Finite Group Databasebeta

← C2×#21460944 #30608312

Subgroups — C2×#21460944 #30608312

Order 15616.

484 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840672C211yesmaximal, characteristic, complemented
2C2×#16840622C211yesmaximal, characteristic, complemented
3#21460944C214yesmaximal, direct product factor
4C2×#16839945C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519838—21no—
7#16840672—21no—
8#16840672C2212yescomplemented
9#16840622—21no—
10#16840622C2212yescomplemented
11C2×#14519807—21no—
12C2×#14519775C2211yescharacteristic
13#16839945—21no—
14#16839945—21no—
15#16839945C412yes—
16#16839945C2212yes—
17C2×#14519704—21no—
18C2×#14519696C411yescharacteristic
19C2×2−1+4×C61C411yescharacteristic
20C2×#11758217—41no—
21C22×#92420—41no—
22#14519844—22no—
23#14519844—41no—
24#14519838—22no—
25#14519838—41no—
26C22×Dic122D411yescharacteristic
27#14519807—22no—
28#14519807—22no—
29#14519807—42no—
30C2×#11758202—41no—
31C2×#11758200—41no—
32C2×#11758194—21no—
33#14519775—41no—
34#14519775C2×C411yescharacteristic
35#14519775D411yescharacteristic
36#14519775D411yescharacteristic
37#14519775C2311yescharacteristic
38C2×#11758196—41no—
39C2×C4×Dic61D411yescharacteristic
40#14519704—22no—
41#14519704—22no—
42#14519696—21no—
43#14519696C2×C412yes—
442−1+4×C61—21no—
452−1+4×C61—41no—
462−1+4×C61—42no—
472−1+4×C61C2×C412yes—
48C2×#41×C61—21no—
49C2×#41×C61—41no—
50C2×#41×C61—41no—
51C22×Q8×C61—41no—
52C22×Q8×C61C2×C411yescharacteristic
53#41×C61—22no—
54#41×C61—22no—
55#41×C61—41no—
56#41×C61—42no—
57#41×C61—42no—
58#41×C61—42no—
59#41×C61—42no—
60#41×C61—44no—
61#41×C61—42no—
62#41×C61—42no—
63#41×C61—41no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—42no—
69C2×Q8×C61—42no—
70C2×Q8×C61—44no—
71C2×Q8×C61—41no—
72C2×Q8×C61C22⋊C411yescharacteristic
73C2×Q8×C61C22×C411yescharacteristic
74C2×D4×C61—21no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61—42no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C2×Dic122—21no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122C22⋊C411yescharacteristic
87C2×Dic122C2×D411yescharacteristic
88#11758217—42no—
89#11758217—81no—
90C2×#92420—42no—
91C2×#92420—82no—
92C2×#92420—81no—
93#11758202—42no—
94#11758202—42no—
95#11758200—42no—
96#11758200—42no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—21no—
102C4×Dic61C22⋊C411yescharacteristic
103C4×Dic61C2×D411yescharacteristic
104#11758194—22no—
105#11758194—41no—
106C2×#92418—41no—
107C23×C61—41no—
108C23×C61#9911yescharacteristic
109Q8×C61—22no—
110Q8×C61—42no—
111Q8×C61—41no—
112Q8×C61—41no—
113Q8×C61—41no—
114Q8×C61—42no—
115Q8×C61—42no—
116D4×C61—22no—
117D4×C61—41no—
118D4×C61—42no—
119D4×C61—42no—
120D4×C61—42no—
121D4×C61—42no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—44no—
129C2×C4×C61—44no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#9911yescharacteristic
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143Dic122—41no—
144Dic122—41no—
145Dic122—81no—
146#92420—82no—
147#92420—82no—
148#92418—42no—
149C2×#1405—611nomaximal, Sylow
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—82no—
153C22×C61AΣL(1,𝔽16)11yescharacteristic
154C22×C61AΣL(1,𝔽16)11yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—42no—
161Dic61—21no—
