Finite Group Databasebeta

← C2×#21462227 #30624319

Subgroups — C2×#21462227 #30624319

Order 15616.

646 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×#16840808C211yesmaximal, characteristic
2C2×#16840802C211yesmaximal, characteristic, complemented
3#21462227C218yesmaximal, direct product factor
4C2×#16840687C211yesmaximal, characteristic, complemented
5C2×#16840681C211yesmaximal, characteristic, complemented
6C2×#16840679C211yesmaximal, characteristic
7C2×#16840653C211yesmaximal, characteristic, complemented
8C2×#16840204C211yesmaximal, characteristic
9C2×#14519865—21no—
10C2×Q8×#6923—21no—
11C2×#14519852C2211yescharacteristic
12#16840808—22no—
13#16840808C2214yes—
14#16840802—22no—
15#16840802C2214yescomplemented
16C2×#14519847C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18C2×#14519842—21no—
19C2×#14519840—21no—
20C2×#14519831C2211yescharacteristic
21#16840687C2214yescomplemented
22#16840681C2214yescomplemented
23#16840679C2214yes—
24#16840653C2214yescomplemented
25C2×#14519800C2211yescharacteristic
26C2×Q16×D61C2211yescharacteristic
27#16840204C414yescomplemented
28#16840204C2214yes—
29C2×#14519723C411yescharacteristic, complemented
30C2×#14519722C411yescharacteristic, complemented
31C2×#14519720C411yescharacteristic, complemented
32C2×#14519716C2211yescharacteristic
33C2×Q32×C61C411yescharacteristic, complemented
34#14519865—24no—
35#14519865—42no—
36C2×#11758213—21no—
37C2×#11758213—41no—
38C2×D61⋊C8—41no—
39C2×D61⋊C8D411yescharacteristic
40Q8×#6923—24no—
41Q8×#6923—42no—
42C2×C4⋊#6923—21no—
43C2×C4⋊#6923—41no—
44C2×C4×#6923—41no—
45C2×C4×#6923D411yescharacteristic
46#14519852—21no—
47#14519852C2312yes—
48C2×#11758187—21no—
49#14519847—21no—
50#14519847C2312yes—
51#14519845—21no—
52#14519845C2312yes—
53#14519842—24no—
54#14519840—24no—
55#14519831D412yes—
56#14519831C2312yes—
57C2×#11758226—21no—
58C2×Q8×D61—21no—
59#14519800—21no—
60#14519800—21no—
61#14519800C2×C412yes—
62#14519800C2312yes—
63C2×Dic244C2×C411yescharacteristic
64C2×#11758202—21no—
65Q16×D61—21no—
66Q16×D61—21no—
67Q16×D61C2×C412yes—
68Q16×D61C2312yes—
69C2×#11758201—21no—
70C2×D488C2×C411yescharacteristic
71C2×C8×D61C2311yescharacteristic
72#14519723C2×C414yescomplemented
73#14519722C2×C414yescomplemented
74#14519720C2×C414yescomplemented
75#14519716C2×C412yes—
76#14519716C2312yes—
77C2×#11758185C2×C411yescharacteristic
78C2×Q16×C61C2×C411yescharacteristic
79C2×Q16×C61C2×C411yescharacteristic
80Q32×C61C2×C414yescomplemented
81C2×C16×C61C2×C411yescharacteristic
82C22×#6923—21no—
83C22×#6923—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86#11758226—22no—
87#11758226—22no—
88#11758226—41no—
89#11758226—41no—
90Q8×D61—22no—
91Q8×D61—22no—
92Q8×D61—41no—
93Q8×D61—41no—
94C2×D244—21no—
95C2×D244—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61C2×D411yescharacteristic
99C2×Dic122—21no—
100C2×Dic122—41no—
101C2×#92420—21no—
102C2×#92420—41no—
103C4⋊#6923—22no—
104C4⋊#6923—44no—
105C4⋊#6923—41no—
106C4×#6923—21no—
107C4×#6923—44no—
108C4×#6923C2×D412yes—
109#11758213—22no—
110#11758213—44no—
