Finite Group Databasebeta

← #24913393

Subgroups — #24913393

Order 10624.

576 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581769C211yesmaximal, characteristic, complemented
2C2×#14581764C211yesmaximal, characteristic
3#19127643C211yesmaximal, characteristic, complemented
4#19127642C211yesmaximal, characteristic, complemented
5#19127630C211yesmaximal, characteristic, complemented
6#19127629C211yesmaximal, characteristic, complemented
7#19127617C211yesmaximal, characteristic, complemented
8#19127616C211yesmaximal, characteristic, complemented
9#19127614C211yesmaximal, characteristic, complemented
10#19127613C211yesmaximal, characteristic, complemented
11#19127581C211yesmaximal, characteristic, complemented
12#19127580C211yesmaximal, characteristic, complemented
13#19127578C211yesmaximal, characteristic, complemented
14C2×C83⋊#95C211yesmaximal, characteristic, complemented
15#386×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C23×Dic83C2211yescharacteristic
20C23×Dic83C2211yescharacteristic
21#14581769—24no—
22#14581764—24no—
23C2×C4⋊Dic83C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C22×D4×C83C2211yescharacteristic
47C23×C4×C83C2211yescharacteristic
48C2×C22⋊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⋊D83—22no—
60C2×C22⋊D83—22no—
61C2×C22⋊D83—41no—
62C2×C22⋊D83—41no—
63C22×Dic83—22no—
64C22×Dic83—41no—
65C22×Dic83—41no—
66C22×Dic83—41no—
67C22×Dic83—41no—
68C22×Dic83D414yes—
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C22×Dic83C2311yescharacteristic
73C22×Dic83C2311yescharacteristic
74C22×Dic83C2311yescharacteristic
75C22×Dic83C2311yescharacteristic
76C4⋊Dic83—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—22no—
79Dic83⋊C4—22no—
80C22⋊Dic83—22no—
81C22⋊Dic83—22no—
82C22⋊Dic83—41no—
83C22⋊Dic83—41no—
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—
89C24×C83C2311yescharacteristic
90C24×C83C2311yescharacteristic
91C2×D4×C83—22no—
92C2×D4×C83—22no—
93C2×D4×C83—22no—
94C22×C4×C83—22no—
95C22×C4×C83—41no—
96C22×C4×C83—41no—
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C22×C4×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C22⋊C4×C83—22no—
103C22⋊C4×C83—41no—
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×C83—21no—
113C23×C83—21no—
114C23×C83—21no—
115C23×C83—21no—
116C23×C83C2×D412yes—
117C23×C83#4112yes—
118C23×C83#4112yes—
119C23×C83C2411yescharacteristic
120C22×D83—21no—
121C22×D83—21no—
122C22×D83—21no—
123C22×D83—21no—
124C22×D83—21no—
125C22×D83—21no—
126C22×D83—21no—
127D4×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—44no—
144C22⋊D83—44no—
145C22⋊D83—44no—
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—44no—
166C2×Dic83—44no—
167C2×Dic83C2×D412yes—
168C2×Dic83C2×D412yes—
169Dic166—44no—
170C22×C83—22no—
171C22×C83—22no—
172C22×C83—22no—
173C22×C83—22no—
174C22×C83—22no—
175C22×C83—22no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—41no—
181C22×C83—41no—
182C22×C83—41no—
183C22×C83#12414yes—
184C22×C83C22×D411yescharacteristic
185C22×C83C2×#4111yescharacteristic
186C22×C83C2×#4111yescharacteristic
187C22×C83H(5,𝔽2)11yescharacteristic
188C22×C83H(5,𝔽2)11yescharacteristic
189C22×C83H(5,𝔽2)11yescharacteristic
190C22×C832−1+411yescharacteristic
191C2×D83—41no—
192C2×D83—41no—
193C2×D83—41no—
194C2×D83—41no—
195C2×D83—41no—
196C2×D83—41no—
197C2×D83—41no—
198C4×C83—41no—
199C4×C83—41no—
200C4×C83—41no—
201C4×C83—41no—
202C4×C83—41no—
203Dic83—22no—
204Dic83—22no—
205Dic83—41no—
206Dic83—41no—
207Dic83—41no—
208Dic83—41no—
209Dic83—41no—
210C2×C83—24no—
211C2×C83—81no—
212C2×C83C2×#12411yescharacteristic
213C2×C83#53411yescharacteristic
214C2×C83#53711yescharacteristic
215C2×C83#53811yescharacteristic
216C2×C83#53811yescharacteristic
217C2×C83#53911yescharacteristic
218C2×C83#53911yescharacteristic
219D83—81no—
220#2639—831nomaximal, Sylow
221C83#263911yescharacteristic, complemented, Sylow
222C2×C22⋊Q8—831no—
