Finite Group Databasebeta

← #11884184

Subgroups — #11884184

Order 1152.

1064 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2C2×#63945C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594383C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4813C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591627C211yesmaximal, characteristic, complemented
10#10590824C211yesmaximal, characteristic, complemented
11#10590760C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590506C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#80771—31nomaximal
17#80627—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3797C2211yescharacteristic, complemented
21C2×D3×Dic6C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24#64106C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#887C2211yescharacteristic, complemented
33#63945—24no—
34#63923—21no—
35#63921—21no—
36#63918—21no—
37#63916C2211yescharacteristic
38#63910—21no—
39C4×#626C2211yescharacteristic
40#63895—21no—
41#63894C2211yescharacteristic
42#63893—21no—
43#63880—21no—
44#63866C2211yescharacteristic, complemented
45#63853—21no—
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×#918—31no—
64C2×#918—31no—
65C2×D3×SD16—31no—
66C22×#204—31no—
67#5676—31no—
68#5632—31no—
69#5630—31no—
70Q8×D12—31no—
71C3×#467—31no—
72C3×#464—31no—
73#5190—31no—
74#5186—31no—
75#5170—31no—
76#5111—31no—
77#5060—31no—
78#5050—31no—
79#5046—31no—
80#5026—31no—
81#4889—31no—
82#4886—31no—
83#4841—31no—
84#4836—31no—
85#4818—31no—
86#4813D311yescharacteristic, complemented
87#4808—31no—
88#4808—31no—
89#4808—61no—
90#4806—31no—
91#4798D311yescharacteristic, complemented
92#4780—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#624—21no—
113C2×#624—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—41no—
117#3797—22no—
118#3797—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3756—41no—
124#3752—21no—
125C4⋊(C3⋊Dic3)—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3744—22no—
128C3×#216—22no—
129C3×#216—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—22no—
143C3×D3×C8—22no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3D411yescharacteristic
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3717D414yescomplemented
153#3716—22no—
154#3715—41no—
155#3712—22no—
156#3266—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—61no—
160C2×D3×Q8—31no—
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C2×D3×D4—31no—
164C22×D12—31no—
165C22×Dic6—31no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C22×C3×C8—31no—
170C3×#124—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C4×Q8—31no—
174#947C2×D311yescharacteristic
175#946C2×D311yescharacteristic
176#944—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—61no—
180C2×#216C2×D311yescharacteristic, complemented
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185#938—31no—
186C2×#214—31no—
187C2×#214—31no—
188C4×#67—31no—
189#918—64no—
190#918—64no—
191D3×SD16—64no—
192C2×#204—31no—
193C2×#204—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—61no—
198C2×#204—64no—
199C2×#204C2×D311yescharacteristic
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×D3×C8C2×D311yescharacteristic
203#897—31no—
204#897—31no—
205#897—61no—
206#897—61no—
207#897—61no—
208#897C2×D311yescharacteristic
209#896—61no—
210#895—31no—
211#895—61no—
212#894—61no—
213#893—31no—
214#888—61no—
215#887C2×D311yescharacteristic, complemented
216#884—61no—
217#883—61no—
218#882—61no—
219#882—61no—
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222D3×C22⋊C4—61no—
223#878—61no—
224C4×D12—31no—
225C4×D12—31no—
226C4×D12—61no—
227#869—31no—
228#869—61no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235C3×#102—31no—
236#835—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—61no—
242#816—31no—
243#816C2×D311yescharacteristic, complemented
244#815—31no—
245Dic3⋊C8C2×D311yescharacteristic, complemented
246#810—31no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic
252#807C2×D311yescharacteristic, complemented
253#803—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×Q8—21no—
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)—42no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C4×C3⋊D3—42no—
274#634—21no—
275#634—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6C2×D412yes—
290#627—42no—
291#627—42no—
292#626—22no—
293#626—42no—
294#626—81no—
295#624—42no—
296#624—81no—
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—31no—
309#464—31no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—31no—
325C22×C3×C4—31no—
326C2×#67—31no—
327C2×#67—61no—
328C2×#67—61no—
329C22×Dic3—61no—
330#239—62no—
331#239—62no—
332#239—122no—
333#239—121no—
334#239—121no—
335#239—122no—
336D3×Q8—62no—
337D3×Q8—62no—
338D3×Q8—62no—
339D3×Q8—121no—
340D3×Q8—121no—
341D3×Q8—121no—
342D3×D4—62no—
343D3×D4—121no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—62no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—121no—
354C2×D12—121no—
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—61no—
371C2×Dic6—62no—
372C2×Dic6—61no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—121no—
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—62no—
380C3×Q16—62no—
381C3×SD16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
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⋊C4—61no—
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400C3×C42—61no—
401#217—31no—
402#217—61no—
403#216—22no—
404#216—22no—
405#216—121no—
406#216—121no—
407#216—122no—
408#215—34no—
409#215—62no—
410#215—121no—
411#214—62no—
412#214—121no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—21no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—121no—
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—31no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439C4×Dic3—21no—
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446#204—22no—
447#204—34no—
448#204—62no—
449#204—62no—
450#204—62no—
