Finite Group Databasebeta

← C2×#21460790 #30604708

Subgroups — C2×#21460790 #30604708

Order 15616.

496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16840659C211yesmaximal, characteristic, complemented
2C2×#16840630C211yesmaximal, characteristic, complemented
3#21460790C214yesmaximal, direct product factor
4C2×#16840016C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519851—21no—
7#16840659—21no—
8#16840659C2212yescomplemented
9#16840630—21no—
10#16840630C2212yescomplemented
11C22×D488C411yescharacteristic, complemented
12C22×#11758189C2211yescharacteristic
13C2×#14519752—21no—
14#16840016—21no—
15#16840016—21no—
16#16840016C412yescomplemented
17#16840016C2212yes—
18C2×#14519697—21no—
19C2×#106×C61C411yescharacteristic, complemented
20#14519856—22no—
21#14519856—22no—
22#14519856—41no—
23#14519856—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—41no—
26C2×C4×#6923—22no—
27#14519851—22no—
28#14519851—41no—
29C2×#11758187—41no—
30C22×D244—21no—
31C22×D244—41no—
32C22×C4×D61D411yescharacteristic
33C2×D488—21no—
34C2×D488—41no—
35C2×D488—41no—
36C2×D488C2×C412yescomplemented
37C2×#11758189—41no—
38C2×#11758189—41no—
39C2×#11758189C2×C411yescharacteristic
40C2×#11758189D411yescharacteristic
41C2×#11758189D411yescharacteristic
42C2×#11758189C2311yescharacteristic
43C22×#92418D411yescharacteristic
44#14519752—22no—
45#14519752—22no—
46#14519752—41no—
47#14519752—41no—
48C2×#11758198—41no—
49#14519697—22no—
50#14519697—22no—
51C22×C8×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53#106×C61—21no—
54#106×C61C2×C412yescomplemented
55C23×D61—41no—
56C23×D61D811yescharacteristic
57C22×#6923—42no—
58C22×C4×C61—41no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×Dic61SD1611yescharacteristic
61C2×D244—22no—
62C2×D244—41no—
63C2×D244—41no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—42no—
67C2×D244—42no—
68C2×D244—41no—
69C2×D244—84no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×C4×D61D811yescharacteristic
76C2×C4×D61SD1611yescharacteristic
77C2×C4×D61C2×D411yescharacteristic
78C22⋊#6923—42no—
79C22⋊#6923—42no—
80C4⋊#6923—42no—
81C4⋊#6923—42no—
82C4×#6923—24no—
83C4×#6923—42no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61C22⋊C411yescharacteristic
87C2×C8×C61C22×C411yescharacteristic
88C4⋊C4×C61—22no—
89C4⋊C4×C61—41no—
90#11758198—42no—
91#11758198—42no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C2×D411yescharacteristic
96D488—42no—
97D488—42no—
98#11758189—41no—
99#11758189—41no—
100#11758189—41no—
101#11758189—41no—
102#11758187—42no—
103C23×C61#10211yescharacteristic
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—82no—
109C22×D61—82no—
110C22×D61—81no—
111C22×D61—81no—
112C22×D61#10211yescharacteristic
113C22×D61C2×D811yescharacteristic
114C2×#6923—44no—
115C2×#6923—84no—
116C2×C4×C61—42no—
117C2×C4×C61—82no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#9911yescharacteristic
120C2×C4×C61#10211yescharacteristic
121C2×C4×C61#10411yescharacteristic
122C2×C4×C61#10411yescharacteristic
123C2×C4×C61C2×C22⋊C411yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61#10211yescharacteristic
127C2×Dic61C2×SD1611yescharacteristic
128D244—42no—
129D244—42no—
130D244—84no—
131D244—84no—
132D244—81no—
133D244—81no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C8×C61—21no—
143C8×C61—21no—
144#92418—21no—
145#92418—21no—
146C2×#1339—611nomaximal, Sylow
147C22×C61—22no—
148C22×C61#32711yescharacteristic
149C22×C61#32711yescharacteristic
150C22×C61C2×#10211yescharacteristic
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—42no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—81no—
157C2×D61—82no—
158C2×D61—82no—
159C2×D61—82no—
160C2×D61—162no—
161C2×D61—162no—
162#6923—84no—
163C4×C61—82no—
164C4×C61#32711yescharacteristic
165C4×C61#32711yescharacteristic
166C4×C61C2×#9911yescharacteristic
167C4×C61C2×#10411yescharacteristic
168Dic61—21no—
