Finite Group Databasebeta

← #24911645

Subgroups — #24911645

Order 10624.

582 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×#14581748C211yesmaximal, characteristic, complemented
2#19127634C211yesmaximal, characteristic, complemented
3#19127615C211yesmaximal, characteristic, complemented
4#19127615C211yesmaximal, characteristic, complemented
5#19127615C211yesmaximal, characteristic, complemented
6#19127604C211yesmaximal, characteristic, complemented
7#19127595C211yesmaximal, characteristic, complemented
8#19127594C211yesmaximal, characteristic, complemented
9#19127589C211yesmaximal, characteristic, complemented
10#19127582C211yesmaximal, characteristic, complemented
11#19127581C211yesmaximal, characteristic, complemented
12#19127581C211yesmaximal, characteristic, complemented
13#19127574C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
15C2×#121×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17#14581748—24no—
18C2×C4⋊Dic83C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×C22⋊Dic83C2211yescharacteristic
24C2×C22⋊Dic83C2211yescharacteristic
25C2×C22⋊Dic83C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×C22⋊Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
35C2×C4×Dic83C2211yescharacteristic
36C2×C4×Dic83C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C22×D4×C83C2211yescharacteristic
46C22×D4×C83C2211yescharacteristic
47C22×D4×C83C2211yescharacteristic
48C23×C4×C83C2211yescharacteristic
49#121×C83—24no—
50C2×C4⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C22×Dic83—22no—
54C22×Dic83—22no—
55C22×Dic83—22no—
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C4⋊Dic83—41no—
65Dic83⋊C4—22no—
66Dic83⋊C4—22no—
67Dic83⋊C4—22no—
68Dic83⋊C4—41no—
69C22⋊Dic83—22no—
70C22⋊Dic83—22no—
71C22⋊Dic83—22no—
72C22⋊Dic83—22no—
73C22⋊Dic83—22no—
74C22⋊Dic83—22no—
75C22⋊Dic83—41no—
76C22⋊Dic83—41no—
77C22⋊Dic83—41no—
78C22⋊Dic83—41no—
79C22⋊Dic83—41no—
80C4×Dic83—22no—
81C4×Dic83—22no—
82C4×Dic83—41no—
83C24×C83C2311yescharacteristic
84C24×C83C2311yescharacteristic
85C24×C83C2311yescharacteristic
86C2×D4×C83—22no—
87C2×D4×C83—22no—
88C2×D4×C83—22no—
89C2×D4×C83—22no—
90C2×D4×C83—22no—
91C2×D4×C83—22no—
92C2×D4×C83—41no—
93C2×D4×C83—41no—
94C2×D4×C83—41no—
95C22×C4×C83—22no—
96C22×C4×C83—22no—
97C22×C4×C83—41no—
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C22×C4×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C4⋊C4×C83—22no—
103C22⋊C4×C83—22no—
104C22⋊C4×C83D414yes—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—21no—
115C23×C83—21no—
116C23×C83—21no—
117C23×C83—21no—
118C23×C83—21no—
119C23×C83—21no—
120C23×C83—21no—
121C23×C83—21no—
122C23×C83—21no—
123C23×C83—21no—
124C23×C83C2×D412yes—
125C23×C83#4112yes—
126C23×C83C2411yescharacteristic
127D4×C83—44no—
128D4×C83—44no—
129D4×C83—44no—
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—44no—
140C2×C4×C83C2×D412yes—
141C2×C4×C83C2×D412yes—
142C2×C4×C83#4112yes—
143C2×Dic83—28no—
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—21no—
162C2×Dic83—21no—
163C2×Dic83—21no—
164C2×Dic83—21no—
165C2×Dic83—21no—
166C2×Dic83#4112yes—
167C2×Dic83#4112yes—
168C22×C83—22no—
169C22×C83—22no—
170C22×C83—22no—
171C22×C83—22no—
172C22×C83—22no—
173C22×C83—22no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—41no—
181C22×C83—41no—
182C22×C83—41no—
183C22×C83—41no—
184C22×C83—41no—
185C22×C83—41no—
186C22×C83—41no—
187C22×C83—41no—
188C22×C83—41no—
189C22×C83C22×D411yescharacteristic
190C22×C83C2×#4111yescharacteristic
191C22×C83C2×#4111yescharacteristic
192C22×C83C2×#4111yescharacteristic
193C22×C83C2×#4111yescharacteristic
194C22×C83H(5,𝔽2)11yescharacteristic
195C22×C83H(5,𝔽2)11yescharacteristic
196C4×C83—22no—
197C4×C83—22no—
198C4×C83—22no—
199C4×C83—41no—
200Dic83—22no—
201Dic83—22no—
202Dic83—41no—
203Dic83—41no—
204Dic83—41no—
205Dic83—41no—
206Dic83—41no—
207Dic83—41no—
