Finite Group Databasebeta

← #24914484

Subgroups — #24914484

Order 10624.

528 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581772C211yesmaximal, characteristic, complemented
2C2×#14581770C211yesmaximal, characteristic, complemented
3#19127636C211yesmaximal, characteristic, complemented
4#19127636C211yesmaximal, characteristic, complemented
5#19127634C211yesmaximal, characteristic, complemented
6#19127625C211yesmaximal, characteristic, complemented
7#19127623C211yesmaximal, characteristic, complemented
8#19127605C211yesmaximal, characteristic, complemented
9#19127602C211yesmaximal, characteristic
10#19127598C211yesmaximal, characteristic, complemented
11#19127579C211yesmaximal, characteristic
12#19127579C211yesmaximal, characteristic
13#19127575C211yesmaximal, characteristic, complemented
14#19127572C211yesmaximal, characteristic, complemented
15#398×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20#14581772—24no—
21#14581770—24no—
22C2×C4⋊Dic83C2211yescharacteristic
23C2×C4⋊Dic83C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×Dic83⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×(C2×D83)⋊C4C2211yescharacteristic
37C2×(C2×D83)⋊C4C2211yescharacteristic
38C2×(C2×D83)⋊C4C2211yescharacteristic
39C2×(C2×D83)⋊C4C2211yescharacteristic
40C2×C4×Dic83C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C23×D83C2311yescharacteristic
55C2×Dic166—41no—
56C2×Dic166—41no—
57C2×Dic166D414yescomplemented
58C2×D332—41no—
59C2×D332—41no—
60C2×D332Q814yescomplemented
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C2×C4×D83—22no—
68C2×C4×D83—22no—
69C2×C4×D83—41no—
70C2×C4×D83—41no—
71C2×C4×D83—41no—
72C2×C4×D83—41no—
73C4⋊Dic83—22no—
74C4⋊Dic83—22no—
75Dic83⋊C4—22no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—41no—
79Dic83⋊C4—41no—
80Dic83⋊C4—41no—
81(C2×D83)⋊C4—22no—
82(C2×D83)⋊C4—22no—
83(C2×D83)⋊C4—22no—
84(C2×D83)⋊C4—22no—
85(C2×D83)⋊C4—22no—
86(C2×D83)⋊C4—22no—
87(C2×D83)⋊C4—41no—
88(C2×D83)⋊C4—41no—
89(C2×D83)⋊C4—41no—
90(C2×D83)⋊C4—41no—
91C4×Dic83—41no—
92C22×C4×C83C2311yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C4⋊C4×C83—22no—
100C4⋊C4×C83—22no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—41no—
103C23×C83C2411yescharacteristic
104C22×D83—21no—
105C22×D83—21no—
106C22×D83—21no—
107C22×D83—21no—
108C22×D83—21no—
109C22×D83—21no—
110C22×D83—21no—
111C22×D83—21no—
112C22×D83—21no—
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83C2×Q812yes—
117C22×D83C2×Q812yes—
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×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83C2×D412yes—
138C2×C4×C83C2×Q812yes—
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×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83C2×D412yes—
155C2×Dic83C2×D412yes—
156C2×Dic83#4112yes—
157D332—44no—
158C4×D83—44no—
159C4×D83—44no—
160Dic166—44no—
161C22×C83C22×D411yescharacteristic
162C22×C83C22×Q811yescharacteristic
163C22×C83C2×#4111yescharacteristic
164C22×C83H(5,𝔽2)11yescharacteristic
165C22×C83H(5,𝔽2)11yescharacteristic
166C22×C83H(5,𝔽2)11yescharacteristic
167C22×C832−1+411yescharacteristic
168C2×D83—22no—
169C2×D83—22no—
170C2×D83—22no—
171C2×D83—22no—
172C2×D83—22no—
173C2×D83—22no—
174C2×D83—41no—
175C2×D83—41no—
176C2×D83—41no—
177C2×D83—41no—
178C2×D83—41no—
179C2×D83—41no—
180C2×D83—41no—
181C2×D83—41no—
182C4×C83—22no—
183C4×C83—22no—
184C4×C83—41no—
185C4×C83—41no—
186C4×C83—41no—
187C4×C83—41no—
188C4×C83—41no—
189Dic83—22no—
190Dic83—22no—
191Dic83—22no—
192Dic83—41no—
193Dic83—41no—
194Dic83—41no—
195C2×C83#53411yescharacteristic
196C2×C83#53911yescharacteristic
197C2×C83#54311yescharacteristic
198C2×C83D4×Q811yescharacteristic
199C2×C83#55011yescharacteristic
200C2×C83#55411yescharacteristic
201C2×C83#56211yescharacteristic
202D83—42no—
203D83—42no—
204#2732—831nomaximal, Sylow
205C83#273211yescharacteristic, complemented, Sylow
206C2×C22⋊Q8—831no—
207C2×C22⋊Q8—831no—
208#399—831no—
209#399—831no—
210#398—831no—
211#398D8311yescharacteristic, complemented
212#396—831no—
213#396—831no—
214#391—831no—
215#390—831no—
216#389—831no—
