Finite Group Databasebeta

← #24913302

Subgroups — #24913302

Order 10624.

562 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×C4×C22⋊D83C211yesmaximal, characteristic, complemented
2#19127634C211yesmaximal, characteristic, complemented
3#19127629C211yesmaximal, characteristic, complemented
4#19127624C211yesmaximal, characteristic, complemented
5#19127623C211yesmaximal, characteristic, complemented
6#19127617C211yesmaximal, characteristic, complemented
7#19127616C211yesmaximal, characteristic, complemented
8#19127615C211yesmaximal, characteristic, complemented
9#19127609C211yesmaximal, characteristic
10#19127589C211yesmaximal, characteristic, complemented
11#19127582C211yesmaximal, characteristic, complemented
12#19127577C211yesmaximal, characteristic, complemented
13#19127572C211yesmaximal, characteristic, complemented
14#19127561C211yesmaximal, characteristic, complemented
15C2×#123×C83C211yesmaximal, characteristic, complemented
16C22×C22⋊D83C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19C4×C22⋊D83—24no—
20C2×C4⋊Dic83C2211yescharacteristic
21C2×C4⋊Dic83C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×C4×Dic83C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C22×D4×C83C2211yescharacteristic
46C23×C4×C83C2211yescharacteristic
47#123×C83—24no—
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C2×C22⋊D83—22no—
55C2×C22⋊D83—22no—
56C2×C22⋊D83—22no—
57C2×C22⋊D83—22no—
58C2×C22⋊D83—41no—
59C2×C22⋊D83—41no—
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C2×C4×D83—22no—
68C2×C4×D83—41no—
69C2×C4×D83—41no—
70C4⋊Dic83—41no—
71C4⋊Dic83—41no—
72Dic83⋊C4—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4—41no—
75Dic83⋊C4—41no—
76C22⋊Dic83—22no—
77C22⋊Dic83—22no—
78C22⋊Dic83—41no—
79C22⋊Dic83—41no—
80C22⋊Dic83—41no—
81C22⋊Dic83—41no—
82(C2×D83)⋊C4—22no—
83(C2×D83)⋊C4—22no—
84(C2×D83)⋊C4—41no—
85(C2×D83)⋊C4—41no—
86C4×Dic83—22no—
87C24×C83C2311yescharacteristic
88C24×C83C2311yescharacteristic
89C2×D4×C83—22no—
90C2×D4×C83—41no—
91C2×D4×C83—41no—
92C22×C4×C83—41no—
93C22×C4×C83—41no—
94C22×C4×C83D414yescomplemented
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C4⋊C4×C83—22no—
101C4⋊C4×C83—22no—
102C22⋊C4×C83—22no—
103C22⋊C4×C83—22no—
104C22⋊C4×C83—22no—
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×C83C2×D412yes—
119C23×C83C2411yescharacteristic
120C22×D83—21no—
121C22×D83—21no—
122C22×D83—21no—
123C22×D83—21no—
124C22×D83—21no—
125C22×D83—21no—
126C22×D83#4112yes—
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—44no—
142C2×C4×C83C2×D412yes—
143C2×C4×C83C2×D412yes—
144C22⋊D83—28no—
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—21no—
166C2×Dic83#4112yes—
167C4×D83—44no—
168C22×C83—22no—
169C22×C83—22no—
170C22×C83—22no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
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×C83C22×D411yescharacteristic
183C22×C83C2×#4111yescharacteristic
184C22×C83C2×#4111yescharacteristic
185C22×C83H(5,𝔽2)11yescharacteristic
186C22×C83H(5,𝔽2)11yescharacteristic
187C22×C83H(5,𝔽2)11yescharacteristic
188C22×C832−1+411yescharacteristic
189C2×D83—22no—
190C2×D83—22no—
191C2×D83—22no—
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—
201Dic83—22no—
202Dic83—41no—
203Dic83—41no—
204Dic83—41no—
205Dic83—41no—
206Dic83—41no—
207Dic83—41no—
208C2×C83—42no—
209C2×C83—81no—
210C2×C83#52511yescharacteristic
211C2×C83#53411yescharacteristic
212C2×C83#53711yescharacteristic
213C2×C83#53811yescharacteristic
214C2×C83#53911yescharacteristic
215C2×C83#54011yescharacteristic
216C2×C83#54211yescharacteristic
217D83—42no—
218#2630—831nomaximal, Sylow
219C83#263011yescharacteristic, complemented, Sylow
220C2×#123D8311yescharacteristic, complemented
221C2×C4×D4—831no—
222#398—831no—
223#397—831no—