451#204—62no—
452#204—122no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—22no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—91no—
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—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—31no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—31no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—31no—
517C4⋊C8—31no—
518#103—31no—
519#103—91no—
520#103—91no—
521#103D3211yescharacteristic, complemented
522#102—31no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
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—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—32no—
549C3×Q8—41no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—61no—
554C3×D4—61no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—62no—
573#67—122no—
574#67—241no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—122no—
585C2×Dic3D3×D411yescharacteristic
586C2×Dic3D3×D411yescharacteristic
587C2×Dic3D3×D411yescharacteristic
588D12—21no—
589D12—21no—
590D12—32no—
591D12—32no—
592D12—62no—
593D12—62no—
594D12—61no—
595D12—61no—
596D12—121no—
597D12—122no—
598D12—122no—
599D12—124no—
600D12—122no—
601D12—241no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—121no—
609C4×D3—121no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—124no—
615C4×D3—122no—
616C4×D3—241no—
617C4×D3—241no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—121no—
626Dic6—121no—
627Dic6—122no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6D3×D412yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8D3×D412yes—
642C2×C32D4211yescharacteristic
643C2×C32C2×#13711yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—41no—
647C3×D3—22no—
648C3×D3—81no—
649C24—181no—
650#41—182no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—91no—
655C2×Q8—181no—
656C2×Q8—181no—
657C2×Q8—182no—
658C2×Q8—182no—
659C2×Q8—361no—
660C2×Q8—361no—
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—91no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—62no—
677Q16—62no—
678Q16—361no—
679SD16—62no—
680SD16—94no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—31no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C22×C3—21no—
712C22×C3—32no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×D3×D411yescharacteristic
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—122no—
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—244no—
744C2×D3—244no—
745C2×D3#91812yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—42no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—62no—
756C3×C4—61no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4C2×D3×D411yescharacteristic
761C3×C4C2×D3×D411yescharacteristic
762C3×C4#100911yescharacteristic
763C3×C4#100911yescharacteristic
764Dic3—21no—
765Dic3—21no—
766Dic3—22no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—61no—
771Dic3—61no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—241no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—31no—
778C23—61no—
779C23—91no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23—721no—
784Q8—21no—
785Q8—21no—
786Q8—32no—
787Q8—61no—
788Q8—61no—
789Q8—61no—
790Q8—181no—
791Q8—181no—
792Q8—362no—
793Q8—362no—
794D4—61no—
795D4—61no—
796D4—92no—
797D4—182no—
798D4—181no—
799D4—362no—
800D4—362no—
801D4—721no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—91no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—362no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—721no—
820C2×C4C22×D3211yescharacteristic
821C8—21no—
822C8—32no—
823C8—61no—
824C8—181no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—62no—
829C2×C3—241no—
830C2×C3#560911yescharacteristic
831C2×C3#560911yescharacteristic
832C2×C3C2×#91811yescharacteristic
833C2×C3#577011yescharacteristic
834C2×C3#577011yescharacteristic
835C2×C3D3×#13711yescharacteristic
836D3—22no—
837D3—81no—
838D3—121no—
839D3—122no—
840D3—121no—
841D3—122no—
842D3—241no—
843D3—242no—
844C22—32no—
845C22—61no—
846C22—61no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—182no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—41no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—62no—
864C4—121no—
865C4—121no—
866C4—181no—
867C4—361no—
868C4#6430811yescharacteristic
869C4D32×D411yescharacteristic
870C3—21no—
871C3#8062711yescharacteristic, complemented
872C3#8077111yescharacteristic, complemented
873C2—62no—
874C2—241no—
875C2—361no—
876C2—362no—
877C2#1059428411yescharacteristic
878C2#1059475711yescharacteristic
879C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595431C2
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
2. C2×#63945C2semidirect
3. C2×D3×#204C2semidirect
4. #10594383C2semidirect
5. #10592507C2semidirect
6. C3×#4813C2semidirect
7. C3×#4798C2semidirect
8. #10591653C2semidirect
9. #10591627C2semidirect
10. #10590824C2semidirect
11. #10590760C2semidirect
12. #10590727C2semidirect
13. #10590596C2semidirect
14. #10590506C2semidirect
15. #10590457C2semidirect
20. C2×#3797C22semidirect
22. C2×#3756C22semidirect
24. #64106C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
32. C3×#887C22semidirect
44. #63866C22semidirect
50. C2×#3712C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
62. #63554C22semidirect
86. #4813D3semidirect
91. #4798D3semidirect
152. #3717D4semidirect
180. C2×#216C2×D3semidirect
181. C2×#216C2×D3semidirect
215. #887C2×D3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
243. #816C2×D3semidirect
245. Dic3⋊C8C2×D3semidirect
252. #807C2×D3semidirect
468. C2×C3×D3#137semidirect
521. #103D32semidirect
745. C2×D3#918semidirect
776. C32#3266semidirect
871. C3#80627semidirect
872. C3#80771semidirect

Maximal subgroups

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

subgroupindex
#105954312
C2×#639452
C2×D3×#2042
#105943832
#105925072
C3×#48132
C3×#47982
#105916532
#105916272
#105908242
#105907602
#105907272
#105905962
#105905062
#105904572
#807713
#806273