Finite Group Databasebeta

← #11884154

Subgroups — #11884154

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×#64127C211yesmaximal, characteristic, complemented
2#10595431C211yesmaximal, characteristic
3#10595361C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5C3×#5190C211yesmaximal, characteristic, complemented
6C3×#5188C211yesmaximal, characteristic, complemented
7#10591653C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591602C211yesmaximal, characteristic, complemented
10#10591592C211yesmaximal, characteristic, complemented
11#10591577C211yesmaximal, characteristic, complemented
12#10591565C211yesmaximal, characteristic, complemented
13#10590845C211yesmaximal, characteristic, complemented
14#10590773C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#81881—31nomaximal
17#80771—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25#64127—24no—
26C2×#3744C2211yescharacteristic
27C2×#3743C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×#946C2211yescharacteristic
31C3×#944C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36#63923—21no—
37#63921—21no—
38#63916C2211yescharacteristic
39#63910—21no—
40C4×#626C2211yescharacteristic
41#63896—21no—
42#63894C2211yescharacteristic
43#63881—21no—
44#63871C2211yescharacteristic, complemented
45#63865—21no—
46#63853—21no—
47#63844C2211yescharacteristic, complemented
48#63840—21no—
49C2×#3717C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51D3×#204—24no—
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×#918—31no—
64C2×#918—31no—
65C2×#918—61no—
66C2×D3×SD16—31no—
67C22×#204—31no—
68#5727—31no—
69#5676—31no—
70#5632—31no—
71#5630—31no—
72C3×#497—31no—
73C3×#467—31no—
74#5190D311yescharacteristic, complemented
75#5188D311yescharacteristic, complemented
76#5187—31no—
77#5186—31no—
78#5174—31no—
79#5170—31no—
80#5169—31no—
81#5111—31no—
82#5083—31no—
83#5054—31no—
84#5050—31no—
85#5046—31no—
86#4889—31no—
87#4886—31no—
88#4818—31no—
89#4808—31no—
90#4806—31no—
91#4798—31no—
92#4710—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—41no—
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634—21no—
107C2×#634C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×Q16—22no—
122C2×C32×C8C2311yescharacteristic
123#3756—22no—
124#3755—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744D414yescomplemented
127#3743—22no—
128C3×#216—41no—
129C3×#215—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145#3724—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722D411yescharacteristic
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153Dic32—21no—
154#3717—22no—
155#3716—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×Q8—61no—
164C2×D3×D4—31no—
165C22×D12—31no—
166C22×Dic6—31no—
167C2×C3×Q16—21no—
168C2×C3×Q16—31no—
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C22×C3×C8—31no—
174C3×C4⋊Q8—31no—
175C3×#124—31no—
176C3×C22⋊Q8—31no—
177C3×C22⋊Q8—31no—
178#947C2×D311yescharacteristic
179#946—31no—
180#946C2×D311yescharacteristic
181#946C2×D311yescharacteristic
182#944C2×D311yescharacteristic, complemented
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic
192#938—31no—
193C2×#214—31no—
194C4×#67—31no—
195#918—64no—
196#918—64no—
197#918—68no—
198D3×SD16—64no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—61no—
204C2×#204—64no—
205C2×#204C2×D311yescharacteristic
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—61no—
209C2×D3×C8C2×D311yescharacteristic
210#897—31no—
211#896—61no—
212#896—61no—
213#896—61no—
214#895—31no—
215#895—61no—
216#894—61no—
217#893—31no—
218#893—61no—
219#888—61no—
220#888—61no—
221#887—31no—
222#884—61no—
223#883—61no—
224#882—61no—
225#882—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229#878—61no—
230C4×D12—31no—
231C4×D12—31no—
232C4×Dic6—31no—
233C3×#107—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#97—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#835C2×D311yescharacteristic, complemented
240#832—31no—
241#830—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246#818C2×D311yescharacteristic, complemented
247#816—31no—
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#810—31no—
252#809—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—42no—
277C4×C3⋊D3—42no—
278#634—21no—
279#634—42no—
280#634C2×D412yes—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#627—42no—
