Finite Group Databasebeta

← #24914839

Subgroups — #24914839

Order 10624.

520 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83⋊#401C211yesmaximal, characteristic, complemented
2C83⋊#401C211yesmaximal, characteristic, complemented
3#19127614C211yesmaximal, characteristic, complemented
4#19127613C211yesmaximal, characteristic, complemented
5#19127613C211yesmaximal, characteristic, complemented
6#19127609C211yesmaximal, characteristic
7#19127581C211yesmaximal, characteristic, complemented
8#19127580C211yesmaximal, characteristic, complemented
9#19127578C211yesmaximal, characteristic, complemented
10#19127577C211yesmaximal, characteristic, complemented
11#19127577C211yesmaximal, characteristic, complemented
12#19127564C211yesmaximal, characteristic, complemented
13#19127563C211yesmaximal, characteristic, complemented
14#19127562C211yesmaximal, characteristic, complemented
15#386×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C23×Dic83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic
21C2×C22⋊Dic83C2211yescharacteristic
22C2×C22⋊Dic83C2211yescharacteristic
23C2×C22⋊Dic83C2211yescharacteristic
24C2×C22⋊Dic83C2211yescharacteristic
25C2×C22⋊Dic83C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
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
44C22×D4×C83C2211yescharacteristic
45C23×C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C2×Dic166—41no—
53C2×Dic166—41no—
54C2×Dic166—41no—
55C2×C22⋊D83—22no—
56C2×C22⋊D83—22no—
57C2×C22⋊D83—22no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83—41no—
60C2×C22⋊D83—41no—
61C22×Dic83—22no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C2×C4×D83—22no—
72C2×C4×D83—41no—
73C2×C4×D83—41no—
74C22⋊Dic83—41no—
75C22⋊Dic83—41no—
76C22⋊Dic83—41no—
77C22⋊Dic83—41no—
78C22⋊Dic83—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81(C2×D83)⋊C4—41no—
82(C2×D83)⋊C4—41no—
83C24×C83C2311yescharacteristic
84C24×C83C2311yescharacteristic
85C2×D4×C83—22no—
86C2×D4×C83—22no—
87C2×D4×C83—41no—
88C22×C4×C83—22no—
89C22×C4×C83—41no—
90C22×C4×C83—41no—
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83#4112yes—
112C23×C83#4112yes—
113C23×C83C2411yescharacteristic
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—21no—
120C22×D83#4112yes—
121D4×C83—44no—
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×C83—44no—
138C22⋊D83—44no—
139C22⋊D83—44no—
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—21no—
156C2×Dic83—21no—
157C2×Dic83—21no—
158C2×Dic83—21no—
159C2×Dic83—21no—
160C2×Dic83—21no—
161C2×Dic83—44no—
162C4×D83—44no—
163Dic166—44no—
164C22×C83—22no—
165C22×C83—22no—
166C22×C83—22no—
167C22×C83—22no—
168C22×C83—22no—
169C22×C83—22no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83C2×#4111yescharacteristic
179C22×C83C2×#4111yescharacteristic
180C22×C83C2×#4111yescharacteristic
181C22×C83H(5,𝔽2)11yescharacteristic
182C22×C83H(5,𝔽2)11yescharacteristic
183C22×C83H(5,𝔽2)11yescharacteristic
184C22×C83H(5,𝔽2)11yescharacteristic
185C2×D83—22no—
186C2×D83—22no—
187C2×D83—22no—
188C2×D83—41no—
189C2×D83—41no—
190C2×D83—41no—
191C2×D83—41no—
192C4×C83—41no—
193C4×C83—41no—
194C4×C83—41no—
195C4×C83—41no—
196C4×C83—41no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200Dic83—41no—
201Dic83—41no—
202Dic83—41no—
203Dic83—41no—
204C2×C83—42no—
205C2×C83—42no—
206C2×C83#53811yescharacteristic
207C2×C83#53811yescharacteristic
208C2×C83#53811yescharacteristic
209C2×C83#55111yescharacteristic
210C2×C83#55111yescharacteristic
211C2×C83#55111yescharacteristic
212C2×C83#56011yescharacteristic
213D83—42no—
214#2760—831nomaximal, Sylow
215C83#276011yescharacteristic, complemented, Sylow
216#401—831no—
217#401—831no—
218#393—831no—
219#393—831no—
220#393—831no—
221#392—831no—
222#386—831no—
223#386—831no—
