Finite Group Databasebeta

← C2×#21461924 #30616139

Subgroups — C2×#21461924 #30616139

Order 15616.

1142 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519845C211yesmaximal, characteristic
2C22×#14519831C211yesmaximal, characteristic
3C2×#16840713C212yesmaximal
4#21461924C218yesmaximal, direct product factor
5C2×#16840635C212yesmaximal
6C2×#107×D61C211yesmaximal, characteristic
7C22×D61⋊C8C2211yescharacteristic
8C22×C4⋊#6923—22no—
9C22×C4⋊#6923C2212yes—
10C22×C4×#6923C2211yescharacteristic
11C2×#14519845—24no—
12C2×#14519845C2214yes—
13C2×#14519831—24no—
14C2×#14519831C2214yes—
15#16840713—24no—
16#16840713C2218yes—
17C2×(C2×#6923)⋊C4—22no—
18#16840635C2218yes—
19C22×C8×D61C2211yescharacteristic
20C2×C4⋊C4×D61C2212yes—
21C2×#14519711C411yescharacteristic, complemented
22C2×#14519710C412yescomplemented
23#107×D61C414yescomplemented
24#107×D61C2214yes—
25C2×#107×C61C411yescharacteristic, complemented
26C23×#6923—22no—
27C23×#6923D412yes—
28C2×D61⋊C8—22no—
29C2×D61⋊C8—21no—
30C2×D61⋊C8Q814yes—
31C2×D61⋊C8C2312yes—
32C22×#92420—21no—
33C2×C4⋊#6923—24no—
34C2×C4⋊#6923—24no—
35C2×C4⋊#6923—28no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—48no—
38C2×C4⋊#6923C2314yes—
39C2×C4×#6923—22no—
40C2×C4×#6923—22no—
41C2×C4×#6923D412yes—
42C2×C4×#6923C2312yes—
43#14519845—28no—
44#14519831—28no—
45(C2×#6923)⋊C4—28no—
46C22×C4×D61—22no—
47C22×C4×D61C2311yescharacteristic
48C22×#92418C2×C411yescharacteristic
49C2×C8×D61C2×C412yes—
50C2×C8×D61D414yes—
51C2×C8×D61Q814yes—
52C2×C8×D61C2312yes—
53C2×C4⋊Dic61C2×C412yes—
54C2×#11758196—22no—
55C4⋊C4×D61—22no—
56C4⋊C4×D61—22no—
57C4⋊C4×D61C2×C414yes—
58C4⋊C4×D61C2314yes—
59#14519711C2×C414yescomplemented
60#14519710C2×C418yescomplemented
61C22×C8×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C412yes—
63#107×C61C2×C414yescomplemented
64C23×D61C2×D411yescharacteristic
65C22×#6923—24no—
66C22×#6923—24no—
67C22×#6923—24no—
68C22×#6923—24no—
69C22×#6923—44no—
70C22×#6923—44no—
71C22×#6923—44no—
72C22×#6923C2×D414yes—
73C22×C4×C61—22no—
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61#4111yescharacteristic
77C2×C4×D61—24no—
78C2×C4×D61—24no—
79C2×C4×D61—44no—
80C2×C4×D61—44no—
81C2×C4×D61C22×C411yescharacteristic
82C2×C4×D61C2×D412yes—
83C2×C4×D61C2×D411yescharacteristic
84C2×C4×D61C2×Q812yes—
85C2×C4×D61C2×Q812yes—
86C2×C4×D61#4112yes—
87C2×C4×D61#4111yescharacteristic
88C2×C4×D61C2411yescharacteristic
89C2×#92420—24no—
90C2×#92420—22no—
91C4⋊#6923—24no—
92C4⋊#6923—24no—
93C4⋊#6923—416no—
94C4⋊#6923—44no—
95C4×#6923—24no—
96C4×#6923—22no—
97C4×#6923—22no—
98D61⋊C8—24no—
99D61⋊C8—22no—
100D61⋊C8C2×Q814yes—
101C2×C8×C61C4⋊C414yescomplemented
102C2×C8×C61C22×C412yes—
103C4⋊C4×C61—22no—
104C4⋊C4×C61C22×C414yes—
105C4⋊Dic61—22no—
106C4⋊Dic61C22×C414yes—
107#11758196—24no—
108#11758196—24no—
109C2×#92418C4⋊C414yescomplemented
110C2×#92418C22×C412yes—
111C8×D61C4⋊C418yescomplemented
112C8×D61C2×D414yes—
113C8×D61C2×Q814yes—
114C23×C61C4×D411yescharacteristic
115C22×D61C4×D411yescharacteristic
116C22×D61#12112yes—
117C22×D61C4⋊Q812yes—
118C22×D61AGL(1,ℤ/8)14yes—
