Finite Group Databasebeta

← C2×#21460658 #30596274

Subgroups — C2×#21460658 #30596274

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840779C211yesmaximal, characteristic
2C22×#14519832C211yesmaximal, characteristic
3#21460658C214yesmaximal, direct product factor
4C2×#16839812C211yesmaximal, characteristic
5C23×#92420C412yes—
6#16840779—21no—
7#16840779—21no—
8#16840779C412yes—
9#16840779C2212yes—
10C2×#14519844—21no—
11C2×C22⋊#92420C412yes—
12C2×#14519832—21no—
13C2×#14519832—21no—
14C2×#14519832—21no—
15C2×#14519832—21no—
16C2×#14519832C412yes—
17C2×#14519832C2212yes—
18C2×C4×#92420—21no—
19C22×C4×Dic61C2211yescharacteristic
20#16839812—21no—
21#16839812—21no—
22#16839812C412yes—
23#16839812C2212yes—
24C2×#14519706—21no—
25C2×C22⋊#92418C411yescharacteristic
26C2×C8×Dic61—21no—
27C2×C22⋊C8×C61C411yescharacteristic
28C22×#92420—22no—
29C22×#92420—22no—
30C22×#92420—24no—
31C22×#92420—22no—
32C22×#92420C818yescomplemented
33C22×#92420C2×C414yes—
34#14519844—22no—
35#14519844—22no—
36C22⋊#92420—22no—
37C22⋊#92420C2×C414yes—
38#14519832—22no—
39#14519832—22no—
40#14519832—22no—
41#14519832—22no—
42C4×#92420—22no—
43C4×#92420—22no—
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C22×#92418—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61Q811yescharacteristic
57C2×C4×Dic61Q811yescharacteristic
58C2×C4×Dic61C2311yescharacteristic
59#14519706—22no—
60#14519706—22no—
61C22⋊#92418—21no—
62C22⋊#92418C2×C412yes—
63C8×Dic61—22no—
64C8×Dic61—22no—
65C23×C4×C61C2×C411yescharacteristic
66C22×C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61C2×C412yes—
69C24×C61C4211yescharacteristic
70C22×C4×C61—42no—
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C4⋊C411yescharacteristic
75C22×C4×C61C4⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×Dic61—42no—
78C22×Dic61C4211yescharacteristic
79C22×Dic61C4211yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C4⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C2×C814yes—
89C22×Dic61M1614yes—
90C22×Dic61C22×C411yescharacteristic
91C22×Dic61C22×C411yescharacteristic
92C2×#92420—28no—
93C2×#92420—28no—
94C2×#92420—24no—
95C2×#92420—24no—
96C2×#92420—24no—
97C2×#92420—44no—
98C2×#92420C2×C818yescomplemented
99C2×C8×C61—22no—
100C2×C8×C61—42no—
101C4×Dic61C22⋊C411yescharacteristic
102C4×Dic61C22⋊C411yescharacteristic
103C4×Dic61C22⋊C411yescharacteristic
104C4×Dic61C22⋊C411yescharacteristic
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C4⋊C411yescharacteristic
108C4×Dic61C4⋊C411yescharacteristic
109C4×Dic61C4⋊C411yescharacteristic
110C4×Dic61C4⋊C411yescharacteristic
111C4×Dic61C4⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61C2×D411yescharacteristic
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61C2×Q811yescharacteristic
117C2×#92418—22no—
118C2×#92418—42no—
119C23×C61—22no—
120C23×C61—22no—
121C23×C61#9511yescharacteristic
122C23×C61#9511yescharacteristic
123C23×C61C4×C812yes—
124C23×C61#9712yes—
125C23×C61C2×C4211yescharacteristic
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61#9511yescharacteristic
133C2×C4×C61#9511yescharacteristic
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C2×C4⋊C411yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9511yescharacteristic
143C2×Dic61#9511yescharacteristic
144C2×Dic61#9511yescharacteristic
145C2×Dic61#9511yescharacteristic
146C2×Dic61C4×C812yes—
147C2×Dic61#9712yes—
148C2×Dic61C22⋊C814yes—
149C2×Dic61C22⋊C814yes—
150C2×Dic61C4⋊C814yes—
151C2×Dic61C4⋊C814yes—
152C2×Dic61C2×C22⋊C411yescharacteristic
153C2×Dic61C2×C22⋊C411yescharacteristic
154C2×Dic61C2×C4⋊C411yescharacteristic
155C2×Dic61C2×C4⋊C411yescharacteristic
156C2×Dic61C22×C812yes—
157C2×Dic61C2×M1612yes—
158#92420—28no—
159#92420—44no—
160C8×C61—42no—
161#92418—42no—
162C2×#1281—611nomaximal, Sylow
163C22×C61—24no—
164C22×C61—24no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#33612yes—
170C22×C61#33612yes—
171C22×C61#34412yes—
