Finite Group Databasebeta

← #11775309

Subgroups — #11775309

Order 1152.

648 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 57 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
2#10593803C211yesmaximal, characteristic, complemented
3#10591219C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3811—21no—
7C2×#3802C411yescharacteristic, complemented
8C2×#3788—21no—
9C3×#930—21no—
10#63980C2212yes—
11C2×#3722—21no—
12#63921—21no—
13#63916—21no—
14#63912C412yescomplemented
15#63900C411yescharacteristic, complemented
16C22⋊#622C2212yescomplemented
17#63778—21no—
18C3×C3⋊#95—21no—
19#63579C2212yescomplemented
20D3×#121—61no—
21#4664—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×D32—21no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C3×#67—22no—
32C22×C3×Dic3—22no—
33C2×C3×D12—21no—
34#3811—44no—
35C2×#626—22no—
36C2×#625C2×C412yes—
37C2×#624—21no—
38#3802—42no—
39C2×#622—22no—
40#3788—42no—
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43#3724C2×C412yes—
44#3722—42no—
45(C2×D3)⋊Dic3—22no—
46#1510—91nomaximal, Sylow
47C2×D3×D4—61no—
48C2×D3×D4—62no—
49C22×C4×D3—61no—
50C22×C4×D3—61no—
51C3×#121—61no—
52#939—62no—
53#938—61no—
54#930—21no—
55C2×(C2×D3)⋊C4—62no—
56#895—61no—
57D3×C4⋊C4—61no—
58#884—62no—
59D3×C22⋊C4—62no—
60C3×#95—61no—
61C3⋊#95—21no—
62C3⋊#95—62no—
63C23×C32C2×D411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3×D3—22no—
70C2×D32—42no—
71C2×D32—42no—
72C2×D32—42no—
73C2×C32×C4—41no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3C22×C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C3×#67—44no—
84C2×C3×Dic3—22no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C3×D12—42no—
89#626—44no—
90#625—42no—
91#624—42no—
92#622—42no—
93C2×#121—91no—
94#407—91no—
95#381—91no—
96#327—94no—
97C23×D3—61no—
98C23×D3—61no—
99C23×D3—62no—
100C2×C3×D4—61no—
101C2×C3×D4—62no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—62no—
105C2×#67—22no—
106C2×#67—62no—
107C2×#67—62no—
108C22×Dic3—22no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111D3×D4—124no—
112D3×D4—128no—
113C2×D12—21no—
114C2×D12—62no—
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—61no—
123C2×C4×D3—62no—
124C2×C4×D3—124no—
125C2×C4×D3—124no—
126C3×C4⋊C4—61no—
127C3×C22⋊C4—62no—
128#217—62no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—62no—
131(C2×D3)⋊C4—124no—
132C4⋊Dic3—21no—
133Dic3⋊C4—62no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32C2×C22⋊C411yescharacteristic
137C22×C32AGL(1,ℤ/8)12yes—
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—44no—
144C2×C3⋊D3#9912yes—
145C2×C3×D3—42no—
146C2×C3×D3—42no—
147C2×C3×D3—42no—
148D32—84no—
149C32×C4—21no—
150C32×C4—21no—
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3×Dic3—42no—
154C3×Dic3—82no—
155C22×D4—91no—
156C22×D4—181no—
157C23×C4—91no—
158C2×M16—181no—
159#121—61no—
160#121—92no—
161#121—92no—
162#121—181no—
163C2×C4⋊C4—91no—
164C2×C22⋊C4—181no—
165C2×C22⋊C4—181no—
166C22⋊C8—92no—
167C22⋊C8—181no—
168#95—61no—
169#95—92no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—62no—
173C22×D3—22no—
174C22×D3—61no—
175C22×D3—61no—
176C22×D3—61no—
177C22×D3—61no—
178C22×D3—64no—
179C22×D3—64no—
