Finite Group Databasebeta

← #46814045

Subgroups — #46814045

Order 34432.

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×#22575430C211yesmaximal, characteristic
2#31770510C211yesmaximal, characteristic, complemented
3#31770509C211yesmaximal, characteristic, complemented
4#31770503C211yesmaximal, characteristic, complemented
5#31770500C211yesmaximal, characteristic, complemented
6#31770498C211yesmaximal, characteristic
7#31770493C211yesmaximal, characteristic
8#31770493C211yesmaximal, characteristic
9#31770492C211yesmaximal, characteristic, complemented
10#31770489C211yesmaximal, characteristic, complemented
11#31770488C211yesmaximal, characteristic, complemented
12#31770487C211yesmaximal, characteristic, complemented
13#31770466C211yesmaximal, characteristic
14#31770463C211yesmaximal, characteristic
15#388×C269C211yesmaximal, characteristic
16C22×Dic538C2211yescharacteristic
17C23×Dic269C2211yescharacteristic
18#22575430C418yescomplemented
19C2×C4⋊Dic269C2211yescharacteristic
20C2×C4⋊Dic269C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×C22⋊Dic269C2211yescharacteristic
28C2×C22⋊Dic269C2211yescharacteristic
29C2×C22⋊Dic269C2211yescharacteristic
30C2×C4×Dic269C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
33#22575360C2211yescharacteristic
34#22575360C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C2×C4⋊C4×C269C2211yescharacteristic
46C2×C22⋊C4×C269C2211yescharacteristic
47C2×C22⋊C4×C269C2211yescharacteristic
48C2×C22⋊C4×C269C2211yescharacteristic
49C2×C42×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C2×Dic538—41no—
53C2×Dic538—41no—
54C2×Dic538C2×C414yes—
55C22×Dic269—41no—
56C22×Dic269—41no—
57C22×Dic269C2×C414yes—
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C22×Dic269C2311yescharacteristic
64C22×Dic269C2311yescharacteristic
65C22×Dic269C2311yescharacteristic
66C4⋊Dic269—41no—
67C4⋊Dic269C2×C414yes—
68#16864381—41no—
69#16864381—41no—
70#16864381—41no—
71#16864381—41no—
72#16864381C2×C414yes—
73#16864381C2×C414yes—
74C22⋊Dic269—41no—
75C22⋊Dic269—41no—
76C22⋊Dic269C2×C414yes—
77C4×Dic269—41no—
78C4×Dic269—41no—
79C4×Dic269—41no—
80C24×C269C2311yescharacteristic
81C22×C4×C269C2311yescharacteristic
82C22×C4×C269C2311yescharacteristic
83C22×C4×C269C2311yescharacteristic
84C22×C4×C269C2311yescharacteristic
85C22×C4×C269C2311yescharacteristic
86C22×C4×C269C2311yescharacteristic
87C4⋊C4×C269—41no—
88C22⋊C4×C269—41no—
89C22⋊C4×C269—41no—
90C22⋊C4×C269C2×C414yes—
91C42×C269—41no—
92Dic538—44no—
93C2×Dic269—21no—
94C2×Dic269—21no—
95C2×Dic269—21no—
96C2×Dic269—21no—
97C2×Dic269—21no—
98C2×Dic269—21no—
99C2×Dic269—21no—
100C2×Dic269—21no—
101C2×Dic269—21no—
102C2×Dic269—21no—
103C2×Dic269—21no—
104C2×Dic269—21no—
105C2×Dic269—21no—
106C2×Dic269—21no—
107C2×Dic269—21no—
108C2×Dic269—21no—
109C2×Dic269—21no—
110C2×Dic269—21no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—44no—
114C2×Dic269C22×C412yes—
115C2×Dic269C22×C412yes—
116C2×Dic269C22×C412yes—
117C2×Dic269C22×C412yes—
118C23×C269—21no—
119C23×C269—21no—
120C23×C269—21no—
121C23×C269—21no—
122C23×C269—21no—
123C23×C269—21no—
124C23×C269C22×C412yes—
125C23×C269C2411yescharacteristic
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269C22×C412yes—
143C2×C4×C269C22×C412yes—
144C22×C269—22no—
145C22×C269—22no—
146C22×C269—22no—
147C22×C269—41no—
148C22×C269—41no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269C23×C411yescharacteristic
152C22×C269H(5,𝔽2)11yescharacteristic
153C22×C269H(5,𝔽2)11yescharacteristic
154C22×C269H(5,𝔽2)11yescharacteristic
155C22×C2692−1+411yescharacteristic
156C22×C2692−1+411yescharacteristic
157C22×C2692−1+411yescharacteristic
158C4×C269—22no—
159C4×C269—22no—
160C4×C269—41no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269—41no—
164Dic269—22no—
165Dic269—22no—
166Dic269—22no—
167Dic269—22no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—42no—
