Finite Group Databasebeta

← #11884303

Subgroups — #11884303

Order 1152.

1094 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3#10595018C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10592745C211yesmaximal, characteristic, complemented
6C3×#5052C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591170C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590577C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80921—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#893C2211yescharacteristic, complemented
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63981—21no—
37#63974—21no—
38#63949—24no—
39#63910—21no—
40#63909C2211yescharacteristic
41#63897—21no—
42#63894C2211yescharacteristic
43#63864C2211yescharacteristic
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48#63825—24no—
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#919—31no—
67C2×#908—31no—
68#5631D311yescharacteristic, complemented
69#5630—31no—
70#5550—31no—
71C3×#470—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5127—31no—
76#5086—31no—
77#5083—31no—
78#5052D311yescharacteristic, complemented
79#5048—31no—
80#5047—31no—
81#5047—31no—
82#5046—31no—
83#5046—31no—
84#5046—61no—
85#5016—31no—
86#5014—31no—
87#5011—31no—
88#4869—31no—
89#4864—31no—
90#4819—31no—
91#4818—31no—
92#4810—31no—
93#4808—31no—
94C23×C3⋊D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C3×#239—22no—
105C3×#239—41no—
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#624—21no—
119C2×#624—21no—
120#3799—22no—
121#3799—41no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3755—22no—
126#3755—41no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C3×#208—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3718—41no—
150#3717—22no—
151#3717—22no—
152#3715—22no—
153#3714—22no—
154#3714D414yescomplemented
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×#235—31no—
162C2×#235C2×D311yescharacteristic
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—61no—
166C2×C3×Q16—31no—
167C2×C3×M16—31no—
168C3×C4⋊Q8—31no—
169C3×#123—61no—
170C3×#123—61no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×C22⋊Q8C2×D311yescharacteristic
176C3×#121—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C4⋊C4—61no—
180#950—64no—
181#949—64no—
182#947—31no—
183#944C2×D311yescharacteristic, complemented
184C2×#216—31no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—61no—
195C2×#215—61no—
196#937—61no—
197C2×#214—31no—
198C2×#213—31no—
199C2×#213—31no—
200#930—31no—
201C4×#67C2×D311yescharacteristic
202#924C2×D311yescharacteristic
203C2×#208C2×D311yescharacteristic
204C22×C3⋊C8—31no—
205#919—64no—
206#908—64no—
207C2×D24—31no—
208C2×D24—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×D3×C8—31no—
212#897C2×D311yescharacteristic, complemented
213#895—31no—
214#895—61no—
215#894—21no—
216#894—61no—
217#894—61no—
218#893—31no—
219#893C2×D311yescharacteristic, complemented
220D3×C4⋊C4—21no—
221#884—21no—
222#884—61no—
223#883—21no—
224#882—61no—
225D3×C22⋊C4—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#106—31no—
230C3×#103—31no—
231C3×#103—31no—
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810C2×D311yescharacteristic, complemented
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809—61no—
251#808C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—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×D3—21no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)C2×D412yes—
275C3×#67—41no—
276C3×#67—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×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296#626—81no—
297#624—42no—
298#624—81no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—31no—
306#546—91no—
307#497—91no—
308#470—31no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—121no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—21no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67#6711yescharacteristic
345#239—22no—
346#239—41no—
347#239—62no—
348#239—121no—
349#235—22no—
350#235—41no—
351#235—62no—
352#235—121no—
353C2×D12—21no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—122no—
367C2×D12—121no—
368C2×D12—121no—
369C2×D12—121no—
370C2×D12—122no—
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—21no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3C22×D311yescharacteristic
380C2×Dic6C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×Q16—62no—
383C3×M16—62no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—41no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—41no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—31no—
407#217—21no—
408#217#6711yescharacteristic
409#216—22no—
410#216—121no—
411#216—121no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—122no—
418#215—121no—
419#215—121no—
420#215—122no—
421#214—62no—
422#213—34no—
423#213—62no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—61no—
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—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4#6711yescharacteristic
435C4⋊Dic3—21no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4#6711yescharacteristic
441C4×Dic3C22×D311yescharacteristic
442#208—22no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—62no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452D24—34no—
453D24—62no—
454#204—62no—
455#204—62no—
456D3×C8—62no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—84no—
468C2×C3×D3—21no—
469C2×C3×D3—22no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8—91no—
500C2×M16—31no—
501C22×C8—91no—
502C4⋊Q8—31no—
503#124—91no—
504#123—61no—
505#123—61no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8D3211yescharacteristic
510#121—61no—
511#121—91no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—181no—
519#106—31no—
520C4⋊C8—91no—
521#103—31no—
522#103—31no—
523#103—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—61no—
533C23×C3D3×D411yescharacteristic
534C23×C3C2×#6711yescharacteristic
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—124no—
