Finite Group Databasebeta

← C2×#21436488 #29467150

Subgroups — C2×#21436488 #29467150

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838113C212yesmaximal
2#21436488C2116yesmaximal, direct product factor
3C2×#16837739C214yesmaximal, complemented
4C2×#16837694C212yesmaximal, complemented
5C2×#16837644C212yesmaximal, complemented
6C2×C4×Dic236C211yesmaximal, characteristic, complemented
7C2×C8×D236C211yesmaximal, characteristic
8C2×#107×D59C212yesmaximal, complemented
9C2×C59×#500C211yesmaximal, characteristic, complemented
10C22×Dic236C2211yescharacteristic
11C22×C8×D59C2212yes—
12#16838113—28no—
13#16838113C22116yes—
14C2×#14273718—22no—
15C2×#14273707C2214yes—
16C2×#14273703—24no—
17C2×C4×Dic118C2212yes—
18C2×C4×D236C2211yescharacteristic
19C2×#14273689—22no—
20C2×C4⋊C4×D59C2214yes—
21#16837739C22132yescomplemented
22#16837694C22116yescomplemented
23#16837644C22116yescomplemented
24C4×Dic236C2218yescomplemented
25C8×D236C2218yes—
26C2×#14273661C2211yescharacteristic
27C2×#14273660C2214yes—
28#107×D59C22116yescomplemented
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×#14273652C2212yes—
31C2×#14273650C2214yes—
32C2×(C2×D59)⋊C8C2212yes—
33C2×C4⋊Q8×C59C2212yes—
34C59×#500C2218yescomplemented
35C2×#107×C59C2212yes—
36C2×#107×C59C2212yes—
37C2×C4×C8×C59C2211yescharacteristic
38C22×Dic118C2312yes—
39C22×D236D411yescharacteristic
40C22×C4×D59—24no—
41C22×C4×D59C2312yes—
42C2×Dic236—24no—
43C2×Dic236C2314yes—
44C22×C59⋊C8C2312yes—
45C2×C8×D59—28no—
46C2×C8×D59C2318yes—
47#14273718—216no—
48#14273707—28no—
49#14273707C23116yes—
50#14273703—232no—
51C4×Dic118—24no—
52C4×Dic118C2318yes—
53C4×D236D414yes—
54C4×D236C2314yes—
55#14273689—216no—
56C2×C4⋊Dic59—24no—
57C2×C4⋊Dic59D411yescharacteristic
58C2×C4⋊Dic59C2312yes—
59C2×Dic59⋊C4—22no—
60C2×Dic59⋊C4—24no—
61C4⋊C4×D59—28no—
62C4⋊C4×D59C23116yes—
63C2×(C2×D59)⋊C4—24no—
64C2×(C2×D59)⋊C4D412yes—
65C2×C4×Dic59—22no—
66#14273661C2314yes—
67#14273660C23116yes—
68C4⋊(C59⋊C8)C2314yes—
69#14273652C2318yes—
70#14273650C23116yes—
71(C2×D59)⋊C8C2318yes—
72C22×Q8×C59—22no—
73C22×C8×C59C2311yescharacteristic
74C22×C8×C59C2311yescharacteristic
75C4⋊Q8×C59—24no—
76C4⋊Q8×C59C2318yes—
77C2×C4⋊C4×C59—22no—
78C2×C4⋊C4×C59C2314yes—
79C2×C42×C59C2311yescharacteristic
80#107×C59C2318yes—
81#107×C59C2318yes—
82C4×C8×C59C2314yes—
83C23×D59C2×D412yes—
84C2×Q8×C59—28no—
85C2×Q8×C59—84no—
86C22×C4×C59—24no—
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2411yescharacteristic
90C22×Dic59—22no—
91C22×Dic59—22no—
92C22×Dic59C2×D412yes—
93C2×D236Q1618yescomplemented
94C2×D236C2×D414yes—
95C2×C4×D59—24no—
96C2×C4×D59—24no—
97C2×C4×D59—216no—
98C2×C4×D59—88no—
99C2×C4×D59C2×D414yes—
100C2×C4×D59C2414yes—
101C2×Dic118—24no—
102C2×Dic118—24no—
103C2×Dic118—22no—
104C2×Dic118C2414yes—
105C2×C8×C59—22no—
106C2×C8×C59#4114yes—
107C2×C8×C59C2412yes—
108C2×C8×C59C2412yes—
109C4⋊C4×C59—28no—
110C4⋊C4×C59—24no—
111C4⋊C4×C59C2418yes—
112C42×C59C2×D412yes—
113C42×C59C2412yes—
114(C2×D59)⋊C4—216no—
115(C2×D59)⋊C4C2×D418yes—
