Finite Group Databasebeta

← C2×#24906879 #35386780

Subgroups — C2×#24906879 #35386780

Order 21248.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128048C211yesmaximal, characteristic
2C2×#19127996C211yesmaximal, characteristic, complemented
3C2×#19127901C211yesmaximal, characteristic
4#24906879C218yesmaximal, direct product factor
5C2×#19127452C211yesmaximal, characteristic, complemented
6C2×#19127449C211yesmaximal, characteristic, complemented
7C2×#19127444C211yesmaximal, characteristic
8C2×C8×Q8×C83C211yesmaximal, characteristic, complemented
9C22×#13050577—21no—
10C2×#14581792C2211yescharacteristic
11C2×#14581789C2211yescharacteristic
12#19128048—22no—
13#19128048C2214yes—
14#19127996—22no—
15#19127996C2214yescomplemented
16#19127901—22no—
17#19127901C2214yes—
18C2×#14581725—21no—
19C2×C4⋊(C83⋊C8)C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×#14581716—21no—
22C2×#14581714—21no—
23C2×#14581714—21no—
24C2×#14581712—21no—
25#19127452C2214yescomplemented
26#19127449C2214yescomplemented
27#19127444C2214yes—
28C2×C4×Q8×C83C2211yescharacteristic
29C8×Q8×C83—22no—
30C8×Q8×C83C2214yescomplemented
31C2×C4⋊C8×C83—21no—
32C2×C4⋊C8×C83C2211yescharacteristic
33C2×C4×C8×C83—21no—
34C2×C4×C8×C83C2211yescharacteristic
35C22×Dic166—21no—
36C22×D332—21no—
37C22×D332—21no—
38C22×D332—21no—
39C2×#13050577—24no—
40C2×#13050577—44no—
41C22×C83⋊C8—21no—
42C22×C83⋊C8—21no—
43#14581792—21no—
44#14581792—21no—
45#14581792—21no—
46#14581792C2312yes—
47#14581789—21no—
48#14581789—21no—
49#14581789—21no—
50#14581789C2312yes—
51C2×C4⋊Dic83—21no—
52C2×C4⋊Dic83—21no—
53#14581725—24no—
54C4⋊(C83⋊C8)—21no—
55C4⋊(C83⋊C8)—21no—
56C4⋊(C83⋊C8)C2312yes—
57C4⋊(C83⋊C8)C2312yes—
58#14581716—24no—
59#14581714—24no—
60#14581714—24no—
61#14581712—24no—
62C22×Q8×C83D411yescharacteristic
63C22×C8×C83—21no—
64C22×C8×C83D411yescharacteristic
65C22×C8×C83D411yescharacteristic
66C4×Q8×C83—21no—
67C4×Q8×C83—21no—
68C4×Q8×C83D412yes—
69C4×Q8×C83C2312yes—
70C2×C4⋊C4×C83—21no—
71C2×C4⋊C4×C83D411yescharacteristic
72C2×C42×C83—21no—
73C2×C42×C83C2311yescharacteristic
74C4⋊C8×C83—24no—
75C4⋊C8×C83—21no—
76C4⋊C8×C83C2312yes—
77C4×C8×C83—24no—
78C4×C8×C83D412yes—
79C4×C8×C83C2312yes—
80C23×D83—41no—
81C2×Dic166—22no—
82C2×Dic166—41no—
83C2×Dic166—82no—
84C2×D332—22no—
85C2×D332—22no—
86C2×D332—22no—
87C2×D332—42no—
88C2×D332—42no—
89C2×D332—42no—
90C2×D332—42no—
91C2×D332—41no—
92C2×D332—41no—
93C2×D332—41no—
94C2×D332—82no—
95C22×Dic83—41no—
96#13050577—48no—
97C2×C83⋊C8—22no—
98C2×C83⋊C8—22no—
99C2×C83⋊C8—42no—
100C2×C83⋊C8—42no—
101C4⋊Dic83—22no—
102C4⋊Dic83—22no—
103C4⋊Dic83—41no—
104C4⋊Dic83—41no—
105C2×Q8×C83—21no—
106C2×Q8×C83—22no—
107C2×Q8×C83SD1614yes—
108C2×Q8×C83C2×D412yes—
109C22×C4×C83—21no—
110C22×C4×C83—21no—
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83C2×D411yescharacteristic
113C22×C4×C83#4111yescharacteristic
114C2×C8×C83—22no—
115C2×C8×C83—22no—
116C2×C8×C83—22no—
117C2×C8×C83—42no—
118C2×C8×C83C2×D412yes—
119C2×C8×C83C2×D412yes—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—21no—
122C4⋊C4×C83—22no—
123C4⋊C4×C83C2×D412yes—
124C42×C83—22no—
125C42×C83—22no—
126C42×C83C2×D411yescharacteristic