169Dic61—21no—
170C2×#469—611no—
171C2×#349—611no—
172C2×H(3,ℤ/4)—611no—
173#1339—614no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#133912yescomplemented
177C2×C61C2×#32711yescharacteristic
178D61—41no—
179D61—41no—
180D61—162no—
181C22×D8—611no—
182C22×M16—611no—
183C2×#121—1221no—
184C2×#117—1221no—
185C2×M32—1221no—
186#469—612no—
187#469—612no—
188#469—1221no—
189#469—1221no—
190C2×#106#692311yescharacteristic, complemented
191C2×#102—1221no—
192#349—612no—
193#349—1221no—
194H(3,ℤ/4)—612no—
195H(3,ℤ/4)—1221no—
196C61C2×#133911yescharacteristic, complemented, Sylow
197C22×D4—1221no—
198C22×D4—2441no—
199C23×C4—611no—
200C2×D8—612no—
201C2×D8—1221no—
202C2×D8—2441no—
203C2×D8—2441no—
204C2×M16—611no—
205C2×M16—611no—
206C2×M16—611no—
207C2×M16—611no—
208C2×M16—2441no—
209C2×M16—2441no—
210C22×C8—611no—
211C22×C8C2×#692311yescharacteristic
212#121—1222no—
213#121—1222no—
214#121—2441no—
215#121—2441no—
216#117—1222no—
217#117—1222no—
218#117—2441no—
219#117—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—2441no—
222C2×C22⋊C4—2441no—
223C2×C22⋊C4—2441no—
224C2×C42—1222no—
225M32—1222no—
226M32—2441no—
227C2×C16—2441no—
228#106—21no—
229#106C2×#692312yescomplemented
230#102—1222no—
231#102—1222no—
232C24—611no—
233C24—2441no—
234C2×D4—1222no—
235C2×D4—4884no—
236C2×D4—2442no—
237C2×D4—2442no—
238C2×D4—2441no—
239C2×D4—2441no—
240C2×D4—2441no—
241C2×D4—2441no—
242C2×D4—2441no—
243C22×C4—41no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4C22⋊#692311yescharacteristic
255D8—2442no—
256D8—2442no—
257M16—2441no—
258M16—2441no—
259M16—2441no—
260M16—2441no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—1221no—
266C2×C8—1221no—
267C2×C8C22⋊#692311yescharacteristic
268C2×C8C22×#692311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C42—1224no—
278C42—2442no—
279C16—2442no—
280C23—611no—
281C23—611no—
282C23—1221no—
283C23—1221no—
284C23—4882no—
285C23—4882no—
286C23—4881no—
287C23—4881no—
288C23—2442no—
289C23—2442no—
290C23#1451983911yescharacteristic
291D4—4884no—
292D4—4884no—
293D4—4881no—
294D4—4881no—
295D4—2442no—
296D4—2442no—
297C2×C4—42no—
298C2×C4—82no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4884no—
312C2×C4—2444no—
313C2×C4#1451983611yescharacteristic
314C2×C4#1451983611yescharacteristic
315C2×C4#1451983911yescharacteristic
316C2×C4#1451984211yescharacteristic
317C2×C4#1451984211yescharacteristic
318C2×C4C2×C22⋊#692311yescharacteristic
319C8—21no—
320C8—21no—
321C8—1221no—
322C8—1221no—
323C22—22no—
324C22—1221no—
325C22—1221no—
326C22—9762no—
327C22—9762no—
328C22—4882no—
329C22—4882no—
330C22—4881no—
331C22—4882no—
332C22—2441no—
333C22—2441no—
334C22—2442no—
335C22#1684061411yescharacteristic
336C22#1684061411yescharacteristic
337C22C2×#1451983911yescharacteristic
338C4—82no—
339C4—1221no—
340C4—1221no—
341C4—4884no—
342C4#1684061411yescharacteristic
343C4#1684061411yescharacteristic
344C4C2×#1451983611yescharacteristic
345C4C2×#1451984211yescharacteristic
346C2—21no—
347C2—21no—
348C2—9762no—
349C2—2441no—
350C2—2441no—
351C2#2146079012yesdirect product factor
352C2C2×#1684061411yescharacteristic
subgroupG/H
centerC22#16840614
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#106×C61C4
socleC22×C61#327
prime radicalC2×#16840016C2
cosocleC2×#11758189C23
hypercenterC2×#106#6923
hypocenterC61C2×#1339
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#16840659C2semidirect
2. C2×#16840630C2semidirect
3. #21460790C2direct (N × H)
8. #16840659C22semidirect
10. #16840630C22semidirect
11. C22×D488C4semidirect
16. #16840016C4semidirect
19. C2×#106×C61C4semidirect
36. C2×D488C2×C4semidirect
54. #106×C61C2×C4semidirect
176. C2×C61#1339semidirect
190. C2×#106#6923semidirect
196. C61C2×#1339semidirect
229. #106C2×#6923semidirect
351. C2#21460790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406592
C2×#168406302
#214607902
C2×#168400162
C2×#133961