547C22×D3—242no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3—242no—
551C22×D3C2×#6711yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—61no—
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×D4—32no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—121no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—122no—
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—41no—
597#67—42no—
598#67—122no—
599#67—241no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605C2×Dic3C2×#6711yescharacteristic
606D12—21no—
607D12—32no—
608D12—32no—
609D12—42no—
610D12—62no—
611D12—62no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—121no—
619D12—121no—
620D12—122no—
621D12—122no—
622D12—124no—
623D12—122no—
624D12—241no—
625D12D3×D412yes—
626C4×D3—21no—
627C4×D3—21no—
628C4×D3—42no—
629C4×D3—42no—
630C4×D3—42no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3—241no—
634C4×D3—241no—
635Dic6—21no—
636Dic6—21no—
637Dic6—21no—
638Dic6—21no—
639C3×C8—32no—
640C3×C8—61no—
641C3⋊C8—21no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—121no—
647C3⋊C8—121no—
648C3⋊C8D3×D412yes—
649C2×C32—41no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57711yescharacteristic
653C3⋊D3—42no—
654C3⋊D3—81no—
655C3×D3—41no—
656C3×D3—42no—
657C24—181no—
658#41—62no—
659#41—62no—
660#41—121no—
661#41—121no—
662#41—182no—
663#41—361no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8C2×D3211yescharacteristic
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—182no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—181no—
677C2×D4—361no—
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—181no—
683C22×C4—181no—
684C22×C4C2×D3211yescharacteristic
685Q16—62no—
686Q16—361no—
687SD16—182no—
688SD16—182no—
689SD16—182no—
690SD16—182no—
691SD16—361no—
692D8—94no—
693D8—182no—
694M16—62no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—91no—
698C2×C8—91no—
699C2×C8—182no—
700C4⋊C4—21no—
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4C2×D3211yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—31no—
710C22⋊C4—31no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C42—31no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—62no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C22×#6711yescharacteristic
737C2×D3—21no—
738C2×D3—22no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—122no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—122no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3—248no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—81no—
777C3×C4—81no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4—121no—
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4#100411yescharacteristic
784C3×C4#100911yescharacteristic
785Dic3—21no—
786Dic3—21no—
787Dic3—21no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791C32#326711yescharacteristic, complemented, Sylow
792C23—31no—
793C23—61no—
794C23—181no—
795C23—181no—
796C23—362no—
797C23—362no—
798C23—721no—
799C23D3×#6711yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—61no—
803Q8—61no—
804Q8—61no—
805Q8—61no—
806D4—32no—
807D4—61no—
808D4—92no—
809D4—122no—
810D4—121no—
811D4—122no—
812D4—181no—
813D4—181no—
814D4—181no—
815D4—362no—
816D4—362no—
817D4—721no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—31no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—122no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—362no—
834C2×C4—721no—
835C2×C4D3×#6711yescharacteristic
836C2×C4C22×D3211yescharacteristic
837C8—32no—
838C8—61no—
839C8—181no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—41no—
846C2×C3—41no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3#560911yescharacteristic
850C2×C3#577711yescharacteristic
851C2×C3#577811yescharacteristic
852C2×C3D4×#6711yescharacteristic
853C2×C3#582211yescharacteristic
854C2×C3#583711yescharacteristic
855D3—41no—
856D3—42no—
857D3—122no—
858D3—122no—
859D3—242no—
860D3—242no—
861D3—241no—
862D3—241no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—61no—
867C22—61no—
868C22—62no—
869C22—61no—
870C22—121no—
871C22—121no—
872C22—182no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22—361no—
877C22—361no—
878C22—724no—
879C22C2×D3×#6711yescharacteristic
880C4—21no—
881C4—41no—
882C4—41no—
883C4—61no—
884C4—61no—
885C4—61no—
886C4—121no—
887C4—121no—
888C4—121no—
889C4D32×D411yescharacteristic
890C4#6431411yescharacteristic
891C3—21no—
892C3#8092111yescharacteristic, complemented
893C3#8352211yescharacteristic, complemented
894C2—41no—
895C2—121no—
896C2—122no—
897C2—362no—
898C2—721no—
899C2#1059529111yescharacteristic
900C2#1059531911yescharacteristic
901C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5631C2semidirect
2. C2×#63949C2semidirect
3. #10595018C2semidirect
4. C2×#63825C2semidirect
5. #10592745C2semidirect
6. C3×#5052C2semidirect
7. #10591608C2semidirect
8. #10591588C2semidirect
9. #10591565C2semidirect
10. #10591170C2semidirect
11. #10591147C2semidirect
12. #10590616C2semidirect
13. #10590589C2semidirect
14. #10590577C2semidirect
15. #10590534C2semidirect
19. C2×C3×#239C22semidirect
25. C3×#944C22semidirect
26. C2×C3×#216C22semidirect
30. C3×#897C22semidirect
32. C3×#893C22semidirect
44. C2×#3718C22semidirect
47. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. C3×#835C22semidirect
56. C3×#810C22semidirect
57. C3×#808C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. #5631D3semidirect
78. #5052D3semidirect
154. #3714D4semidirect
160. C2×#239C2×D3semidirect
183. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
212. #897C2×D3semidirect
219. #893C2×D3semidirect
233. #835C2×D3semidirect
243. #810C2×D3semidirect
251. #808C2×D3semidirect
791. C32#3267semidirect
892. C3#80921semidirect
893. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C2×#639492
#105950182
C2×#638252
#105927452
C3×#50522
#105916082
#105915882
#105915652
#105911702
#105911472
#105906162
#105905892
#105905772
#105905342
#835223
#809213