Finite Group Databasebeta

← #24910608

Subgroups — #24910608

Order 10624.

512 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581777C211yesmaximal, characteristic
2#19127602C211yesmaximal, characteristic
3#19127596C211yesmaximal, characteristic, complemented
4#19127593C211yesmaximal, characteristic, complemented
5#19127592C211yesmaximal, characteristic, complemented
6#19127592C211yesmaximal, characteristic, complemented
7#19127591C211yesmaximal, characteristic, complemented
8#19127587C211yesmaximal, characteristic, complemented
9#19127583C211yesmaximal, characteristic, complemented
10#19127579C211yesmaximal, characteristic
11#19127572C211yesmaximal, characteristic, complemented
12#19127572C211yesmaximal, characteristic, complemented
13#19127560C211yesmaximal, characteristic, complemented
14#19127558C211yesmaximal, characteristic, complemented
15#389×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×C4×D83C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19#14581777C418yescomplemented
20C2×C4⋊Dic83C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×(C2×D83)⋊C4C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×C4×Dic83C2211yescharacteristic
36C2×C4×Dic83C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C42×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52C23×D83C2311yescharacteristic
53C23×D83C2311yescharacteristic
54C2×D332—41no—
55C2×D332—41no—
56C2×D332C2×C414yes—
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C2×C4×D83—41no—
64C2×C4×D83—41no—
65C2×C4×D83—41no—
66C2×C4×D83—41no—
67C2×C4×D83—41no—
68C2×C4×D83C2×C414yescomplemented
69C4⋊Dic83—41no—
70Dic83⋊C4—41no—
71Dic83⋊C4—41no—
72Dic83⋊C4—41no—
73Dic83⋊C4C2×C414yescomplemented
74(C2×D83)⋊C4—41no—
75(C2×D83)⋊C4—41no—
76(C2×D83)⋊C4—41no—
77(C2×D83)⋊C4—41no—
78(C2×D83)⋊C4—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81(C2×D83)⋊C4C2×C414yes—
82(C2×D83)⋊C4C2×C414yes—
83(C2×D83)⋊C4C2×C414yescomplemented
84C4×Dic83—41no—
85C4×Dic83—41no—
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C4⋊C4×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83C2×C414yescomplemented
97C42×C83—41no—
98C23×C83C2411yescharacteristic
99C22×D83—21no—
100C22×D83—21no—
101C22×D83—21no—
102C22×D83—21no—
103C22×D83—21no—
104C22×D83—21no—
105C22×D83—21no—
106C22×D83—21no—
107C22×D83—21no—
108C22×D83—21no—
109C22×D83—21no—
110C22×D83—21no—
111C22×D83C22×C412yes—
112C22×D83C22×C412yes—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83C22×C412yes—
132C2×C4×C83C22×C412yes—
133C2×C4×C83C22×C412yes—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83C22×C412yes—
151C2×Dic83C22×C412yes—
152D332—44no—
153C4×D83—44no—
154C4×D83—44no—
155C22×C83C23×C411yescharacteristic
156C22×C83H(5,𝔽2)11yescharacteristic
157C22×C83H(5,𝔽2)11yescharacteristic
158C22×C83H(5,𝔽2)11yescharacteristic
159C22×C83H(5,𝔽2)11yescharacteristic
160C22×C832−1+411yescharacteristic
161C22×C832−1+411yescharacteristic
162C2×D83—22no—
163C2×D83—22no—
164C2×D83—22no—
165C2×D83—22no—
166C2×D83—22no—
167C2×D83—22no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C2×D83—41no—
172C2×D83—41no—
173C2×D83—41no—
174C2×D83—41no—
175C2×D83—41no—
176C4×C83—22no—
177C4×C83—22no—
178C4×C83—22no—
179C4×C83—41no—
180C4×C83—41no—
181C4×C83—41no—
182C4×C83—41no—
183Dic83—22no—
184Dic83—22no—
185Dic83—41no—
186Dic83—41no—
187Dic83—41no—
188Dic83—41no—
189C2×C83#51811yescharacteristic
190C2×C83#52011yescharacteristic
191C2×C83#52011yescharacteristic
192C2×C83#56011yescharacteristic
193C2×C83#56211yescharacteristic
194C2×C83#56211yescharacteristic
195C2×C83#56311yescharacteristic
196D83—42no—
197D83—42no—
198#2376—831nomaximal, Sylow
199C83#237611yescharacteristic, complemented, Sylow
200C2×#123—831no—
201#390—831no—
202#389—831no—
203#389D8311yescharacteristic, complemented
204#388—831no—
205#388—831no—
206#388—831no—
207#388—831no—
208#387—831no—
209#387—831no—
210#386—831no—
211#385—831no—
212#385—831no—
213#380—831no—
214#380—831no—
215C22×D4—831no—
216C23×C4—831no—
217C23×C4—831no—
218#123—838no—
219C2×C4⋊C4—831no—
