Finite Group Databasebeta

← #44487276

Subgroups — #44487276

Order 30592.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439937C211yesmaximal, characteristic
2#29504678C211yesmaximal, characteristic, complemented
3#29504676C211yesmaximal, characteristic, complemented
4#29504670C211yesmaximal, characteristic, complemented
5#29504669C211yesmaximal, characteristic, complemented
6#29504659C211yesmaximal, characteristic, complemented
7#29504656C211yesmaximal, characteristic, complemented
8#29504656C211yesmaximal, characteristic, complemented
9#29504655C211yesmaximal, characteristic, complemented
10#29504647C211yesmaximal, characteristic
11#29504644C211yesmaximal, characteristic
12#29504630C211yesmaximal, characteristic
13C4×C22⋊Dic239C211yesmaximal, characteristic
14C2×C239⋊#95C211yesmaximal, characteristic
15C4×C22⋊C4×C239C211yesmaximal, characteristic
16C22×Dic478C2211yescharacteristic
17C23×Dic239C2211yescharacteristic
18C23×Dic239C2211yescharacteristic
19#21439937C418yescomplemented
20C2×C4⋊Dic239C2211yescharacteristic
21C2×C4⋊Dic239C2211yescharacteristic
22C2×C4⋊Dic239C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×Dic239⋊C4C2211yescharacteristic
27C2×Dic239⋊C4C2211yescharacteristic
28C2×Dic239⋊C4C2211yescharacteristic
29C2×C22⋊Dic239C2211yescharacteristic
30C2×C22⋊Dic239C2211yescharacteristic
31C2×C4×Dic239C2211yescharacteristic
32C2×C4×Dic239C2211yescharacteristic
33C239⋊#95C2211yescharacteristic
34C239⋊#95C2211yescharacteristic
35C239⋊#95C2211yescharacteristic
36C239⋊#95C2211yescharacteristic
37C239⋊#95C2211yescharacteristic
38C239⋊#95C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C23×C4×C239C2211yescharacteristic
46C2×C22⋊C4×C239C2211yescharacteristic
47C2×C22⋊C4×C239C2211yescharacteristic
48C2×C42×C239C2211yescharacteristic
49C2×C42×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52C2×Dic478—41no—
53C2×Dic478—41no—
54C2×Dic478C2×C414yescomplemented
55C22×Dic239—22no—
56C22×Dic239—41no—
57C22×Dic239—41no—
58C22×Dic239—41no—
59C22×Dic239—41no—
60C22×Dic239C2×C414yes—
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C22×Dic239C2311yescharacteristic
64C22×Dic239C2311yescharacteristic
65C22×Dic239C2311yescharacteristic
66C22×Dic239C2311yescharacteristic
67C22×Dic239C2311yescharacteristic
68C22×Dic239C2311yescharacteristic
69C4⋊Dic239—41no—
70C4⋊Dic239—41no—
71C4⋊Dic239C2×C414yescomplemented
72Dic239⋊C4—41no—
73Dic239⋊C4—41no—
74Dic239⋊C4—41no—
75Dic239⋊C4—41no—
76Dic239⋊C4C2×C414yescomplemented
77Dic239⋊C4C2×C414yescomplemented
78C22⋊Dic239—22no—
79C22⋊Dic239C2×C414yes—
80C4×Dic239—41no—
81C4×Dic239—41no—
82C24×C239C2311yescharacteristic
83C22×C4×C239—41no—
84C22×C4×C239—41no—
85C22×C4×C239Q814yescomplemented
86C22×C4×C239C2311yescharacteristic
87C22×C4×C239C2311yescharacteristic
88C22×C4×C239C2311yescharacteristic
89C22×C4×C239C2311yescharacteristic
90C22×C4×C239C2311yescharacteristic
91C22×C4×C239C2311yescharacteristic
92C22⋊C4×C239—22no—
93C22⋊C4×C239C2×C414yes—
