Finite Group Databasebeta

← #24912658

Subgroups — #24912658

Order 10624.

548 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581782C211yesmaximal, characteristic, complemented
2C2×(C22⋊D83)⋊C4C211yesmaximal, characteristic
3#19127624C211yesmaximal, characteristic, complemented
4#19127623C211yesmaximal, characteristic, complemented
5#19127623C211yesmaximal, characteristic, complemented
6#19127601C211yesmaximal, characteristic
7#19127601C211yesmaximal, characteristic
8#19127576C211yesmaximal, characteristic, complemented
9#19127575C211yesmaximal, characteristic, complemented
10#19127573C211yesmaximal, characteristic, complemented
11#19127572C211yesmaximal, characteristic, complemented
12#19127570C211yesmaximal, characteristic, complemented
13#19127565C211yesmaximal, characteristic, complemented
14C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
15#396×C83C211yesmaximal, characteristic, complemented
16C22×C22⋊D83C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19#14581782—24no—
20(C22⋊D83)⋊C4—24no—
21C2×C4⋊Dic83C2211yescharacteristic
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×Dic83⋊C4C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×(C2×D83)⋊C4C2211yescharacteristic
37C2×(C2×D83)⋊C4C2211yescharacteristic
38C2×C4×Dic83C2211yescharacteristic
39C2×C4×Dic83C2211yescharacteristic
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×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C2×C22⋊D83—22no—
55C2×C22⋊D83—22no—
56C2×C22⋊D83Q814yes—
57C22×Dic83—22no—
58C22×Dic83—41no—
59C22×Dic83—41no—
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C2×C4×D83—22no—
68C2×C4×D83—41no—
69C2×C4×D83—41no—
70C4⋊Dic83—22no—
71C4⋊Dic83—22no—
72C4⋊Dic83—41no—
73Dic83⋊C4—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—22no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—41no—
79Dic83⋊C4—41no—
80C22⋊Dic83—22no—
81C22⋊Dic83—41no—
82(C2×D83)⋊C4—22no—
83(C2×D83)⋊C4—22no—
84(C2×D83)⋊C4—22no—
85(C2×D83)⋊C4—41no—
86(C2×D83)⋊C4—41no—
87C4×Dic83—22no—
88C4×Dic83—22no—
89C4×Dic83D414yes—
90C24×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C4⋊C4×C83—22no—
98C4⋊C4×C83—22no—
99C4⋊C4×C83—41no—
100C22⋊C4×C83—22no—
101C22⋊C4×C83—22no—
102C22⋊C4×C83—41no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83C2×Q812yes—
110C23×C83C2411yescharacteristic
111C22×D83—21no—
112C22×D83—21no—
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
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×C83C2×D412yes—
135C2×C4×C83#4112yes—
136C22⋊D83—28no—
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×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—44no—
154C2×Dic83C2×D412yes—
155C2×Dic83C2×D412yes—
156C2×Dic83C2×Q812yes—
157C2×Dic83#4112yes—
158C2×Dic83#4112yes—
159C4×D83—44no—
160C22×C83—22no—
161C22×C83—22no—
162C22×C83—22no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83C22×D411yescharacteristic
168C22×C83C22×Q811yescharacteristic
169C22×C83C2×#4111yescharacteristic
170C22×C83C2×#4111yescharacteristic
171C22×C83C2×#4111yescharacteristic
172C22×C83H(5,𝔽2)11yescharacteristic
173C22×C83H(5,𝔽2)11yescharacteristic
174C2×D83—22no—
175C2×D83—22no—
176C2×D83—22no—
177C2×D83—41no—
178C2×D83—41no—
179C2×D83—41no—
180C2×D83—41no—
181C4×C83—22no—
182C4×C83—22no—
183C4×C83—41no—
184C4×C83—41no—
185C4×C83—41no—
186C4×C83—41no—
187Dic83—22no—
188Dic83—22no—
189Dic83—41no—
190Dic83—41no—
191Dic83—41no—
192Dic83—41no—
193Dic83C22⋊Q814yes—
194C2×C83—42no—
195C2×C83C2×C22⋊Q811yescharacteristic
196C2×C83#53211yescharacteristic
197C2×C83#53511yescharacteristic
198C2×C83#55311yescharacteristic
199C2×C83#55311yescharacteristic
200C2×C83#55411yescharacteristic
201C2×C83#55411yescharacteristic
202D83—42no—
203#2566—831nomaximal, Sylow
204C83#256611yescharacteristic, complemented, Sylow
