Finite Group Databasebeta

← C2×#20252189 #27080332

Subgroups — C2×#20252189 #27080332

Order 12032.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic47C212yesmaximal, complemented
2#20252189C2116yesmaximal, direct product factor
3C2×#15689235C212yesmaximal, complemented
4C2×#15689230C212yesmaximal, complemented
5C2×#15689224C214yesmaximal, complemented
6C2×#15689161C211yesmaximal, characteristic, complemented
7C2×#15689119C212yesmaximal, complemented
8C22×#13093934C211yesmaximal, characteristic, complemented
9C22×#135×C47C211yesmaximal, characteristic
10C23×C47⋊C8C2211yescharacteristic
11#41×Dic47—28no—
12#41×Dic47C22116yescomplemented
13C2×Q8×Dic47C2214yes—
14C2×D4×Dic47—24no—
15C2×D4×Dic47C2214yes—
16C2×#13093983—22no—
17C2×#13093983C2212yes—
18C22×C4×Dic47—22no—
19C22×C4×Dic47C2211yescharacteristic
20#15689235C22116yescomplemented
21#15689230C22116yescomplemented
22#15689224C22132yescomplemented
23#15689161C2218yescomplemented
24C2×#13093958C2212yes—
25C2×#13093956C2212yes—
26#15689119C22116yescomplemented
27C2×#13093948C2214yes—
28C2×#13093945C2214yes—
29C2×#13093934C2212yes—
30C2×#13093934C2212yes—
31C2×#13093934C2218yescomplemented
32C22×#41×C47C2212yes—
33C2×#135×C47C4116yescomplemented
34C2×#135×C47C2218yes—
35C22×Q16×C47C2211yescharacteristic
36C22×SD16×C47C2212yes—
37C22×D8×C47C2211yescharacteristic
38C23×C8×C47C2211yescharacteristic
39C23×Dic47—24no—
40C23×Dic47D412yes—
41C22×C47⋊C8—24no—
42C22×C47⋊C8C2312yes—
43C22×C47⋊C8C2314yes—
44Q8×Dic47—28no—
45Q8×Dic47C23116yes—
46D4×Dic47—232no—
47D4×Dic47—28no—
48D4×Dic47C23116yes—
49#13093983—24no—
50#13093983—216no—
51#13093983C2318yes—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47C2314yes—
54C2×C22⋊Dic47—22no—
55C2×C22⋊Dic47—24no—
56C2×C4×Dic47—22no—
57C2×C4×Dic47—24no—
58C2×C4×Dic47—216no—
59C2×C4×Dic47D412yes—
60C2×C4×Dic47D414yes—
61C2×C4×Dic47C2312yes—
62C2×C4×Dic47C2314yes—
63#13093958C2318yes—
64#13093956C2318yes—
65#13093948C23116yes—
66#13093945C23116yes—
67#13093934C2318yes—
68#13093934C2318yes—
69C2×#41×C47—24no—
70C2×#41×C47—28no—
71C2×#41×C47C2×C4116yescomplemented
72C2×#41×C47C2318yes—
73C22×Q8×C47C2312yes—
74C22×D4×C47—22no—
75C22×D4×C47C2312yes—
76C23×C4×C47—22no—
77C23×C4×C47C2311yescharacteristic
78#135×C47C2×C4164yescomplemented
79C2×Q16×C47C2×C418yescomplemented
80C2×Q16×C47C2314yes—
81C2×SD16×C47C2×C4116yescomplemented
82C2×SD16×C47C2318yes—
83C2×D8×C47C2×C418yescomplemented
84C2×D8×C47C2314yes—
85C22×C8×C47C2×C418yescomplemented
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2314yes—
89C24×C47—22no—
90C24×C47C2×D411yescharacteristic
91#41×C47—232no—
92#41×C47—216no—
93#41×C47C22×C4132yescomplemented
