Finite Group Databasebeta

← #11884311

Subgroups — #11884311

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic, complemented
2C2×#63795C211yesmaximal, characteristic, complemented
3#10594629C211yesmaximal, characteristic, complemented
4#10594381C211yesmaximal, characteristic, complemented
5#10592563C211yesmaximal, characteristic, complemented
6C3×#4869C211yesmaximal, characteristic, complemented
7C3×#4867C211yesmaximal, characteristic, complemented
8#10590899C211yesmaximal, characteristic, complemented
9#10590736C211yesmaximal, characteristic, complemented
10#10590618C211yesmaximal, characteristic, complemented
11#10590617C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590559C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80921—31nomaximal
17#79879—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3796C2211yescharacteristic, complemented
21C2×#3795C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic, complemented
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63909—21no—
36#63906—21no—
37C4×#626C2211yescharacteristic
38#63891—21no—
39#63890—21no—
40#63890—21no—
41D3×C4⋊Dic3—21no—
42#63866C2211yescharacteristic, complemented
43#63864C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50#63810—24no—
51#63795—24no—
52C32×#106C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×#815C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×#919—31no—
64C2×#912—31no—
65C2×#911—31no—
66C2×#908—31no—
67#5631—31no—
68#5630—31no—
69#5555—31no—
70#5554—31no—
71C3×#470—31no—
72C3×#442—31no—
73#5190—31no—
74#5127—31no—
75#5047—31no—
76#5046—31no—
77#5019—31no—
78#5016—31no—
79#4869D311yescharacteristic, complemented
80#4867D311yescharacteristic, complemented
81#4864—31no—
82#4864—31no—
83#4864—61no—
84#4819—31no—
85#4818—31no—
86#4810—31no—
87#4808—31no—
88#4783—31no—
89#4783—31no—
90#4781—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116#3796—22no—
117#3796—22no—
118#3796—41no—
119#3796—41no—
120#3795—22no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3744—22no—
130C8×C3⋊D3—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—22no—
141C3×D24D414yescomplemented
142C3×ΓL(1,𝔽25)—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—41no—
151#3717—41no—
152#3716—22no—
153#3715—22no—
154#3715—22no—
155#3714—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×D8—31no—
167C2×C3×M16—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#947—31no—
173#944—31no—
174C2×#216—31no—
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178C2×#214—31no—
179C2×#214—31no—
180C2×#214—31no—
181C2×#213—31no—
182#930—61no—
183#930—61no—
184C4×#67—31no—
185C2×(C2×D3)⋊C4—61no—
186C2×C4⋊Dic3—61no—
187#919—64no—
188#912—64no—
189#911—64no—
190#908—64no—
191C2×Dic12—31no—
192C2×Dic12C2×D311yescharacteristic, complemented
193C2×D24—31no—
194C2×D24C2×D311yescharacteristic
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—61no—
200C2×ΓL(1,𝔽25)C2×D311yescharacteristic
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—61no—
204#897—31no—
205#897—31no—
206#897—61no—
207#897C2×D311yescharacteristic
208#897C2×D311yescharacteristic
209#895—31no—
210#895—31no—
211#895—61no—
212#895—61no—
213#894—61no—
214#894—61no—
215#893C2×D311yescharacteristic
216#893C2×D311yescharacteristic, complemented
217D3×C4⋊C4—61no—
218#886—61no—
219#886—61no—
220#886—61no—
221#884—61no—
222#883—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227C4×D12—31no—
228#869—31no—
229C3×#106—21no—
230C3×#106C2×D311yescharacteristic, complemented
231C3×#106C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#97—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#815C2×D311yescharacteristic, complemented
242Dic3⋊C8—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810C2×D311yescharacteristic, complemented
247#810C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic
252#809C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—81no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272#634—21no—
273#634—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×D12C2×D412yes—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×C4×D3—81no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—41no—
292#626—42no—
293#626—42no—
294#626—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
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—31no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C2×#67—31no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336#239—62no—
337#239—62no—
338#239—121no—
339#239—121no—
340#237—62no—
341#237—62no—
342#237—62no—
343#237—121no—
344#237—121no—
345#237—121no—
346D3×D4—62no—
347D3×D4—121no—
348#235—62no—
349#235—121no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—121no—
361C2×D12—121no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×D8—34no—
380C3×M16—62no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399#217—31no—
400#216—121no—
401#215—62no—
402#215—62no—
403#215—121no—
404#214—62no—
405#214—62no—
406#214—62no—
407#213—62no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
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—121no—
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⋊Dic3—121no—
433Dic3⋊C4—31no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436C4×Dic3C22×D311yescharacteristic
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—22no—
