Finite Group Databasebeta

← #24912941

Subgroups — #24912941

Order 10624.

596 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581765C211yesmaximal, characteristic
2C2×C4⋊C4×D83C211yesmaximal, characteristic, complemented
3#19127643C211yesmaximal, characteristic, complemented
4#19127642C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127616C211yesmaximal, characteristic, complemented
7#19127595C211yesmaximal, characteristic, complemented
8#19127592C211yesmaximal, characteristic, complemented
9#19127591C211yesmaximal, characteristic, complemented
10#19127579C211yesmaximal, characteristic, complemented
11#19127579C211yesmaximal, characteristic, complemented
12#19127577C211yesmaximal, characteristic, complemented
13#19127577C211yesmaximal, characteristic, complemented
14C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
15#388×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic
21C22×C4×D83C2211yescharacteristic
22#14581765—24no—
23C2×C4⋊Dic83C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C4⋊C4×D83—24no—
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
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×C4×Dic83C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C42×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C23×D83C2311yescharacteristic
55C2×D332—22no—
56C2×D332—22no—
57C2×D332—22no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83—22no—
60C2×C22⋊D83—22no—
61C2×C22⋊D83—22no—
62C2×C22⋊D83—41no—
63C2×C22⋊D83—41no—
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C2×C4×D83—22no—
71C2×C4×D83—22no—
72C2×C4×D83—22no—
73C2×C4×D83—22no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C2×C4×D83—41no—
77C2×C4×D83—41no—
78C2×C4×D83D414yes—
79C4⋊Dic83—22no—
80Dic83⋊C4—22no—
81Dic83⋊C4—22no—
82Dic83⋊C4—22no—
83C22⋊Dic83—22no—
84C22⋊Dic83—41no—
85(C2×D83)⋊C4—22no—
86(C2×D83)⋊C4—22no—
87(C2×D83)⋊C4—22no—
88(C2×D83)⋊C4—22no—
89(C2×D83)⋊C4—22no—
90(C2×D83)⋊C4—41no—
91(C2×D83)⋊C4—41no—
92C4×Dic83—41no—
93C24×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C4⋊C4×C83—22no—
101C22⋊C4×C83—22no—
102C22⋊C4×C83—22no—
103C22⋊C4×C83—41no—
104C42×C83—41no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83C2411yescharacteristic
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—21no—
120C22×D83—21no—
121C22×D83—21no—
122C22×D83—21no—
123C22×D83—21no—
124C22×D83C2×D412yes—
125C22×D83#4112yes—
126C22×D83#4112yes—
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—21no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83C2×D412yes—
144C2×C4×C83#4112yes—
145C22⋊D83—44no—
146C22⋊D83—44no—
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—21no—
162C2×Dic83—21no—
163C2×Dic83C2×D412yes—
164C2×Dic83#4112yes—
165D332—44no—
166C4×D83—28no—
167C4×D83—44no—
168C4×D83—44no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83C22×D411yescharacteristic
177C22×C83C2×#4111yescharacteristic
178C22×C83C2×#4111yescharacteristic
179C22×C83C2×#4111yescharacteristic
180C22×C83C2×#4111yescharacteristic
181C22×C83H(5,𝔽2)11yescharacteristic
182C22×C83H(5,𝔽2)11yescharacteristic
183C2×D83—22no—
184C2×D83—22no—
185C2×D83—22no—
186C2×D83—22no—
187C2×D83—22no—
188C2×D83—22no—
189C2×D83—41no—
190C2×D83—41no—
191C2×D83—41no—
192C2×D83—41no—
193C2×D83—41no—
194C2×D83—41no—
195C2×D83—41no—
196C2×D83#12414yes—
197C4×C83—22no—
198C4×C83—22no—
199C4×C83—41no—
200C4×C83—41no—
201C4×C83—41no—
202C4×C83—41no—
203Dic83—22no—
204Dic83—22no—
205Dic83—41no—
206Dic83—41no—
207Dic83—41no—
208Dic83—41no—
209C2×C83—81no—
210C2×C83#52511yescharacteristic
211C2×C83C2×#12411yescharacteristic
212C2×C83#53411yescharacteristic
213C2×C83#55311yescharacteristic
214C2×C83#55311yescharacteristic
215C2×C83#55311yescharacteristic
216C2×C83#55311yescharacteristic
217D83—24no—
218D83—81no—
219#2591—831nomaximal, Sylow
220C83#259111yescharacteristic, complemented, Sylow
221C2×#121—831no—
222C22×C4⋊C4—831no—
223#400—831no—
224#400—831no—
225#394—831no—
226#394—831no—
227#388—831no—
228#388—831no—
229#388—831no—
230#388D8311yescharacteristic, complemented
231#386—831no—
232#386—831no—
233#386—831no—
234#386—831no—
235C4×C22⋊C4—831no—
236C22×D4—831no—
237C22×D4—831no—
238C22×D4—831no—
