Finite Group Databasebeta

← #24913435

Subgroups — #24913435

Order 10624.

436 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
1#19127642C211yesmaximal, characteristic, complemented
2#19127642C211yesmaximal, characteristic, complemented
3#19127641C211yesmaximal, characteristic, complemented
4#19127639C211yesmaximal, characteristic, complemented
5#19127635C211yesmaximal, characteristic, complemented
6#19127634C211yesmaximal, characteristic, complemented
7#19127632C211yesmaximal, characteristic, complemented
8#19127631C211yesmaximal, characteristic, complemented
9#19127576C211yesmaximal, characteristic
10#19127574C211yesmaximal, characteristic
11#19127573C211yesmaximal, characteristic
12#19127559C211yesmaximal, characteristic
13#19127559C211yesmaximal, characteristic
14C2×C83⋊#95C211yesmaximal, characteristic
15#385×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18C2×C4⋊Dic83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C83⋊#95C2211yescharacteristic
31C83⋊#95C2211yescharacteristic
32C83⋊#95C2211yescharacteristic
33C83⋊#95C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C23×C4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C22×Dic83—22no—
52C22×Dic83—41no—
53C22×Dic83—41no—
54C22×Dic83—41no—
55C22×Dic83—41no—
56C22×Dic83Q814yes—
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C4⋊Dic83—41no—
66C4⋊Dic83—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69Dic83⋊C4—41no—
70Dic83⋊C4—41no—
71Dic83⋊C4—41no—
72Dic83⋊C4—41no—
73Dic83⋊C4—41no—
74Dic83⋊C4—41no—
75C22⋊Dic83—22no—
76C22⋊Dic83—22no—
77C24×C83C2311yescharacteristic
78C22×C4×C83—22no—
79C22×C4×C83—41no—
80C22×C4×C83—41no—
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C22⋊C4×C83—22no—
90C22⋊C4×C83—22no—
91C23×C83—21no—
92C23×C83—21no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83C2×Q812yes—
96C23×C83#4112yes—
97C23×C83#4112yes—
98C23×C83C2411yescharacteristic
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—44no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—44no—
141C2×Dic83—44no—
142C2×Dic83C2×Q812yes—
143C2×Dic83C2×Q812yes—
144C22×C83—22no—
145C22×C83—22no—
146C22×C83—22no—
147C22×C83—22no—
148C22×C83—22no—
149C22×C83—22no—
150C22×C83#12514yes—
151C22×C83C22×Q811yescharacteristic
152C22×C83C2×#4111yescharacteristic
153C22×C83C2×#4111yescharacteristic
154C22×C83H(5,𝔽2)11yescharacteristic
155C22×C83H(5,𝔽2)11yescharacteristic
156C22×C83H(5,𝔽2)11yescharacteristic
157C22×C832−1+411yescharacteristic
158C4×C83—41no—
159C4×C83—41no—
160C4×C83—41no—
161C4×C83—41no—
162C4×C83—41no—
163C4×C83—41no—
164Dic83—22no—
165Dic83—22no—
166Dic83—41no—
167Dic83—41no—
168Dic83—41no—
169Dic83—41no—
170Dic83—41no—
171Dic83—41no—
172C2×C83—24no—
173C2×C83C2×#12511yescharacteristic
174C2×C83#53811yescharacteristic
175C2×C83#53811yescharacteristic
176C2×C83#53911yescharacteristic
177C2×C83#53911yescharacteristic
178C2×C83#54311yescharacteristic
179C2×C83#54411yescharacteristic
180#2646—831nomaximal, Sylow
181C83#264611yescharacteristic, complemented, Sylow
182#400—831no—
183#400—831no—
184#400—831no—
185#400—831no—
186#398—831no—
187#398—831no—
188#398—831no—
189#398—831no—
190#385—831no—
191#385—831no—
192#385—831no—
193#385D8311yescharacteristic
194#380—831no—
195#380—831no—
196C2×#95—831no—
197C23×C4—831no—
198C23×C4—831no—
199C23×C4C2×D8311yescharacteristic
