Finite Group Databasebeta

← #11796085

Subgroups — #11796085

Order 1152.

581 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 581 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#131C211yesmaximal, characteristic
2#10590625C211yesmaximal, characteristic, complemented
3C2×#63542C211yesmaximal, characteristic, complemented
4C3×#4561C212yesmaximal, complemented
5#10589113C212yesmaximal, complemented
6D3×#350—32nomaximal
7#41×C3⋊D3C411yescharacteristic
8C32×#131C2211yescharacteristic
9#64157C411yescharacteristic
10#64116—21no—
11#64116C411yescharacteristic
12M16×C3⋊D3—21no—
13M16×C3⋊D3C411yescharacteristic
14#64110—21no—
15#64110C2211yescharacteristic
16C2×C8×C3⋊D3—21no—
17C2×C8×C3⋊D3C2211yescharacteristic
18C3×#812C2212yescomplemented
19C2×C3×C3⋊C16C2212yescomplemented
20#63544—21no—
21#63542—21no—
22#63542—21no—
23#63542—21no—
24D3×#131—32no—
25D3×#131—61no—
26D3×M32—32no—
27C2×D3×C16—32no—
28C3×#350—32no—
29#4561D312yescomplemented
30#4515—32no—
31#4508—32no—
32C32×#41C2×C411yescharacteristic
33#3832C811yescharacteristic
34Q8×C3⋊D3C811yescharacteristic
35#3830—21no—
36#3830C811yescharacteristic
37D4×C3⋊D3—21no—
38D4×C3⋊D3C811yescharacteristic
39#3828—21no—
40#3828C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C32×M16—21no—
44C32×M16C2×C411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8C2311yescharacteristic
47#3748—21no—
48#3748C2×C411yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51#3743—21no—
52#3743—21no—
53#3743—21no—
54C8×C3⋊D3—21no—
55C8×C3⋊D3—21no—
56C8×C3⋊D3—21no—
57C8×C3⋊D3D411yescharacteristic
58C8×C3⋊D3D411yescharacteristic
59C8×C3⋊D3D411yescharacteristic
60C8×C3⋊D3D411yescharacteristic
61C3×C3⋊C16—22no—
62C3×C3⋊C16—22no—
63C2×#350—91noSylow
64D3×#41—32no—
65D3×#41—61no—
66C3×#131—21no—
67C3×#131C2×D312yes—
68#948—32no—
69#948—61no—
70#907—32no—
71#907—61no—
72#907—62no—
73#907—62no—
74D3×M16—32no—
75D3×M16—61no—
76D3×M16—62no—
77D3×M16—62no—
78#901—32no—
79#901—61no—
80#901—62no—
81#901—62no—
82C2×D3×C8—32no—
83C2×D3×C8—61no—
84C2×D3×C8—62no—
85C2×D3×C8—62no—
86C3×M32—32no—
87C2×C3×C16—32no—
88#812C2×D312yescomplemented
89C2×C3⋊C16C2×D312yescomplemented
90#798—62no—
91D3×C16—62no—
92D3×C16—62no—
93D3×C16—62no—
94C22×C3⋊D3—21no—
95C22×C3⋊D3M1611yescharacteristic
96C32×Q8C2×C811yescharacteristic
97C32×D4—21no—
98C32×D4C2×C811yescharacteristic
99C2×C32×C4—21no—
100C2×C32×C4C22×C411yescharacteristic
101#638—21no—
102#638—21no—
103#638—21no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3M1611yescharacteristic
106C4⋊(C3⋊D3)—21no—
107C4⋊(C3⋊D3)C2×C811yescharacteristic
108C4×C3⋊D3—21no—
109C4×C3⋊D3—21no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3C22⋊C411yescharacteristic
112C4×C3⋊D3C22⋊C411yescharacteristic
113C4×C3⋊D3C2×C811yescharacteristic
114C4×C3⋊D3C2×C811yescharacteristic
115#634—21no—