111#11758213—41no—
112D61⋊C8—21no—
113D61⋊C8—44no—
114D61⋊C8C2×D412yes—
115Q16×C61—21no—
116Q16×C61—21no—
117Q16×C61C22×C412yes—
118Q16×C61C22×C412yes—
119C2×C8×C61C22×C411yescharacteristic
120#11758202—22no—
121#11758202—22no—
122#11758201—22no—
123#11758201—22no—
124C2×#92418#4111yescharacteristic
125Dic244—21no—
126Dic244C22×C412yes—
127D488—21no—
128D488C22×C412yes—
129C8×D61C22×C411yescharacteristic
130C8×D61C2×D411yescharacteristic
131C8×D61#4111yescharacteristic
132C8×D61C2411yescharacteristic
133#11758187—22no—
134C16×C61C22×C412yes—
135#11758185C22×C412yes—
136C22×D61—41no—
137C22×D61AGL(1,ℤ/8)11yescharacteristic
138C2×#6923—22no—
139C2×#6923—42no—
140C2×#6923—42no—
141C2×#6923—82no—
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61C4×D411yescharacteristic
149C2×Dic61—41no—
150C2×Dic61AGL(1,ℤ/8)11yescharacteristic
151D244—22no—
152D244—42no—
153D244—42no—
154D244—41no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61C4×D411yescharacteristic
160C4×D61AGL(1,ℤ/8)11yescharacteristic
161C4×D61AGL(1,ℤ/8)11yescharacteristic
162C4×D61C22×D411yescharacteristic
163Dic122—22no—
164Dic122—41no—
165Dic122—42no—
166Dic122—42no—
167#92420—22no—
168#92420—42no—
169C8×C61C4×D411yescharacteristic
170C8×C61C23×C411yescharacteristic
171#92418C4×D411yescharacteristic
172#92418C2×#4111yescharacteristic
173C2×#2180—611nomaximal, Sylow
174C22×C61#44211yescharacteristic
175C2×D61—22no—
176C2×D61—42no—
177C2×D61—82no—
178C2×D61#44211yescharacteristic
179C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
180#6923—42no—
181#6923—82no—
182C4×C61—42no—
183C4×C61—42no—
184C4×C61#44211yescharacteristic
185C4×C61C2×C4×D411yescharacteristic
186Dic61—42no—
187Dic61#44211yescharacteristic
188Dic61C2×AGL(1,ℤ/8)11yescharacteristic
189C2×#510—611no—
190C2×#444—611no—
191C2×#441—611no—
192#2180—618no—
193C2×#365—611no—
194C2×#362—611no—
195C2×#360—611no—
196C2×#347—611no—
197C2×C61#218012yescomplemented
198C2×C61C2×#44211yescharacteristic
199D61—21no—
200D61—21no—
201D61—82no—
202C2×#135—611no—
203C22×Q16—611no—
204C2×#131—1221no—
205C2×C4×Q8—1221no—
206#510—614no—
207#510—614no—
208C2×Q32—611no—
209C2×Q32#692311yescharacteristic, complemented
210C2×SD32—611no—
211C2×SD32—611no—
212C2×M32—611no—
213C2×M32—611no—
214#444—614no—
215#444—1222no—
216#441—614no—
217#441—1222no—
218C2×#108—611no—
219C2×#106—611no—
220C2×#104—1221no—
221C2×#103—1221no—
222C2×#97—611no—
223#365—614no—
224#362—614no—
225#360—614no—
226#347—614no—
227C61C2×#218011yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C22×Q8—1221no—
230#135—612no—
231#135—612no—
232#135—1221no—
233#135—1221no—
234C2×Q16—612no—
235C2×Q16—612no—
236C2×Q16—611no—
237C2×Q16—1221no—
238C2×Q16—1221no—
239C2×Q16—1221no—
240C2×Q16C2×#692311yescharacteristic
241C2×Q16C2×#692311yescharacteristic
242C2×SD16—1221no—
243C2×D8—611no—
244#131—1224no—
245#131—2442no—
246C2×M16—1221no—
247C2×M16—2441no—
248C22×C8—611no—
249C22×C8—611no—
250C22×C8—2441no—
251C4×Q8—1224no—
252C4×Q8—2442no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C42—611no—
256C2×C42—2441no—