94C2×Q8×C47—22no—
95C2×Q8×C47—24no—
96C2×Q8×C47C22×C418yes—
97C2×Q8×C47C2414yes—
98C2×D4×C47—216no—
99C2×D4×C47—28no—
100C2×D4×C47—22no—
101C2×D4×C47—24no—
102C2×D4×C47C22×C418yes—
103C2×D4×C47C2414yes—
104C22×C4×C47—22no—
105C22×C4×C47—216no—
106C22×C4×C47—28no—
107C22×C4×C47C22×C414yes—
108C22×C4×C47C2×D412yes—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47#4114yes—
111C22×C4×C47C2411yescharacteristic
112C22×C4×C47C2412yes—
113C22×Dic47—24no—
114C22×Dic47—216no—
115C22×Dic47—44no—
116C22×Dic47—416no—
117C22×Dic47C2×D414yes—
118C22×Dic47C2×D418yes—
119Q16×C47C22×C4116yescomplemented
120SD16×C47C22×C4132yescomplemented
121D8×C47C22×C4116yescomplemented
122C2×C8×C47C22×C414yes—
123C2×C8×C47C22×C414yes—
124C2×C8×C47C22×C4116yescomplemented
125C2×C8×C47C2412yes—
126C2×C8×C47C2412yes—
127C22⋊Dic47—28no—
128C22⋊Dic47—216no—
129C4⋊Dic47—24no—
130C4⋊Dic47—216no—
131C4⋊Dic47C2418yes—
132C4×Dic47—28no—
133C4×Dic47—216no—
134C4×Dic47C2×D418yes—
135C4×Dic47C2×D414yes—
136C4×Dic47C2414yes—
137C2×C47⋊C8—24no—
138C2×C47⋊C8—28no—
139C2×C47⋊C8C2414yes—
140C23×C47—24no—
141C23×C47—28no—
142C23×C47—24no—
143C23×C47—48no—
144C23×C47C4×D414yes—
145C23×C47C22×D412yes—
146C23×C47C22×D411yescharacteristic
147Q8×C47—28no—
148Q8×C47—24no—
149Q8×C47C23×C418yes—
150D4×C47—232no—
151D4×C47—28no—
152D4×C47—24no—
153D4×C47C23×C418yes—
154C2×C4×C47—28no—
155C2×C4×C47—24no—
156C2×C4×C47—232no—
157C2×C4×C47C4×D414yes—
158C2×C4×C47C4×D418yes—
159C2×C4×C47C23×C412yes—
160C2×C4×C47C23×C414yes—
161C2×C4×C47C22×D412yes—
162C2×C4×C47C22×D411yescharacteristic
163C2×C4×C47C2×#4112yes—
164C2×C4×C47C2×#4114yes—
165C2×C4×C47C2511yescharacteristic
166C2×Dic47—28no—
167C2×Dic47—28no—
168C2×Dic47—48no—
169C2×Dic47—432no—
170C2×Dic47—48no—
171C2×Dic47C22×D418yes—
172C8×C47C23×C414yes—
173C8×C47C23×C414yes—
174C47⋊C8—24no—
175C2×#2943—471nomaximal, Sylow
176C22×C47—28no—
177C22×C47—24no—
178C22×C47—28no—
179C22×C47—416no—
180C22×C47—48no—
181C22×C47C2×C4×D414yes—
182C22×C47C2×C4×D412yes—
183C22×C47#57514yes—
184C22×C47C23×D411yescharacteristic
185C4×C47—28no—
186C4×C47C2×C4×D414yes—
187C4×C47C2×C4×D412yes—
188C4×C47C24×C411yescharacteristic
189C4×C47C22×#4111yescharacteristic
190Dic47—28no—
191Dic47—48no—
192C22×#135D4711yescharacteristic
193C2×C4×#41—472no—
194#2943—4716no—
195C2×#442—472no—
196C2×#441—472no—
197C2×#440—474no—
198C2×#427—471no—
199C2×#416—472no—
200C22×#97—471no—
201C2×C47—24no—
202C2×C47—48no—
203C2×C47#294314yescomplemented
204C2×C47C22×C4×D411yescharacteristic
205C2×C47C2×#57512yes—
206C22×#41C2×D4712yes—
207C2×#135Dic47116yescomplemented
208C2×#135C2×D4718yes—
209C22×Q16C2×D4711yescharacteristic
210C22×SD16C2×D4712yes—
