Finite Group Databasebeta

← #11878937

Subgroups — #11878937

Order 1152.

1182 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 233 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
1#10596199C211yesmaximal, characteristic, complemented
2#10596196C211yesmaximal, characteristic
3C32×#494C211yesmaximal, characteristic, complemented
4#10592886C214yesmaximal, complemented
5#10592884C214yesmaximal, complemented
6#10592784C211yesmaximal, characteristic, complemented
7#10592778C211yesmaximal, characteristic, complemented
8#10592393C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81803—34nomaximal
11C2×#3832C2212yes—
12C2×C32×Q16C2214yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16#64155C2212yes—
17Q8×C3⋊Dic3C2212yes—
18C2×#3755C2214yes—
19#64106—21no—
20#64104—21no—
21#64104—21no—
22#64102—21no—
23#64102—21no—
24#64101—21no—
25#64099—21no—
26#64096—21no—
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×C4×C8C2211yescharacteristic
31#63662C2214yes—
32#63648C2214yes—
33#63647C2212yes—
34#63641C2212yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5728—34no—
37#5725—34no—
38C3×#494D314yescomplemented
39#5187—316no—
40#5185—316no—
41#5085—34no—
42#5079—34no—
43#4694—34no—
44#4685—34no—
45C2×C32×Q8C2312yes—
46C2×C32×Q8C2312yes—
47#3832—44no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×#634—21no—
57C32×Q16—44no—
58C2×C32×C8C2312yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C42C2311yescharacteristic
64#3755—44no—
65#3752—22no—
66#3752—22no—
67#3752—22no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—22no—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—22no—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77#3210—91noSylow
78C2×#239—38no—
79C2×C3×Q16C2×D3116yes—
80C3×C4⋊Q8C2×D314yes—
81C3×C4⋊Q8C2×D314yes—
82#947—38no—
83#946—38no—
84Q8×Dic3—38no—
85C2×#215—316no—
86#897—64no—
87#895—64no—
88#895—64no—
89#893—64no—
90#893—64no—
91#892—64no—
92#890—64no—
93#887—64no—
94#874—34no—
95C42×D3—34no—
96#869—34no—
97C3×C4×C8C2×D314yes—
98#835—316no—
99#821—316no—
100(C2×D3)⋊C8—38no—
101Dic3⋊C8—38no—
102C4×C3⋊C8—34no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3C2×D411yescharacteristic
105C32×Q8—24no—
106C32×Q8—24no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2411yescharacteristic
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C4⋊(C3⋊D3)—24no—
117C4⋊(C3⋊D3)—44no—
118C4⋊(C3⋊D3)—42no—
119C4⋊(C3⋊D3)—42no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—44no—
124#634—42no—
125C32×C8—22no—
126C3⋊(C3⋊C8)—22no—
127#533—91no—
128#532—91no—
129#494C3⋊D311yescharacteristic, complemented
130#492—91no—
131#487—91no—
132#486—91no—
133#464—94no—
134#452—94no—
135#431—91no—
136C2×C3×Q8C22×D318yes—
137C2×C3×Q8C22×D318yes—
138#239—1216no—
139C2×D12—38no—
140C2×D12—68no—
141C2×D12—64no—
142C2×D12—64no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—68no—
147C2×Dic6—64no—
148C3×Q16—416no—
149C2×C3×C8C22×D318yes—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4—24no—
153C3×C4⋊C4—24no—
154C3×C42C22×D314yes—
155#215—1216no—
156(C2×D3)⋊C4—68no—
157(C2×D3)⋊C4—68no—
158(C2×D3)⋊C4—68no—
159C4⋊Dic3—38no—
160C4⋊Dic3—68no—
161C4⋊Dic3—64no—
162Dic3⋊C4—68no—
163C4×Dic3—34no—
164C4×Dic3—34no—
165C4×Dic3—34no—
166C4×Dic3—68no—
167C2×C3⋊C8—38no—
168C22×C32C22×D411yescharacteristic
169C2×C3⋊D3—21no—
170C2×C3⋊D3—21no—
171C2×C3⋊D3—21no—
172C2×C3⋊D3—42no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C32×C4—42no—