119C22×D61#13714yes—
120C22×D61C22×D411yescharacteristic
121C2×#6923—24no—
122C2×#6923—24no—
123C2×#6923—24no—
124C2×#6923—48no—
125C2×#6923—44no—
126C2×#6923—44no—
127C2×#6923—44no—
128C2×#6923—88no—
129C2×C4×C61—24no—
130C2×C4×C61—44no—
131C2×C4×C61C2×C4⋊C412yes—
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×Q812yes—
134C2×C4×C61C23×C411yescharacteristic
135C2×Dic61—24no—
136C2×Dic61—44no—
137C2×Dic61C4×D411yescharacteristic
138C2×Dic61C22⋊Q812yes—
139C2×Dic61#12512yes—
140C2×Dic61C2×#4111yescharacteristic
141C4×D61—44no—
142C4×D61—44no—
143C4×D61—48no—
144C4×D61C2×C4⋊C412yes—
145C4×D61C4×Q812yes—
146C4×D61#12112yes—
147C4×D61C22⋊Q812yes—
148C4×D61#12512yes—
149C4×D61C4⋊Q812yes—
150C4×D61C22×D411yescharacteristic
151C4×D61C22×Q811yescharacteristic
152C4×D61C22×Q811yescharacteristic
153C4×D61C2×#4111yescharacteristic
154#92420—24no—
155C8×C61C2×C4⋊C414yescomplemented
156#92418C2×C4⋊C414yescomplemented
157C2×#1943—611nomaximal, Sylow
158C22×C61#38912yes—
159C22×C61#44112yes—
160C22×C61#44212yes—
161C22×C61C2×C4×D411yescharacteristic
162C2×D61#38912yes—
163C2×D61#44112yes—
164C2×D61#44212yes—
165C2×D61#46818yes—
166C2×D61#50118yes—
167C2×D61C2×#12111yescharacteristic
168C2×D61C2×C4⋊Q811yescharacteristic
169C2×D61C2×AGL(1,ℤ/8)12yes—
170C2×D61C2×#13712yes—
171#6923—44no—
172#6923—84no—
173C4×C61—44no—
174C4×C61#38912yes—
175C4×C61C22×C4⋊C411yescharacteristic
176C4×C61C2×C4×Q811yescharacteristic
177Dic61—44no—
178Dic61#38912yes—
179Dic61C2×C22⋊Q811yescharacteristic
180Dic61C2×#12511yescharacteristic
181C22×#107—611no—
182C22×#106—611no—
183C22×#97—611no—
184C2×#389—612no—
185#1943—618no—
186C2×#340—612no—
187C2×C61#194314yescomplemented
188C2×C61C2×#38911yescharacteristic
189C2×C61C2×#44111yescharacteristic
190C2×C61C2×#44211yescharacteristic
191D61#194314yescomplemented
192D61C2×#46812yes—
193D61C2×#50112yes—
194C23×C8—611no—
195C23×C8—611no—
196C22×C4⋊C4—612no—
197C22×C4⋊C4—612no—
198C22×C4⋊C4—1222no—
199C22×C42—611no—
200C2×#107—611no—
201C2×#107—612no—
202C2×#107—614no—
203C2×#107—614no—
204C2×#107#692311yescharacteristic, complemented
205C2×#106—614no—
206C2×#106—1224no—
207C2×#97—614no—
208C2×#97—1224no—
209#389—618no—
210#389—1224no—
211C2×#95—1222no—
212#340—618no—
213C61C2×#194311yescharacteristic, complemented, Sylow
214C23×C4—611no—
215C23×C4—612no—
216C23×C4—1222no—
217C23×C4—1222no—
218C22×C8—611no—
219C22×C8—614no—
220C22×C8—614no—
221C22×C8—612no—
222C22×C8—612no—
223C22×C8—614no—
224C22×C8—612no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8—1222no—
228C22×C8C2×#692311yescharacteristic
229C2×C4⋊C4—612no—
230C2×C4⋊C4—614no—
231C2×C4⋊C4—614no—
232C2×C4⋊C4—614no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1224no—
237C2×C4⋊C4—1224no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1228no—
240C2×C4⋊C4—2448no—
241C2×C4⋊C4C2×#692312yes—
242C2×C42—612no—
243C2×C42—612no—
244C2×C42—1222no—
245C2×C42—1222no—
246#107—614no—
247#107—618no—
248#107C2×#692314yescomplemented
249#106—1228no—
250#97—1228no—
251#95—1228no—
252C24—611no—
253C22×C4—22no—
254C22×C4—611no—