116C4⋊Dic59—22no—
117C4⋊Dic59—216no—
118C4⋊Dic59C2×D414yes—
119C4⋊Dic59C2414yes—
120Dic59⋊C4—28no—
121Dic59⋊C4—216no—
122C4×Dic59—28no—
123C2×C59⋊C8—24no—
124C2×C59⋊C8C2414yes—
125Dic236—28no—
126C8×D59—216no—
127C23×C59C22×D411yescharacteristic
128C22×D59—24no—
129C22×D59—24no—
130C22×D59C2×Q1618yes—
131C22×D59C22×D414yes—
132Q8×C59—88no—
133C2×C4×C59—22no—
134C2×C4×C59—28no—
135C2×C4×C59—48no—
136C2×C4×C59C2×Q1614yes—
137C2×C4×C59C22×D412yes—
138C2×C4×C59C22×D411yescharacteristic
139C2×C4×C59C22×D412yes—
140C2×C4×C59C2×#4112yes—
141C2×C4×C592−1+412yes—
142C2×C4×C59C2511yescharacteristic
143C2×Dic59—24no—
144C2×Dic59—24no—
145C2×Dic59—24no—
146C2×Dic59—44no—
147C2×Dic59—44no—
148C2×Dic59C22×D414yes—
149D236C2×Q16116yescomplemented
150C4×D59—28no—
151C4×D59—24no—
152C4×D59—24no—
153C4×D59—816no—
154Dic118—24no—
155Dic118—24no—
156Dic118—44no—
157C8×C59—22no—
158C8×C59C2×#4114yes—
159C59⋊C8—24no—
160C2×#3338—591nomaximal, Sylow
161C22×C59#54712yes—
162C22×C59C22×Q1612yes—
163C22×C59#57612yes—
164C22×C59C23×D411yescharacteristic
165C2×D59—216no—
166C2×D59—24no—
167C2×D59—24no—
168C2×D59C22×Q1618yes—
169C4×C59—22no—
170C4×C59—48no—
171C4×C59#54712yes—
172C4×C59C22×Q1614yes—
173C4×C59C22×#4111yescharacteristic
174C4×C59C2×2−1+411yescharacteristic
175Dic59—24no—
176Dic59—44no—
177Dic59—44no—
178C2×#554—592no—
179#3338—5916no—
180C2×#500D5911yescharacteristic, complemented
181C2×#484—594no—
182C2×#477—592no—
183C2×#467—592no—
184C2×C4×Q16—591no—
185C2×C8×D4—591no—
186C22×#107—592no—
187C2×C59#333814yescomplemented
188C2×C59C2×#54711yescharacteristic
189C2×C59C23×Q1611yescharacteristic
190C2×C59C2×#57611yescharacteristic
191D59—28no—
192C22×Q16—591no—
193C23×C8—592no—
194#554—5916no—
195#554—1188no—
196C2×C4⋊Q8C2×D5912yes—
197C2×#125—1182no—
198C2×C22⋊Q8—594no—
199C2×C22⋊Q8—1184no—
200C2×C4×Q8—592no—
201C2×C4×D4—591no—
202C2×C4×D4—1182no—
203C22×C4⋊C4—594no—
204#500C2×D5918yescomplemented
205#484—5932no—
206#477—5916no—
207#467—5916no—
208C4×Q16—598no—
209C8×D4—598no—
210C2×#107—591no—
211C2×#107—594no—
212C2×#107—5916no—
213C2×#107C2×D5912yes—
214C2×#107C2×D5912yes—
215C2×C4⋊C8—591no—
216C2×#103—592no—
217C2×#103—594no—
218C2×C22⋊C8—592no—
219C2×C4×C8C2×D5911yescharacteristic
220C59C2×#333811yescharacteristic, complemented, Sylow
221C22×Q8—22no—
222C22×Q8—592no—
223C22×D4—591no—
224C23×C4—592no—
225C23×C4—1184no—
226C2×Q16—594no—
227C2×Q16—1184no—
228C22×C8—592no—
229C22×C8—598no—
230C22×C8—1188no—
231C22×C8C22×D5911yescharacteristic
232C22×C8C22×D5911yescharacteristic
233C4⋊Q8—24no—
234C4⋊Q8C22×D5918yes—
235#125—11816no—
236C22⋊Q8—5916no—
237C22⋊Q8—11832no—
238C22⋊Q8—1188no—
239C4×Q8—598no—
240C4×Q8—1184no—
241C4×D4—594no—
242C4×D4—594no—
243C4×D4—11816no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—592no—
247C2×C4⋊C4—5916no—
248C2×C4⋊C4—1188no—
249C2×C4⋊C4—1184no—
250C2×C4⋊C4—1184no—
251C2×C4⋊C4—1182no—
252C2×C4⋊C4C22×D5914yes—
253C2×C22⋊C4—592no—
254C2×C22⋊C4—1184no—
255C2×C42—1182no—
256C2×C42C22×D5911yescharacteristic
