Finite Group Databasebeta

← #79783

Subgroups — #79783

Order 384.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5578C211yesmaximal, characteristic, complemented
2C4×#237C211yesmaximal, characteristic
3C3×#440C211yesmaximal, characteristic, complemented
4#5173C211yesmaximal, characteristic
5#5162C211yesmaximal, characteristic, complemented
6#5030C211yesmaximal, characteristic, complemented
7#5018C211yesmaximal, characteristic, complemented
8#4888C211yesmaximal, characteristic, complemented
9#4875C211yesmaximal, characteristic, complemented
10#4815C211yesmaximal, characteristic, complemented
11#4795C211yesmaximal, characteristic, complemented
12#4783C211yesmaximal, characteristic
13#4761C211yesmaximal, characteristic, complemented
14#4716C211yesmaximal, characteristic, complemented
15#4705C211yesmaximal, characteristic, complemented
16#3116—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C3×C4×Q8C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21#946C2211yescharacteristic
22#944C2211yescharacteristic
23C2×#216C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C4×#67—21no—
27C2×C4×Dic3—21no—
28C2×Dic12C2211yescharacteristic
29#897C2211yescharacteristic
30#896—21no—
31#892C2211yescharacteristic
32#889—21no—
33#888C2211yescharacteristic
34#887C2211yescharacteristic
35#67⋊C4—21no—
36#877—21no—
37#872—21no—
38C42×D3C2211yescharacteristic
39C4×Dic6—21no—
40C4×Dic6C2211yescharacteristic
41C4×Dic6C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×#97C2211yescharacteristic
46#835C2211yescharacteristic
47#832C2211yescharacteristic
48(C2×D3)⋊C8C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#817C2211yescharacteristic
51#816C2211yescharacteristic
52#816C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54Dic3⋊C8C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59#803C2211yescharacteristic
60#533—31no—
61C4×#41—31no—
62#485—31no—
63#485—31no—
64#477—31no—
65#476—31no—
66#462—31no—
67#461—31no—
68#452—31no—
69#452—31no—
70#441—31no—
71#441—31no—
72#440—31no—
73#440D311yescharacteristic, complemented
74#432—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C2×#67—21no—
79C22×Dic3—21no—
80C22×Dic3—21no—
81#237—22no—
82#237—22no—
83C2×C4×D3D411yescharacteristic
84C2×C4×D3D411yescharacteristic
85C2×C4×D3C2311yescharacteristic
86C2×Dic6—21no—
87C2×Dic6C2311yescharacteristic
88C2×Dic6C2311yescharacteristic
89C3×SD16—22no—
90C2×C3×C8C2311yescharacteristic
91C2×C3×C8C2311yescharacteristic
92C3×C4⋊C4—21no—
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C22⋊C4—21no—
96C3×C42—21no—
97C3×C42C2311yescharacteristic
98#217—21no—
99#216—22no—
100#214—22no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104C4⋊Dic3—21no—
105C4⋊Dic3C2311yescharacteristic
106C4⋊Dic3C2311yescharacteristic
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114C4×Dic3—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3D411yescharacteristic
119C4×Dic3D411yescharacteristic
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123Dic12—22no—
124C2×#41—31no—
125C2×Q16—31no—
126C2×Q16—31no—
127C2×SD16—31no—
128C2×SD16C2×D311yescharacteristic
129C4⋊Q8—31no—
130C4⋊Q8—31no—
131#125—61no—
132C22⋊Q8—31no—
133C22⋊Q8—31no—
134C22⋊Q8—61no—
135C4×Q8—31no—
136C4×Q8—31no—
137C4×Q8—31no—
138C4×Q8—61no—
139C4×Q8C2×D311yescharacteristic
140C4×D4—31no—
141C4×D4—61no—
142C4×D4—61no—
143C4×D4C2×D311yescharacteristic
144#117—31no—
145#117—61no—
146#117—61no—
147C2×C42—31no—
148C2×C42—61no—
149#107—31no—
150#107C2×D311yescharacteristic
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103C2×D311yescharacteristic
161#102—31no—
