Finite Group Databasebeta

← C2×#21445294 #29662608

Subgroups — C2×#21445294 #29662608

Order 15616.

766 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840136C211yesmaximal, characteristic
2C2×#16840044C211yesmaximal, characteristic, complemented
3C2×#16839963C211yesmaximal, characteristic
4C2×#16839889C211yesmaximal, characteristic, complemented
5#21445294C218yesmaximal, direct product factor
6C2×#16839514C211yesmaximal, characteristic, complemented
7C2×#16839505C211yesmaximal, characteristic
8C2×C61×#332C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×#11758201—21no—
11C22×#11758201—21no—
12C2×#14519774C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840136—22no—
15#16840136C2214yes—
16#16840044—22no—
17#16840044C2214yescomplemented
18#16839963—22no—
19#16839963C2214yes—
20#16839889—22no—
21#16839889C2214yescomplemented
22C2×#14519708—21no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706—21no—
25C2×#14519700—21no—
26C2×#14519699—21no—
27C2×#14519687—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839514C2214yescomplemented
30#16839505C2214yes—
31C2×C4⋊Q8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4⋊C8×C61C2211yescharacteristic
34C61×#332C2214yescomplemented
35C22×Dic122D411yescharacteristic
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C2×#11758190—24no—
40C2×#11758190—44no—
41C2×#11758201—24no—
42C2×#11758201—24no—
43C2×#11758201—44no—
44C2×#11758201—44no—
45C22×#92418—21no—
46C22×#92418D411yescharacteristic
47C22×#92418D411yescharacteristic
48#14519774—21no—
49#14519774—21no—
50#14519774—21no—
51#14519774C2312yes—
52C4×Dic122—21no—
53C4×Dic122—21no—
54C4×Dic122D412yes—
55C4×Dic122C2312yes—
56C2×C4⋊Dic61D411yescharacteristic
57C2×#11758196—21no—
58C2×C4×Dic61—21no—
59#14519708—24no—
60C4⋊#92418—21no—
61C4⋊#92418C2312yes—
62#14519706—24no—
63#14519700—24no—
64#14519699—24no—
65#14519687—24no—
66C4×#92418D412yes—
67C4×#92418C2312yes—
68C22×Q8×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C4⋊Q8×C61—21no—
72C4⋊Q8×C61—21no—
73C4⋊Q8×C61—21no—
74C4⋊Q8×C61C2312yes—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61C2312yes—
81C4⋊C8×C61C2312yes—
82C23×D61—41no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—42no—
86C2×Q8×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×Dic61—21no—
92C22×Dic61—21no—
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—22no—
96C2×D244—42no—
97C2×D244—42no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—82no—
104C2×Dic122—22no—
105C2×Dic122—22no—
106C2×Dic122—21no—
107C2×Dic122C2×D412yes—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C2×C8×C61—42no—
111C2×C8×C61—42no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61C2411yescharacteristic
120#11758201—48no—
121#11758201—48no—
122C4⋊Dic61—21no—
123C4⋊Dic61C2×D412yes—
124#11758196—22no—
125#11758196—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—42no—
131C2×#92418SD1614yescomplemented
132C2×#92418C2×D412yes—
133C2×#92418C2×D412yes—
134#11758190—48no—
135C23×C61#12111yescharacteristic
136C22×D61—42no—
137C22×D61—82no—
138C22×D61—82no—
139C22×D61—82no—
140Q8×C61—42no—
141Q8×C61—42no—
142Q8×C61—82no—
143C2×C4×C61—22no—
144C2×C4×C61—42no—
145C2×C4×C61—82no—
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61C2×SD1612yes—
150C2×C4×C61AGL(1,ℤ/8)12yes—
151C2×C4×C61AGL(1,ℤ/8)12yes—
152C2×C4×C61#13712yes—
153C2×C4×C61C22×D411yescharacteristic
154C2×C4×C61C22×D411yescharacteristic
155C2×C4×C61C2×#4111yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160D244—42no—
161D244—42no—
162D244—42no—
163D244—42no—
164D244—82no—
165D244—82no—
166D244—82no—
167D244—82no—
168Dic122—22no—
169Dic122—22no—
170Dic122—42no—
171C8×C61—42no—
172C8×C61—42no—
173#92418—22no—
174#92418—42no—
175#92418C2×SD1614yescomplemented
176C2×#1686—611nomaximal, Sylow
177C22×C61#46012yes—
178C22×C61#46812yes—
179C22×C61#47112yes—
180C22×C61C2×#12111yescharacteristic
181C2×D61—82no—
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—164no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—82no—
188C4×C61#46012yes—
189C4×C61#46812yes—
190C4×C61C22×SD1611yescharacteristic
191C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C4×C61C2×#13711yescharacteristic
194Dic61—42no—
195Dic61—42no—
196C2×#492—611no—
197C2×#475—611no—
198C2×#460—611no—
199C2×#446—611no—
200#1686—618no—
201C2×#335—611no—
202C2×#332D6111yescharacteristic, complemented
203C2×#331—611no—
204C2×C61#168614yescomplemented
