Finite Group Databasebeta

← #24914198

Subgroups — #24914198

Order 10624.

548 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581781C211yesmaximal, characteristic, complemented
2C2×#14581774C211yesmaximal, characteristic, complemented
3#19127638C211yesmaximal, characteristic, complemented
4#19127630C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127616C211yesmaximal, characteristic, complemented
7#19127610C211yesmaximal, characteristic
8#19127608C211yesmaximal, characteristic, complemented
9#19127601C211yesmaximal, characteristic, complemented
10#19127598C211yesmaximal, characteristic, complemented
11#19127594C211yesmaximal, characteristic, complemented
12#19127590C211yesmaximal, characteristic, complemented
13#19127579C211yesmaximal, characteristic, complemented
14#19127575C211yesmaximal, characteristic, complemented
15#393×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20#14581781—24no—
21#14581774—24no—
22C2×C4⋊Dic83C2211yescharacteristic
23C2×C4⋊Dic83C2211yescharacteristic
24C2×C4⋊Dic83C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
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×(C2×D83)⋊C4C2211yescharacteristic
38C2×(C2×D83)⋊C4C2211yescharacteristic
39C2×C4×Dic83C2211yescharacteristic
40C2×C4×Dic83C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C22×Q8×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C23×D83C2311yescharacteristic
55C2×D332—22no—
56C2×D332—22no—
57C2×D332—41no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83—22no—
60C2×C22⋊D83—41no—
61C2×C22⋊D83—41no—
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—41no—
72C2×C4×D83—41no—
73C4⋊Dic83—22no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—41no—
79C22⋊Dic83—22no—
80C22⋊Dic83—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—41no—
86(C2×D83)⋊C4—41no—
87(C2×D83)⋊C4—41no—
88(C2×D83)⋊C4—41no—
89(C2×D83)⋊C4D414yescomplemented
90C4×Dic83—22no—
91C4×Dic83—41no—
92C24×C83C2311yescharacteristic
93C2×Q8×C83—22no—
94C2×Q8×C83—22no—
95C2×Q8×C83—41no—
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C22×C4×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C22⋊C4×C83—22no—
103C22⋊C4×C83—22no—
104C22⋊C4×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×D83—21no—
125C22×D83—21no—
126C22×D83C2×D412yes—
127Q8×C83—44no—
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×C83—21no—
144C2×C4×C83C2×D412yes—
145C2×C4×C83#4112yes—
146C22⋊D83—44no—
147C22⋊D83—44no—
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×Dic83—21no—
164C2×Dic83C2×D412yes—
165C2×Dic83#4112yes—
166D332—44no—
167C4×D83—44no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83C22×D411yescharacteristic
176C22×C83C2×#4111yescharacteristic
177C22×C83C2×#4111yescharacteristic
178C22×C83H(5,𝔽2)11yescharacteristic
179C22×C83H(5,𝔽2)11yescharacteristic
180C22×C83H(5,𝔽2)11yescharacteristic
181C22×C832−1+411yescharacteristic
182C2×D83—22no—
183C2×D83—22no—
184C2×D83—22no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—41no—
189C2×D83—41no—
190C2×D83—41no—
191C2×D83—41no—
192C2×D83—41no—
193C2×D83—41no—
194C2×D83—41no—
195C2×D83—41no—
196C4×C83—22no—
197C4×C83—22no—
198C4×C83—41no—
199C4×C83—41no—
200C4×C83—41no—
201C4×C83—41no—
202Dic83—22no—
203Dic83—22no—
204Dic83—41no—
205Dic83—41no—
206Dic83—41no—
207Dic83—41no—
208C2×C83—81no—
209C2×C83#53511yescharacteristic
210C2×C83#53811yescharacteristic
211C2×C83#54211yescharacteristic
212C2×C83#54611yescharacteristic
213C2×C83#54711yescharacteristic
214C2×C83#55911yescharacteristic
215C2×C83#56211yescharacteristic
216D83—42no—
217D83—81no—
218#2710—831nomaximal, Sylow
219C83#271011yescharacteristic, complemented, Sylow
220C2×#124—831no—
221C2×#123—831no—
222#399—831no—
223#397—831no—
224#394—831no—
225#394—831no—
226#393D8311yescharacteristic, complemented
227#392—831no—
228#391—831no—
229#390—831no—
230#389—831no—
231#388—831no—
232#388—831no—
233#386—831no—
234#385—831no—
235C22×Q8C2×D8311yescharacteristic
