic
374C2×Dic6—21no—
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6—61no—
382C2×Dic6—61no—
383C2×Dic6—121no—
384C2×Dic6C22×D311yescharacteristic
385C3×SD16—24no—
386C3×SD16—62no—
387C3×SD16—62no—
388C3×SD16—62no—
389C3×SD16D1214yescomplemented
390C3×SD16#6714yescomplemented
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—62no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402C3×C42—61no—
403#217—21no—
404#217—31no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#216—64no—
411#216—62no—
412#216—62no—
413#216—121no—
414#215—22no—
415#214—22no—
416#214—64no—
417#214—62no—
418#214—62no—
419#214—121no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430C4⋊Dic3—21no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445C4×Dic3—21no—
446C4×Dic3C22×D311yescharacteristic
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—64no—
453Dic12—62no—
454Dic12—62no—
455Dic12—121no—
456#204—22no—
457#204—121no—
458ΓL(1,𝔽25)—64no—
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461D3×C8—22no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—84no—
475C2×C3×D3#13712yescomplemented
476C32×C4—22no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—21no—
480C3⋊Dic3—41no—
481C3⋊Dic3—41no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C22×Q8—31no—
490C22×Q8—91no—
491C22×D4—31no—
492#137—184no—
493C2×Q16—91no—
494C2×Q16—91no—
495C2×Q16—91no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—64no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16D3211yescharacteristic
503C2×M16—91no—
504C22×C8—31no—
505C4⋊Q8—91no—
506C4⋊Q8—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510C22⋊Q8—91no—
511C22⋊Q8—91no—
512C22⋊Q8—181no—
513C22⋊Q8—181no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—122no—
539C23×C3—122no—
540C23×C3—241no—
541C22×D3—21no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—61no—
547C22×D3—81no—
548C22×D3D3×D411yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—22no—
552C3×Q8—41no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—122no—
556C3×Q8C2×D1212yes—
557C3×Q8C2×#6712yes—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—22no—
561C3×D4—41no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4C2×D1212yes—
566C3×D4C2×#6712yes—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—241no—
581C2×C3×C4C23×D311yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583#67—42no—
584#67—62no—
585#67—122no—
586#67—122no—
587#67—124no—
588#67—241no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—81no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—122no—
603C2×Dic3—122no—
604C2×Dic3—124no—
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607C2×Dic3D3×D411yescharacteristic
608D12—21no—
609D12—21no—
610D12—62no—
611D12—241no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—42no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—61no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—124no—
624Dic6—21no—
625Dic6—21no—
626Dic6—42no—
627Dic6—62no—
628Dic6—62no—
629Dic6—61no—
630Dic6—61no—
631Dic6—61no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638Dic6—121no—
639Dic6—122no—
640Dic6—122no—
641Dic6—124no—
642C3×C8—22no—
643C3×C8—61no—
644C3×C8—61no—
645C3×C8C2×D1212yes—
646C3×C8C2×#6712yes—
647C3⋊C8—21no—
648C3⋊C8—21no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C2×C32—42no—
653C2×C32D4211yescharacteristic
654C2×C32C2×#13711yescharacteristic
655C2×C32#57711yescharacteristic
656C3⋊D3—41no—
657C3×D3—22no—
658C3×D3—81no—
659C24—61no—
660#41—182no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—61no—
664C2×Q8—62no—
665C2×Q8—91no—
666C2×Q8—91no—
667C2×Q8—121no—
668C2×Q8—181no—
669C2×Q8—182no—
670C2×Q8—361no—
671C2×Q8C2×D3211yescharacteristic
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—62no—
675C2×D4—91no—
676C2×D4—121no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4C2×D3211yescharacteristic
680C22×C4—31no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—91no—
684C22×C4—181no—
685C22×C4—181no—
686Q16—182no—
687Q16—182no—
688Q16—361no—
689SD16—62no—
690SD16—62no—
691SD16—62no—
692SD16—182no—
