Finite Group Databasebeta

← C2×#21445195 #29662263

Subgroups — C2×#21445195 #29662263

Order 15616.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840160C211yesmaximal, characteristic, complemented
2C2×#16840053C211yesmaximal, characteristic
3C2×#16839968C211yesmaximal, characteristic
4C2×C8×D244C211yesmaximal, characteristic
5#21445195C218yesmaximal, direct product factor
6C2×#16839510C211yesmaximal, characteristic, complemented
7C2×#16839509C211yesmaximal, characteristic, complemented
8C2×C61×#334C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×C8×D61—21no—
11C2×#14519777C2211yescharacteristic
12C2×#14519777C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14#16840160—22no—
15#16840160C2214yescomplemented
16#16840053—22no—
17#16840053C2214yes—
18#16839968—22no—
19#16839968C2214yes—
20C8×D244—22no—
21C8×D244C2214yes—
22C2×#14519709—21no—
23C2×#14519709—21no—
24C2×#14519709—21no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519702—21no—
27C2×#14519699—21no—
28C2×#14519689—21no—
29#16839510C2214yescomplemented
30#16839509C2214yescomplemented
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×#334C2214yescomplemented
35C22×Dic122—21no—
36C22×Dic122—21no—
37C22×D244D411yescharacteristic
38C22×C4×D61—21no—
39C2×#11758190—24no—
40C2×#11758190—44no—
41C22×#92418—21no—
42C2×C8×D61—24no—
43C2×C8×D61—44no—
44#14519777—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777C2312yes—
51#14519777C2312yes—
52C4×D244—21no—
53C4×D244—21no—
54C4×D244D412yes—
55C4×D244C2312yes—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61D411yescharacteristic
61C2×#11758198—21no—
62#14519709—24no—
63#14519709—24no—
64#14519709—24no—
65C4⋊#92418—21no—
66C4⋊#92418C2312yes—
67#14519702—24no—
68#14519699—24no—
69#14519689—24no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C22×C8×C61D411yescharacteristic
73C22×C8×C61D411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C4⋊C8×C61C2312yes—
78C4⋊C8×C61C2312yes—
79C4×C8×C61D412yes—
80C4×C8×C61C2312yes—
81C23×D61—21no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C2×D244—21no—
89C2×D244—22no—
90C2×D244SD1614yes—
91C2×D244C2×D412yes—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—42no—
95C2×C4×D61—42no—
96C2×Dic122—22no—
97C2×Dic122—22no—
98C2×Dic122—42no—
99C2×Dic122—42no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122—82no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—42no—
107C2×C8×C61—42no—
108C2×C8×C61SD1614yescomplemented
109C2×C8×C61C2×D412yes—
110C2×C8×C61C2×D412yes—
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114C42×C61C2411yescharacteristic
115#11758198—22no—
116#11758198—22no—
117C4⋊Dic61—21no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—22no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126C4⋊Dic61C2×D412yes—
127C2×#92418—22no—
128C2×#92418—42no—
129#11758190—48no—
130C8×D61—48no—
131C23×C61#12111yescharacteristic
132C22×D61—22no—
133C22×D61—24no—
134C22×D61—42no—
135C22×D61—42no—
136C2×C4×C61—22no—
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61C2×SD1612yes—
141C2×C4×C61C2×SD1612yes—
142C2×C4×C61#13512yes—
143C2×C4×C61#13712yes—
144C2×C4×C61C22×D411yescharacteristic
145C2×C4×C61C22×D411yescharacteristic
146C2×C4×C61C2×#4111yescharacteristic
147C2×Dic61—22no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—82no—
152C2×Dic61—82no—
153D244—22no—
154D244—24no—
155D244C2×SD1614yes—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—44no—
159Dic122—42no—
160Dic122—42no—
161Dic122—82no—
162Dic122—82no—
163Dic122—82no—
164C8×C61—22no—
165C8×C61—42no—
166C8×C61—42no—
167C8×C61C2×SD1614yescomplemented
168#92418—42no—
169C2×#1671—611nomaximal, Sylow
170C22×C61#46112yes—
171C22×C61#46512yes—
172C22×C61#47112yes—
173C22×C61C2×#12111yescharacteristic
174C2×D61—24no—
175C2×D61—48no—
176C2×D61—42no—
177C2×D61—42no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61#46112yes—
181C4×C61#46512yes—
182C4×C61C22×SD1611yescharacteristic
183C4×C61C22×SD1611yescharacteristic
184C4×C61C2×#13511yescharacteristic
185C4×C61C2×#13711yescharacteristic
186Dic61—42no—
187Dic61—82no—
188Dic61—82no—
189C2×#498—611no—
190C2×#476—611no—
191C2×#461—611no—
192C2×C8×D4—611no—
193#1671—618no—
194C2×#334D6111yescharacteristic, complemented
195C2×#333—611no—
196C2×#332—611no—
197C2×C61#167114yescomplemented
198C2×C61C2×#46111yescharacteristic
199C2×C61C2×#46511yescharacteristic
200C2×C61C2×#47111yescharacteristic