255C22×C4—612no—
256C22×C4—612no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—612no—
260C22×C4—612no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—614no—
264C22×C4—1224no—
265C22×C4—1224no—
266C22×C4—1224no—
267C22×C4—1224no—
268C22×C4—1224no—
269C22×C4—1222no—
270C22×C4—1224no—
271C22×C4—2444no—
272C22×C4—2444no—
273C22×C4—2444no—
274C22×C4—2444no—
275C22×C4—2444no—
276C22×C4C22×#692311yescharacteristic
277C2×C8—614no—
278C2×C8—612no—
279C2×C8—614no—
280C2×C8—618no—
281C2×C8—614no—
282C2×C8—614no—
283C2×C8—1222no—
284C2×C8—1224no—
285C2×C8—1224no—
286C2×C8—1222no—
287C2×C8C4⋊#692314yescomplemented
288C2×C8C22×#692312yes—
289C4⋊C4—22no—
290C4⋊C4—614no—
291C4⋊C4—1224no—
292C4⋊C4—1224no—
293C4⋊C4—1224no—
294C4⋊C4—1224no—
295C4⋊C4—1222no—
296C4⋊C4—2444no—
297C4⋊C4—24416no—
298C4⋊C4C22×#692314yes—
299C42—1222no—
300C42—1224no—
301C42—1222no—
302C23—612no—
303C23—612no—
304C23—614no—
305C23—614no—
306C23—611no—
307C23—611no—
308C23D4×#692311yescharacteristic
309C2×C4—24no—
310C2×C4—44no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—612no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1224no—
326C2×C4—1224no—
327C2×C4—1224no—
328C2×C4—1224no—
329C2×C4—4888no—
330C2×C4—2444no—
331C2×C4—2444no—
332C2×C4—2448no—
333C2×C4—2444no—
334C2×C4—2444no—
335C2×C4—2444no—
336C2×C4—2448no—
337C2×C4—2444no—
338C2×C4C2×C4⋊#692312yes—
339C2×C4D4×#692311yescharacteristic
340C2×C4Q8×#692312yes—
341C2×C4C23×#692311yescharacteristic
342C8—614no—
343C8—1224no—
344C8C2×C4⋊#692314yescomplemented
345C22—611no—
346C22—611no—
347C22—612no—
348C22—612no—
349C22—612no—
350C22—612no—
351C22—612no—
352C22—618no—
353C22—618no—
354C22#1684071312yes—
355C22#1684080212yes—
356C22#1684080312yes—
357C22C2×D4×#692311yescharacteristic
358C4—44no—
359C4—611no—
360C4—611no—
361C4—612no—
362C4—4884no—
363C4—2444no—
364C4—2444no—
365C4#1684071312yes—
366C4C22×C4⋊#692311yescharacteristic
367C4C2×Q8×#692311yescharacteristic
368C2—612no—
369C2—612no—
370C2—614no—
371C2#2146192414yesdirect product factor
372C2C2×#1684071311yescharacteristic
373C2C2×#1684080211yescharacteristic
374C2C2×#1684080311yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#107×C61C4
socleC23×C61C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×#107#6923
hypocenterC61C2×#1943
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #21461924C2direct (N × H)
21. C2×#14519711C4semidirect
22. C2×#14519710C4semidirect
23. #107×D61C4semidirect
25. C2×#107×C61C4semidirect
59. #14519711C2×C4semidirect
60. #14519710C2×C4semidirect
63. #107×C61C2×C4semidirect
101. C2×C8×C61C4⋊C4semidirect
109. C2×#92418C4⋊C4semidirect
111. C8×D61C4⋊C4semidirect
155. C8×C61C2×C4⋊C4semidirect
156. #92418C2×C4⋊C4semidirect
187. C2×C61#1943semidirect
191. D61#1943semidirect
204. C2×#107#6923semidirect
213. C61C2×#1943semidirect
248. #107C2×#6923semidirect
287. C2×C8C4⋊#6923semidirect
344. C8C2×C4⋊#6923semidirect
371. C2#21461924direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198452
C22×#145198312
C2×#168407132
#214619242
C2×#168406352
C2×#107×D612
C2×#194361