94C42×C239—41no—
95C42×C239—41no—
96Dic478—44no—
97C2×Dic239—21no—
98C2×Dic239—21no—
99C2×Dic239—21no—
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—44no—
118C2×Dic239—44no—
119C2×Dic239C22×C412yes—
120C2×Dic239C22×C412yes—
121C2×Dic239C22×C412yes—
122C2×Dic239C22×C412yes—
123C23×C239—21no—
124C23×C239—21no—
125C23×C239—21no—
126C23×C239—21no—
127C23×C239C22×C412yes—
128C23×C239C2×Q812yes—
129C23×C239#4112yes—
130C23×C239C2411yescharacteristic
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×C239—21no—
142C2×C4×C239—21no—
143C2×C4×C239—21no—
144C2×C4×C239—21no—
145C2×C4×C239—44no—
146C2×C4×C239C22×C412yes—
147C2×C4×C239C22×C412yes—
148C2×C4×C239C2×Q812yes—
149C2×C4×C239C2×Q812yes—
150C22×C239—22no—
151C22×C239—22no—
152C22×C239—22no—
153C22×C239—22no—
154C22×C239—22no—
155C22×C239—22no—
156C22×C239C4×Q814yes—
157C22×C239C23×C411yescharacteristic
158C22×C239C22×Q811yescharacteristic
159C22×C239C2×#4111yescharacteristic
160C22×C239H(5,𝔽2)11yescharacteristic
161C22×C239H(5,𝔽2)11yescharacteristic
162C22×C239H(5,𝔽2)11yescharacteristic
163C22×C2392−1+411yescharacteristic
164C4×C239—22no—
165C4×C239—22no—
166C4×C239—22no—
167C4×C239—22no—
168C4×C239—41no—
169C4×C239—41no—
170Dic239—22no—
171Dic239—22no—
172Dic239—22no—
173Dic239—22no—
174Dic239—41no—
175Dic239—41no—
176Dic239—41no—
177Dic239—41no—
178C2×C239—24no—
179C2×C239C2×C4×Q811yescharacteristic
180C2×C239#51811yescharacteristic
181C2×C239#52011yescharacteristic
182C2×C239#53811yescharacteristic
183C2×C239#53911yescharacteristic
184C2×C239#54311yescharacteristic
185C2×C239#54411yescharacteristic
186C239#232911yescharacteristic, complemented, Sylow
187#2329—2391nomaximal, Sylow
188C2×C22⋊Q8—2391no—
189#391—2391no—
190#391—2391no—
191#389—2391no—
192#389—2391no—
193#387—2391no—
194#387—2391no—
195#387—2391no—
196#387—2391no—
197#385—2391no—
198#385—2391no—
199#380—2391no—
200C4×C22⋊C4—2391no—
201C4×C22⋊C4D23911yescharacteristic
202C2×#95—2391no—
203C22×Q8—2391no—
204C23×C4—2391no—
205C23×C4—2391no—
206C23×C4C2×D23911yescharacteristic
207C22⋊Q8—2398no—
208C2×C4⋊C4—2391no—
209C2×C4⋊C4—2391no—
210C2×C4⋊C4—2391no—
211C2×C4⋊C4—2391no—
212C2×C4⋊C4—2391no—
213C2×C4⋊C4—2391no—
214C2×C4⋊C4—2391no—
215C2×C4⋊C4—2391no—
216C2×C4⋊C4—2391no—
217C2×C22⋊C4—2391no—
218C2×C22⋊C4—2391no—
219C2×C22⋊C4C2×D23911yescharacteristic
220C2×C22⋊C4C2×D23911yescharacteristic
221C2×C42—2391no—
222C2×C42—2391no—
223C2×C42C2×D23911yescharacteristic
224C2×C42C2×D23911yescharacteristic
225#95—2391no—
226#95—2391no—
227#95—2391no—
228#95—2391no—
229#95—2391no—
230#95—2391no—
231#95—2391no—
232#95—2391no—
233#95—2391no—
234#95—2391no—
235#95—2391no—
236#95—2391no—
237#95C2×D23911yescharacteristic
238#95C2×D23911yescharacteristic
239C24C22×D23911yescharacteristic
240C2×Q8—9561no—
241C2×Q8—9561no—
242C2×Q8—2394no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—9561no—
246C22×C4—9561no—
247C22×C4—9561no—
248C22×C4—9561no—
249C22×C4—4782no—
250C22×C4—2394no—
251C22×C4—2391no—