176C32×C4—42no—
177C32×C4#13512yes—
178C32×C4#13712yes—
179C32×C4H(5,𝔽2)12yes—
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3—42no—
184C2×#41—92no—
185C2×Q16C2×C3⋊D314yes—
186C2×SD16—94no—
187C4⋊Q8—91no—
188C4⋊Q8C2×C3⋊D311yescharacteristic
189C4⋊Q8C2×C3⋊D311yescharacteristic
190#127—91no—
191#125—181no—
192#124—92no—
193C22⋊Q8—92no—
194C22⋊Q8—181no—
195#121—181no—
196#121—181no—
197C4×Q8—92no—
198C4×Q8—181no—
199C4×D4—181no—
200C4×D4—181no—
201#117—181no—
202C2×C42—91no—
203C4⋊C8—92no—
204#103—94no—
205#102—94no—
206C22⋊C8—92no—
207C4×C8—91no—
208C4×C8C2×C3⋊D311yescharacteristic
209C22×D3—34no—
210C22×D3—68no—
211C3×Q8—216no—
212C3×Q8—216no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4D3×D414yes—
216C2×C3×C4D3×D414yes—
217C2×C3×C4C23×D314yes—
218C2×Dic3—34no—
219C2×Dic3—34no—
220C2×Dic3—34no—
221C2×Dic3—68no—
222D12—616no—
223D12—1216no—
224D12—128no—
225D12—128no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—68no—
229C4×D3—1216no—
230Dic6—128no—
231C3×C8—28no—
232C3⋊C8—68no—
233C2×C32#53511yescharacteristic
234C2×C32C2×#13511yescharacteristic
235C2×C32C2×#13711yescharacteristic
236C3⋊D3—41no—
237C3⋊D3—82no—
238#41—364no—
239C2×Q8—181no—
240C2×Q8C22×C3⋊D312yes—
241C2×Q8C22×C3⋊D312yes—
242C2×D4—92no—
243C2×D4—182no—
244C2×D4—181no—
245C2×D4—181no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—182no—
250Q16—44no—
251SD16—364no—
252C2×C8—92no—
253C2×C8C22×C3⋊D312yes—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—92no—
259C4⋊C4—182no—
260C4⋊C4—182no—
261C4⋊C4—181no—
262C22⋊C4—182no—
263C22⋊C4—182no—
264C22⋊C4—182no—
265C42—91no—
266C42—91no—
267C42—91no—
268C42—182no—
269C42C22×C3⋊D311yescharacteristic
270C22×C3C2×D3×D414yes—
271C2×D3—64no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—128no—
275C2×D3—128no—
276C2×D3—128no—
277C3×C4—48no—
278C3×C4—48no—
279C3×C4#91818yes—
280C3×C4#91918yes—
281C3×C4#100418yes—
282Dic3—64no—
283Dic3—64no—
284Dic3—64no—
285Dic3—128no—
286C32#321011yescharacteristic, complemented, Sylow
287C23—91no—
288C23—182no—
289Q8—24no—
290Q8—24no—
291Q8—362no—
292D4—184no—
293D4—364no—
294D4—362no—
295D4—362no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—364no—
306C2×C4D4×C3⋊D311yescharacteristic
307C2×C4D4×C3⋊D311yescharacteristic
308C2×C4C23×C3⋊D311yescharacteristic
309C8—22no—
310C8—182no—
311C2×C3#571514yes—
312C2×C3C2×#91814yes—
313C2×C3C2×#91914yes—
314D3—124no—
315D3—248no—
316C22—181no—
317C22—181no—
318C22—181no—
319C22—362no—
320C22—362no—
321C22—362no—
322C22C2×D4×C3⋊D311yescharacteristic
323C4—42no—
324C4—42no—
325C4—181no—
326C4—181no—
327C4—181no—
328C4—362no—
329C4#6412712yes—
330C4#6412812yes—
331C4#6436112yes—
332C3#8180314yescomplemented
333C2—361no—
334C2—722no—
335C2#1059618611yescharacteristic
336C2C2×#6412711yescharacteristic
337C2C2×#6412811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#494C2
socleC22×C32C22×D4
prime radical#10596196C2
hypercenter#494C3⋊D3
hypocenterC32#3210
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#494C2semidirect
4. #10592886C2semidirect
5. #10592884C2semidirect
6. #10592784C2semidirect
7. #10592778C2semidirect
8. #10592393C2semidirect
9. #10592384C2semidirect
38. C3×#494D3semidirect
129. #494C3⋊D3semidirect
286. C32#3210semidirect
332. C3#81803semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105961962
C32×#4942
#105928862
#105928842
#105927842
#105927782
#105923932
#105923842
#818033