162Dic61—22no—
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166C2×#456—611no—
167C2×#356—611no—
168C2×#333—611no—
169#1405—614no—
170C2×C61—21no—
171C2×C61—21no—
172C2×C61—82no—
173C2×C61#140512yescomplemented
174C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
175C2×2−1+4#692311yescharacteristic
176C2×#137—1221no—
177C2×C4⋊Q8—611no—
178#456—612no—
179#456—612no—
180#456—1221no—
181#456—1221no—
182C2×C4⋊C8—1221no—
183C2×#104—1221no—
184C2×#101—611no—
185C2×#101—1221no—
186#356—612no—
187#356—1221no—
188#333—612no—
189#333—1221no—
190C61C2×#140511yescharacteristic, complemented, Sylow
1912−1+4—21no—
1922−1+4—41no—
1932−1+4—42no—
1942−1+4C2×#692312yes—
195C2×#41—21no—
196C2×#41—41no—
197C2×#41—41no—
198C22×Q8—41no—
199C22×Q8—611no—
200C22×Q8C2×#692311yescharacteristic
201#137—1222no—
202#137—1222no—
203#137—2442no—
204C2×Q16—2441no—
205C2×SD16—2441no—
206C2×M16—1221no—
207C2×M16—2441no—
208C22×C8—2441no—
209C4⋊Q8—611no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212C4⋊Q8—611no—
213C4⋊Q8—2441no—
214C2×C4⋊C4—2441no—
215C2×C42—611no—
216C4⋊C8—1222no—
217C4⋊C8—2441no—
218#104—1222no—
219#104—1222no—
220#101—612no—
221#101—1221no—
222#101—1222no—
223#101—2441no—
224#41—22no—
225#41—22no—
226#41—41no—
227#41—42no—
228#41—42no—
229#41—42no—
230#41—42no—
231#41—44no—
232#41—42no—
233#41—42no—
234#41—41no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—44no—
242C2×Q8—41no—
243C2×Q8—611no—
244C2×Q8—611no—
245C2×Q8—1221no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8C22⋊#692311yescharacteristic
249C2×Q8C22×#692311yescharacteristic
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22⋊#692311yescharacteristic
259Q16—2442no—
260Q16—2442no—
261SD16—2442no—
262SD16—2442no—
263M16—1222no—
264M16—4881no—
265M16—2442no—
266M16—2441no—
267C2×C8—4882no—
268C2×C8—4881no—
269C2×C8—2442no—
270C2×C8—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C42—611no—
276C42—611no—
277C42—1221no—
278C23—41no—
279C23#1451983511yescharacteristic
280Q8—22no—
281Q8—41no—
282Q8—41no—
283Q8—42no—
284Q8—41no—
285Q8—42no—
286Q8—42no—
287Q8—4881no—
288Q8—2441no—
289Q8—2441no—
290D4—22no—
291D4—41no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4#1451983511yescharacteristic
316C2×C4C2×C22⋊#692311yescharacteristic
317C8—4882no—
318C8—4882no—
319C8—2442no—
320C22—22no—
321C22—42no—
322C22—82no—
323C22#1684066211yescharacteristic
324C22#1684066211yescharacteristic
325C22C2×#1451983511yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—42no—
331C4—1221no—
332C4—1222no—
333C4—1221no—
334C4—2441no—
335C4—2441no—
336C2—21no—
337C2—21no—
338C2—82no—
339C2#2146094412yesdirect product factor
340C2C2×#1684066211yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×Q8×C61C22×C4
FrattiniC2×Q8C22×#6923
Fitting, prime radicalC2×2−1+4×C61C4
socleC22×C61AΣL(1,𝔽16)
cosocle#14519775C23
hypercenterC2×2−1+4#6923
hypocenterC61C2×#1405
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#16840672C2semidirect
2. C2×#16840622C2semidirect
3. #21460944C2direct (N × H)
8. #16840672C22semidirect
10. #16840622C22semidirect
173. C2×C61#1405semidirect
190. C61C2×#1405semidirect
339. C2#21460944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406722
C2×#168406222
#214609442
C2×#168399452
C2×#140561