Finite Group Databasebeta

← #44487713

Subgroups — #44487713

Order 30592.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439938C211yesmaximal, characteristic
2#29504678C211yesmaximal, characteristic, complemented
3#29504676C211yesmaximal, characteristic, complemented
4#29504671C211yesmaximal, characteristic, complemented
5#29504667C211yesmaximal, characteristic, complemented
6#29504664C211yesmaximal, characteristic
7#29504664C211yesmaximal, characteristic
8#29504663C211yesmaximal, characteristic
9#29504661C211yesmaximal, characteristic
10#29504659C211yesmaximal, characteristic, complemented
11#29504659C211yesmaximal, characteristic, complemented
12#29504654C211yesmaximal, characteristic, complemented
13#29504634C211yesmaximal, characteristic
14#29504629C211yesmaximal, characteristic
15#387×C239C211yesmaximal, characteristic, complemented
16C22×Dic478C2211yescharacteristic
17C22×C4×D239C2211yescharacteristic
18#21439938C418yescomplemented
19C2×C4⋊Dic239C2211yescharacteristic
20C2×C4⋊Dic239C2211yescharacteristic
21C2×C4⋊Dic239C2211yescharacteristic
22C2×Dic239⋊C4C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×(C2×D239)⋊C4C2211yescharacteristic
27C2×(C2×D239)⋊C4C2211yescharacteristic
28C2×(C2×D239)⋊C4C2211yescharacteristic
29C2×(C2×D239)⋊C4C2211yescharacteristic
30C2×(C2×D239)⋊C4C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×C4×Dic239C2211yescharacteristic
33C2×C4×Dic239C2211yescharacteristic
34C2×C4×Dic239C2211yescharacteristic
35C239⋊#95C2211yescharacteristic
36C239⋊#95C2211yescharacteristic
37C239⋊#95C2211yescharacteristic
38C239⋊#95C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C2×C4⋊C4×C239C2211yescharacteristic
46C2×C4⋊C4×C239C2211yescharacteristic
47C2×C42×C239C2211yescharacteristic
48#95×C239C2211yescharacteristic
49#95×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52C23×D239C2311yescharacteristic
53C2×Dic478—41no—
54C2×Dic478—41no—
55C2×Dic478C2×C414yes—
56C22×Dic239C2311yescharacteristic
57C22×Dic239C2311yescharacteristic
58C22×Dic239C2311yescharacteristic
59C22×Dic239C2311yescharacteristic
60C22×Dic239C2311yescharacteristic
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C2×C4×D239—41no—
64C2×C4×D239—41no—
65C2×C4×D239C2×C414yes—
66C4⋊Dic239—41no—
67C4⋊Dic239—41no—
68C4⋊Dic239—41no—
69Dic239⋊C4—41no—
70Dic239⋊C4—41no—
71Dic239⋊C4C2×C414yes—
72Dic239⋊C4C2×C414yes—
73(C2×D239)⋊C4—41no—
74(C2×D239)⋊C4—41no—
75(C2×D239)⋊C4—41no—
76(C2×D239)⋊C4—41no—
77(C2×D239)⋊C4C2×C414yes—
78(C2×D239)⋊C4C2×C414yes—
79C4×Dic239—41no—
80C4×Dic239—41no—
81C4×Dic239—41no—
82C22×C4×C239C2311yescharacteristic
83C22×C4×C239C2311yescharacteristic
84C22×C4×C239C2311yescharacteristic
85C22×C4×C239C2311yescharacteristic
86C22×C4×C239C2311yescharacteristic
87C22×C4×C239C2311yescharacteristic
88C22×C4×C239C2311yescharacteristic
89C4⋊C4×C239—41no—
90C4⋊C4×C239C2×C414yes—
91C42×C239—41no—
92C22×D239—21no—
93C22×D239—21no—
94C22×D239—21no—
95C22×D239—21no—