224#396—831no—
225#396—831no—
226#394—831no—
227#394—831no—
228#394—831no—
229#392—831no—
230#388—831no—
231#387—831no—
232#386—831no—
233#385—831no—
234#380—831no—
235C22×D4—831no—
236C22×D4—831no—
237C22×D4C2×D8311yescharacteristic
238C23×C4—831no—
239C23×C4C2×D8311yescharacteristic
240#123—24no—
241C4×D4—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×C4⋊C4C2×D8311yescharacteristic
249C2×C4⋊C4C2×D8311yescharacteristic
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⋊C4—831no—
260C2×C22⋊C4C2×D8311yescharacteristic
261C2×C22⋊C4C2×D8311yescharacteristic
262C2×C22⋊C4C2×D8311yescharacteristic
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—
272C24—831no—
273C24C22×D8311yescharacteristic
274C24C22×D8311yescharacteristic
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—3321no—
279C2×D4—3321no—
280C2×D4—1662no—
281C2×D4—1662no—
282C2×D4—1662no—
283C2×D4—1662no—
284C22×C4—41no—
285C22×C4—41no—
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×C4C22⋊D8314yescomplemented
297C22×C4C22×D8311yescharacteristic
298C22×C4C22×D8311yescharacteristic
299C22×C4C22×D8311yescharacteristic
300C22×C4C22×D8311yescharacteristic
301C22×C4C22×D8311yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—3321no—
305C4⋊C4—3321no—
306C4⋊C4—3321no—
307C4⋊C4—3321no—
308C4⋊C4—1662no—
309C4⋊C4—1662no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—3321no—
314C22⋊C4—3321no—
315C22⋊C4—3321no—
316C22⋊C4—3321no—
317C22⋊C4—3321no—
318C22⋊C4—3321no—
319C22⋊C4—1662no—
320C22⋊C4—1662no—
321C22⋊C4—1662no—
322C22⋊C4—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—832no—
338C23—1661no—
339C23—1661no—
340C23—1661no—
341C23—1661no—
342C23—1661no—
343C23—1661no—
344C23C2×C22⋊D8312yes—
345C23C23×D8311yescharacteristic
346D4—44no—
347D4—3324no—
348D4—1668no—
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—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—44no—
363C2×C4—3324no—
364C2×C4—832no—
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—1661no—
380C2×C4—1661no—
381C2×C4—1661no—
382C2×C4—1661no—
383C2×C4—1661no—
384C2×C4—1661no—
385C2×C4C2×C22⋊D8312yes—
386C2×C4C2×C22⋊D8312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—3321no—
402C22—3321no—
403C22—3321no—
404C22—3321no—
405C22—1662no—
406C22—1662no—
407C22—1662no—
408C22C22×C22⋊D8311yescharacteristic
409C22#41×D8311yescharacteristic
410C22#41×D8311yescharacteristic
411C22#1458183711yescharacteristic
412C22#1458183711yescharacteristic
413C22#1458183811yescharacteristic
414C22#1458183911yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—3321no—
421C4—3321no—
422C4—3321no—
423C4—3321no—
424C4—3321no—
425C4—3321no—
426C4—1662no—
427C2—42no—
428C2—81no—
429C2—3322no—
430C2#1912820811yescharacteristic
431C2#1912826011yescharacteristic
432C2#1912827911yescharacteristic
433C2#1912828711yescharacteristic
434C2#1912829411yescharacteristic
435C2#1912830311yescharacteristic
436C2#1912831911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
FittingC2×#123×C83C2
prime radical#19127609C2
hypercenterC2×#123D83
hypocenterC83#2630
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D83C2semidirect
2. #19127634C2semidirect
3. #19127629C2semidirect
4. #19127624C2semidirect
5. #19127623C2semidirect
6. #19127617C2semidirect
7. #19127616C2semidirect
8. #19127615C2semidirect
10. #19127589C2semidirect
11. #19127582C2semidirect
12. #19127577C2semidirect
13. #19127572C2semidirect
14. #19127561C2semidirect
15. C2×#123×C83C2semidirect
94. C22×C4×C83D4semidirect
219. C83#2630semidirect
220. C2×#123D83semidirect
296. C22×C4C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D832
#191276342
#191276292
#191276242
#191276232
#191276172
#191276162
#191276152
#191276092
#191275892
#191275822
#191275772
#191275722
#191275612
C2×#123×C832
#263083