Finite Group Databasebeta

← #11859337

Subgroups — #11859337

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic, complemented
2#10595076C211yesmaximal, characteristic
3C2×D32×C8C211yesmaximal, characteristic, complemented
4C3×C8×#67C212yesmaximal, complemented
5#10591153C211yesmaximal, characteristic, complemented
6#10591151C212yesmaximal, complemented
7#10590937C211yesmaximal, characteristic, complemented
8#10590907C212yesmaximal, complemented
9C8×#626C212yesmaximal, complemented
10#10590702C211yesmaximal, characteristic, complemented
11#10590700C211yesmaximal, characteristic, complemented
12#79421—32nomaximal
13C2×#3828C2211yescharacteristic
14C2×C4×D32C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic, complemented
16C2×#3748C2211yescharacteristic, complemented
17#64110—24no—
18C2×#3743C2211yescharacteristic
19C2×#3743C2211yescharacteristic, complemented
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C3×C4×#67C2212yes—
23C2×C3×D3×C8C2212yes—
24#63983C411yescharacteristic
25#63975C411yescharacteristic
26#63971C412yes—
27#63923C411yescharacteristic
28C4×#626C2212yes—
29#63897C411yescharacteristic
30#63896C412yes—
31#63874C2211yescharacteristic
32C2×#3712C2211yescharacteristic
33C2×#3710C2211yescharacteristic
34C2×D3×C3⋊C8C2212yes—
35D32×C8—24no—
36C3×#830C2212yescomplemented
37C3×(C2×D3)⋊C8C2212yes—
38C3×Dic3⋊C8C2212yescomplemented
39C3×C8×Dic3C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63557C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yes—
43#63554C2212yescomplemented
44C2×#901—32no—
45C2×#901—61no—
46C22×D3×C8—32no—
47#5547—32no—
48C3×C8×D4—32no—
49C8×#67—32no—
50C8×#67D312yescomplemented
51#5011—32no—
52#4839—32no—
53#4836—32no—
54#4730—32no—
55#4728—32no—
56#4727—32no—
57#4726—32no—
58#4689—32no—
59C8×D12—32no—
60C22×D32C2×C411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C2×#638C2×C411yescharacteristic
63C2×#638C2×C411yescharacteristic
64#3828—22no—
65#3828—22no—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×#634C2×C411yescharacteristic
70C2×C3×#67C2×C412yes—
71C2×C3×C4×D3C2312yes—
72C2×#626C2×C412yes—
73C2×#624C2×C411yescharacteristic
74C2×D3×Dic3C2×C412yes—
75C4×D32—22no—
76C4×D32—22no—
77C2×C32×C8—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80#3748—22no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3743—22no—
84#3743—22no—
85C8×C3⋊D3—22no—
86C8×C3⋊D3D414yescomplemented
87C3×#217C2×C412yes—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×Dic3⋊C4C2×C412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×D3×C8—24no—
94#3724C2×C412yes—
95Dic3⋊Dic3C2×C412yes—
96#3722C2×C411yescharacteristic
97#3722C2×C411yescharacteristic
98#3722C2×C412yes—
99(C2×D3)⋊Dic3C2×C412yes—
100#3712—22no—
101#3710—22no—
102D3×C3⋊C8—24no—
103#2929—91noSylow
104C2×#235—32no—
105C2×#235—61no—
106C22×C4×D3—32no—
107C22×C3×C8—21no—
108C22×C3×C8—32no—
109C22×C3×C8C2×D312yescomplemented
110C3×C4×D4—32no—
111#939—32no—
112#937—32no—
113C4×#67—32no—
114C4×#67C2×D312yes—
115C2×#208—32no—
116C2×#208—61no—
117C22×C3⋊C8—32no—
118#901—68no—
119#901—68no—
120C2×ΓL(1,𝔽25)—32no—
121C2×ΓL(1,𝔽25)—32no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—61no—
124C2×ΓL(1,𝔽25)—61no—
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—61no—
130C2×D3×C8—61no—
131C2×D3×C8—68no—
132C2×D3×C8C2×D312yes—
133#896—32no—
134#894—32no—
135#884—32no—
136#883—32no—
137#882—32no—
138#878—32no—
139C4×D12—32no—
140#872—32no—
141C3×C4⋊C8—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144C3×C4×C8—32no—
145#830—32no—
146#830C2×D312yescomplemented
147(C2×D3)⋊C8—32no—
148(C2×D3)⋊C8—32no—
149(C2×D3)⋊C8—32no—
150(C2×D3)⋊C8C2×D312yes—
151#815—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8C2×D312yescomplemented
154C8×Dic3C2×D312yescomplemented
155C4⋊(C3⋊C8)—32no—
156#803—32no—
