Finite Group Databasebeta

← #11775858

Subgroups — #11775858

Order 1152.

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

normal subgroups only

This group has 404 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#10591060C211yesmaximal, characteristic, complemented
4#10590036C212yesmaximal, complemented
5#10590035C212yesmaximal, complemented
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×C4×#67—21no—
8C2×C3×#208—21no—
9#63982C411yescharacteristic
10#63980C411yescharacteristic
11#63962—21no—
12C4×#627C411yescharacteristic
13#63915C2211yescharacteristic
14C4×#625C411yescharacteristic
15#63870C2211yescharacteristic
16#63862—21no—
17#63855—21no—
18C22⋊#622—21no—
19#63777C2212yes—
20C4⋊#622—21no—
21#63555C2212yes—
22#63553—21no—
23#5538—61no—
24Dic3×M16—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C3×#67—21no—
29C2×C3×C4×D3—21no—
30C2×#627C2×C411yescharacteristic
31C2×#625C2×C411yescharacteristic
32C2×#622—22no—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×#217—21no—
38C3×(C2×D3)⋊C4—21no—
39C3×Dic3⋊C4—21no—
40C3×C4×Dic3—21no—
41C3×#208—24no—
42C2×C3×C3⋊C8—22no—
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#1529—91nomaximal, Sylow
52C2×C3×M16—61no—
53C3×C4×D4—61no—
54#939—61no—
55#935—61no—
56C4×#67—21no—
57C4×#67—61no—
58#926—61no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61C2×#208—21no—
62#898—61no—
63#889—61no—
64#886—61no—
65#885—61no—
66#879—61no—
67#878—61no—
68#872—61no—
69C4×Dic6—61no—
70#815—62no—
71C8×Dic3—62no—
72C23×C32C22⋊C411yescharacteristic
73C22×C3×D3—21no—
74C2×C32×C4—22no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C3×#67—42no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86C2×C3×Dic3—21no—
87C3×C4×D3—42no—
88#627—41no—
89#625—41no—
90#622—42no—
91C3×C3⋊C8—24no—
92#529—91no—
93#432—91no—
94C4×M16—91no—
95#330—92no—
96#329—92no—
97C2×C3×D4—61no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—61no—
101C2×#67—21no—
102C2×#67—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C2×C4×D3—21no—
108C2×Dic6—61no—
109C3×M16—64no—
110C2×C3×C8—62no—
111C3×C4⋊C4—61no—
112C3×C22⋊C4—61no—
113C3×C22⋊C4—61no—
114C3×C42—61no—
115#217—21no—
116#217—61no—
117#217—61no—
118#217—61no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—61no—
121(C2×D3)⋊C4—61no—
122(C2×D3)⋊C4—61no—
123C4⋊Dic3—61no—
124C4⋊Dic3—61no—
125C4⋊Dic3—61no—
126Dic3⋊C4—21no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131Dic3⋊C4—61no—
132C4×Dic3—21no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141#208—24no—
142C2×C3⋊C8—22no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3×D3—41no—
148C2×C3×D3—41no—
149C2×C3×D3—41no—
150C32×C4—21no—
151C32×C4#10412yes—
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3×Dic3—41no—
157C3×Dic3—41no—
158C3×Dic3—41no—
159C2×M16—61no—
160#126—181no—
161#125—91no—
162#124—91no—
163#123—181no—
164C22⋊Q8—91no—
165#121—91no—
166C4×Q8—91no—
167C4×D4—61no—
168C4×D4—91no—
169#117—181no—
170C2×C42—91no—
171C4⋊C8—181no—
172C22⋊C8—181no—
173#97—92no—
174#97—92no—
175C4×C8—181no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—61no—
179C22×D3—21no—
180C3×D4—122no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4—122no—
192#67—42no—
193#67—122no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—122no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208C2×Dic3—122no—
209C4×D3—42no—
210Dic6—122no—
211C3×C8—64no—
212C3⋊C8—24no—
213C2×C32—41no—
214C2×C32#41311yescharacteristic
215C2×C32C2×#10411yescharacteristic
216C2×C32#42111yescharacteristic
217C3×D3—81no—
218C2×Q8—91no—
219C2×D4—61no—
220C2×D4—91no—
221C22×C4—61no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225M16—64no—
226C2×C8—62no—
227C2×C8—182no—
228C4⋊C4—61no—
229C4⋊C4—91no—
230C4⋊C4—91no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—181no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C42—61no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42—91no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—121no—
253C22×C3—121no—
254C22×C3—121no—
255C2×D3—41no—
256C2×D3—41no—
257C2×D3—41no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—41no—
263C3×C4—121no—
264C3×C4—121no—
265C3×C4—121no—
266Dic3—41no—
267Dic3—41no—
268Dic3—41no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—121no—
273Dic3—121no—
274Dic3—121no—
275Dic3—121no—
276Dic3—121no—
277C32#152911yescharacteristic, complemented, Sylow
278C23—61no—
279C23D32⋊C411yescharacteristic
280Q8—361no—
281D4—122no—
282D4—361no—
283C2×C4—22no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—122no—
292C2×C4—361no—
293C2×C4—361no—
294C2×C4D32⋊C411yescharacteristic
295C2×C4C2×GO+(4,𝔽2)11yescharacteristic
296C8—64no—
297C8—362no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—42no—
305C2×C3—42no—
306C2×C3—241no—
307D3—81no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—121no—
312C22—121no—
313C22—121no—
314C22C2×D32⋊C411yescharacteristic
315C4—21no—
316C4—121no—
317C4—121no—
318C4—121no—
319C4—181no—
320C4—181no—
321C4—181no—
322C4—181no—
323C4#6374112yes—
324C3—21no—
325C3—21no—
326C2—41no—
327C2—241no—
328C2#1059331311yescharacteristic
329C2#1059332311yescharacteristic
330C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1529
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. #10591060C2semidirect
4. #10590036C2semidirect
5. #10590035C2semidirect
277. C32#1529semidirect

Maximal subgroups

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

subgroupindex
#105950332
#105938062
#105910602
#105900362
#105900352
#15299