Finite Group Databasebeta

← C2×#24907032 #35387069

Subgroups — C2×#24907032 #35387069

Order 21248.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128048C211yesmaximal, characteristic
2C2×#19127912C211yesmaximal, characteristic, complemented
3C2×#19127902C211yesmaximal, characteristic
4C2×#19127831C211yesmaximal, characteristic, complemented
5#24907032C218yesmaximal, direct product factor
6C2×#19127448C211yesmaximal, characteristic, complemented
7C2×#19127444C211yesmaximal, characteristic
8C2×#334×C83C211yesmaximal, characteristic, complemented
9C22×Dic332—21no—
10C22×#13050579—21no—
11C2×#14581792C2211yescharacteristic
12C2×#14581789C2211yescharacteristic
13C2×C4×Dic166C2211yescharacteristic
14#19128048—22no—
15#19128048C2214yes—
16#19127912—22no—
17#19127912C2214yescomplemented
18#19127902—22no—
19#19127902C2214yes—
20#19127831—22no—
21#19127831C2214yescomplemented
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×Dic83⋊C8—21no—
24C2×#14581717—21no—
25C2×#14581714—21no—
26C2×#14581714—21no—
27C2×#14581714—21no—
28C2×#14581702—21no—
29#19127448C2214yescomplemented
30#19127444C2214yes—
31C2×C4⋊C8×C83C2211yescharacteristic
32C2×C4⋊C8×C83C2211yescharacteristic
33C2×C4×C8×C83C2211yescharacteristic
34#334×C83C2214yescomplemented
35C22×Dic166—21no—
36C22×Dic166D411yescharacteristic
37C22×D332—21no—
38C22×D332—21no—
39C22×D332—21no—
40C2×Dic332—24no—
41C2×Dic332—44no—
42C2×#13050579—24no—
43C2×#13050579—44no—
44C22×C83⋊C8—21no—
45#14581792—21no—
46#14581792—21no—
47#14581792—21no—
48#14581792C2312yes—
49#14581789—21no—
50#14581789—21no—
51#14581789—21no—
52#14581789C2312yes—
53C4×Dic166—21no—
54C4×Dic166—21no—
55C4×Dic166D412yes—
56C4×Dic166C2312yes—
57C2×C4⋊Dic83—21no—
58C2×C4⋊Dic83—21no—
59C2×C4⋊Dic83D411yescharacteristic
60C2×Dic83⋊C4—21no—
61C2×C4×Dic83—21no—
62C4⋊(C83⋊C8)—21no—
63C4⋊(C83⋊C8)C2312yes—
64Dic83⋊C8—24no—
65#14581717—24no—
66#14581714—24no—
67#14581714—24no—
68#14581714—24no—
69#14581702—24no—
70C22×C8×C83—21no—
71C22×C8×C83—21no—
72C22×C8×C83D411yescharacteristic
73C22×C8×C83D411yescharacteristic
74C2×C42×C83C2311yescharacteristic
75C4⋊C8×C83—21no—
76C4⋊C8×C83—21no—
77C4⋊C8×C83C2312yes—
78C4⋊C8×C83C2312yes—
79C4×C8×C83D412yes—
80C4×C8×C83C2312yes—
81C23×D83—41no—
82C2×Dic166—22no—
83C2×Dic166—22no—
84C2×Dic166—21no—
85C2×Dic166—22no—
86C2×Dic166—42no—
87C2×Dic166—42no—
88C2×Dic166—41no—
89C2×Dic166C2×D412yes—
90C2×D332—22no—
91C2×D332—22no—
92C2×D332—22no—
93C2×D332—42no—
94C2×D332—42no—
95C2×D332—42no—
96C2×D332—42no—
97C2×D332—41no—
98C2×D332—41no—
99C2×D332—41no—
100C2×D332—82no—
101C22×Dic83—21no—
102C22×Dic83—21no—
103C22×Dic83—41no—
104Dic332—48no—
105#13050579—48no—
106C2×C83⋊C8—22no—
107C2×C83⋊C8—42no—
108C4⋊Dic83—21no—
109C4⋊Dic83—22no—
110C4⋊Dic83—22no—
111C4⋊Dic83—41no—
112C4⋊Dic83—41no—
113C4⋊Dic83C2×D412yes—
114Dic83⋊C4—22no—
115Dic83⋊C4—22no—
116C4×Dic83—22no—
117C4×Dic83—22no—
118C22×C4×C83C2×D411yescharacteristic
119C22×C4×C83C2×D411yescharacteristic
120C22×C4×C83#4111yescharacteristic
121C2×C8×C83—22no—
122C2×C8×C83—22no—
123C2×C8×C83—22no—
124C2×C8×C83—22no—
125C2×C8×C83—42no—
126C2×C8×C83—42no—
127C2×C8×C83C2×D412yes—
128C2×C8×C83C2×D412yes—
