Finite Group Databasebeta

← #11775279

Subgroups — #11775279

Order 1152.

601 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 601 conjugacy classes of subgroups — too many to draw. Only its 94 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#10596095C211yesmaximal, characteristic
2#10591257C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4538C212yesmaximal, complemented
5#10589151C212yesmaximal
6#68311—32nomaximal
7C32×C22⋊Q8C2211yescharacteristic
8#64156C411yescharacteristic, complemented
9Q8×C3⋊Dic3C411yescharacteristic, complemented
10#64139C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64107—21no—
13#64102C411yescharacteristic, complemented
14#64101—21no—
15#64099C411yescharacteristic, complemented
16#64095—21no—
17#64090—21no—
18C2×#3724—21no—
19C2×Dic32—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63572—21no—
23#63555—21no—
24#5624—32no—
25#5624—61no—
26#4719—32no—
27#4649—32no—
28C3×#328—32no—
29#4538D312yescomplemented
30#4470—32no—
31#4451—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C22×C3×Dic3—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C22⋊C4—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—22no—
57#3724—24no—
58Dic32—42no—
59#1509—91noSylow
60C3×C22⋊Q8—21no—
61C3×C22⋊Q8C2×D312yes—
62#947—32no—
63#947—61no—
64Q8×Dic3—32no—
65Q8×Dic3—61no—
66#930—32no—
67#930—61no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72#898—62no—
73#898—62no—
74#893—32no—
75#893—61no—
76#892—62no—
77#892—62no—
78#890—32no—
79#890—61no—
80#886—62no—
81#886—62no—
82#67⋊C4—62no—
83#67⋊C4—62no—
84C3×C22⋊C8—32no—
85C3×#95—32no—
86C3⋊#95C2×D312yes—
87#830C2×D312yes—
88#815—62no—
89Dic3⋊C8—62no—
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—21no—
92C32×Q8—41no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—41no—
99#638—41no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C4⋊(C3⋊D3)—41no—
109C4×C3⋊D3—42no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C3×C3⋊C8—42no—
114#529—91no—
115#432—91no—
116C4×C4⋊C4—91no—
117#328—32no—
118#327—92no—
119C2×C3×Q8—21no—
120C2×C3×Q8C4×D312yes—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D312yes—
124C2×#67—62no—
125C2×#67—62no—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C2×D12—32no—
132C2×D12—61no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C3×C8—62no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4C4×D312yes—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—22no—
142(C2×D3)⋊C4—62no—
143(C2×D3)⋊C4—62no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147(C2×D3)⋊C4—62no—
148(C2×D3)⋊C4—62no—
149(C2×D3)⋊C4—62no—
150C4⋊Dic3—32no—
151C4⋊Dic3—61no—
152C4⋊Dic3—62no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156Dic3⋊C4—68no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—32no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—124no—
170C2×C3⋊C8—22no—
171C22×C32—21no—
172C22×C32—21no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32AGL(1,ℤ/8)11yescharacteristic
175C22×C32#13711yescharacteristic
176C2×C3⋊D3—41no—
177C2×C3⋊D3—41no—
178C2×C3⋊D3—41no—
179C32×C4—21no—
180C32×C4—21no—
181C32×C4—41no—
182C32×C4—41no—
183C3⋊Dic3—21no—
184C3⋊Dic3—21no—
185C3⋊Dic3—21no—
186C3⋊Dic3—41no—
187C3⋊Dic3#10412yes—
188C3×Dic3—44no—
189#126—181no—
190#125—91no—
191#124—91no—
192#123—181no—
193C22⋊Q8D3211yescharacteristic
194#121—91no—
195C4×Q8—91no—
196C4×D4—91no—
197C4×D4—181no—
198#117—181no—
199C2×C4⋊C4—181no—