205C2×C61C2×#46011yescharacteristic
206C2×C61C2×#46811yescharacteristic
207C2×C61C2×#47111yescharacteristic
208D61—162no—
209C22×SD16—1221no—
210C22×SD16—1221no—
211C22×SD16—1221no—
212C2×C4⋊Q8C2×D6111yescharacteristic
213C2×#127—611no—
214C2×C4×Q8—611no—
215#492—614no—
216#492—1222no—
217#475—614no—
218#475—1222no—
219#460—614no—
220#460—1222no—
221#446—614no—
222#446—1222no—
223C2×#106—1221no—
224C2×C4⋊C8—611no—
225C2×C4⋊C8—1221no—
226C2×C4⋊C8C2×D6111yescharacteristic
227C2×C4⋊C8C2×D6111yescharacteristic
228C2×#103—1221no—
229C2×#102—1221no—
230C2×#97—1221no—
231C2×C4×C8—611no—
232#335—614no—
233#332C2×D6114yescomplemented
234#331—614no—
235C61C2×#168611yescharacteristic, complemented, Sylow
236C22×Q8—21no—
237C22×Q8—611no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4—1221no—
241C2×SD16—1224no—
242C2×SD16—1224no—
243C2×SD16—1224no—
244C2×SD16—2444no—
245C2×SD16—2444no—
246C2×SD16—2444no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—1221no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C22×D6112yes—
256#127—612no—
257#127—1221no—
258#127—1221no—
259#127—1221no—
260C4×Q8—612no—
261C4×Q8—612no—
262C4×Q8—1221no—
263C4×Q8—1221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C42—1221no—
269C2×C42C22×D6111yescharacteristic
270#106—1224no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—612no—
274C4⋊C8—1224no—
275C4⋊C8—1221no—
276C4⋊C8C22×D6112yes—
277C4⋊C8C22×D6112yes—
278#103—1224no—
279#102—1224no—
280#97—1224no—
281C4×C8—612no—
282C4×C8—612no—
283C24—2441no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8—612no—
289C2×Q8—1221no—
290C2×Q8—1222no—
291C2×Q8—1222no—
292C2×D4—1222no—
293C2×D4—1222no—
294C2×D4—1222no—
295C2×D4—4882no—
296C2×D4—2442no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2442no—
301C2×D4—2442no—
302C2×D4—2442no—
303C22×C4—41no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4#1175822211yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309SD16—2448no—
310SD16—2448no—
311SD16—2448no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—612no—
317C2×C8—614no—
318C2×C8—612no—
319C2×C8—1222no—
320C2×C8—1222no—
321C2×C8—2442no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—612no—
327C4⋊C4—1222no—
328C4⋊C4—1221no—
329C4⋊C4—1222no—
330C42—1222no—
331C42—1222no—
332C42#1175822211yescharacteristic
333C42D4×D6111yescharacteristic
334C42D4×D6111yescharacteristic
335C42C23×D6111yescharacteristic
336C23—4882no—
337C23—4882no—
338C23—4882no—
339C23—2442no—
340C23#1451975011yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—82no—
344Q8—1222no—
345Q8—1222no—
346Q8—2442no—
347D4—4882no—
348D4—4882no—
349D4—4882no—
350D4—4882no—
351D4—2442no—
352D4—2442no—
353D4—2442no—
354D4—2442no—
355C2×C4—22no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4#1451975011yescharacteristic
363C2×C4#1451975011yescharacteristic
364C2×C4#1451975011yescharacteristic
365C2×C4SD16×D6112yes—
366C2×C4#1451980112yes—
367C2×C4#1451980412yes—
368C2×C4#1451980912yes—
369C2×C4C2×D4×D6111yescharacteristic
370C2×C4C2×D4×D6111yescharacteristic
371C2×C4C2×#1175822211yescharacteristic
372C8—42no—
373C8—42no—
374C8—614no—
375C8—1222no—
376C8—2442no—
377C22—9764no—
378C22—4882no—
379C22—4882no—
380C22—4882no—
381C22#1683996112yes—
382C22#1684001112yes—
383C22#1684002812yes—
384C22C2×#1451975011yescharacteristic
385C4—21no—
386C4—21no—
387C4—82no—
388C4—2442no—
389C4—2442no—
390C4#1683996112yes—
391C4#1684001112yes—
392C4C2×SD16×D6111yescharacteristic
393C4C2×#1451980111yescharacteristic
394C4C2×#1451980411yescharacteristic
395C4C2×#1451980911yescharacteristic
396C2—9762no—
397C2#2144529414yesdirect product factor
398C2C2×#1683996111yescharacteristic
399C2C2×#1684001111yescharacteristic
400C2C2×#1684002811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenterC2×#332D61
hypocenterC61C2×#1686
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×#16840044C2semidirect
4. C2×#16839889C2semidirect
5. #21445294C2direct (N × H)
6. C2×#16839514C2semidirect
8. C2×C61×#332C2semidirect
17. #16840044C22semidirect
21. #16839889C22semidirect
29. #16839514C22semidirect
34. C61×#332C22semidirect
131. C2×#92418SD16semidirect
175. #92418C2×SD16semidirect
202. C2×#332D61semidirect
204. C2×C61#1686semidirect
233. #332C2×D61semidirect
235. C61C2×#1686semidirect
397. C2#21445294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401362
C2×#168400442
C2×#168399632
C2×#168398892
#214452942
C2×#168395142
C2×#168395052
C2×C61×#3322
C2×#168661