Finite Group Databasebeta

← #11774294

Subgroups — #11774294

Order 1152.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
2C2×#63779C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C2×#3805C411yescharacteristic
7C22×#622—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10#67⋊Dic3—21no—
11#63957C411yescharacteristic
12C4×#627C411yescharacteristic
13#63902C2211yescharacteristic
14C4×#625C411yescharacteristic
15#63878—21no—
16C4×D3×Dic3—21no—
17#63838C2211yescharacteristic
18#63779—21no—
19#63779C2212yes—
20C3×#830—21no—
21#63572—21no—
22#63553C2212yes—
23C4×#237—61no—
24#4718—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#3805C814yescomplemented
34C2×D3×Dic3—21no—
35C2×D3×Dic3—21no—
36C2×#622—22no—
37C2×#622—42no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C3×#217—21no—
43C3×(C2×D3)⋊C4—21no—
44C3×Dic3⋊C4—21no—
45C3×C4×Dic3—21no—
46C2×C3×C3⋊C8—22no—
47#3724C2×C411yescharacteristic
48#3724C2×C411yescharacteristic
49Dic3⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—21no—
52Dic32—21no—
53#1477—91nomaximal, Sylow
54C2×#237—61no—
55C3×C4×D4—61no—
56D4×Dic3—61no—
57C4×#67—21no—
58C4×#67—61no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—61no—
62#892—61no—
63#887—61no—
64#67⋊C4—61no—
65#67⋊C4—61no—
66#877—61no—
67#877—61no—
68C42×D3—61no—
69C4×Dic6—61no—
70C3×C22⋊C8—61no—
71#830—21no—
72Dic3⋊C8—62no—
73C8×Dic3—62no—
74C23×C32C22⋊C411yescharacteristic
75C22×C3×D3—21no—
76C2×C32×C4—41no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C2×C812yes—
84C2×C3⋊Dic3M1612yes—
85C2×C3⋊Dic3C22×C411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C3×#67—24no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C3×C4×D3—42no—
92#627—21no—
93#627C2×C812yescomplemented
94#625—21no—
95#625C2×C812yescomplemented
96D3×Dic3—24no—
97D3×Dic3—41no—
98D3×Dic3—41no—
99#622—42no—
100C3×C3⋊C8—42no—
101C4×#41—91no—
102#431—91no—
103C2×C4⋊C8—91no—
104Q8⋊C8—92no—
105D4⋊C8—92no—
106C2×C3×D4—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—61no—
110C2×#67—21no—
111C2×#67—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118#237—64no—
119#237—64no—
120C2×C4×D3—21no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×Dic6—61no—
124C2×C3×C8—62no—
125C3×C4⋊C4—61no—
126C3×C22⋊C4—61no—
127C3×C22⋊C4—61no—
128C3×C42—61no—
129#217—21no—
130#217—61no—
131(C2×D3)⋊C4—21no—
132(C2×D3)⋊C4—61no—
133C4⋊Dic3—61no—
134Dic3⋊C4—21no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138C4×Dic3—21no—
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—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—22no—
152C22×C32—21no—
153C22×C32—21no—
154C22×C32C22⋊C812yes—
155C22×C32C2×C22⋊C411yescharacteristic
156C2×C3×D3—22no—
157C2×C3×D3—41no—
158C2×C3×D3—41no—
159C32×C4—21no—
160C32×C4—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3C22⋊C812yes—
163C3⋊Dic3C22×C811yescharacteristic
164C3⋊Dic3C2×M1611yescharacteristic
165C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
166C3⋊Dic3#13711yescharacteristic
167C3×Dic3—22no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C2×#41—91no—
171C22×C8—181no—
172C4×Q8—91no—
173C4×Q8—91no—
174C4×D4—61no—
175C4×D4—91no—
176C4×D4—91no—
177C4×D4—181no—
178#117—91no—
179#117—181no—
180C2×C42—91no—
181C2×C42—181no—
182C4⋊C8—92no—
183C4⋊C8—181no—
184C4⋊C8—181no—
185C22⋊C8—61no—
186C4×C8—92no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—61no—
190C22×D3—21no—
191C3×D4—64no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4—122no—
202#67—24no—
203#67—62no—
204#67—62no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—64no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226C2×Dic3—121no—
227C4×D3—42no—
228C4×D3—64no—
229C4×D3—121no—
230C4×D3—121no—
231Dic6—62no—
232Dic6—62no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32—22no—
236C2×C32C2×C22⋊C811yescharacteristic
237C2×C32#41711yescharacteristic
238C2×C32#42111yescharacteristic
239C3×D3—42no—
240#41—94no—
241#41—182no—
242C2×Q8—91no—
243C2×D4—61no—
244C2×D4—91no—
245C22×C4—61no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4GO+(4,𝔽2)11yescharacteristic
251C2×C8—62no—
252C2×C8—182no—
253C2×C8—362no—
254C4⋊C4—61no—
255C4⋊C4—91no—
256C4⋊C4—91no—
257C4⋊C4—181no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—181no—
261C42—61no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—91no—
266C42—181no—
267C42—181no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—62no—
277C22×C3—121no—
278C22×C3—121no—
279C2×D3—22no—
280C2×D3—41no—
281C2×D3—41no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—62no—
287C3×C4—121no—
288C3×C4—121no—
289Dic3—22no—
290Dic3—41no—
291Dic3—41no—
292Dic3—61no—
293Dic3—61no—
294Dic3—62no—
295Dic3—61no—
296Dic3—61no—
297Dic3—62no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—121no—
303Dic3—121no—
304C32#147711yescharacteristic, complemented, Sylow
305C23—61no—
306C23D32⋊C411yescharacteristic
307Q8—92no—
308Q8—181no—
309D4—64no—
310D4—92no—
311D4—181no—
312C2×C4—41no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—91no—
322C2×C4—122no—
323C2×C4—184no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4—361no—
327C2×C4—361no—
328C2×C4D32⋊C411yescharacteristic
329C2×C4C2×GO+(4,𝔽2)11yescharacteristic
330C8—122no—
331C8—362no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—42no—
339C2×C3—42no—
340C2×C3—122no—
341D3—42no—
342C22—21no—
343C22—21no—
344C22—62no—
345C22—121no—
346C22—121no—
347C22D32⋊C812yes—
348C22C2×D32⋊C411yescharacteristic
349C4—21no—
350C4—21no—
351C4—62no—
352C4—92no—
353C4—91no—
354C4—91no—
355C4—91no—
356C4—91no—
357C4—121no—
358C4—121no—
359C4—181no—
360C3—21no—
361C3—21no—
362C2—22no—
363C2—122no—
364C2C2×D32⋊C811yescharacteristic
365C2#1059331911yescharacteristic
366C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1477
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
3. #10591061C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
33. #3805C8semidirect
93. #627C2×C8semidirect
95. #625C2×C8semidirect
304. C32#1477semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
C2×#637792
#105910612
#105900312
#105900302
#14779