223C2×#121—831no—
224#400—831no—
225#400—831no—
226#397—831no—
227#397—831no—
228#394—831no—
229#394—831no—
230#393—831no—
231#393—831no—
232#386—831no—
233#386—831no—
234#386—831no—
235#386D8311yescharacteristic, complemented
236C2×#95—831no—
237C22×Q8—831no—
238C22×D4—831no—
239C22×D4—831no—
240C22×D4C2×D8311yescharacteristic
241C23×C4—831no—
242C23×C4—831no—
243C23×C4C2×D8311yescharacteristic
244C22⋊Q8—1664no—
245#121—1664no—
246C2×C4⋊C4—831no—
247C2×C4⋊C4—831no—
248C2×C4⋊C4—831no—
249C2×C4⋊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
262#95—831no—
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#95—831no—
272#95C2×D8311yescharacteristic
273#95C2×D8311yescharacteristic
274C24—831no—
275C24C22×D8311yescharacteristic
276C24C22×D8311yescharacteristic
277C2×Q8—3321no—
278C2×Q8—3321no—
279C2×Q8—1662no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—3321no—
284C2×D4—3321no—
285C2×D4—1662no—
286C2×D4—1662no—
287C2×D4—1662no—
288C2×D4—1662no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—3321no—
293C22×C4—3321no—
294C22×C4—3321no—
295C22×C4—3321no—
296C22×C4—834no—
297C22×C4—831no—
298C22×C4—831no—
299C22×C4—831no—
300C22×C4—831no—
301C22×C4—831no—
302C22×C4—831no—
303C22×C4—831no—
304C22×C4—1662no—
305C22×C4C22×D8311yescharacteristic
306C22×C4C22×D8311yescharacteristic
307C22×C4C22×D8311yescharacteristic
308C22×C4C22×D8311yescharacteristic
309C22×C4C22×D8311yescharacteristic
310C4⋊C4—1662no—
311C4⋊C4—1662no—
312C4⋊C4—1662no—
313C4⋊C4—1662no—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—3321no—
318C22⋊C4—3321no—
319C22⋊C4—3321no—
320C22⋊C4—3321no—
321C22⋊C4—3321no—
322C22⋊C4—3321no—
323C22⋊C4—1662no—
324C22⋊C4—1662no—
325C22⋊C4—1662no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—1661no—
338C23—1661no—
339C23—1661no—
340C23—1661no—
341C23—1661no—
342C23—1661no—
343C23—1661no—
344C23D4×D8312yes—
345C23#1305058912yes—
346C23#1305059012yes—
347C23C23×D8311yescharacteristic
348Q8—3324no—
349D4—44no—
350D4—3324no—
351D4—3324no—
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—21no—
367C2×C4—44no—
368C2×C4—3324no—
369C2×C4—3324no—
370C2×C4—832no—
371C2×C4—832no—
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×C4—1661no—
388C2×C4—1661no—
389C2×C4—1661no—
390C2×C4—1661no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—3321no—
405C22—3321no—
406C22—3321no—
407C22—3321no—
408C22—3321no—
409C22—3321no—
410C22—3321no—
411C22#1458177814yes—
412C22C2×D4×D8311yescharacteristic
413C22C2×#1305058911yescharacteristic
414C22C2×#1305059011yescharacteristic
415C22#1458183711yescharacteristic
416C22#1458183711yescharacteristic
417C22#1458183811yescharacteristic
418C22#1458183911yescharacteristic
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—3321no—
425C4—3321no—
426C4—3321no—
427C4—3321no—
428C4—3321no—
429C4—1662no—
430C4—1662no—
431C2—24no—
432C2—81no—
433C2—6641no—
434C2C2×#1458177811yescharacteristic
435C2#1912825911yescharacteristic
436C2#1912827811yescharacteristic
437C2#1912828411yescharacteristic
438C2#1912828611yescharacteristic
439C2#1912829311yescharacteristic
440C2#1912829511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#386×C83C2
prime radicalC2×#14581764C2
hypercenter#386D83
hypocenterC83#2639
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14581769C2semidirect
3. #19127643C2semidirect
4. #19127642C2semidirect
5. #19127630C2semidirect
6. #19127629C2semidirect
7. #19127617C2semidirect
8. #19127616C2semidirect
9. #19127614C2semidirect
10. #19127613C2semidirect
11. #19127581C2semidirect
12. #19127580C2semidirect
13. #19127578C2semidirect
14. C2×C83⋊#95C2semidirect
15. #386×C83C2semidirect
221. C83#2639semidirect
235. #386D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817692
C2×#145817642
#191276432
#191276422
#191276302
#191276292
#191276172
#191276162
#191276142
#191276132
#191275812
#191275802
#191275782
C2×C83⋊#952
#386×C832
#263983