Finite Group Databasebeta

← #11884095

Subgroups — #11884095

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#626C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4817C211yesmaximal, characteristic, complemented
7C3×#4809C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10590965C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590559C211yesmaximal, characteristic, complemented
15#10590522C211yesmaximal, characteristic, complemented
16#80204—31nomaximal
17#79795—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64104C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63951—24no—
32D3×#215—24no—
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63909—21no—
36C4×#626—21no—
37C4×#626C2211yescharacteristic
38#63890—21no—
39#63871—21no—
40#63871C2211yescharacteristic, complemented
41#63866—21no—
42#63866C2211yescharacteristic, complemented
43#63864C2211yescharacteristic
44#63857—21no—
45#63857C2211yescharacteristic
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63Q8×#67—31no—
64C22×#215—31no—
65C2×#918—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5630—31no—
69Q8×D12—31no—
70#5554—31no—
71C3×#451—31no—
72C3×#440—31no—
73#5190—31no—
74#5187—31no—
75#5185—31no—
76#5051—31no—
77#5028—31no—
78#5019—31no—
79#4887—31no—
80#4886—31no—
81#4818—31no—
82#4817D311yescharacteristic, complemented
83#4812—31no—
84#4809D311yescharacteristic, complemented
85#4806—31no—
86#4806—31no—
87#4806—61no—
88#4783—31no—
89#4776—31no—
90#4731—31no—
91#4730—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634—21no—
103C2×#634C2311yescharacteristic
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3796—22no—
120#3796—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—41no—
127C3×#216—22no—
128C3×#215D414yescomplemented
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×Dic12—41no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722—21no—
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—22no—
151#3717—22no—
152#3716—22no—
153#3715—22no—
154#3712—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—61no—
162C2×D3×Q8C2×D311yescharacteristic
163C2×#237—31no—
164C2×D3×D4—31no—
165C22×D12—31no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C3×C22⋊Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172#947—31no—
173#946—31no—
174#946—61no—
175Q8×Dic3C2×D311yescharacteristic, complemented
176#944—31no—
177#944—61no—
178C2×#216—31no—
179C2×#216C2×D311yescharacteristic, complemented
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—61no—
185C2×#215—64no—
186C2×#215C2×D311yescharacteristic
187C2×#214—31no—
188C2×#214—31no—
189#930—61no—
190C4×#67—31no—
191C4×#67—61no—
192C2×(C2×D3)⋊C4—61no—
193#924—31no—
194#924—61no—
195C22×C3⋊C8—31no—
196#918—64no—
197#915—64no—
198D3×SD16—64no—
199C2×Dic12—31no—
200C2×Dic12C2×D311yescharacteristic, complemented
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—61no—
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×D3×C8—31no—
209#897—31no—
210#897—31no—
211#897—61no—
212#897—61no—
213#897C2×D311yescharacteristic
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#894—61no—
219#893C2×D311yescharacteristic
220#886—61no—
221#882—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224#875—31no—
225C4×D12—31no—
226C4×D12—61no—
227#869—31no—
228#869—61no—
229C3×#107—31no—
230C3×#103—21no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C2×D311yescharacteristic, complemented
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243(C2×D3)⋊C8C2×D311yescharacteristic
244#815C2×D311yescharacteristic, complemented
245Dic3⋊C8—31no—
246#810—31no—
247#810—31no—
248#810—31no—
249#810—61no—
250#810C2×D311yescharacteristic, complemented
251#809—31no—
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—81no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C4×C3⋊D3—42no—
274#634—21no—
275#634—21no—
276#634—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—81no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—42no—
294#626—22no—
295#626—42no—
296#626—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊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—31no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
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—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C2×#67—31no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—61no—
335#239—62no—
336#239—121no—
337D3×Q8—22no—
338D3×Q8—41no—
339D3×Q8—62no—
340D3×Q8—62no—
341D3×Q8—122no—
342D3×Q8—121no—
343D3×Q8—121no—
344D3×Q8—122no—
345#237—62no—
346#237—121no—
347D3×D4—62no—
348D3×D4—121no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12—121no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—121no—
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—21no—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—121no—
378C2×Dic6C22×D311yescharacteristic
379C2×Dic6C22×D311yescharacteristic
380C3×Q16—62no—
381C3×Q16—121no—
382C3×SD16—34no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397C3×C42—61no—
398#217—31no—
399#217—61no—
400#216—22no—
401#216—62no—
402#215—62no—
403#215—62no—
404#215—62no—
405#215—62no—
406#215—122no—
407#215D1214yescomplemented
408#214—62no—
409#214—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—31no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C4×Dic3—21no—
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—41no—
447Dic12—62no—
448#204—62no—
449#204—62no—
450#204—121no—
451#204—121no—
452#204—122no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—22no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—41no—
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—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—91no—