173C2×C269#51811yescharacteristic
174C2×C269#51911yescharacteristic
175C2×C269#52011yescharacteristic
176C2×C269#56211yescharacteristic
177C2×C269#56211yescharacteristic
178C2×C269#56311yescharacteristic
179C2×C269#56311yescharacteristic
180C269#237811yescharacteristic, complemented, Sylow
181#2378—2691nomaximal, Sylow
182C2×C22⋊Q8—2691no—
183#391—2691no—
184#391—2691no—
185#389—2691no—
186#389—2691no—
187#388—2691no—
188#388—2691no—
189#388—2691no—
190#388D26911yescharacteristic
191#387—2691no—
192#387—2691no—
193#387—2691no—
194#387—2691no—
195#381—2691no—
196#380—2691no—
197C22×Q8—2691no—
198C23×C4—2691no—
199C22⋊Q8—2698no—
200C2×C4⋊C4—2691no—
201C2×C4⋊C4—2691no—
202C2×C4⋊C4—2691no—
203C2×C4⋊C4—2691no—
204C2×C4⋊C4—2691no—
205C2×C4⋊C4—2691no—
206C2×C4⋊C4—2691no—
207C2×C4⋊C4—2691no—
208C2×C4⋊C4C2×D26911yescharacteristic
209C2×C22⋊C4—2691no—
210C2×C22⋊C4—2691no—
211C2×C22⋊C4—2691no—
212C2×C22⋊C4C2×D26911yescharacteristic
213C2×C22⋊C4C2×D26911yescharacteristic
214C2×C22⋊C4C2×D26911yescharacteristic
215C2×C42—2691no—
216C2×C42—2691no—
217C2×C42—2691no—
218C2×C42C2×D26911yescharacteristic
219#95—2691no—
220#95—2691no—
221#95—2691no—
222#95—2691no—
223#95—2691no—
224#95—2691no—
225#95—2691no—
226#95—2691no—
227#95—2691no—
228#95—2691no—
229#95—2691no—
230#95—2691no—
231#95C2×D26911yescharacteristic
232#95C2×D26911yescharacteristic
233C24C22×D26911yescharacteristic
234C2×Q8—2694no—
235C2×Q8—10761no—
236C2×Q8—10761no—
237C22×C4—2691no—
238C22×C4—2691no—
239C22×C4—2691no—
240C22×C4—2691no—
241C22×C4—2694no—
242C22×C4—2691no—
243C22×C4—2691no—
244C22×C4—2691no—
245C22×C4—2691no—
246C22×C4—10761no—
247C22×C4—10761no—
248C22×C4C22×D26911yescharacteristic
249C22×C4C22×D26911yescharacteristic
250C22×C4C22×D26911yescharacteristic
251C22×C4C22×D26911yescharacteristic
252C22×C4C22×D26911yescharacteristic
253C22×C4C22×D26911yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—2694no—
256C4⋊C4—2694no—
257C4⋊C4—2694no—
258C4⋊C4—10761no—
259C4⋊C4—10761no—
260C4⋊C4—10761no—
261C4⋊C4—10761no—
262C4⋊C4—10761no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—2694no—
266C22⋊C4—10761no—
267C22⋊C4—10761no—
268C22⋊C4C4×D26914yes—
269C42—41no—
270C42—10761no—
271C42—10761no—
272C42—10761no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C4×D26912yes—
280C23C23×D26911yescharacteristic
281Q8—10764no—
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—2692no—
299C2×C4—2692no—
300C2×C4—2692no—
301C2×C4—2692no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—10764no—
323C2×C4C2×C4×D26912yes—
324C2×C4C2×C4×D26912yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C22×C4×D26911yescharacteristic
333C22#2257549811yescharacteristic
334C22#2257549811yescharacteristic
335C22#2257549911yescharacteristic
336C22#2257550011yescharacteristic
337C22#2257550011yescharacteristic
338C22#2257550011yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—5382no—
346C4—5382no—
347C4—5382no—
348C4—5382no—
349C4—10761no—
350C4—10761no—
351C4—10761no—
352C4—10761no—
353C2—42no—
354C2#3177107711yescharacteristic
355C2#3177108211yescharacteristic
356C2#3177108411yescharacteristic
357C2#3177135011yescharacteristic
358C2#3177135211yescharacteristic
359C2#3177135511yescharacteristic
360C2#3177135711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#388×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenter#388D269
hypocenterC269#2378
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #31770510C2semidirect
3. #31770509C2semidirect
4. #31770503C2semidirect
5. #31770500C2semidirect
9. #31770492C2semidirect
10. #31770489C2semidirect
11. #31770488C2semidirect
12. #31770487C2semidirect
18. #22575430C4semidirect
180. C269#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#225754302
#317705102
#317705092
#317705032
#317705002
#317704982
#317704932
#317704922
#317704892
#317704882
#317704872
#317704662
#317704632
#388×C2692
#2378269