Finite Group Databasebeta

← C2×#10592760 #11864807

Subgroups — C2×#10592760 #11864807

Order 1152.

2280 conjugacy classes of subgroups; only the 313 normal subgroups are shown.

normal subgroups only

This group has 2280 conjugacy classes of subgroups — too many to draw. Only its 313 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic
2C2×C32×#124C211yesmaximal, characteristic, complemented
3C2×#64151C212yesmaximal, complemented
4C2×#63660C211yesmaximal, characteristic, complemented
5#10592760C218yesmaximal, direct product factor
6C2×#63632C212yesmaximal, complemented
7C2×#5061—34nomaximal
8C22×C32×Q8C2211yescharacteristic, complemented
9C22×C32×D4C2211yescharacteristic
10C22×#638—22no—
11#64361—22no—
12#64361—24no—
13#64361C2214yes—
14C2×#3830—22no—
15C2×D4×C3⋊D3—22no—
16C2×#3828C2212yes—
17C32×#124—22no—
18C32×#124C2214yescomplemented
19C2×C32×C22⋊C4—22no—
20C2×C32×C42C2211yescharacteristic, complemented
21C2×#3756—22no—
22#64151—24no—
23#64151C2218yescomplemented
24C2×#3755—22no—
25C2×#3748C2212yescomplemented
26#63660C2214yescomplemented
27#63632C2218yescomplemented
28C2×#1004—34no—
29C2×C3×#124D314yescomplemented
30C2×#942—38no—
31C2×#833—34no—
32#5061—332no—
33C2×#805—38no—
34C24×C32D412yes—
35C23×C3⋊D3—22no—
36C2×C32×Q8—21no—
37C2×C32×Q8—22no—
38C2×C32×Q8—22no—
39C2×C32×Q8C2312yescomplemented
40C2×C32×D4—22no—
41C2×C32×D4—22no—
42C2×C32×D4D412yes—
43C2×C32×D4C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—24no—
48C2×#638—28no—
49C2×#638—22no—
50C2×#638—28no—
51C22×C3⋊Dic3—22no—
52#3830—28no—
53#3830—28no—
54D4×C3⋊D3—28no—
55D4×C3⋊D3—28no—
56#3828—22no—
57#3828—22no—
58#3828D414yes—
59#3828C2314yes—
60C2×C4⋊(C3⋊D3)D412yes—
61C2×C4×C3⋊D3—22no—
62C2×#634D412yes—
63C32×C22⋊C4—28no—
64C32×C42—21no—
65C32×C42C2312yescomplemented
66#3756—28no—
67#3755—28no—
68#3748—22no—
69#3748C2314yescomplemented
70C2×C3⋊(C3⋊C8)—22no—
71C2×#455—91noSylow
72C22×C3×Q8C2×D314yescomplemented
73C22×C3×D4C2×D314yes—
74C22×#67—68no—
75#1004—316no—
76#1004—616no—
77#1004—68no—
78C2×#237—68no—
79C2×D3×D4—68no—
80C2×#235—38no—
81C3×#124—28no—
82C3×#124C2×D3116yescomplemented
83C2×C3×C22⋊C4—28no—
84C2×C3×C42C2×D314yescomplemented
85C2×#216—68no—
86#942—332no—
87#942—616no—
88C2×#215—68no—
89C2×#208—38no—
90#833—316no—
91#805—332no—
92C23×C32—22no—
93C23×C32—22no—
94C23×C32—44no—
95C23×C32C2×D411yescharacteristic
96C23×C32C2×D414yes—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—28no—
99C22×C3⋊D3—84no—
100C32×Q8—24no—
101C32×Q8—42no—
102C32×D4—24no—
103C32×D4—24no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—42no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2411yescharacteristic
113#638—216no—
114#638—24no—
115#638—24no—
116C2×C3⋊Dic3—28no—
117C2×C3⋊Dic3—22no—
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)C2×D414yes—