172C22×C61#34412yes—
173C22×C61C2×#9511yescharacteristic
174C22×C61C2×C4×C811yescharacteristic
175C22×C61C2×#9711yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180Dic61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61—21no—
184Dic61#33612yes—
185Dic61#33612yes—
186Dic61C2×C22⋊C812yes—
187Dic61C2×C4⋊C812yes—
188C2×#431—611no—
189C2×#431—611no—
190C22×#97—611no—
191#1281—614no—
192C2×C61—22no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#128114yescomplemented
196C2×C61C2×#33611yescharacteristic
197C2×C61C2×#34411yescharacteristic
198C2×C61C2×#34411yescharacteristic
199C23×C8—612no—
200C22×C42—611no—
201#431—612no—
202#431—612no—
203#431—612no—
204#431—612no—
205#431—1221no—
206#431—1221no—
207#431—1221no—
208#431—1221no—
209C2×C4⋊C8—1221no—
210C2×C4⋊C8—1221no—
211C2×C22⋊C8—612no—
212C2×C22⋊C8—611no—
213C2×C22⋊C8#692311yescharacteristic
214C2×#97—612no—
215C2×#97—612no—
216C2×#97—1221no—
217C2×#97—1221no—
218C2×#97—1221no—
219C2×#97—1221no—
220C2×C4×C8—1221no—
221C2×C4×C8—1221no—
222C61C2×#128111yescharacteristic, complemented, Sylow
223C23×C4—611no—
224C23×C4—611no—
225C23×C4C2×#692311yescharacteristic
226C22×C8—21no—
227C22×C8—618no—
228C22×C8—614no—
229C22×C8—1224no—
230C22×C8—1222no—
231C22×C8—1222no—
232C22×C8—1222no—
233C22×C8—1221no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C4⋊C8—1222no—
247C4⋊C8—1222no—
248C4⋊C8—1222no—
249C4⋊C8—1222no—
250C22⋊C8—21no—
251C22⋊C8—614no—
252C22⋊C8—612no—
253C22⋊C8—1222no—
254C22⋊C8—1221no—
255C22⋊C8C2×#692312yes—
256#97—1222no—
257#97—1222no—
258#97—1222no—
259#97—1222no—
260C4×C8—1222no—
261C4×C8—1222no—
262C4×C8—1222no—
263C4×C8—1222no—
264C24C4×#692311yescharacteristic
265C22×C4—42no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—614no—
271C22×C4—614no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—2442no—
281C22×C4C4×#692311yescharacteristic
282C22×C4C4⋊#692311yescharacteristic
283C22×C4C4⋊#692311yescharacteristic
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287C2×C8—22no—
288C2×C8—42no—
289C2×C8—618no—
290C2×C8—1224no—
291C2×C8—1224no—
292C2×C8—1228no—
293C2×C8—1228no—
294C2×C8—1224no—
295C2×C8—1222no—
296C2×C8—2442no—
297C2×C8—2444no—
298C42—611no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C23—22no—
315C23—22no—
316C23(C2×#6923)⋊C411yescharacteristic
317C23(C2×#6923)⋊C411yescharacteristic
318C23C8×#692312yes—
319C23#1451983112yes—
320C23C2×C4×#692311yescharacteristic
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—614no—
332C2×C4—614no—
333C2×C4—614no—
334C2×C4—614no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4(C2×#6923)⋊C411yescharacteristic
350C2×C4(C2×#6923)⋊C411yescharacteristic
351C2×C4C2×C22⋊#692311yescharacteristic
352C2×C4C2×C4⋊#692311yescharacteristic
353C8—42no—
354C8—1228no—
355C8—2442no—
356C8—2444no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—24no—
362C22—24no—
363C22(C2×#6923)⋊C812yes—
364C22(C2×#6923)⋊C812yes—
365C22#1684064312yes—
366C22#1684064512yes—
367C22C2×(C2×#6923)⋊C411yescharacteristic
368C22C2×C8×#692311yescharacteristic
369C22C2×#1451983111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—612no—
375C4—612no—
376C4—612no—
377C4—612no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—1221no—
382C2—21no—
383C2—21no—
384C2—22no—
385C2#2146065814yesdirect product factor
386C2C2×(C2×#6923)⋊C811yescharacteristic
387C2C2×#1684064311yescharacteristic
388C2C2×#1684064511yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C61C2×C4×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61#95
prime radicalC24×C61C42
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61C2×#1281
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460658C2direct (N × H)
32. C22×#92420C8semidirect
98. C2×#92420C2×C8semidirect
195. C2×C61#1281semidirect
222. C61C2×#1281semidirect
385. C2#21460658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407792
C22×#145198322
#214606582
C2×#168398122
C2×#128161