200C2×C4⋊C4—831no—
201C2×C4⋊C4—831no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4—831no—
209C2×C4⋊C4—831no—
210C2×C4⋊C4C2×D8311yescharacteristic
211C2×C4⋊C4C2×D8311yescharacteristic
212C2×C22⋊C4—831no—
213C2×C22⋊C4—831no—
214C2×C22⋊C4C2×D8311yescharacteristic
215C2×C22⋊C4C2×D8311yescharacteristic
216#95—831no—
217#95—831no—
218#95—831no—
219#95—831no—
220#95—831no—
221#95—831no—
222#95—831no—
223#95—831no—
224#95—831no—
225#95—831no—
226#95—831no—
227#95—831no—
228#95—831no—
229#95—831no—
230#95C2×D8311yescharacteristic
231#95C2×D8311yescharacteristic
232C24C22×D8311yescharacteristic
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—3321no—
237C22×C4—3321no—
238C22×C4—3321no—
239C22×C4—3321no—
240C22×C4—834no—
241C22×C4—831no—
242C22×C4—831no—
243C22×C4—831no—
244C22×C4—831no—
245C22×C4—831no—
246C22×C4—831no—
247C22×C4—831no—
248C22×C4—831no—
249C22×C4—1662no—
250C22×C4C22×D8311yescharacteristic
251C22×C4C22×D8311yescharacteristic
252C22×C4C22×D8311yescharacteristic
253C22×C4C22×D8311yescharacteristic
254C22×C4C22×D8311yescharacteristic
255C22×C4C22×D8311yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—3321no—
262C4⋊C4—3321no—
263C4⋊C4—3321no—
264C4⋊C4—3321no—
265C4⋊C4—3321no—
266C4⋊C4—3321no—
267C4⋊C4—3321no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—1662no—
271C22⋊C4—1662no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23Q8×D8312yes—
277C23#1305058912yes—
278C23#1305059012yes—
279C23C23×D8311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
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—44no—
299C2×C4—3324no—
300C2×C4—3324no—
301C2×C4—832no—
302C2×C4—832no—
303C2×C4—1661no—
304C2×C4—1661no—
305C2×C4—1661no—
306C2×C4—1661no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4—1661no—
311C2×C4—1661no—
312C2×C4—1661no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4—1661no—
317C2×C4—1661no—
318C2×C4—1661no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4—1661no—
324C2×C4—1661no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22#1458178214yes—
332C22C2×Q8×D8311yescharacteristic
333C22C2×#1305058911yescharacteristic
334C22C2×#1305059011yescharacteristic
335C22#1458183711yescharacteristic
336C22#1458183711yescharacteristic
337C22#1458183811yescharacteristic
338C22#1458183911yescharacteristic
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—3321no—
346C4—3321no—
347C4—3321no—
348C4—3321no—
349C4—3321no—
350C4—3321no—
351C4—1662no—
352C4—1662no—
353C2—24no—
354C2C2×#1458178211yescharacteristic
355C2#1912828411yescharacteristic
356C2#1912828611yescharacteristic
357C2#1912829311yescharacteristic
358C2#1912829511yescharacteristic
359C2#1912832611yescharacteristic
360C2#1912833011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#385×C83C2
prime radicalC24×C83C23
hypercenter#385D83
hypocenterC83#2646
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #19127642C2semidirect
2. #19127642C2semidirect
3. #19127641C2semidirect
4. #19127639C2semidirect
5. #19127635C2semidirect
6. #19127634C2semidirect
7. #19127632C2semidirect
8. #19127631C2semidirect
181. C83#2646semidirect

Maximal subgroups

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

subgroupindex
#191276422
#191276412
#191276392
#191276352
#191276342
#191276322
#191276312
#191275762
#191275742
#191275732
#191275592
C2×C83⋊#952
#385×C832
#264683