Finite Group Databasebeta

← #11774630

Subgroups — #11774630

Order 1152.

456 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C4×#3798C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590032C212yesmaximal, complemented
5#10590029C212yesmaximal, complemented
6C2×#3798C411yescharacteristic
7C42×C3⋊D3C2211yescharacteristic
8C3×C42×D3—21no—
9C4×#627C411yescharacteristic
10C4×#627C2211yescharacteristic
11C4×#626—21no—
12C4×#626—21no—
13C4×#625C411yescharacteristic
14C4×#625C2211yescharacteristic
15#63874C411yescharacteristic
16#63855—21no—
17#63779—21no—
18#63778—21no—
19C4×#622C2212yes—
20C3×#803—21no—
21#63572C2212yes—
22#63557—21no—
23C4×#235—61no—
24#4705—61no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×C4×D3—21no—
29C2×C3×C4×D3—21no—
30C2×C3×C4×D3—21no—
31C2×#627C2×C411yescharacteristic
32C2×#626—21no—
33C2×#625C2×C411yescharacteristic
34#3798—22no—
35#3798—22no—
36C2×#622—22no—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3C2311yescharacteristic
41C3×C4×Dic3—21no—
42C3×C4×Dic3—21no—
43C3×C4×Dic3—21no—
44C2×C3×C3⋊C8—22no—
45#3724C2×C411yescharacteristic
46#3724C2×C411yescharacteristic
47Dic3⋊Dic3—21no—
48Dic3⋊Dic3—21no—
49#3722—21no—
50(C2×D3)⋊Dic3—21no—
51(C2×D3)⋊Dic3—21no—
52#1488—91nomaximal, Sylow
53C2×#235—61no—
54C2×C3×C42—61no—
55C4×#67—61no—
56C4×#67—61no—
57C4×#67—61no—
58C4×#67—61no—
59#926—61no—
60C4×D12—61no—
61C4×D12—61no—
62#872—61no—
63#872—61no—
64C42×D3—21no—
65C42×D3—61no—
66C42×D3—61no—
67C4×Dic6—61no—
68C4×Dic6—61no—
69C3×#97—61no—
70(C2×D3)⋊C8—62no—
71Dic3⋊C8—62no—
72#803—21no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3×D3—21no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22×C411yescharacteristic
80C2×C3⋊Dic3C2×D411yescharacteristic
81C4×C3⋊D3—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—41no—
85C2×C3×Dic3—21no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C3×C4×D3—24no—
89C3×C4×D3—42no—
90C3×C4×D3—42no—
91#627—21no—
92#627M1612yes—
93#626—24no—
94#625—21no—
95#625M1612yes—
96#622—42no—
97C3×C3⋊C8—42no—
98C4×#41—91no—
99#432—91no—
100#431—91no—
101Q8⋊C8—92no—
102D4⋊C8—92no—
103C22×C3×C4—61no—
104C22×C3×C4—61no—
105C22×C3×C4—61no—
106C2×#67—61no—
107C2×#67—61no—
108#235—64no—
109#235—64no—
110C2×D12—61no—
111C2×C4×D3—21no—
112C2×C4×D3—21no—
113C2×C4×D3—21no—
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×Dic6—61no—
121C2×C3×C8—62no—
122C3×C42—21no—
123C3×C42—21no—
124C3×C42—61no—
125C3×C42—61no—
126C3×C42—61no—
127#217—61no—
128#217—61no—
129(C2×D3)⋊C4—61no—
130(C2×D3)⋊C4—61no—
131(C2×D3)⋊C4—61no—
132(C2×D3)⋊C4—61no—
133C4⋊Dic3—61no—
134C4⋊Dic3—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139C4×Dic3—21no—
140C4×Dic3—21no—
141C4×Dic3—21no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C2×C3⋊C8—22no—
149C22×C32C2×C22⋊C411yescharacteristic
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3⋊D3—21no—
153C2×C3×D3—22no—
154C2×C3×D3—41no—
155C2×C3×D3—41no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4#13512yes—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3C2×M1611yescharacteristic
162C3⋊Dic3C2×M1611yescharacteristic
163C3×Dic3—22no—
164C3×Dic3—41no—
165C3×Dic3—41no—
166C2×#41—91no—
167C4×Q8—91no—
168C4×Q8—91no—
169C4×D4—91no—
170C4×D4—91no—
171C4×D4—181no—
172C4×D4—181no—
173#117—91no—
174#117—181no—
175C2×C42—61no—
176C2×C42—91no—
177C4⋊C8—92no—
178C4⋊C8—181no—
179C22⋊C8—181no—
180C22⋊C8—181no—
181#97—61no—
182C4×C8—92no—
183C23×C3—61no—
184C22×D3—21no—
185C22×D3—61no—
186C22×D3—61no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—64no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199#67—62no—
200#67—64no—
201#67—62no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211D12—64no—
212C4×D3—24no—
213C4×D3—42no—
214C4×D3—42no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—121no—
218C4×D3—121no—
219C4×D3—122no—
220C4×D3—122no—
221C4×D3—122no—
222C4×D3—122no—
223Dic6—62no—
224Dic6—62no—
225C3×C8—122no—
226C3⋊C8—42no—
227C2×C32#40711yescharacteristic
228C2×C32#41611yescharacteristic
229C2×C32#42111yescharacteristic
230C3⋊D3—41no—
231C3×D3—42no—
232#41—182no—
233#41—182no—
234C2×Q8—91no—
235C2×D4—91no—
236C2×D4—181no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C2×C8—62no—
244C2×C8—182no—
245C4⋊C4—91no—
246C4⋊C4—91no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C22⋊C4—181no—
250C22⋊C4—181no—
251C22⋊C4—181no—
252C42—61no—
253C42—61no—
254C42—61no—
255C42—91no—
256C42—91no—
257C42—91no—
258C42GO+(4,𝔽2)11yescharacteristic
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—62no—
262C22×C3—121no—
263C22×C3—121no—
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—121no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—62no—
280C3×C4—121no—
281C3×C4—121no—
282Dic3—22no—
283Dic3—41no—
284Dic3—41no—
285Dic3—61no—
286Dic3—61no—
287Dic3—61no—
288Dic3—61no—
289Dic3—121no—
290Dic3—121no—
291Dic3—121no—
292Dic3—121no—
293C32#148811yescharacteristic, complemented, Sylow
294C23—61no—
295C23—91no—
296Q8—92no—
297Q8—181no—
298D4—92no—
299D4—184no—
300D4—181no—
301C2×C4—64no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4—182no—
313C2×C4—361no—
314C2×C4D32⋊C411yescharacteristic
315C2×C4D32⋊C411yescharacteristic
316C2×C4C2×GO+(4,𝔽2)11yescharacteristic
317C8—122no—
318C8—362no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—122no—
326D3—42no—
327D3—122no—
328D3—122no—
329C22—62no—
330C22—121no—
331C22—121no—
332C22—181no—
333C22—181no—
334C22—181no—
335C22C2×D32⋊C411yescharacteristic
336C4—21no—
337C4—21no—
338C4—62no—
339C4—91no—
340C4—91no—
341C4—121no—
342C4—121no—
343C4—181no—
344C4—181no—
345C4#6422312yes—
346C3—21no—
347C3—21no—
348C2—122no—
349C2—361no—
350C2#1059330711yescharacteristic
351C2#1059332311yescharacteristic
352C2#1059334911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1488
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593725C2semidirect
3. #10590299C2semidirect
4. #10590032C2semidirect
5. #10590029C2semidirect
293. C32#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
#105937252
#105902992
#105900322
#105900292
#14889