96C22×D239—21no—
97C22×D239—21no—
98C22×D239C22×C412yes—
99Dic478—44no—
100C2×Dic239—21no—
101C2×Dic239—21no—
102C2×Dic239—21no—
103C2×Dic239—21no—
104C2×Dic239—21no—
105C2×Dic239—21no—
106C2×Dic239—21no—
107C2×Dic239—21no—
108C2×Dic239—21no—
109C2×Dic239—21no—
110C2×Dic239—21no—
111C2×Dic239—21no—
112C2×Dic239—21no—
113C2×Dic239—21no—
114C2×Dic239—21no—
115C2×Dic239—21no—
116C2×Dic239—21no—
117C2×Dic239—21no—
118C2×Dic239C22×C412yes—
119C2×Dic239C22×C412yes—
120C2×Dic239C22×C412yes—
121C4×D239—44no—
122C23×C239C2411yescharacteristic
123C2×C4×C239—21no—
124C2×C4×C239—21no—
125C2×C4×C239—21no—
126C2×C4×C239—21no—
127C2×C4×C239—21no—
128C2×C4×C239—21no—
129C2×C4×C239—21no—
130C2×C4×C239—21no—
131C2×C4×C239—21no—
132C2×C4×C239—21no—
133C2×C4×C239—21no—
134C2×C4×C239—21no—
135C2×C4×C239—21no—
136C2×C4×C239—21no—
137C2×C4×C239—21no—
138C2×C4×C239—21no—
139C2×C4×C239—21no—
140C2×C4×C239—21no—
141C2×C4×C239C22×C412yes—
142C2×C4×C239C22×C412yes—
143C2×C4×C239C22×C412yes—
144C22×C239C23×C411yescharacteristic
145C22×C239H(5,𝔽2)11yescharacteristic
146C22×C239H(5,𝔽2)11yescharacteristic
147C22×C239H(5,𝔽2)11yescharacteristic
148C22×C2392−1+411yescharacteristic
149C22×C2392−1+411yescharacteristic
150C22×C2392−1+411yescharacteristic
151C2×D239—22no—
152C2×D239—22no—
153C2×D239—22no—
154C2×D239—41no—
155C2×D239—41no—
156C2×D239—41no—
157C2×D239—41no—
158C4×C239—22no—
159C4×C239—22no—
160C4×C239—22no—
161C4×C239—41no—
162C4×C239—41no—
163C4×C239—41no—
164C4×C239—41no—
165Dic239—22no—
166Dic239—22no—
167Dic239—22no—
168Dic239—41no—
169Dic239—41no—
170Dic239—41no—
171Dic239—41no—
172C2×C239#51811yescharacteristic
173C2×C239#51911yescharacteristic
174C2×C239#52011yescharacteristic
175C2×C239#56211yescharacteristic
176C2×C239#56211yescharacteristic
177C2×C239#56311yescharacteristic
178C2×C239#56311yescharacteristic
179D239—42no—
180C239#237811yescharacteristic, complemented, Sylow
181#2378—2391nomaximal, Sylow
182C2×C22⋊Q8—2391no—
183#391—2391no—
184#391—2391no—
185#389—2391no—
186#389—2391no—
187#388—2391no—
188#388—2391no—
189#388—2391no—
190#388—2391no—
191#387—2391no—
192#387—2391no—
193#387—2391no—
194#387D23911yescharacteristic, complemented
195#381—2391no—
196#380—2391no—
197C22×Q8—2391no—
198C23×C4—2391no—
199C22⋊Q8—2398no—
200C2×C4⋊C4—2391no—
201C2×C4⋊C4—2391no—
202C2×C4⋊C4—2391no—
203C2×C4⋊C4—2391no—
204C2×C4⋊C4—2391no—
205C2×C4⋊C4—2391no—
206C2×C4⋊C4—2391no—
207C2×C4⋊C4C2×D23911yescharacteristic
208C2×C4⋊C4C2×D23911yescharacteristic
209C2×C22⋊C4—2391no—
210C2×C22⋊C4—2391no—
211C2×C22⋊C4—2391no—
212C2×C22⋊C4—2391no—
213C2×C22⋊C4—2391no—
214C2×C22⋊C4—2391no—
215C2×C42—2391no—
216C2×C42—2391no—
217C2×C42—2391no—
218C2×C42C2×D23911yescharacteristic
219#95—2391no—
220#95—2391no—
221#95—2391no—
222#95—2391no—
223#95—2391no—
224#95—2391no—
225#95—2391no—
226#95—2391no—
227#95—2391no—
228#95—2391no—
229#95C2×D23911yescharacteristic
230#95C2×D23911yescharacteristic
231#95C2×D23911yescharacteristic