443Dic12—121no—
444D24—62no—
445D24D1214yescomplemented
446#204—62no—
447#204—62no—
448#204—62no—
449#204—122no—
450#204—121no—
451ΓL(1,𝔽25)—22no—
452D3×C8—62no—
453D3×C8—62no—
454D3×C8—122no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—91no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—31no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106D3211yescharacteristic, complemented
518C4⋊C8—91no—
519#103—31no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3D3×D411yescharacteristic
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—32no—
552C3×D4—61no—
553C3×D4—61no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—122no—
569C2×C3×C4—241no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—121no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—121no—
586C2×Dic3—122no—
587C2×Dic3—122no—
588C2×Dic3—122no—
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591C2×Dic3D3×D411yescharacteristic
592D12—21no—
593D12—21no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—121no—
599D12—121no—
600D12—121no—
601D12—122no—
602D12—122no—
603D12—122no—
604D12—241no—
605D12—241no—
606D12—242no—
607D12C2×D1212yes—
608D12C2×D1212yes—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—42no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—81no—
617C4×D3—121no—
618C4×D3—121no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622Dic6—21no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—22no—
633C3×C8—61no—
634C3×C8—61no—
635C3×C8C2×D1212yes—
636C3×C8D3×D412yes—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—41no—
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—42no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—91no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—91no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—361no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—182no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—91no—
706C22⋊C4—91no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C22×C3—21no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—21no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—62no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—81no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C22×D1211yescharacteristic
767C3×C4C2×D3×D411yescharacteristic
768C3×C4#100911yescharacteristic
769C3×C4#100911yescharacteristic
770Dic3—21no—
771Dic3—21no—
772Dic3—21no—
773Dic3—41no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—31no—
783C23—61no—
784C23—61no—
785C23—91no—
786C23—181no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—181no—
795Q8—181no—
796D4—32no—
797D4—32no—
798D4—61no—
799D4—61no—
800D4—181no—
801D4—181no—
802D4—361no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—91no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—241no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4—362no—
826C2×C4C22×D3211yescharacteristic
827C8—61no—
828C8—61no—
829C8—181no—
830C8D3×D1212yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—121no—
835C2×C3—122no—
836C2×C3—122no—
837C2×C3D4×D1211yescharacteristic
838C2×C3#560911yescharacteristic
839C2×C3#577311yescharacteristic
840C2×C3#577511yescharacteristic
841C2×C3#577711yescharacteristic
842C2×C3#577811yescharacteristic
843D3—42no—
844D3—42no—
845D3—41no—
846D3—122no—
847D3—121no—
848D3—121no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—61no—
853C22—62no—
854C22—62no—
855C22—61no—
856C22—61no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22D32×D411yescharacteristic
869C4—41no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—361no—
878C4C2×D3×D1211yescharacteristic
879C4#6432011yescharacteristic
880C3—21no—
881C3#7987911yescharacteristic, complemented
882C3#8092111yescharacteristic, complemented
883C2—121no—
884C2—122no—
885C2—122no—
886C2—361no—
887C2—721no—
888C2#1059462111yescharacteristic
889C2#1059474411yescharacteristic
890C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63810C2semidirect
2. C2×#63795C2semidirect
3. #10594629C2semidirect
4. #10594381C2semidirect
5. #10592563C2semidirect
6. C3×#4869C2semidirect
7. C3×#4867C2semidirect
8. #10590899C2semidirect
9. #10590736C2semidirect
10. #10590618C2semidirect
11. #10590617C2semidirect
12. #10590614C2semidirect
13. #10590596C2semidirect
14. #10590559C2semidirect
15. #10590534C2semidirect
20. C2×#3796C22semidirect
23. C2×C8×C3⋊D3C22semidirect
24. #64106C22semidirect
26. C2×C3×Dic12C22semidirect
32. C3×#893C22semidirect
42. #63866C22semidirect
44. C2×#3719C22semidirect
48. C2×#3715C22semidirect
52. C32×#106C22semidirect
53. #63637C22semidirect
55. C3×#815C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
59. C3×#809C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63557C22semidirect
79. #4869D3semidirect
80. #4867D3semidirect
141. C3×D24D4semidirect
192. C2×Dic12C2×D3semidirect
216. #893C2×D3semidirect
230. C3×#106C2×D3semidirect
231. C3×#106C2×D3semidirect
241. #815C2×D3semidirect
246. #810C2×D3semidirect
247. #810C2×D3semidirect
252. #809C2×D3semidirect
445. D24D12semidirect
517. #106D32semidirect
781. C32#3267semidirect
881. C3#79879semidirect
882. C3#80921semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C2×#637952
#105946292
#105943812
#105925632
C3×#48692
C3×#48672
#105908992
#105907362
#105906182
#105906172
#105906142
#105905962
#105905592
#105905342
#809213
#798793