129C42×C83C2×D411yescharacteristic
130C42×C83C2×D411yescharacteristic
131C42×C83#4111yescharacteristic
132C42×C83C2411yescharacteristic
133C23×C83#12111yescharacteristic
134C22×D83—42no—
135C22×D83—82no—
136C22×D83—82no—
137C22×D83—82no—
138C2×C4×C83—22no—
139C2×C4×C83#12111yescharacteristic
140C2×C4×C83#12111yescharacteristic
141C2×C4×C83#12111yescharacteristic
142C2×C4×C83#13512yes—
143C2×C4×C83AGL(1,ℤ/8)12yes—
144C2×C4×C83AGL(1,ℤ/8)12yes—
145C2×C4×C83#13712yes—
146C2×C4×C83C22×D411yescharacteristic
147C2×C4×C83C22×D411yescharacteristic
148C2×C4×C83C2×#4111yescharacteristic
149C2×Dic83—22no—
150C2×Dic83—22no—
151C2×Dic83—42no—
152C2×Dic83—42no—
153C2×Dic83—42no—
154C2×Dic83—82no—
155D332—42no—
156D332—42no—
157D332—42no—
158D332—42no—
159D332—82no—
160D332—82no—
161D332—82no—
162D332—82no—
163Dic166—22no—
164Dic166—22no—
165Dic166—42no—
166Dic166—42no—
167Dic166—42no—
168Dic166—82no—
169C8×C83—22no—
170C8×C83—22no—
171C8×C83—42no—
172C8×C83—42no—
173C83⋊C8—42no—
174C22×C83#46412yes—
175C22×C83#46912yes—
176C22×C83#47112yes—
177C22×C83C2×#12111yescharacteristic
178C2×D83—82no—
179C2×D83—82no—
180C2×D83—82no—
181C2×D83—164no—
182C4×C83—21no—
183C4×C83—21no—
184C4×C83#46412yes—
185C4×C83#46912yes—
186C4×C83C2×#13511yescharacteristic
187C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
188C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C83C2×#13711yescharacteristic
190Dic83—42no—
191Dic83—42no—
192Dic83—82no—
193C2×#1702—831nomaximal, Sylow
194C2×C83#170214yescomplemented
195C2×C83C2×#46411yescharacteristic
196C2×C83C2×#46911yescharacteristic
197C2×C83C2×#47111yescharacteristic
198D83—162no—
199C2×#486—831no—
200C2×#462—831no—
201C2×#460—831no—
202C2×#446—831no—
203#1702—838no—
204C2×#334D8311yescharacteristic, complemented
205C2×#332—831no—
206C2×#331—831no—
207C83C2×#170211yescharacteristic, complemented, Sylow
208C22×Q16—1661no—
209C22×SD16—1661no—
210C2×C4⋊Q8—831no—
211C2×#127—831no—
212C2×C4×Q8—831no—
213#486—834no—
214#486—1662no—
215#462—834no—
216#462—1662no—
217#460—834no—
218#460—1662no—
219#446—834no—
220#446—1662no—
221C2×C4⋊C8—831no—
222C2×C4⋊C8—1661no—
223C2×C4⋊C8C2×D8311yescharacteristic
224C2×C4⋊C8C2×D8311yescharacteristic
225C2×#103—1661no—
226C2×#102—1661no—
227C2×#102—1661no—
228C2×#102—1661no—
229C2×#97—1661no—
230C2×C4×C8C2×D8311yescharacteristic
231#334C2×D8314yescomplemented
232#332—834no—
233#331—834no—
234C22×Q8—831no—
235C22×Q8—1661no—
236C22×D4—1661no—
237C22×D4—1661no—
238C22×D4—1661no—
239C2×Q16—3324no—
240C2×Q16—1664no—
241C2×SD16—3324no—
242C2×SD16—1664no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—1661no—
246C22×C8D33211yescharacteristic
247C22×C8D33211yescharacteristic
248C4⋊Q8—832no—
249C4⋊Q8—1661no—
250C4⋊Q8—1661no—
251C4⋊Q8—1661no—
252#127—832no—
253#127—1661no—
254#127—1661no—
255#127—1661no—
256C4×Q8—832no—
257C4×Q8—832no—
258C4×Q8—1661no—
259C4×Q8—1661no—
260C2×C4⋊C4—831no—
261C2×C4⋊C4—1661no—
262C2×C4⋊C4—1661no—
263C2×C4⋊C4—1661no—
264C2×C42—1661no—
265C2×C42C22×D8311yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—832no—
269C4⋊C8—1664no—
270C4⋊C8—1661no—
271C4⋊C8C22×D8312yes—
272C4⋊C8C22×D8312yes—
273#103—1664no—
274#102—1664no—
275#102—1664no—