127C42×C83C2×D411yescharacteristic
128C42×C83#4111yescharacteristic
129C42×C83C2411yescharacteristic
130C23×C83#12111yescharacteristic
131C22×D83—42no—
132C22×D83—82no—
133C22×D83—82no—
134C22×D83—82no—
135Q8×C83—22no—
136Q8×C83—24no—
137Q8×C83C2×SD1614yes—
138C2×C4×C83—22no—
139C2×C4×C83—24no—
140C2×C4×C83—22no—
141C2×C4×C83—22no—
142C2×C4×C83—42no—
143C2×C4×C83#12111yescharacteristic
144C2×C4×C83#12111yescharacteristic
145C2×C4×C83#12111yescharacteristic
146C2×C4×C83C2×SD1612yes—
147C2×C4×C83#13512yes—
148C2×C4×C83#13512yes—
149C2×C4×C83#13712yes—
150C2×C4×C83C22×D411yescharacteristic
151C2×C4×C83C22×D411yescharacteristic
152C2×C4×C83C2×#4111yescharacteristic
153C2×Dic83—42no—
154C2×Dic83—82no—
155D332—42no—
156D332—42no—
157D332—42no—
158D332—42no—
159D332—82no—
160D332—82no—
161D332—82no—
162D332—82no—
163Dic166—82no—
164Dic166—82no—
165C8×C83—22no—
166C8×C83—22no—
167C8×C83—42no—
168C83⋊C8—42no—
169C83⋊C8—42no—
170C22×C83#46412yes—
171C22×C83#46512yes—
172C22×C83#47212yes—
173C22×C83C2×#12111yescharacteristic
174C2×D83—82no—
175C2×D83—82no—
176C2×D83—82no—
177C2×D83—164no—
178C4×C83—24no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—42no—
182C4×C83#46412yes—
183C4×C83#46512yes—
184C4×C83C22×SD1611yescharacteristic
185C4×C83C2×#13511yescharacteristic
186C4×C83C2×#13511yescharacteristic
187C4×C83C2×#13711yescharacteristic
188Dic83—82no—
189C2×#1678—831nomaximal, Sylow
190C2×C83#167814yescomplemented
191C2×C83C2×#46411yescharacteristic
192C2×C83C2×#46511yescharacteristic
193C2×C83C2×#47211yescharacteristic
194D83—162no—
195C2×#486—831no—
196C2×#477—831no—
197C2×#460—831no—
198C2×C8×Q8D8311yescharacteristic, complemented
199#1678—838no—
200C2×#334—831no—
201C2×#333—831no—
202C2×#331—831no—
203C83C2×#167811yescharacteristic, complemented, Sylow
204C22×SD16—1661no—
205C2×C4⋊Q8—831no—
206C2×#127—831no—
207C2×C4×Q8C2×D8311yescharacteristic
208#486—834no—
209#486—1662no—
210#477—834no—
211#477—1662no—
212#460—834no—
213#460—1662no—
214C8×Q8—22no—
215C8×Q8C2×D8314yescomplemented
216C2×#107—1661no—
217C2×C4⋊C8—21no—
218C2×C4⋊C8—831no—
219C2×C4⋊C8—831no—
220C2×C4⋊C8C2×D8311yescharacteristic
221C2×#103—1661no—
222C2×#102—1661no—
223C2×#102—1661no—
224C2×#102—1661no—
225C2×C4×C8—21no—
226C2×C4×C8C2×D8311yescharacteristic
227#334—834no—
228#333—834no—
229#331—834no—
230C22×Q8—1661no—
231C22×Q8D33211yescharacteristic
232C22×D4—1661no—
233C22×D4—1661no—
234C22×D4—1661no—
235C2×SD16—3324no—
236C2×SD16—1664no—
237C22×C8—21no—
238C22×C8—1661no—
239C22×C8—1661no—
240C22×C8C22⋊D8311yescharacteristic
241C22×C8C22⋊D8311yescharacteristic
242C4⋊Q8—832no—
243C4⋊Q8—1661no—
244C4⋊Q8—1661no—
245C4⋊Q8—1661no—
246#127—832no—
247#127—1661no—
248#127—1661no—
249#127—1661no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D33212yes—
253C4×Q8C22×D8312yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—1661no—
256C2×C4⋊C4—1661no—
257C2×C4⋊C4D33211yescharacteristic
258C2×C42—21no—
259C2×C42C22×D8311yescharacteristic
260#107—1664no—
261C4⋊C8—24no—
262C4⋊C8—21no—
263C4⋊C8—832no—
264C4⋊C8—832no—
265C4⋊C8—1661no—
266C4⋊C8—1661no—
267C4⋊C8C22×D8312yes—
268#103—1664no—
269#102—1664no—
270#102—1664no—
271#102—1664no—
272C4×C8—24no—