693SD16—361no—
694SD16#62614yescomplemented
695M16—182no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—62no—
699C2×C8—91no—
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C22⋊C4—61no—
711C22⋊C4—91no—
712C22⋊C4—91no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—31no—
720C42—61no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—32no—
725C22×C3—42no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—244no—
738C22×C3C2×D3×D411yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—62no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—84no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3#91512yescomplemented
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—42no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C22×D1211yescharacteristic
768C3×C4#100411yescharacteristic
769C3×C4#100911yescharacteristic
770C3×C4C22×#6711yescharacteristic
771Dic3—21no—
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777Dic3—62no—
778Dic3—61no—
779Dic3—61no—
780Dic3—122no—
781Dic3—122no—
782Dic3—121no—
783Dic3—121no—
784Dic3—121no—
785Dic3—121no—
786C32#326611yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—91no—
791C23—122no—
792C23—122no—
793C23—241no—
794Q8—21no—
795Q8—61no—
796Q8—61no—
797Q8—122no—
798Q8—181no—
799Q8—181no—
800Q8—181no—
801Q8—181no—
802Q8—362no—
803Q8C2×#62612yes—
804D4—21no—
805D4—61no—
806D4—61no—
807D4—122no—
808D4—182no—
809D4—362no—
810D4—721no—
811D4C2×#62612yes—
812C2×C4—21no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—91no—
822C2×C4—122no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—241no—
828C2×C4—362no—
829C2×C4—362no—
830C2×C4C22×D3211yescharacteristic
831C8—61no—
832C8—61no—
833C8—181no—
834C8C2×#62612yes—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—42no—
840C2×C3—62no—
841C2×C3—82no—
842C2×C3—241no—
843C2×C3D4×D1211yescharacteristic
844C2×C3C2×#91511yescharacteristic
845C2×C3#576211yescharacteristic
846C2×C3#577511yescharacteristic
847C2×C3D3×#13711yescharacteristic
848C2×C3D4×#6711yescharacteristic
849D3—22no—
850D3—81no—
851D3—122no—
852D3—121no—
853D3—121no—
854C22—22no—
855C22—32no—
856C22—41no—
857C22—41no—
858C22—61no—
859C22—61no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—244no—
867C22D32×D411yescharacteristic
868C4—22no—
869C4—61no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—361no—
877C4—361no—
878C4#6431411yescharacteristic
879C4C22×#62611yescharacteristic
880C3—21no—
881C3#7979511yescharacteristic, complemented
882C3#8386611yescharacteristic, complemented
883C2—42no—
884C2—62no—
885C2—241no—
886C2—361no—
887C2D3×#91511yescharacteristic
888C2#1059474911yescharacteristic
889C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595246C2
hypercenterC2×SD16D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#64124C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. Q8×#626C2semidirect
5. C3×#5164C2semidirect
6. #10591604C2semidirect
7. #10591595C2semidirect
8. #10591592C2semidirect
9. #10591489C2semidirect
10. #10591466C2semidirect
11. #10591459C2semidirect
12. #10590897C2semidirect
13. #10590852C2semidirect
14. #10590845C2semidirect
15. #10590726C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
23. C2×#3756C22semidirect
26. C2×#3746C22semidirect
27. C2×#3743C22semidirect
28. C3×Q8×Dic3C22semidirect
43. #63871C22semidirect
45. #63866C22semidirect
50. C2×#3719C22semidirect
52. C3×#835C22semidirect
54. C3×#818C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63565C22semidirect
61. #63557C22semidirect
69. C2×D3×SD16D3semidirect
80. #5164D3semidirect
121. C32×SD16D4semidirect
181. Q8×Dic3C2×D3semidirect
238. #835C2×D3semidirect
245. #818C2×D3semidirect
248. #815C2×D3semidirect
389. C3×SD16D12semidirect
390. C3×SD16#67semidirect
475. C2×C3×D3#137semidirect
694. SD16#626semidirect
755. C2×D3#915semidirect
786. C32#3266semidirect
881. C3#79795semidirect
882. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C2×#641242
C2×C3×D3×SD162
Q8×#6262
#105952462
C3×#51642
#105916042
#105915952
#105915922
#105914892
#105914662
#105914592
#105908972
#105908522
#105908452
#105907262
#838663
#797953