Finite Group Databasebeta

← #80214

Subgroups — #80214

Order 384.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#41C211yesmaximal, characteristic, complemented
2#5624C211yesmaximal, characteristic, complemented
3C3×#452C211yesmaximal, characteristic, complemented
4#5238C211yesmaximal, characteristic
5#5185C211yesmaximal, characteristic, complemented
6#5184C211yesmaximal, characteristic, complemented
7#5165C211yesmaximal, characteristic, complemented
8#5164C211yesmaximal, characteristic, complemented
9#5045C211yesmaximal, characteristic, complemented
10#4817C211yesmaximal, characteristic, complemented
11#4796C211yesmaximal, characteristic, complemented
12#4785C211yesmaximal, characteristic, complemented
13#4763C211yesmaximal, characteristic, complemented
14#4737C211yesmaximal, characteristic, complemented
15#4719C211yesmaximal, characteristic, complemented
16#3111—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×Q16C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C22⋊Q8C2211yescharacteristic
21#947C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic
24Q8×Dic3C2211yescharacteristic
25C2×#215C2211yescharacteristic
26D4×Dic3—21no—
27D4×Dic3—21no—
28D4×Dic3C2211yescharacteristic
29D4×Dic3C2211yescharacteristic
30C2×#213C2211yescharacteristic
31#930C2211yescharacteristic
32#926—21no—
33#926C2211yescharacteristic
34C2×C4×Dic3—21no—
35C2×C4×Dic3C2211yescharacteristic
36#898—21no—
37#893C2211yescharacteristic
38#892—21no—
39#890C2211yescharacteristic
40#886—21no—
41#67⋊C4—21no—
42C3×#103C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic
46#835C2211yescharacteristic
47#835C2211yescharacteristic
48#832C2211yescharacteristic
49#830C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#818C2211yescharacteristic
53#817C2211yescharacteristic
54#815C2211yescharacteristic
55#815C2211yescharacteristic
56Dic3⋊C8C2211yescharacteristic
57Dic3⋊C8C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#529—31no—
61C4×#41—31no—
62#485—31no—
63#482—31no—
64#479—31no—
65#478—31no—
66#464—31no—
67#463—31no—
68#452D311yescharacteristic, complemented
69#449—31no—
70#442—31no—
71#441—31no—
72#440—31no—
73#440—31no—
74#432—31no—
75C3×#41—22no—
76C3×#41—22no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C22×C3×C4—21no—
82C22×C3×C4C2311yescharacteristic
83C2×#67—21no—
84C22×Dic3—21no—
85C22×Dic3—21no—
86C22×Dic3D411yescharacteristic
87C22×Dic3D411yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C3×Q16—22no—
91C3×SD16—22no—
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C3×C4⋊C4—21no—
95C3×C4⋊C4C2311yescharacteristic
96C3×C22⋊C4—21no—
97#217—21no—
98#217—21no—
99#217—21no—
100#215—22no—
101#213—22no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106C4⋊Dic3—21no—
107C4⋊Dic3—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114C4×Dic3—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3D411yescharacteristic
119C4×Dic3D411yescharacteristic
120C4×Dic3C2311yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×#41C2×D311yescharacteristic
125C2×Q16C2×D311yescharacteristic
126C2×SD16—31no—
127C2×SD16C2×D311yescharacteristic
128C2×D8—31no—
129#126—61no—
130#125—31no—
131#124—31no—
132#123—61no—
133C22⋊Q8C2×D311yescharacteristic
134#121—31no—
135C4×Q8—31no—
136C4×Q8—31no—
137C4×Q8—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—61no—
142C4×D4—61no—
143C4×D4—61no—
144#117—31no—
145#117—61no—
146#117—61no—
147C2×C42—31no—
148C2×C42—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#103C2×D311yescharacteristic
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8C2×D311yescharacteristic
165#97—31no—
166#97—31no—
167C23×C3—21no—
168C23×C3C2×D411yescharacteristic
169C22×D3—21no—
170C3×Q8—21no—
171C3×Q8—21no—
172C3×Q8—21no—
173C3×Q8#4112yes—
174C3×D4—24no—
175C3×D4—21no—
176C3×D4#4112yes—
177C2×C3×C4—24no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2411yescharacteristic
185#67—42no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—42no—
192C2×Dic3—42no—
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197D12—21no—
198D12—21no—
199C4×D3—42no—
200C3×C8—21no—
201C3×C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204#41—22no—
205#41—22no—
206C2×Q8C22×D311yescharacteristic
207C2×Q8C22×D311yescharacteristic
208C2×D4—21no—
209C2×D4—31no—
210C2×D4—61no—
211C2×D4C22×D311yescharacteristic
212C22×C4—21no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219Q16—22no—
220SD16—22no—
221SD16—62no—
222D8—62no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8C22×D311yescharacteristic
226C2×C8C22×D311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—31no—
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4C22×D311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C42—31no—
246C42—31no—
247C42—31no—
248C42—31no—
249C42—61no—
250C42—61no—
251C42—61no—
252C42—61no—
253C22×C3—21no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3C22×D411yescharacteristic
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—21no—
264C3×C4—22no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4C2×#4111yescharacteristic
268C3×C4C2×#4111yescharacteristic
269Dic3—21no—
270Dic3—21no—
271Dic3—21no—
272Dic3—21no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276C23—21no—
277C23—61no—
278C23D3×D411yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8#23712yes—
283D4—24no—
284D4—21no—
285D4—61no—
286D4—61no—
287D4—122no—
288D4#23712yes—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—122no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4—122no—
306C2×C4—122no—
307C2×C4D3×D411yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—21no—
310C8—21no—
311C8—61no—
312C8—61no—
313C2×C3—41no—
314C2×C3—42no—
315C2×C3#52511yescharacteristic
316C2×C3#57511yescharacteristic
317C2×C3#57511yescharacteristic
318D3—81no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22C2×D3×D411yescharacteristic
329C4—21no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—61no—
334C4—61no—
335C4—61no—
336C4—61no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4C2×#23711yescharacteristic
341C4C2×#23711yescharacteristic
342C3#311111yescharacteristic, complemented, Sylow
343C2—41no—
344C2—42no—
345C2—241no—
346C2#558611yescharacteristic
347C2#576811yescharacteristic
348C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#452C2
socleC22×C3C22×D4
prime radical#5238C2
hypercenter#452D3
hypocenterC3#3111
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. Dic3×#41C2semidirect
2. #5624C2semidirect
3. C3×#452C2semidirect
5. #5185C2semidirect
6. #5184C2semidirect
7. #5165C2semidirect
8. #5164C2semidirect
9. #5045C2semidirect
10. #4817C2semidirect
11. #4796C2semidirect
12. #4785C2semidirect
13. #4763C2semidirect
14. #4737C2semidirect
15. #4719C2semidirect
68. #452D3semidirect
342. C3#3111semidirect

Maximal subgroups

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

subgroupindex
Dic3×#412
#56242
C3×#4522
#52382
#51852
#51842
#51652
#51642
#50452
#48172
#47962
#47852
#47632
#47372
#47192
#31113