180C22×D3—122no—
181C22×D3—122no—
182C22×D3—124no—
183C22×D3—124no—
184C22×D3—124no—
185C22×D3—122no—
186C22×D3—121no—
187C22×D3—121no—
188C3×D4—122no—
189C3×D4—124no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4—62no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200#67—44no—
201#67—124no—
202#67—124no—
203C2×Dic3—22no—
204C2×Dic3—42no—
205C2×Dic3—42no—
206C2×Dic3—42no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213D12—42no—
214D12—124no—
215C4×D3—64no—
216C4×D3—122no—
217C4×D3—122no—
218C4×D3—122no—
219C4×D3—124no—
220C4×D3—122no—
221C4×D3—122no—
222C4×D3—122no—
223C4×D3—122no—
224C2×C32—22no—
225C2×C32C2×#9911yescharacteristic
226C2×C32#41811yescharacteristic
227C2×C32#42111yescharacteristic
228C3⋊D3—22no—
229C3⋊D3—41no—
230C3×D3—82no—
231C24—91no—
232C24—181no—
233C2×D4—62no—
234C2×D4—61no—
235C2×D4—92no—
236C2×D4—182no—
237C2×D4—362no—
238C2×D4—364no—
239C22×C4—62no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—181no—
246C22×C4—362no—
247C22×C4GO+(4,𝔽2)11yescharacteristic
248M16—362no—
249C2×C8—182no—
250C4⋊C4—61no—
251C4⋊C4—92no—
252C22⋊C4—62no—
253C22⋊C4—182no—
254C22⋊C4—362no—
255C22×C3—21no—
256C22×C3—22no—
257C22×C3—21no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—122no—
265C22×C3—122no—
266C22×C3—122no—
267C2×D3—42no—
268C2×D3—42no—
269C2×D3—42no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—128no—
283C2×D3—124no—
284C2×D3—124no—
285C2×D3—248no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—122no—
291C3×C4—242no—
292Dic3—42no—
293Dic3—62no—
294Dic3—82no—
295Dic3—121no—
296Dic3—121no—
297Dic3—121no—
298C32#151011yescharacteristic, complemented, Sylow
299C23—62no—
300C23—91no—
301C23—91no—
302C23—182no—
303C23—182no—
304C23—361no—
305C23—362no—
306C23—362no—
307C23—362no—
308C23C2×GO+(4,𝔽2)11yescharacteristic
309D4—122no—
310D4—124no—
311D4—364no—
312D4—362no—
313C2×C4—41no—
314C2×C4—62no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—182no—
321C2×C4—182no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4—362no—
325C2×C4—361no—
326C2×C4D32⋊C411yescharacteristic
327C2×C4D32⋊C411yescharacteristic
328C8—362no—
329C2×C3—22no—
330C2×C3—22no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—42no—
338C2×C3—242no—
339D3—64no—
340D3—82no—
341D3—122no—
342D3—122no—
343D3—122no—
344C22—21no—
345C22—21no—
346C22—92no—
347C22—122no—
348C22—122no—
349C22—122no—
350C22—181no—
351C22—181no—
352C22—181no—
353C22—181no—
354C22—181no—
355C22—364no—
356C22—724no—
357C22#6422412yes—
358C22C2×D32⋊C411yescharacteristic
359C4—21no—
360C4—21no—
361C4—122no—
362C4—181no—
363C4—181no—
364C4—242no—
365C3—21no—
366C3—21no—
367C2—22no—
368C2—182no—
369C2—242no—
370C2—361no—
371C2#1059336311yescharacteristic
372C2#1059338111yescharacteristic
373C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1510
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. #10593803C2semidirect
3. #10591219C2semidirect
4. #10590071C2semidirect
7. C2×#3802C4semidirect
14. #63912C4semidirect
15. #63900C4semidirect
16. C22⋊#622C22semidirect
19. #63579C22semidirect
298. C32#1510semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105938032
#105912192
#105900712
#15109