273C4×C8C22⋊D8312yes—
274C4×C8C22×D8312yes—
275C24—3321no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—3321no—
279C2×Q8—6642no—
280C2×Q8—1662no—
281C2×Q8#1305057914yes—
282C2×Q8C2×D33212yes—
283C2×D4—3321no—
284C2×D4—3321no—
285C2×D4—3321no—
286C2×D4—3322no—
287C2×D4—3322no—
288C2×D4—3322no—
289C2×D4—3322no—
290C2×D4—6642no—
291C2×D4—1662no—
292C2×D4—1662no—
293C2×D4—1662no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—3321no—
297C22×C4C2×C22⋊D8311yescharacteristic
298C22×C4C2×D33211yescharacteristic
299C22×C4#1305059011yescharacteristic
300SD16—3328no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—3322no—
306C2×C8—3322no—
307C2×C8—1662no—
308C2×C8—1662no—
309C2×C8C2×C22⋊D8312yes—
310C2×C8C2×C22⋊D8312yes—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—3321no—
315C4⋊C4—3321no—
316C4⋊C4—1662no—
317C4⋊C4—1662no—
318C4⋊C4C2×D33212yes—
319C42—22no—
320C42—22no—
321C42C2×C22⋊D8311yescharacteristic
322C42C2×D33211yescharacteristic
323C42#1305059011yescharacteristic
324C42C23×D8311yescharacteristic
325C23—3322no—
326C23—6642no—
327C23—6642no—
328C23—6642no—
329C23#1458176611yescharacteristic
330Q8—24no—
331Q8—22no—
332Q8—6642no—
333Q8—6642no—
334Q8C2×#1305057914yes—
335D4—3322no—
336D4—3322no—
337D4—3322no—
338D4—3322no—
339D4—6642no—
340D4—6642no—
341D4—6642no—
342D4—6642no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—3322no—
349C2×C4—6642no—
350C2×C4#1458176611yescharacteristic
351C2×C4#1458176611yescharacteristic
352C2×C4#1458176611yescharacteristic
353C2×C4C2×#1305057912yes—
354C2×C4#1458181212yes—
355C2×C4#1458181412yes—
356C2×C4#1458182312yes—
357C2×C4C22×C22⋊D8311yescharacteristic
358C2×C4C22×D33211yescharacteristic
359C2×C4C2×#1305059011yescharacteristic
360C8—22no—
361C8—22no—
362C8—42no—
363C8—3322no—
364C8—3322no—
365C22—13284no—
366C22—6642no—
367C22—6642no—
368C22—6642no—
369C22#1912792312yes—
370C22#1912793012yes—
371C22#1912797112yes—
372C22C2×#1458176611yescharacteristic
373C4—24no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—6642no—
378C4#1912792312yes—
379C4#1912793012yes—
380C4C22×#1305057911yescharacteristic
381C4C2×#1458181211yescharacteristic
382C4C2×#1458181411yescharacteristic
383C4C2×#1458182311yescharacteristic
384C2—13282no—
385C2#2490687914yesdirect product factor
386C2C2×#1912792311yescharacteristic
387C2C2×#1912793011yescharacteristic
388C2C2×#1912797111yescharacteristic
subgroupG/H
centerC23#14581766
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×C8×Q8×C83C2
socleC23×C83#121
prime radicalC2×#14581789C22
hypercenterC2×C8×Q8D83
hypocenterC83C2×#1678
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#19127996C2semidirect
4. #24906879C2direct (N × H)
5. C2×#19127452C2semidirect
6. C2×#19127449C2semidirect
8. C2×C8×Q8×C83C2semidirect
15. #19127996C22semidirect
25. #19127452C22semidirect
26. #19127449C22semidirect
30. C8×Q8×C83C22semidirect
190. C2×C83#1678semidirect
198. C2×C8×Q8D83semidirect
203. C83C2×#1678semidirect
215. C8×Q8C2×D83semidirect
385. C2#24906879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191280482
C2×#191279962
C2×#191279012
#249068792
C2×#191274522
C2×#191274492
C2×#191274442
C2×C8×Q8×C832
C2×#167883