120C4×C3⋊D3—24no—
121C4×C3⋊D3—24no—
122#634—22no—
123#634C2×D414yes—
124C3⋊(C3⋊C8)—24no—
125C2×H(5,𝔽2)—91no—
126C2×#137—92no—
127C2×#124C3⋊D311yescharacteristic, complemented
128#455—98no—
129C2×#104—92no—
130C2×#100—91no—
131C24×C3#6718yes—
132C23×D3—68no—
133C2×C3×Q8—24no—
134C2×C3×Q8—28no—
135C2×C3×Q8—28no—
136C2×C3×Q8C22×D318yescomplemented
137C2×C3×D4—28no—
138C2×C3×D4—28no—
139C2×C3×D4#6718yes—
140C2×C3×D4C22×D318yes—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4C22×D314yes—
144C2×#67—616no—
145C2×#67—632no—
146C2×#67—68no—
147C2×#67—632no—
148C22×Dic3—68no—
149#237—632no—
150#237—632no—
151D3×D4—632no—
152D3×D4—632no—
153#235—316no—
154#235—316no—
155#235—68no—
156#235—68no—
157C2×D12—38no—
158C2×C4×D3—68no—
159C2×Dic6—38no—
160C3×C22⋊C4—232no—
161C3×C42—24no—
162C3×C42C22×D318yescomplemented
163#216—632no—
164#215—632no—
165#208—316no—
166#208—68no—
167C2×C3⋊C8—68no—
168C22×C32—22no—
169C22×C32—24no—
170C22×C32—44no—
171C22×C32—44no—
172C22×C32—82no—
173C22×C32#12011yescharacteristic
174C22×C32#12011yescharacteristic
175C22×C32C22×D411yescharacteristic
176C2×C3⋊D3—24no—
177C2×C3⋊D3—44no—
178C2×C3⋊D3—88no—
179C32×C4—42no—
180C32×C4—42no—
181C32×C4#12012yes—
182C32×C4C22×D412yes—
183C3⋊Dic3—24no—
184H(5,𝔽2)—94no—
185H(5,𝔽2)—184no—
186H(5,𝔽2)—182no—
187C2×#41—92no—
188C2×#41—182no—
189C22×Q8C2×C3⋊D311yescharacteristic, complemented
190C22×D4—182no—
191C22×D4—182no—
192C22×D4C2×C3⋊D311yescharacteristic
193#137—98no—
194#137—184no—
195C2×Q16—182no—
196C2×SD16—182no—
197C2×M16—92no—
198#124—22no—
199#124C2×C3⋊D314yescomplemented
200C2×C22⋊C4—22no—
201C2×C42C2×C3⋊D311yescharacteristic, complemented
202#104—98no—
203#100—94no—
204C23×C3—28no—
205C23×C3—28no—
206C23×C3—416no—
207C23×C3C2×#6714yes—
208C23×C3C2×#67116yes—
209C22×D3—68no—
210C22×D3—632no—
211C22×D3—2416no—
212C3×Q8—216no—
213C3×Q8—48no—
214C3×D4—216no—
215C3×D4—216no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—48no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4D3×D418yes—
222C2×C3×C4D3×D418yes—
223C2×C3×C4C2×#6714yes—
224C2×C3×C4C23×D314yes—
225#67—664no—
226#67—616no—
227#67—616no—
228C2×Dic3—632no—
229C2×Dic3—68no—
230D12—316no—
231D12—68no—
232C4×D3—616no—
233C4×D3—616no—
234Dic6—316no—
235Dic6—68no—
236C3⋊C8—616no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32—44no—
240C2×C32#45512yescomplemented
241C2×C32C2×#12011yescharacteristic
242C3⋊D3—44no—
243C24—182no—
244C24#63812yes—
245#41—94no—
246#41—94no—
247#41—188no—
248#41—188no—
249#41—182no—
250#41—182no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—92no—
255C2×Q8C22×C3⋊D312yescomplemented
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—92no—
259C2×D4—188no—
260C2×D4—188no—
261C2×D4—184no—
262C2×D4—188no—
263C2×D4—182no—
264C2×D4—188no—
265C2×D4#63812yes—
