Finite Group Databasebeta

← #11775219

Subgroups — #11775219

Order 1152.

654 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 59 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#10595081C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic, complemented
3#10591074C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3811—21no—
7C2×#3802C411yescharacteristic, complemented
8C2×C22⋊#157—21no—
9C2×C4×#157—21no—
10C3×#930—21no—
11C2×C3×#208—21no—
12#63980C412yescomplemented
13#63921—21no—
14#63916—21no—
15#63912C2212yes—
16#63900C411yescharacteristic, complemented
17#63781C2212yescomplemented
18#63557—21no—
19#63557C2212yescomplemented
20D3×#121—61no—
21#5126—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×D32—21no—
24C22×#157—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3—42no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×#67—22no—
33C2×C3×D12—21no—
34#3811—44no—
35C2×#626—22no—
36C2×#625C2×C412yes—
37C2×#624—21no—
38#3802—42no—
39C22⋊#157—24no—
40C4×#157—42no—
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C3×#208—42no—
44C2×C3×C3⋊C8—22no—
45#3724C2×C412yes—
46(C2×D3)⋊Dic3—22no—
47#1507—91nomaximal, Sylow
48C2×D3×D4—61no—
49C2×D3×D4—62no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C2×C3×M16—61no—
53C3×#121—61no—
54#939—62no—
55#938—61no—
56#930—21no—
57C2×#208—21no—
58#895—61no—
59D3×C4⋊C4—61no—
60#884—62no—
61D3×C22⋊C4—62no—
62(C2×D3)⋊C8—62no—
63(C2×D3)⋊C8—62no—
64C23×C32C22⋊C411yescharacteristic
65C22×C3⋊D3—22no—
66C22×C3⋊D3—22no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C2×D411yescharacteristic
70C22×C3×D3—22no—
71C2×D32—42no—
72C2×D32—42no—
73C2×D32—42no—
74C2×#157—24no—
75C2×#157—42no—
76C2×#157—42no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C4×C3⋊D3—22no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3—41no—
87C3×#67—44no—
88C2×C3×Dic3—22no—
89C3×D12—42no—
90#626—44no—
91#625—42no—
92#624—42no—
93C3×C3⋊C8—42no—
94C2×#121—91no—
95#407—91no—
96C4×C22⋊C4—91no—
97#327—94no—
98C23×D3—61no—
99C23×D3—61no—
100C23×D3—62no—
101C2×C3×D4—61no—
102C2×C3×D4—62no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C2×#67—22no—
106C2×#67—62no—
107C2×#67—62no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110D3×D4—124no—
111D3×D4—128no—
112C2×D12—21no—
113C2×D12—62no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—124no—
124C2×C4×D3—122no—
125C2×C4×D3—122no—
126C3×M16—122no—
127C2×C3×C8—62no—
128C3×C4⋊C4—61no—
129C3×C22⋊C4—62no—
130#217—62no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—62no—
133C4⋊Dic3—21no—
134Dic3⋊C4—62no—
135#208—42no—
136C2×C3⋊C8—22no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—44no—
146C2×C3⋊D3#10412yes—
147C2×C3⋊D3AGL(1,ℤ/8)12yes—
148C2×C3×D3—42no—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151D32—84no—
152#157—44no—
153C32×C4—21no—
154C32×C4#9912yes—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3×Dic3—42no—
158C22×D4—91no—
159C22×D4—181no—
160C23×C4—91no—
161C2×M16—61no—
162#121—61no—
163#121—92no—
164#121—92no—
165#121—181no—
166C2×C4⋊C4—91no—
167C2×C22⋊C4—181no—
168C2×C22⋊C4—181no—
169C2×C42—181no—
170C22⋊C8—92no—
171C22⋊C8—181no—
172#95—92no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—62no—
176C22×D3—22no—