257#107—594no—
258#107—5916no—
259#107C22×D5918yes—
260#107C22×D5918yes—
261C4⋊C8—594no—
262#103—598no—
263#103—5916no—
264C22⋊C8—598no—
265C4×C8C22×D5914yes—
266C24—592no—
267C2×Q8—28no—
268C2×Q8—84no—
269C2×Q8—594no—
270C2×Q8—1182no—
271C2×Q8—1184no—
272C2×Q8—1184no—
273C2×D4—598no—
274C2×D4—594no—
275C22×C4—24no—
276C22×C4—592no—
277C22×C4—594no—
278C22×C4—594no—
279C22×C4—11816no—
280C22×C4—1184no—
281C22×C4—1184no—
282C22×C4—1182no—
283C22×C4—1182no—
284C22×C4—4728no—
285C22×C4D4×D5911yescharacteristic
286C22×C4D4×D5911yescharacteristic
287C22×C4C23×D5911yescharacteristic
288Q16—1188no—
289C2×C8—22no—
290C2×C8—594no—
291C2×C8—1184no—
292C2×C8—11816no—
293C2×C8#1174568914yes—
294C2×C8C23×D5912yes—
295C2×C8C23×D5912yes—
296C4⋊C4—28no—
297C4⋊C4—24no—
298C4⋊C4—594no—
299C4⋊C4—594no—
300C4⋊C4—11816no—
301C4⋊C4—11816no—
302C4⋊C4—1182no—
303C4⋊C4—1188no—
304C4⋊C4C23×D5918yes—
305C22⋊C4—598no—
306C22⋊C4—11816no—
307C42—1188no—
308C42D4×D5912yes—
309C42C23×D5912yes—
310C23—598no—
311C23—594no—
312C23—1184no—
313C23—1184no—
314C23C2×D4×D5911yescharacteristic
315Q8—88no—
316Q8—1184no—
317Q8—1184no—
318Q8—2364no—
319D4—5916no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—594no—
324C2×C4—1184no—
325C2×C4—1184no—
326C2×C4—1184no—
327C2×C4—1188no—
328C2×C4—1184no—
329C2×C4—1184no—
330C2×C4—47216no—
331C2×C4—2364no—
332C2×C4—2364no—
333C2×C4Q16×D5914yes—
334C2×C4C2×D4×D5912yes—
335C2×C4C2×D4×D5912yes—
336C2×C4C2×D4×D5911yescharacteristic
337C2×C4C2×#1174568912yes—
338C2×C4#1427377512yes—
339C2×C4C24×D5911yescharacteristic
340C8—22no—
341C8—1184no—
342C8C2×#1174568914yes—
343C22—598no—
344C22—11816no—
345C22—1184no—
346C22—1184no—
347C22#1683805512yes—
348C22C2×Q16×D5912yes—
349C22#1683820312yes—
350C22C22×D4×D5911yescharacteristic
351C4—22no—
352C4—48no—
353C4—1184no—
354C4—2364no—
355C4—2364no—
356C4#1683805512yes—
357C4C2×Q16×D5914yes—
358C4C22×#1174568911yescharacteristic
359C4C2×#1427377511yescharacteristic
360C2—1188no—
361C2#2143648814yesdirect product factor
362C2C2×#1683805511yescharacteristic
363C2C22×Q16×D5911yescharacteristic
364C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#500C2
socleC23×C59C22×D4
prime radicalC22×D236D4
hypercenterC2×#500D59
hypocenterC59C2×#3338
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #21436488C2direct (N × H)
3. C2×#16837739C2semidirect
4. C2×#16837694C2semidirect
5. C2×#16837644C2semidirect
6. C2×C4×Dic236C2semidirect
8. C2×#107×D59C2semidirect
9. C2×C59×#500C2semidirect
21. #16837739C22semidirect
22. #16837694C22semidirect
23. #16837644C22semidirect
24. C4×Dic236C22semidirect
28. #107×D59C22semidirect
34. C59×#500C22semidirect
93. C2×D236Q16semidirect
149. D236C2×Q16semidirect
180. C2×#500D59semidirect
187. C2×C59#3338semidirect
204. #500C2×D59semidirect
220. C59C2×#3338semidirect
361. C2#21436488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381132
#214364882
C2×#168377392
C2×#168376942
C2×#168376442
C2×C4×Dic2362
C2×C8×D2362
C2×#107×D592
C2×C59×#5002
C2×#333859