294#626—22no—
295#626—42no—
296#626—81no—
297#624—81no—
298D3×Dic3—42no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—91no—
304C22×SD16—91no—
305D4×Q8—91no—
306#546—91no—
307#497—31no—
308#468—91no—
309#467—31no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—91no—
314#450—91no—
315#448—91no—
316#440—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—21no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—31no—
328C22×C3×C4—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67—61no—
332C22×Dic3—61no—
333#239—62no—
334#239—62no—
335#239—64no—
336#239—121no—
337#239—121no—
338#239—122no—
339D3×Q8—62no—
340D3×Q8—62no—
341D3×Q8—62no—
342D3×Q8—64no—
343D3×Q8—121no—
344D3×Q8—121no—
345D3×Q8—121no—
346D3×Q8—122no—
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—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—121no—
372C2×C4×D3—121no—
373C2×C4×D3C22×D311yescharacteristic
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—61no—
377C2×Dic6—62no—
378C2×Dic6—61no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6—61no—
382C2×Dic6—121no—
383C2×Dic6—121no—
384C2×Dic6C22×D311yescharacteristic
385C3×Q16—24no—
386C3×Q16—22no—
387C3×Q16—22no—
388C3×Q16—121no—
389C3×SD16—62no—
390C3×SD16—121no—
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×C4⋊C4—61no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—31no—
408#217—31no—
409#217—61no—
410#216—41no—
411#216—62no—
412#216—62no—
413#216—64no—
414#215—41no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—64no—
419#214—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—31no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3C22×D311yescharacteristic
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452#204—22no—
453#204—34no—
454#204—34no—
455#204—64no—
456#204—62no—
457#204—62no—
458ΓL(1,𝔽25)—64no—
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461D3×C8—22no—
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3#13712yescomplemented
475D32—84no—
476C32×C4—41no—
477C32×C4—41no—
478C32×C4C22×D411yescharacteristic
479C32×C4H(5,𝔽2)11yescharacteristic
480C3⋊Dic3—21no—
481C3⋊Dic3—22no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C22×Q8—91no—
490C22×Q8—91no—
491C22×D4—91no—
492#137—184no—
493C2×Q16—31no—
494C2×Q16—91no—
495C2×Q16D3211yescharacteristic, complemented
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—184no—
503C2×M16—91no—
504C22×C8—31no—
505C4⋊Q8—31no—
506C4⋊Q8—181no—
507#124—31no—
508#123—181no—
509C22⋊Q8—31no—
510C22⋊Q8—31no—
511C22⋊Q8—91no—
512C22⋊Q8—181no—
513C22⋊Q8—181no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—31no—
525#103—31no—
526#103—91no—
527#103—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—31no—
534C23×C3—61no—
535C22×D3—21no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3D3×D411yescharacteristic
549C3×Q8—22no—
550C3×Q8—22no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—41no—
560C3×Q8—41no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—61no—
564C3×D4—61no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
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—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—62no—
583#67—122no—
584#67—241no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598D12—21no—
599D12—21no—
600D12—32no—
601D12—32no—
602D12—62no—
603D12—62no—
604D12—61no—
605D12—61no—
606D12—121no—
607D12—122no—
608D12—122no—
609D12—124no—
610D12—122no—
611D12—241no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—124no—
625C4×D3—122no—
626C4×D3—124no—
627C4×D3—241no—
628C4×D3—241no—
629Dic6—21no—
630Dic6—21no—
631Dic6—32no—
632Dic6—32no—
633Dic6—62no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637Dic6—122no—
638Dic6—122no—
639Dic6—122no—
640Dic6—122no—
641Dic6—124no—
642C3×C8—22no—
643C3×C8—61no—
644C3×C8—61no—
645C3×C8D3×D412yes—
646C3×C8D3×D412yes—
647C3⋊C8—21no—
648C3⋊C8—21no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C2×C32D4211yescharacteristic
653C2×C32C2×#13711yescharacteristic
654C2×C32#57711yescharacteristic
655C3⋊D3—41no—
656C3⋊D3—42no—
657C3×D3—22no—
658C3×D3—81no—
659C24—181no—
660#41—182no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8—181no—
665C2×Q8—181no—
666C2×Q8—182no—
667C2×Q8—182no—
668C2×Q8—361no—
669C2×Q8—361no—
670C2×Q8C2×D3211yescharacteristic
671C2×Q8C2×D3211yescharacteristic