201D61—44no—
202C22×SD16—1221no—
203C23×C8—1221no—
204C2×C4⋊Q8—611no—
205C2×C4⋊Q8—611no—
206C2×C4×D4—611no—
207#498—614no—
208#498—1222no—
209#476—614no—
210#476—1222no—
211#461—614no—
212#461—1222no—
213C8×D4—614no—
214C8×D4—1222no—
215C2×#106—1221no—
216C2×#106—1221no—
217C2×#106—1221no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#103—1221no—
222C2×#102—1221no—
223C2×C22⋊C8—1221no—
224C2×C4×C8C2×D6111yescharacteristic
225#334C2×D6114yescomplemented
226#333—614no—
227#332—614no—
228C61C2×#167111yescharacteristic, complemented, Sylow
229C22×Q8—1221no—
230C22×Q8—1221no—
231C22×D4—611no—
232C23×C4—1221no—
233C2×SD16—1224no—
234C2×SD16—2444no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—1221no—
238C22×C8—1224no—
239C22×C8—2444no—
240C22×C8D24411yescharacteristic
241C22×C8D24411yescharacteristic
242C4⋊Q8—612no—
243C4⋊Q8—612no—
244C4⋊Q8—1221no—
245C4⋊Q8—1221no—
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250C4×D4—612no—
251C4×D4—612no—
252C4×D4—1221no—
253C4×D4—1221no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C42C22×D6111yescharacteristic
261#106—1224no—
262#106—1224no—
263#106—1224no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—612no—
267C4⋊C8—1221no—
268C4⋊C8C22×D6112yes—
269C4⋊C8C22×D6112yes—
270#103—1224no—
271#102—1224no—
272C22⋊C8—1224no—
273C4×C8D24412yes—
274C4×C8C22×D6112yes—
275C24—1221no—
276C2×Q8—1222no—
277C2×Q8—1222no—
278C2×Q8—4882no—
279C2×Q8—2442no—
280C2×Q8—2442no—
281C2×Q8—2441no—
282C2×Q8—2441no—
283C2×D4—612no—
284C2×D4—614no—
285C2×D4—1221no—
286C2×D4—1222no—
287C22×C4—1221no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4C2×D24411yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4#1175822611yescharacteristic
297SD16—2448no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—1222no—
304C2×C8—2442no—
305C2×C8—2448no—
306C2×C8#1175819014yescomplemented
307C2×C8C2×D24412yes—
308C2×C8C2×D24412yes—
309C4⋊C4—612no—
310C4⋊C4—1221no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C4⋊C4—1222no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C42C2×D24411yescharacteristic
322C42D4×D6111yescharacteristic
323C42#1175822611yescharacteristic
324C42C23×D6111yescharacteristic
325C23—1224no—
326C23—1222no—
327C23—2442no—
328C23—2442no—
329C23#1451975211yescharacteristic
330Q8—4882no—
331Q8—4882no—
332Q8—4882no—
333Q8—2442no—
334Q8—2442no—
335D4—614no—
336D4—1224no—
337D4—1222no—
338C2×C4—22no—
339C2×C4—1222no—
340C2×C4—4882no—
341C2×C4—4882no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2444no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4#1451975211yescharacteristic
349C2×C4#1451975211yescharacteristic
350C2×C4#1451975211yescharacteristic
351C2×C4SD16×D6112yes—
352C2×C4C2×#1175819012yes—
353C2×C4#1451979812yes—
354C2×C4#1451981012yes—
355C2×C4C2×D4×D6111yescharacteristic
356C2×C4C22×D24411yescharacteristic
357C2×C4C2×#1175822611yescharacteristic
358C8—22no—
359C8—42no—
360C8—42no—
361C8—2442no—
362C8C2×#1175819014yescomplemented
363C22—1224no—
364C22—2448no—
365C22—2442no—
366C22—2442no—
367C22#1683996812yes—
368C22#1683999212yes—
369C22#1684002612yes—
370C22C2×#1451975211yescharacteristic
371C4—21no—
372C4—21no—
373C4—4882no—
374C4—4882no—
375C4—2442no—
376C4#1683996812yes—
377C4#1683999212yes—
378C4C2×SD16×D6111yescharacteristic
379C4C22×#1175819011yescharacteristic
380C4C2×#1451979811yescharacteristic
381C4C2×#1451981011yescharacteristic
382C2—2444no—
383C2#2144519514yesdirect product factor
384C2C2×#1683996811yescharacteristic
385C2C2×#1683999211yescharacteristic
386C2C2×#1684002611yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#334C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#334D61
hypocenterC61C2×#1671
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. C2×#16840160C2semidirect
5. #21445195C2direct (N × H)
6. C2×#16839510C2semidirect
7. C2×#16839509C2semidirect
8. C2×C61×#334C2semidirect
15. #16840160C22semidirect
29. #16839510C22semidirect
30. #16839509C22semidirect
34. C61×#334C22semidirect
108. C2×C8×C61SD16semidirect
167. C8×C61C2×SD16semidirect
194. C2×#334D61semidirect
197. C2×C61#1671semidirect
225. #334C2×D61semidirect
228. C61C2×#1671semidirect
306. C2×C8#11758190semidirect
362. C8C2×#11758190semidirect
383. C2#21445195direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401602
C2×#168400532
C2×#168399682
C2×C8×D2442
#214451952
C2×#168395102
C2×#168395092
C2×C61×#3342
C2×#167161