217#386—831no—
218#386—831no—
219#385—831no—
220#385—831no—
221C22×Q8—831no—
222C22×D4—831no—
223C23×C4—831no—
224C23×C4—831no—
225C22⋊Q8—1664no—
226C22⋊Q8—1664no—
227C2×C4⋊C4—831no—
228C2×C4⋊C4—831no—
229C2×C4⋊C4—831no—
230C2×C4⋊C4—831no—
231C2×C4⋊C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4C2×D8311yescharacteristic
236C2×C4⋊C4C2×D8311yescharacteristic
237C2×C4⋊C4C2×D8311yescharacteristic
238C2×C4⋊C4C2×D8311yescharacteristic
239C2×C22⋊C4—831no—
240C2×C22⋊C4—831no—
241C2×C22⋊C4—831no—
242C2×C22⋊C4—831no—
243C2×C22⋊C4—831no—
244C2×C22⋊C4—831no—
245C2×C22⋊C4—831no—
246C2×C22⋊C4—831no—
247C2×C22⋊C4—831no—
248C2×C22⋊C4—831no—
249C2×C42—831no—
250#95—831no—
251#95—831no—
252#95—831no—
253#95—831no—
254#95—831no—
255#95C2×D8311yescharacteristic
256#95C2×D8311yescharacteristic
257#95C2×D8311yescharacteristic
258C24—831no—
259C24—831no—
260C2×Q8—3321no—
261C2×Q8—3321no—
262C2×Q8—834no—
263C2×D4—3321no—
264C2×D4—3321no—
265C2×D4—834no—
266C22×C4—3321no—
267C22×C4—3321no—
268C22×C4—3321no—
269C22×C4—3321no—
270C22×C4—831no—
271C22×C4—831no—
272C22×C4—831no—
273C22×C4—831no—
274C22×C4—831no—
275C22×C4—831no—
276C22×C4—1662no—
277C22×C4—1662no—
278C22×C4C22×D8311yescharacteristic
279C22×C4C22×D8311yescharacteristic
280C22×C4C22×D8311yescharacteristic
281C22×C4C22×D8311yescharacteristic
282C22×C4C22×D8311yescharacteristic
283C22×C4C22×D8311yescharacteristic
284C22×C4C22×D8311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—3321no—
290C4⋊C4—3321no—
291C4⋊C4—3321no—
292C4⋊C4—1662no—
293C4⋊C4—1662no—
294C4⋊C4—1662no—
295C4⋊C4—1662no—
296C4⋊C4—1662no—
297C22⋊C4—3321no—
298C22⋊C4—3321no—
299C22⋊C4—3321no—
300C22⋊C4—3321no—
301C22⋊C4—1662no—
302C22⋊C4—1662no—
303C22⋊C4—1662no—
304C22⋊C4—1662no—
305C22⋊C4—1662no—
306C22⋊C4—1662no—
307C42—3321no—
308C23—832no—
309C23—832no—
310C23—1661no—
311C23—1661no—
312C23—1661no—
313C23—1661no—
314C23—1661no—
315C23—1661no—
316C23—1661no—
317C23—1661no—
318C23—1661no—
319C23—1661no—
320C23—1661no—
321C23—1661no—
322C23C23×D8311yescharacteristic
323Q8—3324no—
324D4—3324no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—3324no—
345C2×C4—3324no—
346C2×C4—832no—
347C2×C4—832no—
348C2×C4—832no—
349C2×C4—1661no—
350C2×C4—1661no—
351C2×C4—1661no—
352C2×C4—1661no—
353C2×C4—1661no—
354C2×C4—1661no—
355C2×C4—1661no—
356C2×C4—1661no—
357C2×C4—1661no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4—1661no—
361C2×C4—1661no—
362C2×C4—1661no—
363C2×C4—1661no—
364C2×C4D4×D8312yes—
365C2×C4Q8×D8312yes—
366C22—3321no—
367C22—3321no—
368C22—3321no—
369C22—3321no—
370C22—3321no—
371C22—3321no—
372C22—3321no—
373C22—3321no—
374C22—1662no—
375C22—1662no—
376C22—1662no—
377C22—1662no—
378C22—1662no—
379C22—1662no—
380C22C2×D4×D8311yescharacteristic
381C22C2×Q8×D8311yescharacteristic
382C22#41×D8311yescharacteristic
383C22#1458183711yescharacteristic
384C22#1458183811yescharacteristic
385C22#1458183811yescharacteristic
386C22#1458184011yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—3321no—
395C4—3321no—
396C4—3321no—
397C4—1662no—
398C4—1662no—
399C4—1662no—
400C2—3322no—
401C2—3322no—
402C2#1912826211yescharacteristic
403C2#1912829911yescharacteristic
404C2#1912832611yescharacteristic
405C2#1912836611yescharacteristic
406C2#1912836911yescharacteristic
407C2#1912840711yescharacteristic
408C2#1912844711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#398×C83C2
prime radicalC22×D332C22
hypercenter#398D83
hypocenterC83#2732
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14581772C2semidirect
2. C2×#14581770C2semidirect
3. #19127636C2semidirect
4. #19127636C2semidirect
5. #19127634C2semidirect
6. #19127625C2semidirect
7. #19127623C2semidirect
8. #19127605C2semidirect
10. #19127598C2semidirect
13. #19127575C2semidirect
14. #19127572C2semidirect
15. #398×C83C2semidirect
57. C2×Dic166D4semidirect
60. C2×D332Q8semidirect
205. C83#2732semidirect
211. #398D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817722
C2×#145817702
#191276362
#191276342
#191276252
#191276232
#191276052
#191276022
#191275982
#191275792
#191275752
#191275722
#398×C832
#273283