276#102—1664no—
277#97—1664no—
278C4×C8D33212yes—
279C4×C8C22×D8312yes—
280C24—3321no—
281C2×Q8—3321no—
282C2×Q8—3322no—
283C2×Q8—3322no—
284C2×Q8—832no—
285C2×Q8—1662no—
286C2×Q8—1662no—
287C2×Q8—1662no—
288C2×Q8—1661no—
289C2×D4—3321no—
290C2×D4—3321no—
291C2×D4—3321no—
292C2×D4—3322no—
293C2×D4—3322no—
294C2×D4—3322no—
295C2×D4—3322no—
296C2×D4—6642no—
297C2×D4—1662no—
298C2×D4—1662no—
299C2×D4—1662no—
300C22×C4—3321no—
301C22×C4—1661no—
302C22×C4—1661no—
303C22×C4D4×D8311yescharacteristic
304C22×C4C2×D33211yescharacteristic
305C22×C4#1305059111yescharacteristic
306Q16—3328no—
307SD16—3328no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—3322no—
315C2×C8—1662no—
316C2×C8C2×D33212yes—
317C2×C8C2×D33212yes—
318C4⋊C4—3321no—
319C4⋊C4—3321no—
320C4⋊C4—832no—
321C4⋊C4—1662no—
322C4⋊C4—1662no—
323C4⋊C4—1661no—
324C4⋊C4—1662no—
325C4⋊C4—1662no—
326C42—1662no—
327C42—1662no—
328C42D4×D8311yescharacteristic
329C42C2×D33211yescharacteristic
330C42#1305059111yescharacteristic
331C42C23×D8311yescharacteristic
332C23—3322no—
333C23—6642no—
334C23—6642no—
335C23—6642no—
336C23#1458176711yescharacteristic
337Q8—3322no—
338Q8—3322no—
339Q8—3322no—
340Q8—6642no—
341Q8—1662no—
342Q8—1662no—
343D4—3322no—
344D4—3322no—
345D4—3322no—
346D4—3322no—
347D4—6642no—
348D4—6642no—
349D4—6642no—
350D4—6642no—
351C2×C4—22no—
352C2×C4—3322no—
353C2×C4—3322no—
354C2×C4—3322no—
355C2×C4—6642no—
356C2×C4—1662no—
357C2×C4—1662no—
358C2×C4#1458176711yescharacteristic
359C2×C4#1458176711yescharacteristic
360C2×C4#1458176711yescharacteristic
361C2×C4#1458181412yes—
362C2×C4#1458181912yes—
363C2×C4#1458181912yes—
364C2×C4#1458182512yes—
365C2×C4C2×D4×D8311yescharacteristic
366C2×C4C22×D33211yescharacteristic
367C2×C4C2×#1305059111yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—42no—
372C8—3322no—
373C22—13284no—
374C22—6642no—
375C22—6642no—
376C22—6642no—
377C22#1912792412yes—
378C22#1912795512yes—
379C22#1912796512yes—
380C22C2×#1458176711yescharacteristic
381C4—21no—
382C4—21no—
383C4—3322no—
384C4—3322no—
385C4—6642no—
386C4#1912792412yes—
387C4#1912795512yes—
388C4C2×#1458181411yescharacteristic
389C4C2×#1458181911yescharacteristic
390C4C2×#1458181911yescharacteristic
391C4C2×#1458182511yescharacteristic
392C2—13282no—
393C2#2490703214yesdirect product factor
394C2C2×#1912792411yescharacteristic
395C2C2×#1912795511yescharacteristic
396C2C2×#1912796511yescharacteristic
subgroupG/H
centerC23#14581767
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#334×C83C2
socleC23×C83#121
prime radicalC2×#14581789C22
hypercenterC2×#334D83
hypocenterC83C2×#1702
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. C2×#19127912C2semidirect
4. C2×#19127831C2semidirect
5. #24907032C2direct (N × H)
6. C2×#19127448C2semidirect
8. C2×#334×C83C2semidirect
17. #19127912C22semidirect
21. #19127831C22semidirect
29. #19127448C22semidirect
34. #334×C83C22semidirect
194. C2×C83#1702semidirect
204. C2×#334D83semidirect
207. C83C2×#1702semidirect
231. #334C2×D83semidirect
393. C2#24907032direct (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×#191279122
C2×#191279022
C2×#191278312
#249070322
C2×#191274482
C2×#191274442
C2×#334×C832
C2×#170283