157C23×C32C22×C411yescharacteristic
158C22×C3⋊D3C22×C411yescharacteristic
159C22×C3⋊D3C22×C411yescharacteristic
160C22×C3×D3C22×C412yes—
161C2×D32—22no—
162C2×D32—24no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167#638—22no—
168#638—22no—
169C2×C3⋊Dic3C22×C411yescharacteristic
170C2×C3⋊Dic3C22×C411yescharacteristic
171C4⋊(C3⋊D3)—22no—
172C4×C3⋊D3—21no—
173C4×C3⋊D3—21no—
174C4×C3⋊D3C2×D412yes—
175C4×C3⋊D3#4112yes—
176#634—22no—
177C3×#67—24no—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183#626—24no—
184#624—22no—
185D3×Dic3—24no—
186C32×C8—21no—
187C32×C8C2×D412yes—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)C2×D412yes—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—22no—
192C2×#131—91no—
193C23×C8—91no—
194#525—91no—
195#435—92no—
196#435—92no—
197C8×D4—32no—
198C8×D4—92no—
199#424—91no—
200#408—91no—
201#407—91no—
202#405—91no—
203C23×D3—32no—
204C2×C3×D4—32no—
205C22×C3×C4—21no—
206C22×C3×C4—32no—
207C22×C3×C4C22×D312yes—
208C2×#67—32no—
209C2×#67—32no—
210C2×#67—32no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67C4×D312yes—
214C22×Dic3—32no—
215#235—64no—
216#235—64no—
217#235—64no—
218#235—64no—
219C2×D12—32no—
220C2×D12—32no—
221C2×D12—61no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3C22×D312yes—
231C2×Dic6—32no—
232C2×Dic6—61no—
233C2×C3×C8—24no—
234C2×C3×C8—24no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8—32no—
239C2×C3×C8—64no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C22×D312yes—
242C3×C4⋊C4—32no—
243C3×C22⋊C4—32no—
244C3×C22⋊C4—32no—
245C3×C42—32no—
246#217—32no—
247#217C4×D312yes—
248(C2×D3)⋊C4—32no—
249(C2×D3)⋊C4—32no—
250(C2×D3)⋊C4—32no—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253(C2×D3)⋊C4C4×D312yes—
254C4⋊Dic3—32no—
255Dic3⋊C4—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4C4×D312yes—
259C4×Dic3C22×D312yes—
260#208—64no—
261#208—64no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269ΓL(1,𝔽25)—64no—
270ΓL(1,𝔽25)—64no—
271ΓL(1,𝔽25)—64no—
272ΓL(1,𝔽25)—64no—
273ΓL(1,𝔽25)—64no—
274D3×C8—24no—
275D3×C8—38no—
276D3×C8—64no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—64no—
280D3×C8—64no—
281C22×C32—21no—
282C22×C32—22no—
283C22×C32C23×C411yescharacteristic
284C2×C3⋊D3—21no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3C4×D412yes—
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3#13114yescomplemented
291D32—28no—
292C32×C4—21no—
293C32×C4C22×D411yescharacteristic
294C32×C4C2×#4111yescharacteristic
295C3⋊Dic3—21no—
296C3⋊Dic3C4×D412yes—
297C3×Dic3—22no—
298C3×Dic3—22no—
299C3×Dic3—22no—
300C2×#41—91no—
301C23×C4—91no—
302#131—184no—
303C2×M16—91no—
304C2×M16—91no—
305C2×M16—91no—
306C2×M16—91no—
307C22×C8—32no—
308C22×C8—91no—
309C22×C8—92no—
310C22×C8—91no—
311C22×C8—91no—
312C22×C8—184no—
313C22×C8D3211yescharacteristic, complemented
314#123—91no—
315#123—91no—
316C22⋊Q8—92no—
317#121—92no—
318#120—91no—
319#120—91no—
320C4×D4—32no—
321C4×D4—92no—
322#117—91no—
323C4⋊C8—32no—
324C4⋊C8—92no—
325C22⋊C8—32no—
326C22⋊C8—32no—
327C22⋊C8—92no—
328C22⋊C8—92no—
329#97—92no—
330C4×C8—32no—
331C23×C3—21no—
332C23×C3—32no—
333C23×C3C2×C4×D312yes—
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—64no—
341C22×D3C2×C4×D312yes—
342C3×D4—64no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C23×D312yes—
356#67—24no—
357#67—64no—
358#67—64no—
359#67—64no—
360#67—64no—
361#67—64no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—64no—
367C2×Dic3C2×C4×D312yes—
368C2×Dic3C2×C4×D312yes—
369C2×Dic3C2×C4×D312yes—
370D12—64no—
371D12—64no—
372D12—64no—
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—34no—
376C4×D3—34no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385Dic6—64no—
386Dic6—64no—
387C3×C8—22no—
388C3×C8—22no—
389C3×C8—22no—
390C3×C8—62no—
391C3×C8—62no—
392C3×C8D3×D414yes—
393C3⋊C8—22no—