205C2×#125—831no—
206C2×C4×D4—831no—
207#396—831no—
208#396—831no—
209#396—831no—
210#396D8311yescharacteristic, complemented
211#390—831no—
212#390—831no—
213#385—831no—
214#385—831no—
215#385—831no—
216#385—831no—
217#384—831no—
218#382—831no—
219C4×C4⋊C4—831no—
220C22×D4—831no—
221C23×C4—831no—
222C23×C4—831no—
223#125—1664no—
224C4×D4—1664no—
225C2×C4⋊C4—831no—
226C2×C4⋊C4—831no—
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×C22⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
246C2×C22⋊C4C2×D8311yescharacteristic
247C2×C22⋊C4C2×D8311yescharacteristic
248C2×C42—831no—
249C2×C42—831no—
250C2×C42—831no—
251#95—831no—
252#95—831no—
253#95—831no—
254#95—831no—
255#95—831no—
256#95C2×D8311yescharacteristic
257C24—831no—
258C24C22×D8311yescharacteristic
259C2×D4—834no—
260C2×D4—1662no—
261C2×D4—1662no—
262C22×C4—3321no—
263C22×C4—3321no—
264C22×C4—3321no—
265C22×C4—3321no—
266C22×C4—831no—
267C22×C4—831no—
268C22×C4—831no—
269C22×C4—831no—
270C22×C4—831no—
271C22×C4—831no—
272C22×C4—831no—
273C22×C4—1662no—
274C22×C4—1662no—
275C22×C4C22×D8311yescharacteristic
276C22×C4C22×D8311yescharacteristic
277C22×C4C22×D8311yescharacteristic
278C22×C4C22×D8311yescharacteristic
279C22×C4C22×D8311yescharacteristic
280C22×C4C22×D8311yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—3321no—
285C4⋊C4—3321no—
286C4⋊C4—3321no—
287C4⋊C4—1662no—
288C4⋊C4—1662no—
289C4⋊C4—1662no—
290C4⋊C4—1662no—
291C4⋊C4—1662no—
292C4⋊C4—1662no—
293C4⋊C4—1662no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—3321no—
298C22⋊C4—3321no—
299C22⋊C4—3321no—
300C22⋊C4—1662no—
301C22⋊C4—1662no—
302C22⋊C4—1662no—
303C22⋊C4—1662no—
304C42—834no—
305C42—1662no—
306C42—1662no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—832no—
314C23—1661no—
315C23—1661no—
316C23—1661no—
317C23—1661no—
318C23—1661no—
319C23—1661no—
320C23Q8×D8312yes—
321C23C23×D8311yescharacteristic
322D4—1668no—
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—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3324no—
340C2×C4—3324no—
341C2×C4—832no—
342C2×C4—832no—
343C2×C4—832no—
344C2×C4—832no—
345C2×C4—832no—
346C2×C4—1661no—
347C2×C4—1661no—
348C2×C4—1661no—
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×C4D4×D8312yes—
363C2×C4#1305058912yes—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—3321no—
372C22—3321no—
373C22—3321no—
374C22—3321no—
375C22—1662no—
376C22—1662no—
377C22—1662no—
378C22C2×D4×D8311yescharacteristic
379C22C2×Q8×D8311yescharacteristic
380C22#41×D8311yescharacteristic
381C22#41×D8311yescharacteristic
382C22C2×#1305058911yescharacteristic
383C22#1458183711yescharacteristic
384C22#1458183811yescharacteristic
385C4—22no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—3321no—
392C4—3321no—
393C4—3321no—
394C4—3321no—
395C4—834no—
396C4—1662no—
397C4—1662no—
398C2—42no—
399C2—3322no—
400C2C22⋊Q8×D8311yescharacteristic
401C2#1912824611yescharacteristic
402C2#1912826711yescharacteristic
403C2#1912839411yescharacteristic
404C2#1912840211yescharacteristic
405C2#1912840511yescharacteristic
406C2#1912840911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#396×C83C2
prime radicalC22×C22⋊D83C22
hypercenter#396D83
hypocenterC83#2566
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14581782C2semidirect
3. #19127624C2semidirect
4. #19127623C2semidirect
5. #19127623C2semidirect
8. #19127576C2semidirect
9. #19127575C2semidirect
10. #19127573C2semidirect
11. #19127572C2semidirect
12. #19127570C2semidirect
13. #19127565C2semidirect
14. C4⋊C4×Dic83C2semidirect
15. #396×C83C2semidirect
204. C83#2566semidirect
210. #396D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
C2×(C22⋊D83)⋊C42
#191276242
#191276232
#191276012
#191275762
#191275752
#191275732
#191275722
#191275702
#191275652
C4⋊C4×Dic832
#396×C832
#256683