Finite Group Databasebeta

← #83461

Subgroups — #83461

Order 384.

384 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
1C3×#542C211yesmaximal, characteristic, complemented
2#5523C211yesmaximal, characteristic, complemented
3#5091C211yesmaximal, characteristic, complemented
4#5087C211yesmaximal, characteristic, complemented
5#5057C211yesmaximal, characteristic, complemented
6#5054C211yesmaximal, characteristic, complemented
7#5047C211yesmaximal, characteristic, complemented
8#5044C211yesmaximal, characteristic, complemented
9#5037C211yesmaximal, characteristic
10#5033C211yesmaximal, characteristic, complemented
11C4×#216C211yesmaximal, characteristic, complemented
12#5026C211yesmaximal, characteristic, complemented
13#5018C211yesmaximal, characteristic, complemented
14C4×#213C211yesmaximal, characteristic, complemented
15#5000C211yesmaximal, characteristic, complemented
16#3124—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C3×C4⋊Q8C2211yescharacteristic
19C3×#126—21no—
20C3×#124—21no—
21C3×#124C2211yescharacteristic
22C3×#123—21no—
23C3×C22⋊Q8—21no—
24C3×C22⋊Q8C2211yescharacteristic
25C3×#121C2211yescharacteristic
26C3×C4×Q8C2211yescharacteristic
27C3×C4×D4C2211yescharacteristic
28C3×#117C2211yescharacteristic
29C2×#216C2211yescharacteristic
30C2×#215C2211yescharacteristic
31C2×#214C2211yescharacteristic
32C2×#213C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34#892—21no—
35D3×C4⋊C4—21no—
36#67⋊C4—21no—
37#67⋊C4—21no—
38C4×D12C2211yescharacteristic
39C4×D12C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41C4×Dic6C2211yescharacteristic
42#835C2211yescharacteristic
43#835C2211yescharacteristic
44#832C2211yescharacteristic
45#832C2211yescharacteristic
46#830C2211yescharacteristic
47#830C2211yescharacteristic
48#810C2211yescharacteristic
49#810C2211yescharacteristic
50#809C2211yescharacteristic
51#809C2211yescharacteristic
52#807C2211yescharacteristic
53#807C2211yescharacteristic
54#807C2211yescharacteristic
55#807C2211yescharacteristic
56C4⋊(C3⋊C8)C2211yescharacteristic
57C4⋊(C3⋊C8)C2211yescharacteristic
58#803C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#542D311yescharacteristic, complemented
61#520—31no—
62#484—31no—
63#480—31no—
64#477—31no—
65#474—31no—
66#464—31no—
67#463—31no—
68#452—31no—
69#449—31no—
70#440—31no—
71#440—31no—
72C4×Q16—31no—
73C4×D8—31no—
74#433—31no—
75C2×C3×Q8—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4—21no—
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C22×C3×C4C2311yescharacteristic
81C2×#67—21no—
82C22×Dic3—21no—
83#235—22no—
84#235—22no—
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×Dic6C2311yescharacteristic
90C3×C4⋊C4—21no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4D411yescharacteristic
94C3×C4⋊C4D411yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C22⋊C4—21no—
98C3×C22⋊C4—21no—
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C22⋊C4D411yescharacteristic
103C3×C22⋊C4D411yescharacteristic
104C3×C42—21no—
105C3×C42C2311yescharacteristic
106C3×C42C2311yescharacteristic
107#216—22no—
108#215—22no—
109#214—22no—
110#213—22no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×#41—31no—
125C2×Q16—31no—
126C2×SD16—31no—
127C2×SD16—31no—
128C2×D8—31no—
129C4⋊Q8C2×D311yescharacteristic
130#126—21no—
131#124—21no—
132#124C2×D311yescharacteristic
133#123—21no—
134C22⋊Q8—21no—
135C22⋊Q8C2×D311yescharacteristic
136#121C2×D311yescharacteristic
137C4×Q8—31no—
138C4×Q8—31no—
139C4×Q8C2×D311yescharacteristic
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—61no—
143C4×D4—61no—
144C4×D4C2×D311yescharacteristic
145#117—61no—