239C23×C4—831no—
240C23×C4—831no—
241C23×C4—831no—
242#121—1664no—
243C2×C4⋊C4—831no—
244C2×C4⋊C4—831no—
245C2×C4⋊C4—831no—
246C2×C4⋊C4—831no—
247C2×C4⋊C4—1664no—
248C2×C4⋊C4C2×D8311yescharacteristic
249C2×C22⋊C4—831no—
250C2×C22⋊C4—831no—
251C2×C22⋊C4—831no—
252C2×C22⋊C4—831no—
253C2×C22⋊C4—831no—
254C2×C22⋊C4—831no—
255C2×C22⋊C4—831no—
256C2×C22⋊C4—831no—
257C2×C22⋊C4—831no—
258C2×C22⋊C4C2×D8311yescharacteristic
259C2×C22⋊C4C2×D8311yescharacteristic
260C2×C22⋊C4C2×D8311yescharacteristic
261C2×C42—831no—
262C2×C42C2×D8311yescharacteristic
263#95—831no—
264#95—831no—
265#95—831no—
266#95—831no—
267#95—831no—
268#95—831no—
269#95—831no—
270#95—831no—
271#95C2×D8311yescharacteristic
272#95C2×D8311yescharacteristic
273C24—831no—
274C24—831no—
275C24C22×D8311yescharacteristic
276C2×D4—3321no—
277C2×D4—3321no—
278C2×D4—1662no—
279C2×D4—1662no—
280C2×D4—1662no—
281C2×D4—1662no—
282C2×D4—1662no—
283C2×D4—1662no—
284C2×D4—1662no—
285C22×C4—3321no—
286C22×C4—3321no—
287C22×C4—3321no—
288C22×C4—3321no—
289C22×C4—834no—
290C22×C4—831no—
291C22×C4—831no—
292C22×C4—831no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—831no—
296C22×C4—1662no—
297C22×C4—1662no—
298C22×C4—1662no—
299C22×C4—1662no—
300C22×C4C22×D8311yescharacteristic
301C22×C4C22×D8311yescharacteristic
302C22×C4C22×D8311yescharacteristic
303C22×C4C22×D8311yescharacteristic
304C22×C4C22×D8311yescharacteristic
305C22×C4C22×D8311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—1662no—
308C4⋊C4—1662no—
309C4⋊C4—1662no—
310C4⋊C4—1662no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—3321no—
315C22⋊C4—3321no—
316C22⋊C4—3321no—
317C22⋊C4—1662no—
318C22⋊C4—1662no—
319C22⋊C4—1662no—
320C22⋊C4—1662no—
321C22⋊C4—1662no—
322C22⋊C4—1662no—
323C42—41no—
324C42—3321no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—832no—
333C23—832no—
334C23—832no—
335C23—1661no—
336C23—1661no—
337C23—1661no—
338C23—1661no—
339C23—1661no—
340C23—1661no—
341C23—1661no—
342C23—1661no—
343C23—1661no—
344C23—1661no—
345C23—1661no—
346C23C23×D8311yescharacteristic
347D4—3324no—
348D4—3324no—
349D4—3324no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—3324no—
367C2×C4—3324no—
368C2×C4—832no—
369C2×C4—832no—
370C2×C4—1668no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4—1661no—
376C2×C4—1661no—
377C2×C4—1661no—
378C2×C4—1661no—
379C2×C4—1661no—
380C2×C4—1661no—
381C2×C4—1661no—
382C2×C4—1661no—
383C2×C4—1661no—
384C2×C4—1661no—
385C2×C4—1661no—
386C2×C4—1661no—
387C2×C4D4×D8312yes—
388C2×C4#1305059012yes—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—3321no—
397C22—3321no—
398C22—3321no—
399C22—3321no—
400C22—3321no—
401C22—3321no—
402C22—3321no—
403C22—834no—
404C22—1662no—
405C22—1662no—
406C22—1662no—
407C22—1662no—
408C22—1662no—
409C22—1662no—
410C22C2×D4×D8311yescharacteristic
411C22#41×D8311yescharacteristic
412C22#41×D8311yescharacteristic
413C22#41×D8311yescharacteristic
414C22C2×#1305059011yescharacteristic
415C22#1458183711yescharacteristic
416C22#1458183811yescharacteristic
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—3321no—
424C4—3321no—
425C4—3321no—
426C4—3321no—
427C4—1662no—
428C4—1662no—
429C2—81no—
430C2—6641no—
431C2—1664no—
432C2#1912821011yescharacteristic
433C2#124×D8311yescharacteristic
434C2#1912825911yescharacteristic
435C2#1912839511yescharacteristic
436C2#1912839611yescharacteristic
437C2#1912840111yescharacteristic
438C2#1912840211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#388×C83C2
prime radicalC2×#14581765C2
hypercenter#388D83
hypocenterC83#2591
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D83C2semidirect
3. #19127643C2semidirect
4. #19127642C2semidirect
5. #19127617C2semidirect
6. #19127616C2semidirect
7. #19127595C2semidirect
8. #19127592C2semidirect
9. #19127591C2semidirect
10. #19127579C2semidirect
11. #19127579C2semidirect
12. #19127577C2semidirect
13. #19127577C2semidirect
14. C4×(C2×D83)⋊C4C2semidirect
15. #388×C83C2semidirect
220. C83#2591semidirect
230. #388D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817652
C2×C4⋊C4×D832
#191276432
#191276422
#191276172
#191276162
#191275952
#191275922
#191275912
#191275792
#191275772
C4×(C2×D83)⋊C42
#388×C832
#259183