211C22×D8C2×D4711yescharacteristic
212C23×C8—471no—
213C23×C8C2×D4711yescharacteristic
214C4×#41—4716no—
215C4×#41—948no—
216C2×C4×Q8—474no—
217C2×C4×D4—474no—
218C2×C4×D4—944no—
219C2×#117—472no—
220C2×#117—942no—
221C22×C42—471no—
222C22×C42—942no—
223#442—4716no—
224#441—4716no—
225#440—4732no—
226#427—478no—
227C2×#107—472no—
228C2×#106—472no—
229#416—4716no—
230C2×#103—474no—
231C2×#102—474no—
232C2×#97—472no—
233C2×#97—472no—
234C2×#97—478no—
235C47C2×#294311yescharacteristic, complemented, Sylow
236C2×#41—24no—
237C2×#41—28no—
238C2×#41C2×Dic47116yescomplemented
239C2×#41C22×D4718yes—
240C22×Q8C22×D4712yes—
241C22×D4—22no—
242C22×D4C22×D4712yes—
243C23×C4—22no—
244C23×C4—472no—
245C23×C4—944no—
246C23×C4C22×D4711yescharacteristic
247#135C2×Dic47164yescomplemented
248C2×Q16C2×Dic4718yescomplemented
249C2×Q16C22×D4714yes—
250C2×SD16C2×Dic47116yescomplemented
251C2×SD16C22×D4718yes—
252C2×D8C2×Dic4718yescomplemented
253C2×D8C22×D4714yes—
254C22×C8—472no—
255C22×C8—474no—
256C22×C8—944no—
257C22×C8C2×Dic4718yescomplemented
258C22×C8C22×D4711yescharacteristic
259C22×C8C22×D4711yescharacteristic
260C22×C8C22×D4714yes—
261C4×Q8—4716no—
262C4×Q8—948no—
263C4×D4—4716no—
264C4×D4—948no—
265C4×D4—9432no—
266#117—478no—
267#117—9416no—
268#117—944no—
269C2×C4⋊C4—474no—
270C2×C4⋊C4—944no—
271C2×C22⋊C4—944no—
272C2×C22⋊C4—942no—
273C2×C42—474no—
274C2×C42—472no—
275C2×C42—472no—
276C2×C42—474no—
277C2×C42—9416no—
278C2×C42—944no—
279C2×C42—942no—
280#107—478no—
281#106—478no—
282#103—4716no—
283#102—4716no—
284#97—478no—
285#97—478no—
286C24—22no—
287C24D4×D4711yescharacteristic
288#41—232no—
289#41—216no—
290#41C22×Dic47132yescomplemented
291C2×Q8—22no—
292C2×Q8—24no—
293C2×Q8C22×Dic4718yes—
294C2×Q8C23×D4714yes—
295C2×D4—216no—
296C2×D4—28no—
297C2×D4—22no—
298C2×D4—24no—
299C2×D4C22×Dic4718yes—
300C2×D4C23×D4714yes—
301C22×C4—22no—
302C22×C4—216no—
303C22×C4—28no—
304C22×C4—474no—
305C22×C4—478no—
306C22×C4—9416no—
307C22×C4—944no—
308C22×C4—1884no—
309C22×C4—18816no—
310C22×C4D4×D4712yes—
311C22×C4D4×D4711yescharacteristic
312C22×C4#1062535214yes—
313C22×C4C22×Dic4714yes—
314C22×C4C23×D4711yescharacteristic
315C22×C4C23×D4712yes—
316Q16C22×Dic47116yescomplemented
317SD16C22×Dic47132yescomplemented
318D8C22×Dic47116yescomplemented
319C2×C8—474no—
320C2×C8—944no—
321C2×C8—948no—
322C2×C8C22×Dic4714yes—
323C2×C8C22×Dic4714yes—
324C2×C8C22×Dic47116yescomplemented
325C2×C8C23×D4712yes—
326C2×C8C23×D4712yes—
327C4⋊C4—478no—
328C4⋊C4—9416no—
329C4⋊C4—944no—
330C22⋊C4—9416no—
331C22⋊C4—948no—
332C42—478no—
333C42—474no—
334C42—474no—
335C42—9416no—
336C42—948no—
337C23—24no—
338C23—28no—
339C23—24no—
340C23—48no—