224#386—831no—
225#386—831no—
226#386—831no—
227#386D8311yescharacteristic, complemented
228#381—831no—
229#381—831no—
230#381—831no—
231C22×Q8—831no—
232C22×D4—831no—
233C22×D4—831no—
234C22×D4C2×D8311yescharacteristic
235C23×C4—831no—
236C23×C4—831no—
237C23×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⋊C4—831no—
246C2×C22⋊C4—831no—
247C2×C22⋊C4C2×D8311yescharacteristic
248C2×C22⋊C4C2×D8311yescharacteristic
249C2×C22⋊C4C2×D8311yescharacteristic
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#95—831no—
259#95—831no—
260#95—831no—
261#95—831no—
262#95—831no—
263#95—831no—
264#95C2×D8311yescharacteristic
265#95C2×D8311yescharacteristic
266C24—831no—
267C24C22×D8311yescharacteristic
268C24C22×D8311yescharacteristic
269C2×Q8—3321no—
270C2×Q8—3321no—
271C2×Q8—3321no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—3321no—
276C2×D4—3321no—
277C2×D4—1662no—
278C2×D4—1662no—
279C2×D4—1662no—
280C2×D4—1662no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—3321no—
285C22×C4—3321no—
286C22×C4—3321no—
287C22×C4—3321no—
288C22×C4—831no—
289C22×C4—831no—
290C22×C4—831no—
291C22×C4—831no—
292C22×C4—831no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—1662no—
296C22×C4—1662no—
297C22×C4C22×D8311yescharacteristic
298C22×C4C22×D8311yescharacteristic
299C22×C4C22×D8311yescharacteristic
300C22×C4C22×D8311yescharacteristic
301C22×C4C22×D8311yescharacteristic
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—3321no—
306C22⋊C4—3321no—
307C22⋊C4—3321no—
308C22⋊C4—3321no—
309C22⋊C4—3321no—
310C22⋊C4—3321no—
311C22⋊C4—3321no—
312C22⋊C4—3321no—
313C22⋊C4—3321no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—832no—
327C23—1661no—
328C23—1661no—
329C23—1661no—
330C23—1661no—
331C23—1661no—
332C23—1661no—
333C23#1305058912yes—
334C23#1305059012yes—
335C23C23×D8311yescharacteristic
336Q8—3324no—
337D4—44no—
338D4—3324no—
339D4—3324no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—3324no—
357C2×C4—3324no—
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—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4—1661no—
376C2×C4—1661no—
377C2×C4—1661no—
378C2×C4—1661no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—3321no—
394C22—3321no—
395C22—3321no—
396C22—3321no—
397C22—1662no—
398C22—1662no—
399C22—1662no—
400C22#41×D8311yescharacteristic
401C22C2×#1305058911yescharacteristic
402C22C2×#1305059011yescharacteristic
403C22#1458183711yescharacteristic
404C22#1458183711yescharacteristic
405C22#1458183711yescharacteristic
406C22#1458183811yescharacteristic
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—3321no—
413C4—3321no—
414C4—3321no—
415C4—3321no—
416C4—3321no—
417C4—3321no—
418C4—3321no—
419C2—42no—
420C2—42no—
421C2—3322no—
422C2#1912828311yescharacteristic
423C2#1912828411yescharacteristic
424C2#1912828611yescharacteristic
425C2#1912837411yescharacteristic
426C2#1912837711yescharacteristic
427C2#1912838011yescharacteristic
428C2#1912843911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#386×C83C2
prime radical#19127609C2
hypercenter#386D83
hypocenterC83#2760
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C83⋊#401C2semidirect
2. C83⋊#401C2semidirect
3. #19127614C2semidirect
4. #19127613C2semidirect
5. #19127613C2semidirect
7. #19127581C2semidirect
8. #19127580C2semidirect
9. #19127578C2semidirect
10. #19127577C2semidirect
11. #19127577C2semidirect
12. #19127564C2semidirect
13. #19127563C2semidirect
14. #19127562C2semidirect
15. #386×C83C2semidirect
215. C83#2760semidirect
227. #386D83semidirect

Maximal subgroups

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

subgroupindex
C83⋊#4012
#191276142
#191276132
#191276092
#191275812
#191275802
#191275782
#191275772
#191275642
#191275632
#191275622
#386×C832
#276083