Finite Group Databasebeta

← #24912641

Subgroups — #24912641

Order 10624.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581769C211yesmaximal, characteristic, complemented
2C2×(C22⋊D83)⋊C4C211yesmaximal, characteristic
3#19127642C211yesmaximal, characteristic, complemented
4#19127636C211yesmaximal, characteristic, complemented
5#19127621C211yesmaximal, characteristic, complemented
6#19127614C211yesmaximal, characteristic, complemented
7#19127587C211yesmaximal, characteristic, complemented
8#19127583C211yesmaximal, characteristic, complemented
9#19127580C211yesmaximal, characteristic
10#19127578C211yesmaximal, characteristic
11#19127575C211yesmaximal, characteristic, complemented
12#19127572C211yesmaximal, characteristic, complemented
13#19127559C211yesmaximal, characteristic, complemented
14C2×C83⋊#95C211yesmaximal, characteristic, complemented
15#380×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C23×Dic83C2211yescharacteristic
19C23×Dic83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic
21#14581769—24no—
22(C22⋊D83)⋊C4—24no—
23C2×C4⋊Dic83C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×C4×Dic83C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C23×C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C2×Dic166—22no—
55C2×Dic166—41no—
56C2×Dic166—41no—
57C2×C22⋊D83—22no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83Q814yescomplemented
60C22×Dic83—22no—
61C22×Dic83—22no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83—41no—
65C22×Dic83D414yes—
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C22×Dic83C2311yescharacteristic
73C2×C4×D83—22no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C4⋊Dic83—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—22no—
79Dic83⋊C4—22no—
80Dic83⋊C4—22no—
81Dic83⋊C4—41no—
82C22⋊Dic83—22no—
83(C2×D83)⋊C4—22no—
84(C2×D83)⋊C4—22no—
85(C2×D83)⋊C4—22no—
86(C2×D83)⋊C4—41no—
87(C2×D83)⋊C4—41no—
88C4×Dic83—22no—
89C24×C83C2311yescharacteristic
90C22×C4×C83—22no—
91C22×C4×C83—22no—
92C22×C4×C83—41no—
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—41no—
101C22⋊C4×C83—22no—
102C22⋊C4×C83—22no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83C2×D412yes—
108C23×C83C2×Q812yes—
109C23×C83#4112yes—
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×C83—21no—
135C2×C4×C83—44no—
136C2×C4×C83#4112yes—
137C22⋊D83—28no—
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—21no—
154C2×Dic83—21no—
155C2×Dic83—44no—
156C2×Dic83—44no—
157C2×Dic83C2×D412yes—
158C2×Dic83C2×D412yes—
159C2×Dic83C2×Q812yes—
160C2×Dic83#4112yes—
161C4×D83—44no—
162Dic166—44no—
163C22×C83—22no—
164C22×C83—22no—
165C22×C83—22no—
166C22×C83—22no—
167C22×C83—22no—
168C22×C83—22no—
169C22×C83C22⋊Q814yes—
170C22×C83C22×D411yescharacteristic
171C22×C83C22×Q811yescharacteristic
172C22×C83C2×#4111yescharacteristic
173C22×C83C2×#4111yescharacteristic
174C22×C83C2×#4111yescharacteristic
175C22×C83H(5,𝔽2)11yescharacteristic
176C22×C83H(5,𝔽2)11yescharacteristic
177C2×D83—22no—
178C2×D83—22no—
179C2×D83—22no—
180C2×D83—41no—
181C2×D83—41no—
182C2×D83—41no—
183C2×D83—41no—
184C4×C83—22no—
185C4×C83—41no—
186C4×C83—41no—
187C4×C83—41no—
188C4×C83—41no—
189C4×C83—41no—
190Dic83—22no—
191Dic83—22no—
192Dic83—22no—
193Dic83—22no—
194Dic83—41no—
195Dic83—41no—
196Dic83—41no—
197C2×C83—24no—
198C2×C83C2×C22⋊Q811yescharacteristic
199C2×C83#53211yescharacteristic
200C2×C83#53411yescharacteristic
201C2×C83#55111yescharacteristic
202C2×C83#55111yescharacteristic
203C2×C83#55411yescharacteristic
204C2×C83#55411yescharacteristic
205D83—42no—
206#2564—831nomaximal, Sylow
207C83#256411yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—831no—
209C2×C4×D4—831no—
210#400—831no—
211#399—831no—
212#395—831no—
213#393—831no—
214#387—831no—
215#387—831no—