341C23D4×Dic4714yes—
342C23C2×D4×D4712yes—
343C23C2×D4×D4711yescharacteristic
344Q8—28no—
345Q8—24no—
346Q8C23×Dic4718yes—
347D4—232no—
348D4—28no—
349D4—24no—
350D4C23×Dic4718yes—
351C2×C4—28no—
352C2×C4—24no—
353C2×C4—232no—
354C2×C4—478no—
355C2×C4—948no—
356C2×C4—948no—
357C2×C4—1888no—
358C2×C4—18832no—
359C2×C4—1888no—
360C2×C4D4×Dic4714yes—
361C2×C4D4×Dic4718yes—
362C2×C4C23×Dic4712yes—
363C2×C4C23×Dic4714yes—
364C2×C4C2×D4×D4712yes—
365C2×C4C2×D4×D4711yescharacteristic
366C2×C4C2×#1062535212yes—
367C2×C4C2×#1062535214yes—
368C2×C4C24×D4711yescharacteristic
369C8—944no—
370C8C23×Dic4714yes—
371C8C23×Dic4714yes—
372C22—28no—
373C22—24no—
374C22—28no—
375C22—416no—
376C22—48no—
377C22C2×D4×Dic4714yes—
378C22C2×D4×Dic4712yes—
379C22#1568992014yes—
380C22C22×D4×D4711yescharacteristic
381C4—28no—
382C4—948no—
383C4—1888no—
384C4C2×D4×Dic4714yes—
385C4C2×D4×Dic4712yes—
386C4C24×Dic4711yescharacteristic
387C4C22×#1062535211yescharacteristic
388C2—24no—
389C2—48no—
390C2#2025218914yesdirect product factor
391C2C22×D4×Dic4711yescharacteristic
392C2C2×#1568992012yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
Fitting, prime radicalC22×#135×C47C2
socleC23×C47C22×D4
cosocleC2×C4×C47C25
hypercenterC22×#135D47
hypocenterC47C2×#2943
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic47C2semidirect
2. #20252189C2direct (N × H)
3. C2×#15689235C2semidirect
4. C2×#15689230C2semidirect
5. C2×#15689224C2semidirect
6. C2×#15689161C2semidirect
7. C2×#15689119C2semidirect
8. C22×#13093934C2semidirect
12. #41×Dic47C22semidirect
20. #15689235C22semidirect
21. #15689230C22semidirect
22. #15689224C22semidirect
23. #15689161C22semidirect
26. #15689119C22semidirect
31. C2×#13093934C22semidirect
33. C2×#135×C47C4semidirect
71. C2×#41×C47C2×C4semidirect
78. #135×C47C2×C4semidirect
79. C2×Q16×C47C2×C4semidirect
81. C2×SD16×C47C2×C4semidirect
83. C2×D8×C47C2×C4semidirect
85. C22×C8×C47C2×C4semidirect
93. #41×C47C22×C4semidirect
119. Q16×C47C22×C4semidirect
120. SD16×C47C22×C4semidirect
121. D8×C47C22×C4semidirect
124. C2×C8×C47C22×C4semidirect
203. C2×C47#2943semidirect
207. C2×#135Dic47semidirect
235. C47C2×#2943semidirect
238. C2×#41C2×Dic47semidirect
247. #135C2×Dic47semidirect
248. C2×Q16C2×Dic47semidirect
250. C2×SD16C2×Dic47semidirect
252. C2×D8C2×Dic47semidirect
257. C22×C8C2×Dic47semidirect
290. #41C22×Dic47semidirect
316. Q16C22×Dic47semidirect
317. SD16C22×Dic47semidirect
318. D8C22×Dic47semidirect
324. C2×C8C22×Dic47semidirect
390. C2#20252189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic472
#202521892
C2×#156892352
C2×#156892302
C2×#156892242
C2×#156891612
C2×#156891192
C22×#130939342
C22×#135×C472
C2×#294347