236C22×D4—831no—
237C22×D4—831no—
238C22×D4—831no—
239C23×C4—831no—
240#124—1664no—
241#123—1664no—
242C2×C4⋊C4—831no—
243C2×C4⋊C4—831no—
244C2×C4⋊C4—831no—
245C2×C4⋊C4—831no—
246C2×C4⋊C4—831no—
247C2×C4⋊C4—831no—
248C2×C22⋊C4—831no—
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⋊C4—831no—
259C2×C22⋊C4C2×D8311yescharacteristic
260C2×C22⋊C4C2×D8311yescharacteristic
261C2×C22⋊C4C2×D8311yescharacteristic
262C2×C42—831no—
263C2×C42—831no—
264#95—831no—
265#95—831no—
266#95—831no—
267#95—831no—
268#95—831no—
269#95C2×D8311yescharacteristic
270#95C2×D8311yescharacteristic
271#95C2×D8311yescharacteristic
272C24—831no—
273C24—831no—
274C24C22×D8311yescharacteristic
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×D4—3321no—
279C2×D4—3321no—
280C2×D4—3321no—
281C2×D4—3321no—
282C2×D4—3321no—
283C2×D4—1662no—
284C2×D4—1662no—
285C2×D4—1662no—
286C2×D4—1662no—
287C22×C4—3321no—
288C22×C4—3321no—
289C22×C4—831no—
290C22×C4—831no—
291C22×C4—831no—
292C22×C4—831no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—1662no—
296C22×C4C22×D8311yescharacteristic
297C22×C4C22×D8311yescharacteristic
298C22×C4C22×D8311yescharacteristic
299C22×C4C22×D8311yescharacteristic
300C22×C4C22×D8311yescharacteristic
301C22×C4C22×D8311yescharacteristic
302C4⋊C4—3321no—
303C4⋊C4—3321no—
304C4⋊C4—3321no—
305C4⋊C4—1662no—
306C4⋊C4—1662no—
307C4⋊C4—1662no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—3321no—
312C22⋊C4—3321no—
313C22⋊C4—3321no—
314C22⋊C4—3321no—
315C22⋊C4—3321no—
316C22⋊C4—834no—
317C22⋊C4—1662no—
318C22⋊C4—1662no—
319C22⋊C4—1662no—
320C22⋊C4—1662no—
321C22⋊C4—1662no—
322C42—3321no—
323C42—1662no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—832no—
332C23—1661no—
333C23—1661no—
334C23—1661no—
335C23—1661no—
336C23—1661no—
337C23—1661no—
338C23—1661no—
339C23—1661no—
340C23—1661no—
341C23—1661no—
342C23—1661no—
343C23—1661no—
344C23—1661no—
345C23C23×D8311yescharacteristic
346Q8—44no—
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—832no—
368C2×C4—832no—
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—
379C2×C4—1661no—
380C2×C4—1661no—
381C2×C4—1661no—
382C2×C4—1661no—
383C2×C4—1661no—
384C2×C4—1661no—
385C2×C4D4×D8312yes—
386C2×C4#1305058912yes—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—3321no—
395C22—3321no—
396C22—3321no—
397C22—3321no—
398C22—3321no—
399C22—3321no—
400C22—3321no—
401C22—3321no—
402C22—3321no—
403C22—3321no—
404C22—3321no—
405C22—1662no—
406C22—1662no—
407C22—1662no—
408C22C2×D4×D8311yescharacteristic
409C22#41×D8311yescharacteristic
410C22C2×#1305058911yescharacteristic
411C22#1458183711yescharacteristic
412C22#1458183811yescharacteristic
413C22#1458183811yescharacteristic
414C22#1458184011yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—3321no—
422C4—3321no—
423C4—3321no—
424C4—3321no—
425C4—1662no—
426C4—1662no—
427C2—81no—
428C2—3322no—
429C2—6641no—
430C2#1912826911yescharacteristic
431C2#1912828511yescharacteristic
432C2#1912832411yescharacteristic
433C2#1912833811yescharacteristic
434C2#1912835311yescharacteristic
435C2#1912843311yescharacteristic
436C2#1912844711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#393×C83C2
prime radical#19127610C2
hypercenter#393D83
hypocenterC83#2710
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14581781C2semidirect
2. C2×#14581774C2semidirect
3. #19127638C2semidirect
4. #19127630C2semidirect
5. #19127617C2semidirect
6. #19127616C2semidirect
8. #19127608C2semidirect
9. #19127601C2semidirect
10. #19127598C2semidirect
11. #19127594C2semidirect
12. #19127590C2semidirect
13. #19127579C2semidirect
14. #19127575C2semidirect
15. #393×C83C2semidirect
89. (C2×D83)⋊C4D4semidirect
219. C83#2710semidirect
226. #393D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817812
C2×#145817742
#191276382
#191276302
#191276172
#191276162
#191276102
#191276082
#191276012
#191275982
#191275942
#191275902
#191275792
#191275752
#393×C832
#271083