116#634C2×C811yescharacteristic
117C32×C8—21no—
118C32×C8C2×D411yescharacteristic
119C32×C8C2×D411yescharacteristic
120C3⋊(C3⋊C8)—21no—
121C3⋊(C3⋊C8)C22⋊C411yescharacteristic
122C3⋊(C3⋊C8)C22⋊C411yescharacteristic
123C2×#131—91no—
124C2×M32—91no—
125C22×C16—91no—
126#350—32no—
127#350—92no—
128C3×#41—21no—
129C3×#41C4×D312yes—
130#239—32no—
131#239—61no—
132D3×Q8—32no—
133D3×Q8—61no—
134#237—32no—
135#237—61no—
136#237—62no—
137#237—62no—
138D3×D4—32no—
139D3×D4—61no—
140D3×D4—62no—
141D3×D4—62no—
142#235—32no—
143#235—61no—
144#235—62no—
145#235—62no—
146C2×C4×D3—32no—
147C2×C4×D3—61no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C3×M16—22no—
151C3×M16—22no—
152C3×M16—21no—
153C3×M16C4×D312yes—
154C2×C3×C8—22no—
155C2×C3×C8—22no—
156C2×C3×C8—21no—
157C2×C3×C8C22×D312yes—
158#208—32no—
159#208—61no—
160#208—62no—
161#208—62no—
162C2×C3⋊C8—32no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—62no—
166ΓL(1,𝔽25)—62no—
167ΓL(1,𝔽25)—62no—
168ΓL(1,𝔽25)—62no—
169ΓL(1,𝔽25)—62no—
170ΓL(1,𝔽25)—62no—
171ΓL(1,𝔽25)—62no—
172D3×C8—32no—
173D3×C8—32no—
174D3×C8—32no—
175D3×C8—32no—
176D3×C8—61no—
177D3×C8—61no—
178D3×C8—61no—
179D3×C8—61no—
180D3×C8—62no—
181D3×C8—62no—
182D3×C8—62no—
183D3×C8—62no—
184D3×C8—62no—
185D3×C8—62no—
186C3×C16—62no—
187C3×C16—62no—
188C3⋊C16—22no—
189C3⋊C16—22no—
190C22×C32—21no—
191C22×C32C2×M1611yescharacteristic
192C2×C3⋊D3—21no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3C22⋊C811yescharacteristic
196C2×C3⋊D3C22⋊C811yescharacteristic
197C32×C4—21no—
198C32×C4C2×C22⋊C411yescharacteristic
199C32×C4C22×C811yescharacteristic
200C3⋊Dic3—21no—
201C3⋊Dic3C22⋊C811yescharacteristic
202C3⋊Dic3C22⋊C811yescharacteristic
203C2×#41—91no—
204#131—91no—
205#131—91no—
206#131—91no—
207#131—181no—
208#131—181no—
209#131D3211yescharacteristic
210C2×M16—91no—
211C2×M16—181no—
212C22×C8—91no—
213C22×C8—181no—
214M32—32no—
215M32—181no—
216C2×C16—32no—
217C2×C16—181no—
218C2×C16—181no—
219C2×C16—181no—
220C22×D3—32no—
221C22×D3—61no—
222C22×D3—62no—
223C22×D3—62no—
224C3×Q8—21no—
225C3×Q8D3×C812yes—
226C3×D4—22no—
227C3×D4—22no—
228C3×D4—21no—
229C3×D4D3×C812yes—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4C2×C4×D312yes—
234#67—62no—
235#67—62no—
236#67—62no—
237#67—62no—
238#67—62no—
239#67—62no—
240C2×Dic3—32no—
241C2×Dic3—61no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244D12—32no—
245D12—61no—
246D12—62no—
247D12—62no—
248C4×D3—32no—
249C4×D3—32no—
250C4×D3—32no—
251C4×D3—32no—
252C4×D3—61no—
253C4×D3—61no—
254C4×D3—61no—
255C4×D3—61no—
256C4×D3—62no—
257C4×D3—62no—
258C4×D3—62no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—62no—
262Dic6—32no—
263Dic6—61no—
264Dic6—62no—
265Dic6—62no—
266C3×C8—22no—
267C3×C8—22no—
268C3×C8—21no—
269C3×C8—21no—
270C3×C8D3×D412yes—
271C3×C8D3×D412yes—
272C3⋊C8—32no—
