Finite Group Databasebeta

← #11774631

Subgroups — #11774631

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×#3805C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4#10590032C212yesmaximal, complemented
5#10590029C212yesmaximal, complemented
6C2×#3805C411yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×C4×#67—21no—
9#67⋊Dic3—21no—
10#63957C411yescharacteristic
11C4×#627C2211yescharacteristic
12#63902C411yescharacteristic
13C4×#625C2211yescharacteristic
14#63878—21no—
15C4×D3×Dic3—21no—
16#63838C411yescharacteristic
17C22⋊#622—21no—
18C4⋊#622—21no—
19C4×#622C2212yes—
20C3×#830—21no—
21#63572C2212yes—
22#63555—21no—
23C4×#237—61no—
24#4719—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
32#3805—22no—
33#3805—22no—
34C2×D3×Dic3—21no—
35C2×D3×Dic3—21no—
36C2×#622—22no—
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3C2311yescharacteristic
41C3×#217—21no—
42C3×(C2×D3)⋊C4—21no—
43C3×Dic3⋊C4—21no—
44C3×C4×Dic3—21no—
45C2×C3×C3⋊C8—22no—
46#3724C2×C411yescharacteristic
47#3724C2×C411yescharacteristic
48Dic3⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50Dic32—21no—
51Dic32—21no—
52#1488—91nomaximal, Sylow
53C2×#237—61no—
54C3×C4×D4—61no—
55D4×Dic3—61no—
56C4×#67—21no—
57C4×#67—61no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61#892—61no—
62#887—61no—
63#67⋊C4—61no—
64#67⋊C4—61no—
65#877—61no—
66#877—61no—
67C42×D3—61no—
68C4×Dic6—61no—
69C3×C22⋊C8—61no—
70#830—21no—
71#815—62no—
72Dic3⋊C8—62no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3×D3—21no—
75C2×C32×C4—22no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C3×#67—24no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—21no—
89C3×C4×D3—42no—
90#627—21no—
91#627M1612yes—
92#625—21no—
93#625M1612yes—
94D3×Dic3—24no—
95D3×Dic3—42no—
96#622—42no—
97C3×C3⋊C8—42no—
98C4×#41—91no—
99#432—91no—
100#431—91no—
101Q8⋊C8—92no—
102D4⋊C8—92no—
103C2×C3×D4—61no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—61no—
107C2×#67—21no—
108C2×#67—61no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115#237—64no—
116#237—64no—
117C2×C4×D3—21no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×Dic6—61no—
121C2×C3×C8—62no—
122C3×C4⋊C4—61no—
123C3×C22⋊C4—61no—
124C3×C22⋊C4—61no—
125C3×C42—61no—
126#217—21no—
127#217—61no—
128(C2×D3)⋊C4—21no—
129(C2×D3)⋊C4—61no—
130C4⋊Dic3—61no—
131Dic3⋊C4—21no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135C4×Dic3—21no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C2×C3⋊C8—22no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32C2×C22⋊C411yescharacteristic
153C2×C3×D3—22no—
154C2×C3×D3—41no—
155C2×C3×D3—41no—
156C32×C4—21no—
157C32×C4#13512yes—
158C3⋊Dic3—21no—
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—61no—
170C4×D4—91no—
171C4×D4—91no—
172C4×D4—181no—
173#117—91no—
174#117—181no—
175C2×C42—91no—
176C2×C42—181no—
177C4⋊C8—92no—
178C4⋊C8—181no—
179C22⋊C8—61no—
180C22⋊C8—181no—
181#97—181no—
182C4×C8—92no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—61no—
186C22×D3—21no—
187C3×D4—64no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—122no—
198#67—24no—
199#67—62no—
200#67—62no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C4×D3—42no—
221C4×D3—64no—
222C4×D3—122no—
223Dic6—62no—
224Dic6—62no—
225C3×C8—122no—
226C3⋊C8—42no—
227C2×C32—41no—
228C2×C32#40711yescharacteristic
229C2×C32#41611yescharacteristic
230C2×C32#42111yescharacteristic
231C3×D3—42no—
232#41—182no—
233#41—182no—
234C2×Q8—91no—
235C2×D4—61no—
236C2×D4—91no—
237C22×C4—61no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4GO+(4,𝔽2)11yescharacteristic
243C2×C8—62no—
244C2×C8—182no—
245C4⋊C4—61no—
246C4⋊C4—91no—
247C4⋊C4—91no—
248C4⋊C4—181no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—181no—
252C42—61no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42—91no—
257C42—181no—
258C42—181no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—62no—
268C22×C3—121no—
269C22×C3—121no—
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—62no—
278C3×C4—121no—
279C3×C4—121no—
280Dic3—22no—
281Dic3—41no—
282Dic3—41no—
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286Dic3—61no—
287Dic3—62no—
288Dic3—62no—
289Dic3—121no—
290Dic3—121no—
291Dic3—121no—
292Dic3—121no—
293C32#148811yescharacteristic, complemented, Sylow
294C23—61no—
295C23D32⋊C411yescharacteristic
296Q8—92no—
297Q8—181no—
298D4—64no—
299D4—92no—
300D4—181no—
301C2×C4—22no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—122no—
310C2×C4—184no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—362no—
314C2×C4—361no—
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—42no—
326C2×C3—42no—
327C2×C3—122no—
328D3—42no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—62no—
333C22—121no—
334C22—121no—
335C22C2×D32⋊C411yescharacteristic
336C4—21no—
337C4—62no—
338C4—91no—
339C4—91no—
340C4—121no—
341C4—121no—
342C4—181no—
343C4—181no—
344C4—181no—
345C4#6423712yes—
346C3—21no—
347C3—21no—
348C2—41no—
349C2—122no—
350C2#1059330711yescharacteristic
351C2#1059332411yescharacteristic
352C2#1059349811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1488
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
3. #10591066C2semidirect
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×#38052
#105937952
#105910662
#105900322
#105900292
#14889