Finite Group Databasebeta

← #11775574

Subgroups — #11775574

Order 1152.

766 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3⋊D3×#121C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic, complemented
3C2×#63778C211yesmaximal, characteristic, complemented
4#10590209C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×D4×C3⋊D3—21no—
7C2×D4×C3⋊D3C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157—21no—
10C22×#622—21no—
11C2×C4⋊#157—21no—
12C32×#121C411yescharacteristic, complemented
13#64148—21no—
14#64147C2211yescharacteristic
15#64139C411yescharacteristic, complemented
16#64104C2211yescharacteristic
17C4⋊C4×C3⋊D3C411yescharacteristic, complemented
18#64093—21no—
19C22⋊C4×C3⋊D3—21no—
20#63781C2212yescomplemented
21#63778—21no—
22#63778C2212yescomplemented
23D3×#121—62no—
24C23×C3⋊D3—21no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C2×C32×D4—21no—
28C2×C32×D4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C2×#638—21no—
31C2×#638—21no—
32C2×#638—21no—
33C22×C3⋊Dic3D411yescharacteristic
34D4×C3⋊D3—42no—
35D4×C3⋊D3—42no—
36D4×C3⋊D3—42no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C22⋊#157—42no—
46C2×#622—22no—
47C2×#622—42no—
48C4⋊#157—42no—
49C32×C4⋊C4C2×C411yescharacteristic
50C32×C22⋊C4—21no—
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#1519—91nomaximal, Sylow
57C2×D3×D4—62no—
58C2×D3×D4—64no—
59C22×C4×D3—62no—
60C3×#121—22no—
61#939—64no—
62#938—62no—
63#930—62no—
64#895—62no—
65D3×C4⋊C4—62no—
66#884—64no—
67D3×C22⋊C4—64no—
68C23×C32—21no—
69C23×C32C22⋊C411yescharacteristic
70C22×C3⋊D3—21no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3—42no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3C22⋊C411yescharacteristic
77C22×C3⋊D3D812yes—
78C22×C3⋊D3SD1612yes—
79C22×C3⋊D3C2×D411yescharacteristic
80C2×#157—42no—
81C2×#157—42no—
82C2×#157—42no—
83C32×D4—41no—
84C32×D4—42no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22×C411yescharacteristic
89#638—42no—
90#638—41no—
91#638—41no—
92#638—42no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3C2×D411yescharacteristic
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104C4×C3⋊D3—42no—
105#622—42no—
106C2×#121—91no—
107C2×C22⋊C8—91no—
108#380—91no—
109#327—92no—
110#327—92no—
111C23×D3—62no—
112C23×D3—64no—
113C2×C3×D4—24no—
114C2×C3×D4—22no—
115C22×C3×C4—22no—
116C2×#67—64no—
117C2×#67—64no—
118C2×#67—64no—
119C22×Dic3—62no—
120D3×D4—128no—
121D3×D4—128no—
122D3×D4—128no—
123C2×D12—62no—
124C2×D12—64no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—64no—
130C2×C4×D3—128no—
131C3×C4⋊C4—22no—
132C3×C22⋊C4—24no—
133#217—64no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136C4⋊Dic3—62no—
137Dic3⋊C4—64no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—41no—
141C22×C32—41no—
142C22×C32—41no—
143C22×C32#10212yes—
144C22×C32C2×C22⋊C411yescharacteristic
145C2×C3⋊D3—21no—
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3—41no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—84no—
155C2×C3⋊D3#10212yes—
156C2×C3⋊D3C2×D811yescharacteristic
157C2×C3⋊D3C2×SD1611yescharacteristic
158#157—82no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—41no—
162C3⋊Dic3—21no—
163C3⋊Dic3—41no—
164C3⋊Dic3#9912yes—
165C22×D4—91no—
166C22×D4—181no—
167C23×C4—91no—
168C22×C8—181no—
169#121—91no—
170#121—91no—
171#121—91no—
172#121—181no—
173#121—181no—
174#121#15711yescharacteristic, complemented
175C2×C4⋊C4—91no—
176C2×C4⋊C4—181no—
177C2×C22⋊C4—181no—
178C2×C22⋊C4—181no—
179C22⋊C8—92no—
180C22⋊C8—181no—
181#95—92no—
182C23×C3—24no—
