Finite Group Databasebeta

← #11883989

Subgroups — #11883989

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595362C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4812C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591619C211yesmaximal, characteristic, complemented
10#10590945C211yesmaximal, characteristic, complemented
11#10590879C211yesmaximal, characteristic, complemented
12#10590738C211yesmaximal, characteristic, complemented
13#10590613C211yesmaximal, characteristic, complemented
14#10590590C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#80553—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3795C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#947C2211yescharacteristic, complemented
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34#63940—24no—
35#63923—21no—
36#63922—21no—
37#63916C2211yescharacteristic, complemented
38#63913—21no—
39#63912—21no—
40#63911C2211yescharacteristic
41#63906—21no—
42C4×#626C2211yescharacteristic
43#63896—21no—
44#63881—21no—
45#63844C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3710C2211yescharacteristic, complemented
51#63795—24no—
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×D3×SD16—31no—
65C2×#911—31no—
66C2×#908—31no—
67#5677—31no—
68#5633—31no—
69#5609—31no—
70D4×D12—31no—
71C3×#468—31no—
72C3×#463—31no—
73#5176—31no—
74#5169—31no—
75#5156—31no—
76#5127—31no—
77#5058—31no—
78#5046—31no—
79#5037—31no—
80#5018—31no—
81#4889—31no—
82#4883—31no—
83#4848—31no—
84#4836—31no—
85#4819D311yescharacteristic, complemented
86#4812D311yescharacteristic, complemented
87#4806—31no—
88#4806—31no—
89#4806—61no—
90#4781—31no—
91#4775—31no—
92#4773—31no—
93#4762—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97Q8×C3⋊D3—22no—
98Q8×C3⋊D3—41no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634—21no—
104C2×#634C2311yescharacteristic
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626D411yescharacteristic
116C2×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121D3×D12—22no—
122D3×D12—44no—
123D3×D12—41no—
124#3795—22no—
125#3795—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3755—41no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—22no—
132C3×#215—22no—
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24—22no—
145C3×ΓL(1,𝔽25)—22no—
146#3724—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3716—22no—
153#3716D414yescomplemented
154#3714—22no—
155#3713—41no—
156#3710—22no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—61no—
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×#235—31no—
167C22×D12—31no—
168C22×D12—61no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C2×C3×M16—31no—
173C3×#124—31no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×C4×D4—31no—
177#947C2×D311yescharacteristic, complemented
178#946C2×D311yescharacteristic, complemented
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—61no—
182C2×#215C2×D311yescharacteristic
183C2×#215C2×D311yescharacteristic, complemented
184#940—31no—
185#938—31no—
186#937—61no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192#930—61no—
193C4×#67—31no—
194D3×SD16—64no—
195D3×SD16—64no—
196#911—64no—
197#908—64no—
198C2×D24—31no—
199C2×D24C2×D311yescharacteristic
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208#896—61no—
209#895—31no—
210#895—31no—
211#895—31no—
212#895—61no—
213#895C2×D311yescharacteristic
214#893—61no—
215#893C2×D311yescharacteristic
216#887—31no—
217#885—61no—
218#885—61no—
219#884—61no—
220#884—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#878—61no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×#107—31no—
231C3×C4⋊C8—31no—
232C3×#103—21no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235C3×#102—31no—
236C3×#102—31no—
237#832—31no—
238#830—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—61no—
245#815—31no—
246Dic3⋊C8C2×D311yescharacteristic, complemented
247#810—31no—
248#810—31no—
249#810—61no—
250#809—31no—
251#809—31no—
252#809C2×D311yescharacteristic, complemented
253#807C2×D311yescharacteristic, complemented
254#803—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280#634—21no—
281#634—42no—
282#634C2×D412yescomplemented
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
302#625—42no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—31no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—21no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—31no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C22×Dic3—61no—
347D3×Q8—62no—
348D3×Q8—62no—
349D3×Q8—122no—
350D3×Q8—121no—
351D3×Q8—121no—
352D3×Q8—122no—
353#237—62no—
354#237—121no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—121no—
359D3×D4—124no—
360D3×D4—121no—
361D3×D4—121no—
362#235—62no—
363#235—121no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12—124no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—31no—
392C2×Dic6—31no—
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6—61no—
396C2×Dic6—121no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×D8—62no—
400C3×M16—62no—
401C2×C3×C8—21no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8C22×D311yescharacteristic
405C2×C3×C8C22×D311yescharacteristic
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C4⋊C4C22×D311yescharacteristic
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C42—31no—
417#217—31no—
418#217—61no—
419#215—22no—
420#215—22no—
421#215—121no—
422#215—121no—
423#215—122no—
424#214—34no—
425#214—62no—
426#213—62no—
427#213—121no—
428#213—121no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—121no—
441C4⋊Dic3—31no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—31no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3—61no—
448C4×Dic3—61no—
449C4×Dic3C22×D311yescharacteristic
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—22no—
456D24—62no—
457#204—34no—
458#204—62no—
459#204—62no—
460#204—62no—
461#204—122no—
462ΓL(1,𝔽25)—22no—
463D3×C8—62no—
464D3×C8—62no—
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484D32—84no—
485D32—84no—
486C32×C4—41no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—22no—
491C3⋊Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—91no—
515#124—31no—
516#124—181no—
517C22⋊Q8—31no—