672C2×D4—31no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—181no—
676C2×D4—181no—
677C2×D4—182no—
678C2×D4—181no—
679C2×D4—361no—
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—181no—
683C22×C4—181no—
684C22×C4—181no—
685C22×C4—181no—
686Q16—22no—
687Q16—121no—
688Q16—182no—
689SD16—62no—
690SD16—94no—
691SD16—121no—
692SD16—182no—
693SD16—182no—
694SD16—182no—
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—61no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—91no—
715C22⋊C4—91no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—31no—
720C42—181no—
721C22×C3—21no—
722C22×C3—32no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—62no—
736C2×D3—61no—
737C2×D3—62no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—62no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—122no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—244no—
754C2×D3—244no—
755C2×D3#91812yescomplemented
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4C2×D3×D411yescharacteristic
772C3×C4#100411yescharacteristic
773C3×C4#100911yescharacteristic
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779Dic3—41no—
780Dic3—62no—
781Dic3—62no—
782Dic3—61no—
783Dic3—62no—
784Dic3—61no—
785Dic3—122no—
786C32#326611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—61no—
789C23—91no—
790C23—181no—
791C23—362no—
792C23—362no—
793C23—721no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—61no—
799Q8—61no—
800Q8—92no—
801Q8—181no—
802Q8—362no—
803Q8—362no—
804D4—61no—
805D4—61no—
806D4—92no—
807D4—182no—
808D4—181no—
809D4—362no—
810D4—362no—
811D4—721no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—91no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—362no—
827C2×C4—362no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4C22×D3211yescharacteristic
831C8—61no—
832C8—61no—
833C8—181no—
834C8#381112yes—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—62no—
839C2×C3—241no—
840C2×C3#560911yescharacteristic
841C2×C3#571711yescharacteristic
842C2×C3C2×#91811yescharacteristic
843C2×C3#577011yescharacteristic
844C2×C3D3×#13711yescharacteristic
845C2×C3#577811yescharacteristic
846D3—22no—
847D3—81no—
848D3—122no—
849D3—121no—
850D3—122no—
851D3—121no—
852D3—122no—
853D3—242no—
854C22—32no—
855C22—61no—
856C22—61no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—182no—
864C22—361no—
865C22—361no—
866C22—724no—
867C22D32×D411yescharacteristic
868C4—41no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—182no—
878C4#6431411yescharacteristic
879C4C2×#381111yescharacteristic
880C3—21no—
881C3#8077111yescharacteristic, complemented
882C3#8188111yescharacteristic, complemented
883C2—62no—
884C2—241no—
885C2—361no—
886C2—362no—
887C2D3×#91811yescharacteristic
888C2#1059477011yescharacteristic
889C2#1059529711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenterC2×Q16D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64127C2semidirect
3. #10595361C2semidirect
4. C2×D3×#204C2semidirect
5. C3×#5190C2semidirect
6. C3×#5188C2semidirect
7. #10591653C2semidirect
8. #10591651C2semidirect
9. #10591602C2semidirect
10. #10591592C2semidirect
11. #10591577C2semidirect
12. #10591565C2semidirect
13. #10590845C2semidirect
14. #10590773C2semidirect
15. #10590726C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C2×C32×Q16C22semidirect
23. C2×#3756C22semidirect
27. C2×#3743C22semidirect
31. C3×#944C22semidirect
32. C2×C3×#216C22semidirect
44. #63871C22semidirect
47. #63844C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#818C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
61. #63557C22semidirect
74. #5190D3semidirect
75. #5188D3semidirect
126. #3744D4semidirect
169. C2×C3×Q16C2×D3semidirect
170. C2×C3×Q16C2×D3semidirect
182. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
238. #835C2×D3semidirect
239. #835C2×D3semidirect
246. #818C2×D3semidirect
248. #815C2×D3semidirect
474. C2×C3×D3#137semidirect
495. C2×Q16D32semidirect
755. C2×D3#918semidirect
786. C32#3266semidirect
881. C3#80771semidirect
882. C3#81881semidirect

Maximal subgroups

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

subgroupindex
C2×#641272
#105954312
#105953612
C2×D3×#2042
C3×#51902
C3×#51882
#105916532
#105916512
#105916022
#105915922
#105915772
#105915652
#105908452
#105907732
#105907262
#818813
#807713