257Q32—614no—
258Q32C2×#692314yescomplemented
259SD32—614no—
260SD32—614no—
261M32—612no—
262M32—612no—
263M32—612no—
264M32—1221no—
265C2×C16—611no—
266C2×C16—1221no—
267C2×C16C2×#692311yescharacteristic
268#108—612no—
269#108—1221no—
270#106—612no—
271#106—1221no—
272#104—1224no—
273#103—1224no—
274#97—612no—
275#97—612no—
276#41—1222no—
277#41—1222no—
278#41—2441no—
279#41—2441no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—1222no—
283C2×Q8—1222no—
284C2×Q8—1221no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×D4—1221no—
289C2×D4—2441no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295Q16—21no—
296Q16—21no—
297Q16—612no—
298Q16—1222no—
299Q16—1222no—
300Q16—1221no—
301Q16C22×#692312yes—
302Q16C22×#692312yes—
303SD16—1222no—
304SD16—1222no—
305D8—612no—
306D8—1221no—
307M16—1222no—
308M16—2444no—
309M16—2441no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—612no—
316C2×C8—1221no—
317C2×C8—1221no—
318C2×C8—2444no—
319C2×C8—2441no—
320C2×C8C22×#692311yescharacteristic
321C4⋊C4—1222no—
322C4⋊C4—2441no—
323C4⋊C4—2444no—
324C42—612no—
325C42—1221no—
326C42—2444no—
327C16—612no—
328C16—1222no—
329C16C22×#692312yes—
330C23—611no—
331C23—2441no—
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—1222no—
337Q8—2442no—
338Q8—2442no—
339Q8—2441no—
340D4—1222no—
341D4—2442no—
342D4—2442no—
343D4—2441no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—1222no—
352C2×C4—4882no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2441no—
360C2×C4D4×#692311yescharacteristic
361C8—611no—
362C8—611no—
363C8—1222no—
364C8—2442no—
365C8D4×#692311yescharacteristic
366C8C23×#692311yescharacteristic
367C22—611no—
368C22—611no—
369C22—1222no—
370C22—4882no—
371C22—2442no—
372C22#1684080311yescharacteristic
373C4—42no—
374C4—42no—
375C4—611no—
376C4—611no—
377C4—4882no—
378C4—2442no—
379C4—2442no—
380C4#1684080311yescharacteristic
381C4C2×D4×#692311yescharacteristic
382C2—1221no—
383C2—1221no—
384C2—4882no—
385C2#2146222712yesdirect product factor
386C2C2×#1684080311yescharacteristic
subgroupG/H
centerC22#16840803
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC2×Q32×C61C4
socleC22×C61#442
prime radicalC2×#14519800C22
cosocleC8×D61C24
hypercenterC2×Q32#6923
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. C2×#16840802C2semidirect
3. #21462227C2direct (N × H)
4. C2×#16840687C2semidirect
5. C2×#16840681C2semidirect
7. C2×#16840653C2semidirect
15. #16840802C22semidirect
21. #16840687C22semidirect
22. #16840681C22semidirect
24. #16840653C22semidirect
27. #16840204C4semidirect
29. C2×#14519723C4semidirect
30. C2×#14519722C4semidirect
31. C2×#14519720C4semidirect
33. C2×Q32×C61C4semidirect
72. #14519723C2×C4semidirect
73. #14519722C2×C4semidirect
74. #14519720C2×C4semidirect
80. Q32×C61C2×C4semidirect
197. C2×C61#2180semidirect
209. C2×Q32#6923semidirect
227. C61C2×#2180semidirect
258. Q32C2×#6923semidirect
385. C2#21462227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408082
C2×#168408022
#214622272
C2×#168406872
C2×#168406812
C2×#168406792
C2×#168406532
C2×#168402042
C2×#218061