183C23×C3—22no—
184C22×D3—62no—
185C22×D3—64no—
186C22×D3—64no—
187C22×D3—62no—
188C22×D3—64no—
189C22×D3—124no—
190C22×D3—124no—
191C22×D3—128no—
192C22×D3—128no—
193C22×D3—128no—
194C3×D4—44no—
195C3×D4—48no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—44no—
200#67—128no—
201#67—124no—
202#67—124no—
203#67—128no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—64no—
207C2×Dic3—124no—
208D12—124no—
209D12—124no—
210D12—124no—
211C4×D3—68no—
212C4×D3—124no—
213C4×D3—124no—
214C4×D3—124no—
215C4×D3—128no—
216C2×C32—22no—
217C2×C32—81no—
218C2×C32C2×#9911yescharacteristic
219C2×C32C2×#10211yescharacteristic
220C2×C32#42111yescharacteristic
221C3⋊D3—22no—
222C3⋊D3—21no—
223C3⋊D3—21no—
224C3⋊D3—81no—
225C24—91no—
226C24—181no—
227C2×D4—21no—
228C2×D4—91no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—181no—
232C2×D4—181no—
233C2×D4—362no—
234C2×D4—362no—
235C2×D4—362no—
236C2×D4C2×#15711yescharacteristic
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—181no—
243C22×C4—182no—
244C22×C4—362no—
245C22×C4C2×#15711yescharacteristic
246C2×C8—182no—
247C2×C8—362no—
248C4⋊C4—91no—
249C4⋊C4—181no—
250C4⋊C4—362no—
251C4⋊C4C2×#15711yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—181no—
254C22⋊C4—181no—
255C22⋊C4—181no—
256C22⋊C4—362no—
257C22×C3—22no—
258C22×C3—24no—
259C22×C3—42no—
260C22×C3—42no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—44no—
264C2×D3—64no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—122no—
270C2×D3—122no—
271C2×D3—128no—
272C2×D3—128no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C2×D3—2416no—
277C3×C4—24no—
278C3×C4—42no—
279C3×C4—44no—
280Dic3—64no—
281Dic3—122no—
282Dic3—124no—
283C32#151911yescharacteristic, complemented, Sylow
284C23—21no—
285C23—91no—
286C23—91no—
287C23—92no—
288C23—92no—
289C23—181no—
290C23—361no—
291C23—361no—
292C23—362no—
293C23—362no—
294C23—362no—
295C23C22⋊#15711yescharacteristic
296D4—41no—
297D4—42no—
298D4—361no—
299D4—361no—
300D4—361no—
301D4—362no—
302D4—361no—
303D4—361no—
304D4—362no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—181no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4—362no—
318C2×C4—362no—
319C2×C4C22⋊#15711yescharacteristic
320C2×C4C22×#15711yescharacteristic
321C8—362no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—44no—
326C2×C3—84no—
327D3—68no—
328D3—122no—
329D3—122no—
330D3—244no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—91no—
337C22—92no—
338C22—91no—
339C22—181no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—362no—
344C22—362no—
345C22—361no—
346C22—361no—
347C22—361no—
348C22—724no—
349C22#6378212yes—
350C22C2×C22⋊#15711yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—92no—
355C4—181no—
356C4—361no—
357C4—722no—
358C3—22no—
359C2—22no—
360C2—81no—
361C2—181no—
362C2—182no—
363C2—181no—
364C2—721no—
365C2C2×#6378211yescharacteristic
366C2#1059381711yescharacteristic
367C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#121C4
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#121C2
cosocleC2×C4×C3⋊D3C23
hypercenter#121#157
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10593812C2semidirect
3. C2×#63778C2semidirect
4. #10590209C2semidirect
5. #10590157C2semidirect
7. C2×D4×C3⋊D3C4semidirect
12. C32×#121C4semidirect
15. #64139C4semidirect
17. C4⋊C4×C3⋊D3C4semidirect
20. #63781C22semidirect
22. #63778C22semidirect
174. #121#157semidirect
283. C32#1519semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
#105938122
C2×#637782
#105902092
#105901572
#15199