146#117C2×D311yescharacteristic
147C2×C4⋊C4—31no—
148C2×C4⋊C4—61no—
149#107—31no—
150#107—31no—
151#107—31no—
152#107—31no—
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97—31no—
166C4×C8—31no—
167C23×C3—21no—
168C23×C3C2×D411yescharacteristic
169C22×D3—21no—
170C3×Q8—21no—
171C3×Q8—21no—
172C3×Q8—81no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4—81no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—81no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—24no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—81no—
193D12—21no—
194D12#4112yes—
195C4×D3—24no—
196C4×D3—81no—
197C4×D3—81no—
198Dic6—21no—
199Dic6#4112yes—
200C3⋊C8—21no—
201C3⋊C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204#41—62no—
205#41—62no—
206C2×Q8—21no—
207C2×Q8—31no—
208C2×Q8C22×D311yescharacteristic
209C2×D4—21no—
210C2×D4—31no—
211C2×D4—61no—
212C2×D4C22×D311yescharacteristic
213C22×C4—21no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219Q16—62no—
220SD16—62no—
221SD16—62no—
222D8—62no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8—31no—
226C2×C8—31no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4#6711yescharacteristic
236C4⋊C4#6711yescharacteristic
237C4⋊C4C22×D311yescharacteristic
238C4⋊C4C22×D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4#6711yescharacteristic
247C22⋊C4#6711yescharacteristic
248C42—21no—
249C42—61no—
250C42—61no—
251C42C22×D311yescharacteristic
252C42C22×D311yescharacteristic
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3C22×D411yescharacteristic
260C2×D3—22no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4C2×#4111yescharacteristic
272C3×C4C2×#4111yescharacteristic
273Dic3—22no—
274Dic3—41no—
275Dic3—41no—
276C23—21no—
277C23—61no—
278C23C2×#6711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—32no—
282Q8—61no—
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—32no—
287D4—64no—
288D4—61no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—64no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—81no—
300C2×C4—241no—
301C2×C4—241no—
302C2×C4—241no—
303C2×C4C2×#6711yescharacteristic
304C2×C4C2×#6711yescharacteristic
305C2×C4C2×#6711yescharacteristic
306C2×C4C2×#6711yescharacteristic
307C2×C4C2×#6711yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—61no—
310C8—61no—
311C8—61no—
312C8—61no—
313C2×C3—41no—
314C2×C3—81no—
315C2×C3#52511yescharacteristic
316C2×C3#57611yescharacteristic
317C2×C3#57811yescharacteristic
318D3—42no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—62no—
326C22—121no—
327C22—121no—
328C22C22×#6711yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—62no—
338C4—121no—
339C4—121no—
340C4D3×#4111yescharacteristic
341C4D3×#4111yescharacteristic
342C3#312411yescharacteristic, complemented, Sylow
343C2—41no—
344C2—81no—
345C2—122no—
346C2#582811yescharacteristic
347C2#583511yescharacteristic
348C2#583811yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#542C2
socleC22×C3C22×D4
prime radical#5037C2
hypercenter#542D3
hypocenterC3#3124
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C3×#542C2semidirect
2. #5523C2semidirect
3. #5091C2semidirect
4. #5087C2semidirect
5. #5057C2semidirect
6. #5054C2semidirect
7. #5047C2semidirect
8. #5044C2semidirect
10. #5033C2semidirect
11. C4×#216C2semidirect
12. #5026C2semidirect
13. #5018C2semidirect
14. C4×#213C2semidirect
15. #5000C2semidirect
60. #542D3semidirect
342. C3#3124semidirect

Maximal subgroups

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

subgroupindex
C3×#5422
#55232
#50912
#50872
#50572
#50542
#50472
#50442
#50372
#50332
C4×#2162
#50262
#50182
C4×#2132
#50002
#31243