232#95C2×D23911yescharacteristic
233C24—2391no—
234C2×Q8—9561no—
235C2×Q8—9561no—
236C2×Q8—2394no—
237C22×C4—9561no—
238C22×C4—9561no—
239C22×C4—2394no—
240C22×C4—2391no—
241C22×C4—2391no—
242C22×C4—2391no—
243C22×C4—2391no—
244C22×C4—2391no—
245C22×C4—2391no—
246C22×C4—2391no—
247C22×C4C22×D23911yescharacteristic
248C22×C4C22×D23911yescharacteristic
249C22×C4C22×D23911yescharacteristic
250C22×C4C22×D23911yescharacteristic
251C22×C4C22×D23911yescharacteristic
252C22×C4C22×D23911yescharacteristic
253C22×C4C22×D23911yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—9561no—
256C4⋊C4—9561no—
257C4⋊C4—9561no—
258C4⋊C4—9561no—
259C4⋊C4—9561no—
260C4⋊C4—2394no—
261C4⋊C4—2394no—
262C4⋊C4C4×D23914yes—
263C22⋊C4—9561no—
264C22⋊C4—9561no—
265C22⋊C4—9561no—
266C22⋊C4—9561no—
267C22⋊C4—2394no—
268C22⋊C4—2394no—
269C42—41no—
270C42—9561no—
271C42—9561no—
272C42—9561no—
273C23—4781no—
274C23—4781no—
275C23—4781no—
276C23—4781no—
277C23—4781no—
278C23—4781no—
279C23—2392no—
280C23C23×D23911yescharacteristic
281Q8—9564no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—9564no—
301C2×C4—4781no—
302C2×C4—4781no—
303C2×C4—4781no—
304C2×C4—4781no—
305C2×C4—4781no—
306C2×C4—4781no—
307C2×C4—4781no—
308C2×C4—4781no—
309C2×C4—4781no—
310C2×C4—4781no—
311C2×C4—4781no—
312C2×C4—4781no—
313C2×C4—4781no—
314C2×C4—4781no—
315C2×C4—4781no—
316C2×C4—4781no—
317C2×C4—4781no—
318C2×C4—4781no—
319C2×C4—2392no—
320C2×C4—2392no—
321C2×C4—2392no—
322C2×C4C2×C4×D23912yes—
323C2×C4C2×C4×D23912yes—
324C2×C4C2×C4×D23912yes—
325C22—9561no—
326C22—9561no—
327C22—9561no—
328C22—9561no—
329C22—4782no—
330C22—4782no—
331C22—4782no—
332C22C22×C4×D23911yescharacteristic
333C22#2144000511yescharacteristic
334C22#2144000611yescharacteristic
335C22#2144000611yescharacteristic
336C22#2144000711yescharacteristic
337C22#2144000711yescharacteristic
338C22#2144000811yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—9561no—
347C4—9561no—
348C4—9561no—
349C4—9561no—
350C4—4782no—
351C4—4782no—
352C4—4782no—
353C2—9562no—
354C2#2950524411yescharacteristic
355C2#2950524811yescharacteristic
356C2#2950525211yescharacteristic
357C2#2950551911yescharacteristic
358C2#2950552011yescharacteristic
359C2#2950552311yescharacteristic
360C2#2950552411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#387×C239C2
socle, cosocleC23×C239C24
prime radicalC23×D239C23
hypercenter#387D239
hypocenterC239#2378
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #29504678C2semidirect
3. #29504676C2semidirect
4. #29504671C2semidirect
5. #29504667C2semidirect
10. #29504659C2semidirect
11. #29504659C2semidirect
12. #29504654C2semidirect
15. #387×C239C2semidirect
18. #21439938C4semidirect
180. C239#2378semidirect
194. #387D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399382
#295046782
#295046762
#295046712
#295046672
#295046642
#295046632
#295046612
#295046592
#295046542
#295046342
#295046292
#387×C2392
#2378239