252C22×C4—2391no—
253C22×C4—2391no—
254C22×C4—2391no—
255C22×C4—2391no—
256C22×C4—2391no—
257C22×C4—2391no—
258C22×C4—2391no—
259C22×C4Dic47814yescomplemented
260C22×C4C22×D23911yescharacteristic
261C22×C4C22×D23911yescharacteristic
262C22×C4C22×D23911yescharacteristic
263C22×C4C22×D23911yescharacteristic
264C22×C4C22×D23911yescharacteristic
265C22×C4C22×D23911yescharacteristic
266C4⋊C4—9561no—
267C4⋊C4—9561no—
268C4⋊C4—9561no—
269C4⋊C4—9561no—
270C4⋊C4—9561no—
271C4⋊C4—9561no—
272C4⋊C4—2394no—
273C4⋊C4—2394no—
274C4⋊C4—2394no—
275C22⋊C4—22no—
276C22⋊C4—4782no—
277C22⋊C4—2394no—
278C22⋊C4C4×D23914yes—
279C42—41no—
280C42—41no—
281C42—9561no—
282C42—9561no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C4×D23912yes—
288C23C2×Dic47812yes—
289C23#1683854812yes—
290C23C23×D23911yescharacteristic
291Q8—9564no—
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—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—44no—
307C2×C4—9564no—
308C2×C4—9564no—
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—4781no—
320C2×C4—4781no—
321C2×C4—4781no—
322C2×C4—4781no—
323C2×C4—4781no—
324C2×C4—4781no—
325C2×C4—4781no—
326C2×C4—4781no—
327C2×C4—4781no—
328C2×C4—4781no—
329C2×C4—2392no—
330C2×C4—2392no—
331C2×C4—2392no—
332C2×C4—2392no—
333C2×C4C2×C4×D23912yes—
334C2×C4C2×C4×D23912yes—
335C2×C4C2×Dic47812yes—
336C2×C4C2×Dic47812yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22C4×Dic47814yes—
344C22C22×C4×D23911yescharacteristic
345C22C22×Dic47811yescharacteristic
346C22C2×#1683854811yescharacteristic
347C22#2144000511yescharacteristic
348C22#2144000511yescharacteristic
349C22#2144000611yescharacteristic
350C22#2144000711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—9561no—
358C4—9561no—
359C4—9561no—
360C4—9561no—
361C4—4782no—
362C4—4782no—
363C4—4782no—
364C4—4782no—
365C2—24no—
366C2C2×C4×Dic47811yescharacteristic
367C2#2950524411yescharacteristic
368C2#2950525111yescharacteristic
369C2#2950535511yescharacteristic
370C2#2950536411yescharacteristic
371C2#2950539811yescharacteristic
372C2#2950540011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC4×C22⋊C4×C239C2
socle, cosocleC23×C239C24
prime radicalC24×C239C23
hypercenterC4×C22⋊C4D239
hypocenterC239#2329
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #29504678C2semidirect
3. #29504676C2semidirect
4. #29504670C2semidirect
5. #29504669C2semidirect
6. #29504659C2semidirect
7. #29504656C2semidirect
8. #29504656C2semidirect
9. #29504655C2semidirect
19. #21439937C4semidirect
54. C2×Dic478C2×C4semidirect
71. C4⋊Dic239C2×C4semidirect
76. Dic239⋊C4C2×C4semidirect
77. Dic239⋊C4C2×C4semidirect
85. C22×C4×C239Q8semidirect
186. C239#2329semidirect
259. C22×C4Dic478semidirect

Maximal subgroups

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

subgroupindex
C2×#214399372
#295046782
#295046762
#295046702
#295046692
#295046592
#295046562
#295046552
#295046472
#295046442
#295046302
C4×C22⋊Dic2392
C2×C239⋊#952
C4×C22⋊C4×C2392
#2329239