Finite Group Databasebeta

← #11775372

Subgroups — #11775372

Order 1152.

416 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 55 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#10595033C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic, complemented
3#10591360C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×C4×#67—21no—
8#63982C2211yescharacteristic
9#63980C2211yescharacteristic
10C2×#3724—21no—
11#63962—21no—
12C4×#627C411yescharacteristic, complemented
13#63915C411yescharacteristic, complemented
14C4×#625C411yescharacteristic, complemented
15#63870C411yescharacteristic, complemented
16#63862—21no—
17#63855—21no—
18C22⋊#622C2212yes—
19#63777—21no—
20C4⋊#622—21no—
21C3×C3⋊#95—21no—
22#63579C2212yes—
23#5538—61no—
24#4650—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C3×#67—21no—
29C22×C3×Dic3—22no—
30C2×C3×C4×D3—21no—
31C2×#627C2×C411yescharacteristic
32C2×#625C2×C411yescharacteristic
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×#217—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×Dic3⋊C4—21no—
41C3×C4×Dic3—21no—
42#3724—42no—
43#3724C2×C411yescharacteristic
44#3724C2×C411yescharacteristic
45Dic3⋊Dic3—21no—
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48(C2×D3)⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51#1512—91nomaximal, Sylow
52C3×C4×D4—61no—
53#939—61no—
54#935—61no—
55C4×#67—21no—
56C4×#67—61no—
57#926—61no—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61#898—61no—
62#889—61no—
63#886—61no—
64#885—61no—
65#879—61no—
66#878—61no—
67#872—61no—
68C4×Dic6—61no—
69C3×#95—61no—
70C3⋊#95—21no—
71C3⋊#95—62no—
72C23×C32C2×D411yescharacteristic
73C22×C3×D3—21no—
74C2×C32×C4—41no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C3×#67—41no—
85C3×#67—41no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×C4×D3—42no—
93#627—41no—
94#625—41no—
95#622—42no—
96#529—91no—
97#432—91no—
98#382—91no—
99#328—92no—
100#327—92no—
101C2×C3×D4—61no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—61no—
105C22×C3×C4—62no—
106C2×#67—21no—
107C2×#67—61no—
108C22×Dic3—22no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—21no—
114C2×Dic6—61no—
115C3×C4⋊C4—61no—
116C3×C22⋊C4—61no—
117C3×C22⋊C4—61no—
118C3×C42—61no—
119#217—21no—
120#217—61no—
121#217—61no—
122#217—61no—
123(C2×D3)⋊C4—21no—
124(C2×D3)⋊C4—61no—
125(C2×D3)⋊C4—61no—
126(C2×D3)⋊C4—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130Dic3⋊C4—21no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—124no—
137C4×Dic3—21no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32AGL(1,ℤ/8)11yescharacteristic
150C22×C32#13711yescharacteristic
151C2×C3×D3—41no—
152C2×C3×D3—41no—
153C2×C3×D3—41no—
154C32×C4—21no—
155C32×C4—21no—
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3—21no—
159C3⋊Dic3—21no—
160C3×Dic3—41no—
161C3×Dic3—41no—
162C3×Dic3—41no—
163C3×Dic3—82no—
164#126—181no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8—91no—
171C4×D4—61no—
172C4×D4—91no—
173#117—181no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C4⋊C8—181no—
177C22⋊C8—92no—
178#97—181no—
179#95—61no—
180#95—92no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—61no—
184C22×D3—21no—
185C3×D4—121no—
186C3×D4—121no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—122no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200#67—41no—
201#67—41no—
202#67—122no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—42no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—121no—
220C2×Dic3—121no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C4×D3—42no—
224Dic6—122no—
225C2×C32—21no—
226C2×C32—21no—
227C2×C32#41011yescharacteristic
228C2×C32#41711yescharacteristic
229C2×C32#42111yescharacteristic
230C3×D3—81no—
231C2×Q8—91no—
232C2×D4—61no—
233C2×D4—91no—
234C22×C4—61no—
235C22×C4—62no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4GO+(4,𝔽2)11yescharacteristic
239C2×C8—182no—
240C4⋊C4—61no—
241C4⋊C4—91no—
242C4⋊C4—91no—
243C4⋊C4—181no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—362no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—181no—
250C22⋊C4—181no—
251C22⋊C4—181no—
252C42—61no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42—91no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—121no—
268C22×C3—121no—
269C22×C3—121no—
270C2×D3—41no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—22no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—121no—
278C3×C4—121no—
279C3×C4—121no—
280C3×C4—242no—
281Dic3—41no—
282Dic3—41no—
283Dic3—41no—
284Dic3—62no—
285Dic3—62no—
286Dic3—62no—
287Dic3—82no—
288Dic3—121no—
289Dic3—121no—
290Dic3—121no—
291Dic3—121no—
292Dic3—121no—
293C32#151211yescharacteristic, complemented, Sylow
294C23—61no—
295C23C2×GO+(4,𝔽2)11yescharacteristic
296Q8—361no—
297D4—121no—
298D4—121no—
299D4—361no—
300C2×C4—41no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4—122no—
311C2×C4—122no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—361no—
315C2×C4D32⋊C411yescharacteristic
316C2×C4D32⋊C411yescharacteristic
317C8—362no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—41no—
327C2×C3—41no—
328C2×C3—241no—
329D3—81no—
330C22—21no—
331C22—21no—
332C22—121no—
333C22—121no—
334C22—121no—
335C22#6422411yescharacteristic
336C22#6422611yescharacteristic
337C22C2×D32⋊C411yescharacteristic
338C4—21no—
339C4—21no—
340C4—121no—
341C4—121no—
342C4—121no—
343C4—181no—
344C4—181no—
345C4—181no—
346C4—181no—
347C4—242no—
348C3—21no—
349C3—21no—
350C2—21no—
351C2—21no—
352C2—241no—
353C2#1059334511yescharacteristic
354C2#1059336011yescharacteristic
355C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1512
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. #10593806C2semidirect
3. #10591360C2semidirect
4. #10590072C2semidirect
12. C4×#627C4semidirect
13. #63915C4semidirect
14. C4×#625C4semidirect
15. #63870C4semidirect
293. C32#1512semidirect

Maximal subgroups

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

subgroupindex
#105950332
#105938062
#105913602
#105900722
#105900712
#15129