208C2×C83—42no—
209C2×C83—42no—
210C2×C83—81no—
211C2×C83#52511yescharacteristic
212C2×C83#52911yescharacteristic
213C2×C83#54011yescharacteristic
214C2×C83#54611yescharacteristic
215C2×C83#54611yescharacteristic
216C2×C83#55311yescharacteristic
217C2×C83#55511yescharacteristic
218#2476—831nomaximal, Sylow
219C83#247611yescharacteristic, complemented, Sylow
220C2×#121D8311yescharacteristic
221C2×#117—831no—
222#398—831no—
223#394—831no—
224#394—831no—
225#394—831no—
226#390—831no—
227#388—831no—
228#388—831no—
229#388—831no—
230#387—831no—
231#386—831no—
232#386—831no—
233#385—831no—
234C4×C22⋊C4—831no—
235C22×D4C2×D8311yescharacteristic
236C22×D4C2×D8311yescharacteristic
237C22×D4C2×D8311yescharacteristic
238C23×C4—831no—
239C23×C4C2×D8311yescharacteristic
240#121—24no—
241#117—1664no—
242C2×C4⋊C4—831no—
243C2×C4⋊C4—831no—
244C2×C4⋊C4—831no—
245C2×C4⋊C4—831no—
246C2×C4⋊C4—831no—
247C2×C4⋊C4C2×D8311yescharacteristic
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×C42—831no—
262C2×C42—831no—
263C2×C42—831no—
264#95—831no—
265#95—831no—
266#95—831no—
267#95—831no—
268#95—831no—
269#95—831no—
270#95—831no—
271#95—831no—
272C24C22×D8311yescharacteristic
273C24C22×D8311yescharacteristic
274C24C22×D8311yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—831no—
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×C4—1662no—
298C22×C4C22×D8311yescharacteristic
299C22×C4C22×D8311yescharacteristic
300C22×C4C22×D8311yescharacteristic
301C22×C4C22×D8311yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—3321no—
304C4⋊C4—3321no—
305C4⋊C4—1662no—
306C4⋊C4—1662no—
307C4⋊C4—1662no—
308C22⋊C4—22no—
309C22⋊C4—3321no—
310C22⋊C4—3321no—
311C22⋊C4—3321no—
312C22⋊C4—3321no—
313C22⋊C4—3321no—
314C22⋊C4—1662no—
315C22⋊C4—1662no—
316C22⋊C4—1662no—
317C22⋊C4—1662no—
318C22⋊C4—1662no—
319C22⋊C4—1662no—
320C22⋊C4C22⋊D8314yes—
321C42—3321no—
322C42—1662no—
323C42—1662no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23C2×C22⋊D8312yes—
344C23#1305058912yes—
345C23C23×D8311yescharacteristic
346D4—44no—
347D4—44no—
348D4—44no—
349C2×C4—21no—
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—44no—
359C2×C4—832no—
360C2×C4—832no—
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—
379C2×C4—1668no—
380C2×C4—1661no—
381C2×C4—1661no—
382C2×C4—1661no—
383C2×C4—1661no—
384C2×C4C2×C22⋊D8312yes—
385C2×C4C2×C22⋊D8312yes—
386C2×C4#1305058912yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C22×C22⋊D8311yescharacteristic
409C22#41×D8311yescharacteristic
410C22#41×D8311yescharacteristic
411C22C2×#1305058911yescharacteristic
412C22C2×#1305058911yescharacteristic
413C22#1458183711yescharacteristic
414C22#1458183711yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—3321no—
420C4—3321no—
421C4—3321no—
422C4—3321no—
423C4—3321no—
424C4—3321no—
425C4—1662no—
426C4—1662no—
427C2—42no—
428C2—42no—
429C2—81no—
430C2#1912820811yescharacteristic
431C2#1912823211yescharacteristic
432C2#1912830111yescharacteristic
433C2#1912834511yescharacteristic
434C2#1912834511yescharacteristic
435C2#1912839411yescharacteristic
436C2#1912841511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting, prime radicalC2×#121×C83C2
hypercenterC2×#121D83
hypocenterC83#2476
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14581748C2semidirect
2. #19127634C2semidirect
3. #19127615C2semidirect
4. #19127615C2semidirect
5. #19127615C2semidirect
6. #19127604C2semidirect
7. #19127595C2semidirect
8. #19127594C2semidirect
9. #19127589C2semidirect
10. #19127582C2semidirect
11. #19127581C2semidirect
12. #19127581C2semidirect
13. #19127574C2semidirect
14. C4×C22⋊Dic83C2semidirect
219. C83#2476semidirect

Maximal subgroups

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

subgroupindex
C2×#145817482
#191276342
#191276152
#191276042
#191275952
#191275942
#191275892
#191275822
#191275812
#191275742
C4×C22⋊Dic832
C2×#121×C832
#247683