216#386—831no—
217#386—831no—
218#385—831no—
219#385—831no—
220#380—831no—
221#380D8311yescharacteristic, complemented
222C2×#95—831no—
223C22×Q8—831no—
224C22×D4—831no—
225C23×C4—831no—
226C23×C4—831no—
227C23×C4—831no—
228C23×C4C2×D8311yescharacteristic
229C22⋊Q8—1664no—
230C4×D4—1664no—
231C2×C4⋊C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
246C2×C22⋊C4C2×D8311yescharacteristic
247C2×C42—831no—
248#95—831no—
249#95—831no—
250#95—831no—
251#95—831no—
252#95—831no—
253#95—831no—
254#95—831no—
255#95—831no—
256#95—831no—
257#95—831no—
258#95C2×D8311yescharacteristic
259#95C2×D8311yescharacteristic
260C24—831no—
261C24C22×D8311yescharacteristic
262C2×Q8—3321no—
263C2×Q8—3321no—
264C2×Q8—1662no—
265C2×D4—834no—
266C2×D4—1662no—
267C2×D4—1662no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—3321no—
272C22×C4—3321no—
273C22×C4—3321no—
274C22×C4—3321no—
275C22×C4—3321no—
276C22×C4—834no—
277C22×C4—831no—
278C22×C4—831no—
279C22×C4—831no—
280C22×C4—831no—
281C22×C4—831no—
282C22×C4—831no—
283C22×C4—831no—
284C22×C4—1662no—
285C22×C4—1662no—
286C22×C4—1662no—
287C22×C4C22×D8311yescharacteristic
288C22×C4C22×D8311yescharacteristic
289C22×C4C22×D8311yescharacteristic
290C22×C4C22×D8311yescharacteristic
291C22×C4C22×D8311yescharacteristic
292C22×C4C22×D8311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—3321no—
296C4⋊C4—1662no—
297C4⋊C4—1662no—
298C4⋊C4—1662no—
299C4⋊C4—1662no—
300C4⋊C4—1662no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—3321no—
304C22⋊C4—3321no—
305C22⋊C4—1662no—
306C22⋊C4—1662no—
307C22⋊C4—1662no—
308C22⋊C4—1662no—
309C42—1662no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—832no—
315C23—1661no—
316C23—1661no—
317C23—1661no—
318C23—1661no—
319C23—1661no—
320C23—1661no—
321C23D4×D8312yes—
322C23Q8×D8312yes—
323C23#1305059012yes—
324C23C23×D8311yescharacteristic
325Q8—3324no—
326D4—1668no—
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—44no—
345C2×C4—3324no—
346C2×C4—3324no—
347C2×C4—3324no—
348C2×C4—832no—
349C2×C4—832no—
350C2×C4—832no—
351C2×C4—832no—
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×C4—1661no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4#1305058912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—3321no—
377C22—3321no—
378C22—3321no—
379C22—3321no—
380C22—1662no—
381C22—1662no—
382C22—1662no—
383C22#1458177014yes—
384C22C2×D4×D8311yescharacteristic
385C22C2×Q8×D8311yescharacteristic
386C22#41×D8311yescharacteristic
387C22C2×#1305058911yescharacteristic
388C22C2×#1305059011yescharacteristic
389C22#1458183711yescharacteristic
390C22#1458183811yescharacteristic
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—3321no—
398C4—3321no—
399C4—3321no—
400C4—1662no—
401C4—1662no—
402C4—1662no—
403C4—1662no—
404C2—24no—
405C2—3322no—
406C2C2×#1458177011yescharacteristic
407C2#1912824611yescharacteristic
408C2#1912825911yescharacteristic
409C2#1912837511yescharacteristic
410C2#1912837711yescharacteristic
411C2#1912840511yescharacteristic
412C2#1912840911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#380×C83C2
prime radicalC22×C22⋊D83C22
hypercenter#380D83
hypocenterC83#2564
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14581769C2semidirect
3. #19127642C2semidirect
4. #19127636C2semidirect
5. #19127621C2semidirect
6. #19127614C2semidirect
7. #19127587C2semidirect
8. #19127583C2semidirect
11. #19127575C2semidirect
12. #19127572C2semidirect
13. #19127559C2semidirect
14. C2×C83⋊#95C2semidirect
15. #380×C83C2semidirect
59. C2×C22⋊D83Q8semidirect
207. C83#2564semidirect
221. #380D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817692
C2×(C22⋊D83)⋊C42
#191276422
#191276362
#191276212
#191276142
#191275872
#191275832
#191275802
#191275782
#191275752
#191275722
#191275592
C2×C83⋊#952
#380×C832
#256483