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—31no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—31no—
517C4⋊C8—91no—
518#103—31no—
519#103—91no—
520#103—91no—
521#103D3211yescharacteristic, complemented
522#102—31no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8—91no—
526#97—31no—
527C23×C3—31no—
528C23×C3—61no—
529C22×D3—21no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3D3×D411yescharacteristic
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—22no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—122no—
552C3×Q8C2×D1212yes—
553C3×Q8D3×D412yes—
554C3×D4—32no—
555C3×D4—61no—
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—122no—
572C2×C3×C4—241no—
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575#67—62no—
576#67—122no—
577#67—122no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591D12—21no—
592D12—62no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—121no—
598D12—121no—
599D12—122no—
600D12—122no—
601D12—241no—
602D12—241no—
603D12—242no—
604D12C2×D1212yes—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—42no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—81no—
613C4×D3—121no—
614C4×D3—121no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—124no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—42no—
624Dic6—62no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—122no—
631Dic6—122no—
632Dic6—124no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—32no—
636C3×C8—41no—
637C3×C8—61no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8C2×D1212yes—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—41no—
647C3⋊D3—81no—
648C3×D3—22no—
649C3×D3—42no—
650C24—181no—
651#41—182no—
652#41—361no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—61no—
656C2×Q8—62no—
657C2×Q8—91no—
658C2×Q8—121no—
659C2×Q8—181no—
660C2×Q8—182no—
661C2×Q8—361no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—91no—
675C22×C4—181no—
676C22×C4—181no—
677Q16—62no—
678Q16—121no—
679Q16—182no—
680SD16—34no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685SD16—361no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C42—61no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—22no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—62no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3#91812yescomplemented
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C22×D1211yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4#100911yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771Dic3—61no—
772Dic3—61no—
773Dic3—121no—
774Dic3—122no—
775Dic3—121no—
776Dic3—121no—
777C32#326611yescharacteristic, complemented, Sylow
778C23—31no—
779C23—61no—
780C23—91no—
781C23—181no—
782C23—362no—
783C23—362no—
784C23—721no—
785Q8—21no—
786Q8—61no—
787Q8—61no—
788Q8—61no—
789Q8—61no—
790Q8—122no—
791Q8—181no—
792Q8—181no—
793Q8—362no—
794Q8D3×D1212yes—
795D4—32no—
796D4—61no—
797D4—182no—
798D4—181no—
799D4—181no—
800D4—362no—
801D4—362no—
802D4—721no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—122no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—241no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4C22×D3211yescharacteristic
822C8—21no—
823C8—32no—
824C8—61no—
825C8—181no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—62no—
830C2×C3—122no—
831C2×C3D4×D1211yescharacteristic
832C2×C3#559011yescharacteristic
833C2×C3C2×#91811yescharacteristic
834C2×C3#577511yescharacteristic
835C2×C3D3×#13711yescharacteristic
836C2×C3#577811yescharacteristic
837D3—22no—
838D3—42no—
839D3—122no—
840D3—121no—
841D3—121no—
842D3—241no—
843D3—241no—
844D3—481no—
845C22—32no—
846C22—61no—
847C22—61no—
848C22—62no—
849C22—121no—
850C22—121no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—724no—
858C22D32×D411yescharacteristic
859C4—22no—
860C4—41no—
861C4—61no—
862C4—61no—
863C4—61no—
864C4—121no—
865C4—121no—
866C4—121no—
867C4—181no—
868C4—361no—
869C4C2×D3×D1211yescharacteristic
870C4#6431411yescharacteristic
871C3—21no—
872C3#7979511yescharacteristic, complemented
873C3#8020411yescharacteristic, complemented
874C2—62no—
875C2—122no—
876C2—361no—
877C2—721no—
878C2#1059427711yescharacteristic
879C2#1059475411yescharacteristic
880C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594629C2
hypercenter#103D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×#626C2semidirect
2. C2×#63951C2semidirect
3. C2×D3×#215C2semidirect
5. #10592505C2semidirect
6. C3×#4817C2semidirect
7. C3×#4809C2semidirect
8. #10591607C2semidirect
9. #10590965C2semidirect
10. #10590946C2semidirect
11. #10590899C2semidirect
12. #10590728C2semidirect
13. #10590579C2semidirect
14. #10590559C2semidirect
15. #10590522C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
28. C2×C3×Dic12C22semidirect
40. #63871C22semidirect
42. #63866C22semidirect
46. C2×#3719C22semidirect
50. C2×#3712C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
57. C3×#815C22semidirect
58. C3×#810C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
82. #4817D3semidirect
84. #4809D3semidirect
128. C3×#215D4semidirect
175. Q8×Dic3C2×D3semidirect
179. C2×#216C2×D3semidirect
200. C2×Dic12C2×D3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C2×D3semidirect
244. #815C2×D3semidirect
250. #810C2×D3semidirect
252. #807C2×D3semidirect
407. #215D12semidirect
468. C2×C3×D3#137semidirect
521. #103D32semidirect
746. C2×D3#918semidirect
777. C32#3266semidirect
872. C3#79795semidirect
873. C3#80204semidirect

Maximal subgroups

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

subgroupindex
Q8×#6262
C2×#639512
C2×D3×#2152
#105946292
#105925052
C3×#48172
C3×#48092
#105916072
#105909652
#105909462
#105908992
#105907282
#105905792
#105905592
#105905222
#802043
#797953