394C3⋊C8—22no—
395C3⋊C8—34no—
396C3⋊C8—62no—
397C3⋊C8—62no—
398C3⋊C8—62no—
399C2×C32—41no—
400C2×C32C2×C4×D411yescharacteristic
401C2×C32C2×#13112yes—
402C3⋊D3—22no—
403C3⋊D3—41no—
404C3×D3—24no—
405C24—91no—
406#41—182no—
407#41—182no—
408C2×Q8—91no—
409C2×D4—32no—
410C2×D4—92no—
411C2×D4—91no—
412C2×D4—91no—
413C2×D4—91no—
414C22×C4—32no—
415C22×C4—91no—
416C22×C4—92no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4C2×D3211yescharacteristic
422M16—182no—
423M16—182no—
424M16—182no—
425M16—182no—
426C2×C8—22no—
427C2×C8—32no—
428C2×C8—32no—
429C2×C8—64no—
430C2×C8—91no—
431C2×C8—94no—
432C2×C8—91no—
433C2×C8—182no—
434C2×C8—184no—
435C2×C8—182no—
436C2×C8C2×D3211yescharacteristic
437C2×C8C2×D3211yescharacteristic
438C4⋊C4—32no—
439C4⋊C4—92no—
440C4⋊C4—92no—
441C22⋊C4—32no—
442C22⋊C4—32no—
443C22⋊C4—91no—
444C22⋊C4—91no—
445C22⋊C4—92no—
446C22⋊C4—92no—
447C42—32no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—34no—
454C22×C3—42no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3C22×C4×D312yes—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—34no—
461C2×D3—62no—
462C2×D3—616no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3#90114yescomplemented
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—62no—
477C3×C4—62no—
478C3×C4—62no—
479C3×C4C2×D3×D412yes—
480C3×C4D3×#4112yes—
481Dic3—22no—
482Dic3—22no—
483Dic3—22no—
484Dic3—34no—
485Dic3—62no—
486Dic3—62no—
487Dic3—62no—
488C32#292911yescharacteristic, complemented, Sylow
489C23—32no—
490C23—91no—
491C23—91no—
492C23—184no—
493C23—182no—
494C23C4×D3211yescharacteristic
495Q8—182no—
496D4—64no—
497D4—182no—
498D4—184no—
499D4—182no—
500D4—182no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—32no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—91no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—91no—
512C2×C4—182no—
513C2×C4—184no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4C4×D3211yescharacteristic
517C2×C4C22×D3211yescharacteristic
518C8—21no—
519C8—62no—
520C8—62no—
521C8—92no—
522C8—181no—
523C8#381112yes—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3—42no—
527C2×C3—42no—
528C2×C3—64no—
529C2×C3C4×D3×D412yes—
530C2×C3C2×#90112yes—
531C2×C3D3×#13112yes—
532D3—24no—
533D3—64no—
534D3—122no—
535D3—122no—
536D3—122no—
537C22—22no—
538C22—21no—
539C22—34no—
540C22—62no—
541C22—62no—
542C22—92no—
543C22—188no—
544C22—182no—
545C22—182no—
546C22—181no—
547C22C2×C4×D3211yescharacteristic
548C4—21no—
549C4—62no—
550C4—62no—
551C4—62no—
552C4—92no—
553C4—181no—
554C4#6430611yescharacteristic
555C4C2×#381111yescharacteristic
556C3—21no—
557C3#7942112yescomplemented
558C2—41no—
559C2—64no—
560C2—182no—
561C2—361no—
562C2D3×#90112yes—
563C2C4×#381111yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595076C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64110C2semidirect
3. C2×D32×C8C2semidirect
4. C3×C8×#67C2semidirect
5. #10591153C2semidirect
6. #10591151C2semidirect
7. #10590937C2semidirect
8. #10590907C2semidirect
9. C8×#626C2semidirect
10. #10590702C2semidirect
11. #10590700C2semidirect
15. C22×C32×C8C22semidirect
16. C2×#3748C22semidirect
19. C2×#3743C22semidirect
21. C2×C8×C3⋊D3C22semidirect
36. C3×#830C22semidirect
38. C3×Dic3⋊C8C22semidirect
39. C3×C8×Dic3C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
41. #63557C22semidirect
43. #63554C22semidirect
50. C8×#67D3semidirect
86. C8×C3⋊D3D4semidirect
109. C22×C3×C8C2×D3semidirect
146. #830C2×D3semidirect
153. Dic3⋊C8C2×D3semidirect
154. C8×Dic3C2×D3semidirect
290. C2×C3×D3#131semidirect
313. C22×C8D32semidirect
471. C2×D3#901semidirect
488. C32#2929semidirect
557. C3#79421semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105950762
C2×D32×C82
C3×C8×#672
#105911532
#105911512
#105909372
#105909072
C8×#6262
#105907022
#105907002
#794213