177C22×D3—61no—
178C22×D3—61no—
179C22×D3—61no—
180C22×D3—61no—
181C22×D3—64no—
182C22×D3—122no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—124no—
186C22×D3—124no—
187C22×D3—124no—
188C22×D3—122no—
189C22×D3—122no—
190C3×D4—122no—
191C3×D4—124no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—42no—
199C2×C3×C4—62no—
200#67—44no—
201#67—124no—
202#67—124no—
203C2×Dic3—22no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—122no—
209C2×Dic3—122no—
210D12—42no—
211D12—124no—
212C4×D3—64no—
213C4×D3—122no—
214C4×D3—122no—
215C4×D3—122no—
216C4×D3—124no—
217C4×D3—122no—
218C4×D3—121no—
219C4×D3—121no—
220C4×D3—121no—
221C4×D3—121no—
222C4×D3—122no—
223C3×C8—122no—
224C3⋊C8—42no—
225C2×C32—41no—
226C2×C32C2×#9911yescharacteristic
227C2×C32#41811yescharacteristic
228C2×C32C2×#10411yescharacteristic
229C3⋊D3—22no—
230C3⋊D3—22no—
231C3×D3—82no—
232C24—91no—
233C24—181no—
234C2×D4—62no—
235C2×D4—61no—
236C2×D4—92no—
237C2×D4—182no—
238C2×D4—362no—
239C2×D4—364no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—181no—
246C22×C4—182no—
247C22×C4—362no—
248C22×C4GO+(4,𝔽2)11yescharacteristic
249M16—122no—
250C2×C8—62no—
251C4⋊C4—61no—
252C4⋊C4—92no—
253C22⋊C4—62no—
254C22⋊C4—182no—
255C22⋊C4—184no—
256C42—362no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—122no—
266C22×C3—122no—
267C22×C3—122no—
268C2×D3—42no—
269C2×D3—42no—
270C2×D3—42no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—128no—
284C2×D3—128no—
285C2×D3—248no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—122no—
292Dic3—42no—
293Dic3—62no—
294Dic3—121no—
295Dic3—121no—
296Dic3—121no—
297C32#150711yescharacteristic, complemented, Sylow
298C23—62no—
299C23—91no—
300C23—91no—
301C23—182no—
302C23—182no—
303C23—361no—
304C23—362no—
305C23—362no—
306C23—362no—
307C23D32⋊C411yescharacteristic
308D4—124no—
309D4—122no—
310D4—364no—
311D4—362no—
312C2×C4—22no—
313C2×C4—62no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—184no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—362no—
322C2×C4—361no—
323C2×C4—362no—
324C2×C4—362no—
325C2×C4D32⋊C411yescharacteristic
326C2×C4C2×GO+(4,𝔽2)11yescharacteristic
327C8—122no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—42no—
335C2×C3—42no—
336C2×C3—242no—
337D3—64no—
338D3—82no—
339D3—122no—
340D3—122no—
341D3—122no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—92no—
346C22—92no—
347C22—122no—
348C22—122no—
349C22—122no—
350C22—181no—
351C22—181no—
352C22—181no—
353C22—181no—
354C22—364no—
355C22—724no—
356C22C2×D32⋊C411yescharacteristic
357C4—21no—
358C4—122no—
359C4—181no—
360C4—181no—
361C4—364no—
362C4#6373812yes—
363C3—21no—
364C3—21no—
365C2—41no—
366C2—182no—
367C2—182no—
368C2—242no—
369C2#1059331811yescharacteristic
370C2#1059332511yescharacteristic
371C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1507
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#157C2semidirect
3. #10591074C2semidirect
4. #10590033C2semidirect
7. C2×#3802C4semidirect
12. #63980C4semidirect
16. #63900C4semidirect
17. #63781C22semidirect
19. #63557C22semidirect
297. C32#1507semidirect

Maximal subgroups

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

subgroupindex
#105950812
C4×C22⋊#1572
#105910742
#105900332
#15079