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97—31no—
166#97C2×D311yescharacteristic
167C23×C3—21no—
168C22×D3C2×D411yescharacteristic
169C3×Q8—21no—
170C3×Q8—21no—
171C3×D4—21no—
172C3×D4#4112yes—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—42no—
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2411yescharacteristic
180#67—24no—
181C2×Dic3—24no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—42no—
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189C2×Dic3C2×D411yescharacteristic
190C4×D3—21no—
191C4×D3—21no—
192C4×D3—22no—
193C4×D3—41no—
194Dic6—21no—
195Dic6—21no—
196Dic6—21no—
197Dic6—42no—
198Dic6#4112yes—
199C3×C8—21no—
200C3×C8—21no—
201C3⋊C8—21no—
202C3⋊C8—21no—
203#41—62no—
204#41—62no—
205C2×Q8—31no—
206C2×Q8—31no—
207C2×Q8—61no—
208C2×Q8C22×D311yescharacteristic
209C2×D4—61no—
210C2×D4C22×D311yescharacteristic
211C22×C4—21no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—61no—
216C22×C4—61no—
217Q16—62no—
218Q16—62no—
219SD16—22no—
220SD16—62no—
221C2×C8—31no—
222C2×C8—31no—
223C2×C8C22×D311yescharacteristic
224C2×C8C22×D311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—31no—
227C4⋊C4—31no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4C22×D311yescharacteristic
237C4⋊C4C22×D311yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C42—21no—
244C42—31no—
245C42—31no—
246C42—31no—
247C42—61no—
248C42—61no—
249C42—61no—
250C42—61no—
251C42C22×D311yescharacteristic
252C22×C3—22no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3C22×D411yescharacteristic
256C2×D3—21no—
257C2×D3—21no—
258C2×D3—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4C2×#4111yescharacteristic
265C3×C4C2×#4111yescharacteristic
266Dic3—22no—
267Dic3—21no—
268Dic3—21no—
269Dic3—41no—
270Dic3—41no—
271Dic3—41no—
272Dic3#13712yes—
273C23—21no—
274C23—31no—
275Q8—21no—
276Q8—21no—
277Q8—32no—
278Q8—61no—
279Q8—61no—
280Q8—61no—
281Q8—122no—
282D4—21no—
283D4—64no—
284D4#23512yes—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—31no—
289C2×C4—31no—
290C2×C4—31no—
291C2×C4—42no—
292C2×C4—62no—
293C2×C4—64no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—121no—
301C2×C4—122no—
302C2×C4D3×D411yescharacteristic
303C2×C4D3×D411yescharacteristic
304C2×C4C23×D311yescharacteristic
305C8—21no—
306C8—21no—
307C8—61no—
308C8—61no—
309C2×C3—42no—
310C2×C3#52511yescharacteristic
311C2×C3C2×#13711yescharacteristic
312C2×C3#57511yescharacteristic
313D3—41no—
314C22—22no—
315C22—41no—
316C22—41no—
317C22—61no—
318C22—61no—
319C22—61no—
320C22C2×D3×D411yescharacteristic
321C4—21no—
322C4—21no—
323C4—32no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—61no—
328C4—61no—
329C4—62no—
330C4—121no—
331C4—121no—
332C4—121no—
333C4C2×#23511yescharacteristic
334C4D3×#4111yescharacteristic
335C3#311611yescharacteristic, complemented, Sylow
336C2—42no—
337C2—121no—
338C2#554711yescharacteristic
339C2#577311yescharacteristic
340C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#440C2
socleC22×C3C22×D4
prime radicalC2×#237C22
hypercenter#440D3
hypocenterC3#3116
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #5578C2semidirect
3. C3×#440C2semidirect
5. #5162C2semidirect
6. #5030C2semidirect
7. #5018C2semidirect
8. #4888C2semidirect
9. #4875C2semidirect
10. #4815C2semidirect
11. #4795C2semidirect
13. #4761C2semidirect
14. #4716C2semidirect
15. #4705C2semidirect
73. #440D3semidirect
335. C3#3116semidirect

Maximal subgroups

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

subgroupindex
#55782
C4×#2372
C3×#4402
#51732
#51622
#50302
#50182
#48882
#48752
#48152
#47952
#47832
#47612
#47162
#47052
#31163