273C3⋊C8—32no—
274C3⋊C8—61no—
275C3⋊C8—61no—
276C3⋊C8—62no—
277C3⋊C8—62no—
278C2×C32—21no—
279C2×C32—41no—
280C2×C32C2×C22⋊C811yescharacteristic
281C3⋊D3—21no—
282C3⋊D3—41no—
283C3⋊D3#35012yescomplemented
284#41—91no—
285#41—91no—
286#41—91no—
287#41—181no—
288#41—181no—
289#41#62411yescharacteristic
290C2×Q8—91no—
291C2×D4—91no—
292C2×D4—181no—
293C22×C4—91no—
294C22×C4—181no—
295M16—21no—
296M16—91no—
297M16—181no—
298M16—181no—
299M16—181no—
300M16—181no—
301M16#62411yescharacteristic
302C2×C8—21no—
303C2×C8—91no—
304C2×C8—91no—
305C2×C8—91no—
306C2×C8—91no—
307C2×C8—91no—
308C2×C8—181no—
309C2×C8—181no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8C2×D3211yescharacteristic
313C16—62no—
314C16—62no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3D3×M1612yes—
319C2×D3—32no—
320C2×D3—32no—
321C2×D3—61no—
322C2×D3—61no—
323C2×D3—64no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—122no—
327C2×D3—124no—
328C2×D3—124no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4D3×C22⋊C412yes—
334C3×C4C2×D3×C812yes—
335Dic3—32no—
336Dic3—32no—
337Dic3—61no—
338Dic3—61no—
339Dic3—62no—
340Dic3—62no—
341C32C2×#35011yescharacteristic, complemented, Sylow
342C23—91no—
343C23—181no—
344Q8—91no—
345Q8—181no—
346Q8#371011yescharacteristic
347D4—21no—
348D4—91no—
349D4—181no—
350D4—181no—
351D4—181no—
352D4—181no—
353D4#371011yescharacteristic
354C2×C4—21no—
355C2×C4—91no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4C2×#62411yescharacteristic
365C8—21no—
366C8—91no—
367C8—91no—
368C8—181no—
369C8#381111yescharacteristic
370C8#381111yescharacteristic
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—41no—
374C2×C3—42no—
375C2×C3—42no—
376C2×C3D3×C22⋊C812yes—
377D3—34no—
378D3—62no—
379D3—62no—
380D3—121no—
381D3—122no—
382D3—122no—
383C22—21no—
384C22—91no—
385C22—91no—
386C22—182no—
387C22—181no—
388C22—362no—
389C22#6381811yescharacteristic
390C4—21no—
391C4—91no—
392C4—91no—
393C4—181no—
394C4C2×#371011yescharacteristic
395C4#6397411yescharacteristic
396C3—21no—
397C3D3×#35012yescomplemented
398C2—21no—
399C2—41no—
400C2—92no—
401C2—181no—
402C2—361no—
403C2#1059115211yescharacteristic
subgroupG/H
centerC8#3811
commutatorC32×C4C22×C8
FrattiniC2×C8C2×D32
FittingC32×#131C22
socleC2×C32C2×C22⋊C8
prime radical#41×C3⋊D3C4
cosocleC2×C32×C8C23
hypercenter#131D32
hypocenterC32C2×#350
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
2. #10590625C2semidirect
3. C2×#63542C2semidirect
4. C3×#4561C2semidirect
5. #10589113C2semidirect
18. C3×#812C22semidirect
19. C2×C3×C3⋊C16C22semidirect
29. #4561D3semidirect
88. #812C2×D3semidirect
89. C2×C3⋊C16C2×D3semidirect
283. C3⋊D3#350semidirect
341. C32C2×#350semidirect
397. C3D3×#350semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1312
#105906252
C2×#635422
C3×#45612
#105891132
D3×#3503