518C22⋊Q8—181no—
519#121—31no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—31no—
532#103—91no—
533#103D3211yescharacteristic, complemented
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—31no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3D3×D411yescharacteristic
567C3×Q8—22no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—41no—
573C3×D4—32no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—62no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615C2×Dic3D3×D411yescharacteristic
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—42no—
622D12—62no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—242no—
635D12—241no—
636D12D3×D412yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—42no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—121no—
645C4×D3—121no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—122no—
649C4×D3—124no—
650Dic6—32no—
651Dic6—32no—
652Dic6—62no—
653Dic6—61no—
654Dic6—61no—
655Dic6—121no—
656Dic6—122no—
657Dic6—122no—
658Dic6—124no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—32no—
662C3×C8—41no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8D3×D412yescomplemented
669C2×C32D4211yescharacteristic
670C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
671C2×C32#57711yescharacteristic
672C3⋊D3—22no—
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—42no—
676C3×D3—81no—
677C3×D3—81no—
678C24—181no—
679C24—181no—
680#41—182no—
681#41—361no—
682C2×Q8—91no—
683C2×Q8—181no—
684C2×Q8—182no—
685C2×Q8—361no—
686C2×Q8C2×D3211yescharacteristic
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—182no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4—364no—
704C2×D4—361no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—91no—
708C22×C4—181no—
709C22×C4—181no—
710SD16—62no—
711SD16—62no—
712SD16—94no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—182no—
718D8—361no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—91no—
723C2×C8—182no—
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—181no—
729C4⋊C4C2×D3211yescharacteristic
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—91no—
736C22⋊C4—91no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—181no—
741C22×C3—21no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—22no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C2×D3—244no—
789C2×D3—244no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—42no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100911yescharacteristic
805C3×C4#100911yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—62no—
811Dic3—62no—
812Dic3—61no—
813Dic3—61no—
814Dic3—122no—
815Dic3—121no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—31no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—91no—
822C23—181no—
823C23—362no—
824C23—362no—
825C23—362no—
826C23—362no—
827C23—721no—
828C23—721no—
829Q8—21no—
830Q8—21no—
831Q8—92no—
832Q8—181no—
833Q8—362no—
834D4—32no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—61no—
840D4—122no—
841D4—182no—
842D4—181no—
843D4—181no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—721no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—91no—
860C2×C4—122no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—362no—
865C2×C4—362no—
866C2×C4C22×D3211yescharacteristic
867C8—21no—
868C8—32no—
869C8—61no—
870C8—181no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—121no—
875C2×C3—122no—
876C2×C3—241no—
877C2×C3—241no—
878C2×C3#560911yescharacteristic
879C2×C3#560911yescharacteristic
880C2×C3#577011yescharacteristic
881C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883C2×C3#577811yescharacteristic
884D3—42no—
885D3—41no—
886D3—62no—
887D3—62no—
888D3—81no—
889D3—81no—
890D3—122no—
891D3—241no—
892D3—241no—
893D3—481no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—62no—
898C22—92no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—181no—
908C22—181no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—724no—
913C22—724no—
914C22D32×D411yescharacteristic
915C4—41no—
916C4—41no—
917C4—61no—
918C4—61no—
919C4—61no—
920C4—121no—
921C4—181no—
922C4—182no—
923C4#6430811yescharacteristic
924C4D32×D411yescharacteristic
925C3—21no—
926C3#8055311yescharacteristic, complemented
927C3#8083411yescharacteristic, complemented
928C2—121no—
929C2—122no—
930C2—182no—
931C2—241no—
932C2—241no—
933C2—721no—
934C2#1059428411yescharacteristic
935C2#1059474011yescharacteristic
936C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3265
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. #10595362C2semidirect
2. C2×#63940C2semidirect
3. C2×#63795C2semidirect
4. #10594621C2semidirect
5. #10592505C2semidirect
6. C3×#4819C2semidirect
7. C3×#4812C2semidirect
8. #10591651C2semidirect
9. #10591619C2semidirect
10. #10590945C2semidirect
11. #10590879C2semidirect
12. #10590738C2semidirect
13. #10590613C2semidirect
14. #10590590C2semidirect
15. #10590509C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
22. C2×#3795C22semidirect
23. C2×#3755C22semidirect
24. C2×#3744C22semidirect
26. C3×#947C22semidirect
27. C3×#946C22semidirect
29. C2×C3×#215C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
37. #63916C22semidirect
45. #63844C22semidirect
47. C2×#3716C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3710C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. #63564C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
85. #4819D3semidirect
86. #4812D3semidirect
153. #3716D4semidirect
177. #947C2×D3semidirect
178. #946C2×D3semidirect
183. C2×#215C2×D3semidirect
205. C2×ΓL(1,𝔽25)C2×D3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
240. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
252. #809C2×D3semidirect
253. #807C2×D3semidirect
282. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
471. C2×C3⋊D3AGL(1,ℤ/8)semidirect
533. #103D32semidirect
668. C3⋊C8D3×D4semidirect
816. C32#3265semidirect
926. C3#80553semidirect
927. C3#80834semidirect

Maximal subgroups

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

subgroupindex
#105953622
C2×#639402
C2×#637952
#105946212
#105925052
C3×#48192
C3×#48122
#105916512
#105916192
#105909452
#105908792
#105907382
#105906132
#105905902
#105905092
#808343
#805533