220C2×C4⋊C4—831no—
221C2×C4⋊C4—831no—
222C2×C4⋊C4—831no—
223C2×C4⋊C4—831no—
224C2×C4⋊C4C2×D8311yescharacteristic
225C2×C4⋊C4C2×D8311yescharacteristic
226C2×C4⋊C4C2×D8311yescharacteristic
227C2×C4⋊C4C2×D8311yescharacteristic
228C2×C22⋊C4—831no—
229C2×C22⋊C4—831no—
230C2×C22⋊C4—831no—
231C2×C22⋊C4—831no—
232C2×C22⋊C4—831no—
233C2×C22⋊C4—831no—
234C2×C22⋊C4—831no—
235C2×C22⋊C4—831no—
236C2×C22⋊C4—831no—
237C2×C22⋊C4—831no—
238C2×C42—831no—
239C2×C42—831no—
240C2×C42C2×D8311yescharacteristic
241#95—831no—
242#95—831no—
243#95—831no—
244#95—831no—
245#95—831no—
246#95—831no—
247#95—831no—
248#95—831no—
249#95C2×D8311yescharacteristic
250#95C2×D8311yescharacteristic
251C24—831no—
252C24—831no—
253C2×D4—3321no—
254C2×D4—3321no—
255C2×D4—834no—
256C22×C4—3321no—
257C22×C4—3321no—
258C22×C4—3321no—
259C22×C4—3321no—
260C22×C4—3321no—
261C22×C4—834no—
262C22×C4—831no—
263C22×C4—831no—
264C22×C4—831no—
265C22×C4—831no—
266C22×C4—831no—
267C22×C4—831no—
268C22×C4C22×D8311yescharacteristic
269C22×C4C22×D8311yescharacteristic
270C22×C4C22×D8311yescharacteristic
271C22×C4C22×D8311yescharacteristic
272C22×C4C22×D8311yescharacteristic
273C22×C4C22×D8311yescharacteristic
274C22×C4C22×D8311yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—3321no—
279C4⋊C4—3321no—
280C4⋊C4—3321no—
281C4⋊C4—3321no—
282C4⋊C4—834no—
283C4⋊C4C4×D8314yescomplemented
284C22⋊C4—3321no—
285C22⋊C4—3321no—
286C22⋊C4—3321no—
287C22⋊C4—3321no—
288C22⋊C4—3321no—
289C22⋊C4—3321no—
290C22⋊C4—3321no—
291C22⋊C4—834no—
292C22⋊C4—834no—
293C22⋊C4—834no—
294C42—41no—
295C42—3321no—
296C42—3321no—
297C23—832no—
298C23—832no—
299C23—1661no—
300C23—1661no—
301C23—1661no—
302C23—1661no—
303C23—1661no—
304C23—1661no—
305C23—1661no—
306C23—1661no—
307C23—1661no—
308C23—1661no—
309C23—1661no—
310C23—1661no—
311C23C23×D8311yescharacteristic
312D4—3324no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3324no—
332C2×C4—3324no—
333C2×C4—832no—
334C2×C4—832no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4—1661no—
338C2×C4—1661no—
339C2×C4—1661no—
340C2×C4—1661no—
341C2×C4—1661no—
342C2×C4—1661no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4—1661no—
346C2×C4—1661no—
347C2×C4—1661no—
348C2×C4—1661no—
349C2×C4—1661no—
350C2×C4—1661no—
351C2×C4C2×C4×D8312yes—
352C2×C4C2×C4×D8312yes—
353C2×C4C2×C4×D8312yes—
354C22—3321no—
355C22—3321no—
356C22—3321no—
357C22—3321no—
358C22—3321no—
359C22—3321no—
360C22—3321no—
361C22—3321no—
362C22—1662no—
363C22—1662no—
364C22—1662no—
365C22—1662no—
366C22—1662no—
367C22—1662no—
368C22C22×C4×D8311yescharacteristic
369C22#1458183711yescharacteristic
370C22#1458183711yescharacteristic
371C22#1458183811yescharacteristic
372C22#1458183811yescharacteristic
373C22#1458184011yescharacteristic
374C22#1458184011yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3321no—
383C4—3321no—
384C4—3321no—
385C4—3321no—
386C4—1662no—
387C4—1662no—
388C2—3322no—
389C2—3322no—
390C2#1912817311yescharacteristic
391C2#1912818211yescharacteristic
392C2#1912818311yescharacteristic
393C2#1912843911yescharacteristic
394C2#1912844711yescharacteristic
395C2#1912844911yescharacteristic
396C2#1912845011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
Fitting#389×C83C2
socle, cosocleC23×C83C24
prime radicalC22×D332C22
hypercenter#389D83
hypocenterC83#2376
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #19127596C2semidirect
4. #19127593C2semidirect
5. #19127592C2semidirect
6. #19127592C2semidirect
7. #19127591C2semidirect
8. #19127587C2semidirect
9. #19127583C2semidirect
11. #19127572C2semidirect
12. #19127572C2semidirect
13. #19127560C2semidirect
14. #19127558C2semidirect
15. #389×C83C2semidirect
19. #14581777C4semidirect
68. C2×C4×D83C2×C4semidirect
73. Dic83⋊C4C2×C4semidirect
83. (C2×D83)⋊C4C2×C4semidirect
96. C4⋊C4×C83C2×C4semidirect
199. C83#2376semidirect
203. #389D83semidirect
283. C4⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817772
#191276022
#191275962
#191275932
#191275922
#191275912
#191275872
#191275832
#191275792
#191275722
#191275602
#191275582
#389×C832
#237683