200C2×C42—91no—
201C2×C42—181no—
202C4⋊C8—181no—
203C22⋊C8—32no—
204#97—181no—
205#95—32no—
206C23×C3—21no—
207C23×C3D3×D412yes—
208C22×D3—62no—
209C22×D3—62no—
210C3×Q8—42no—
211C3×Q8—42no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—42no—
219C2×C3×C4—42no—
220C2×C3×C4—64no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4C2×C4×D312yes—
224C2×C3×C4D3×D412yes—
225#67—122no—
226#67—122no—
227#67—122no—
228#67—122no—
229C2×Dic3—24no—
230C2×Dic3—32no—
231C2×Dic3—32no—
232C2×Dic3—32no—
233C2×Dic3—32no—
234C2×Dic3—42no—
235C2×Dic3—42no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—64no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248D12—122no—
249D12—122no—
250C4×D3—124no—
251C4×D3—124no—
252C3×C8—122no—
253C3⋊C8—42no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32#41011yescharacteristic
257C2×C32#41711yescharacteristic
258C2×C32C2×#10411yescharacteristic
259C3⋊D3—81no—
260C2×Q8#62411yescharacteristic
261C2×D4—91no—
262C2×D4—181no—
263C22×C4—62no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—181no—
267C22×C4C2×D3211yescharacteristic
268C2×C8—62no—
269C4⋊C4—21no—
270C4⋊C4—91no—
271C4⋊C4—181no—
272C4⋊C4—181no—
273C4⋊C4—181no—
274C4⋊C4—184no—
275C4⋊C4#62411yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—181no—
278C22⋊C4—181no—
279C22⋊C4—181no—
280C22⋊C4—181no—
281C42—91no—
282C42—91no—
283C42—91no—
284C42—91no—
285C42—181no—
286C42—362no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3D3×C22⋊C412yes—
295C22×C3#91412yes—
296C22×C3#91812yes—
297C2×D3—122no—
298C2×D3—122no—
299C2×D3—122no—
300C2×D3—122no—
301C2×D3—122no—
302C2×D3—122no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—41no—
307C3×C4—42no—
308C3×C4—42no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4—124no—
312Dic3—34no—
313Dic3—44no—
314Dic3—62no—
315Dic3—62no—
316Dic3—62no—
317Dic3—62no—
318Dic3—121no—
319Dic3—121no—
320Dic3—121no—
321Dic3—122no—
322Dic3—122no—
323C32#150911yescharacteristic, complemented, Sylow
324C23—181no—
325C23#381111yescharacteristic
326Q8—41no—
327D4—361no—
328D4—361no—
329D4—361no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—64no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—122no—
339C2×C4—122no—
340C2×C4—182no—
341C2×C4—181no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—362no—
345C2×C4C2×#62411yescharacteristic
346C2×C4#381111yescharacteristic
347C8—122no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—41no—
354C2×C3—41no—
355C2×C3#474012yes—
356C2×C3#480312yes—
357C2×C3D3×#10412yes—
358D3—242no—
359D3—242no—
360C22—21no—
361C22—21no—
362C22—361no—
363C22—361no—
364C22—361no—
365C22#6394111yescharacteristic
366C22#6394511yescharacteristic
367C22#6397411yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—92no—
373C4—124no—
374C4—181no—
375C4—181no—
376C4—181no—
377C4—361no—
378C3—21no—
379C3#6831112yescomplemented
380C2—21no—
381C2—21no—
382C2—721no—
383C2#1059152911yescharacteristic
384C2#1059155411yescharacteristic
385C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591257C2semidirect
3. #10591066C2semidirect
4. C3×#4538C2semidirect
8. #64156C4semidirect
9. Q8×C3⋊Dic3C4semidirect
13. #64102C4semidirect
15. #64099C4semidirect
29. #4538D3semidirect
323. C32#1509semidirect
379. C3#68311semidirect

Maximal subgroups

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

subgroupindex
#105960952
#105912572
#105910662
C3×#45382
#105891512
#683113