Finite Group Databasebeta

← #11774293

Subgroups — #11774293

Order 1152.

488 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 75 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#10593727C211yesmaximal, characteristic, complemented
3#10590331C211yesmaximal, 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—
17C2×#3710—21no—
18#63778—21no—
19C4⋊#622—21no—
20C4×#622C2212yes—
21C3×C4⋊(C3⋊C8)—21no—
22#63572C2212yes—
23C4×#235—61no—
24D3×C4⋊C8—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#3798C814yescomplemented
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#3710—42no—
53#1477—91nomaximal, Sylow
54C2×#235—61no—
55C2×C3×C42—61no—
56C4×#67—61no—
57C4×#67—61no—
58C4×#67—61no—
59C4×#67—61no—
60#926—61no—
61C2×D3×C8—62no—
62C4×D12—61no—
63C4×D12—61no—
64#872—61no—
65#872—61no—
66C42×D3—21no—
67C42×D3—61no—
68C42×D3—61no—
69C4×Dic6—61no—
70C4×Dic6—61no—
71C3×C4⋊C8—61no—
72Dic3⋊C8—62no—
73C4⋊(C3⋊C8)—21no—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3×D3—21no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22×C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3C2×C812yes—
86C4×C3⋊D3M1612yes—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C3×C4×D3—24no—
91C3×C4×D3—42no—
92C3×C4×D3—41no—
93C3×C4×D3—41no—
94#627—21no—
95#627C2×C812yescomplemented
96#626—24no—
97#625—21no—
98#625C2×C812yescomplemented
99#622—42no—
100C3×C3⋊C8—42no—
101C4×#41—91no—
102#431—91no—
103C2×C4⋊C8—91no—
104Q8⋊C8—92no—
105D4⋊C8—92no—
106C22×C3×C4—61no—
107C22×C3×C4—61no—
108C22×C3×C4—61no—
109C2×#67—61no—
110C2×#67—61no—
111#235—64no—
112#235—64no—
113C2×D12—61no—
114C2×C4×D3—21no—
115C2×C4×D3—21no—
116C2×C4×D3—21no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×Dic6—61no—
124C2×C3×C8—62no—
125C3×C42—21no—
126C3×C42—21no—
127C3×C42—61no—
128C3×C42—61no—
129C3×C42—61no—
130#217—61no—
131#217—61no—
132(C2×D3)⋊C4—61no—
133(C2×D3)⋊C4—61no—
134(C2×D3)⋊C4—61no—
135(C2×D3)⋊C4—61no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138Dic3⋊C4—61no—
139Dic3⋊C4—61no—
140Dic3⋊C4—61no—
141Dic3⋊C4—61no—
142C4×Dic3—21no—
143C4×Dic3—21no—
144C4×Dic3—21no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—22no—
152D3×C8—124no—
153C22×C32C2×C22⋊C411yescharacteristic
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3C22⋊C812yes—
157C2×C3×D3—22no—
158C2×C3×D3—41no—
159C2×C3×D3—41no—
160C32×C4—21no—
161C32×C4C22⋊C812yes—
162C32×C4AGL(1,ℤ/8)11yescharacteristic
163C32×C4#13711yescharacteristic
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3C22×C811yescharacteristic
167C3⋊Dic3C2×M1611yescharacteristic
168C3×Dic3—22no—
169C3×Dic3—41no—
170C3×Dic3—41no—
171C2×#41—91no—
172C22×C8—181no—
173C4×Q8—91no—
174C4×Q8—91no—
175C4×D4—91no—
176C4×D4—91no—
177C4×D4—181no—
178C4×D4—181no—
179#117—91no—
180#117—181no—
181C2×C42—61no—
182C2×C42—91no—
183C4⋊C8—61no—
184C4⋊C8—92no—
185C4⋊C8—181no—
186C22⋊C8—181no—
187C4×C8—92no—
188C23×C3—61no—
189C22×D3—21no—
190C22×D3—61no—
191C22×D3—61no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—64no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4—61no—
202C2×C3×C4—122no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205#67—62no—
206#67—64no—
207#67—62no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217D12—64no—
218C4×D3—24no—
219C4×D3—42no—
220C4×D3—41no—
221C4×D3—41no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—121no—
229C4×D3—121no—
230C4×D3—122no—
231C4×D3—122no—
232Dic6—62no—
233Dic6—62no—
234C3×C8—122no—
235C3⋊C8—42no—
236C2×C32C2×C22⋊C811yescharacteristic
237C2×C32#41711yescharacteristic
238C2×C32#42111yescharacteristic
239C3⋊D3—22no—
240C3×D3—42no—
241#41—94no—
242#41—182no—
243C2×Q8—91no—
244C2×D4—91no—
245C2×D4—181no—
246C22×C4—61no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C2×C8—62no—
253C2×C8—182no—
254C2×C8—362no—
255C4⋊C4—91no—
256C4⋊C4—91no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C22⋊C4—181no—
260C22⋊C4—181no—
261C22⋊C4—181no—
262C42—61no—
263C42—61no—
264C42—61no—
265C42—91no—
266C42—91no—
267C42—91no—
268C42GO+(4,𝔽2)11yescharacteristic
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—62no—
272C22×C3—121no—
273C22×C3—121no—
274C2×D3—22no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—121no—
282C2×D3—121no—
283C3×C4—22no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—62no—
292C3×C4—121no—
293C3×C4—121no—
294Dic3—22no—
295Dic3—41no—
296Dic3—41no—
297Dic3—61no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—62no—
302Dic3—121no—
303Dic3—121no—
304Dic3—121no—
305C32#147711yescharacteristic, complemented, Sylow
306C23—61no—
307C23—91no—
308Q8—92no—
309Q8—181no—
310D4—92no—
311D4—184no—
312D4—181no—
313C2×C4—61no—
314C2×C4—64no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—91no—
318C2×C4—92no—
319C2×C4—92no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—122no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—361no—
328C2×C4D32⋊C411yescharacteristic
329C2×C4D32⋊C411yescharacteristic
330C2×C4C2×GO+(4,𝔽2)11yescharacteristic
331C8—122no—
332C8—362no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—122no—
340D3—42no—
341D3—64no—
342D3—122no—
343C22—62no—
344C22—92no—
345C22—121no—
346C22—121no—
347C22—181no—
348C22—181no—
349C22C2×D32⋊C411yescharacteristic
350C4—21no—
351C4—62no—
352C4—91no—
353C4—91no—
354C4—121no—
355C4—121no—
356C4—181no—
357C4—181no—
358C4D32⋊C812yes—
359C4#6422411yescharacteristic
360C4#6422611yescharacteristic
361C3—21no—
362C3—21no—
363C2—122no—
364C2—182no—
365C2C2×D32⋊C811yescharacteristic
366C2#1059332311yescharacteristic
367C2#1059336011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1477
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593727C2semidirect
3. #10590331C2semidirect
4. #10590032C2semidirect
5. #10590029C2semidirect
35. #3798C8semidirect
95. #627C2×C8semidirect
98. #625C2×C8semidirect
305. C32#1477semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
#105937272
#105903312
#105900322
#105900292
#14779