266C2×D4C22×C3⋊D312yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4C22×C3⋊D311yescharacteristic
272Q16—188no—
273SD16—188no—
274M16—94no—
275M16—182no—
276C2×C8—182no—
277C22⋊C4—28no—
278C42—21no—
279C42C22×C3⋊D312yescomplemented
280C22×C3—28no—
281C22×C3—216no—
282C22×C3—416no—
283C22×C3—416no—
284C22×C3—88no—
285C22×C3#93714yes—
286C22×C3#93714yes—
287C22×C3C22×#6714yes—
288C2×D3—616no—
289C2×D3—1216no—
290C2×D3—2432no—
291C3×C4—48no—
292C3×C4—48no—
293C3×C4#93718yes—
294C3×C4C2×D3×D418yes—
295Dic3—616no—
296C32C2×#45511yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—44no—
300C23—188no—
301C23—182no—
302C23—724no—
303C23C2×#63811yescharacteristic
304C23C2×#63814yes—
305Q8—24no—
306Q8—42no—
307Q8—94no—
308Q8—182no—
309D4—24no—
310D4—24no—
311D4—94no—
312D4—1816no—
313D4—184no—
314D4—184no—
315D4—182no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—188no—
322C2×C4—182no—
323C2×C4—184no—
324C2×C4—184no—
325C2×C4D4×C3⋊D312yes—
326C2×C4D4×C3⋊D312yes—
327C2×C4C2×#63811yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—184no—
330C2×C3—24no—
331C2×C3—24no—
332C2×C3—416no—
333C2×C3#506118yescomplemented
334C2×C3C2×#93714yes—
335D3—1216no—
336C22—22no—
337C22—24no—
338C22—44no—
339C22—44no—
340C22—82no—
341C22—184no—
342C22—364no—
343C22—728no—
344C22#6414611yescharacteristic
345C22#6414611yescharacteristic
346C22C22×#63811yescharacteristic
347C4—42no—
348C4—42no—
349C4—184no—
350C4#6414612yes—
351C4C2×D4×C3⋊D312yes—
352C3C2×#506114yescomplemented
353C2—21no—
354C2—21no—
355C2—44no—
356C2—364no—
357C2#1059276012yesdirect product factor
358C2C2×#6414611yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#124C2
socleC22×C32#120
prime radicalC2×#64361C2
hypercenterC2×#124C3⋊D3
hypocenterC32C2×#455
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×C32×#124C2semidirect
3. C2×#64151C2semidirect
4. C2×#63660C2semidirect
5. #10592760C2direct (N × H)
6. C2×#63632C2semidirect
8. C22×C32×Q8C22semidirect
18. C32×#124C22semidirect
20. C2×C32×C42C22semidirect
23. #64151C22semidirect
25. C2×#3748C22semidirect
26. #63660C22semidirect
27. #63632C22semidirect
29. C2×C3×#124D3semidirect
39. C2×C32×Q8C23semidirect
65. C32×C42C23semidirect
69. #3748C23semidirect
72. C22×C3×Q8C2×D3semidirect
82. C3×#124C2×D3semidirect
84. C2×C3×C42C2×D3semidirect
127. C2×#124C3⋊D3semidirect
136. C2×C3×Q8C22×D3semidirect
162. C3×C42C22×D3semidirect
189. C22×Q8C2×C3⋊D3semidirect
199. #124C2×C3⋊D3semidirect
201. C2×C42C2×C3⋊D3semidirect
240. C2×C32#455semidirect
255. C2×Q8C22×C3⋊D3semidirect
279. C42C22×C3⋊D3semidirect
296. C32C2×#455semidirect
333. C2×C3#5061semidirect
352. C3C2×#5061semidirect
357. C2#10592760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643612
C2×C32×#1242
C2×#641512
C2×#636602
#105927602
C2×#636322
C2×#50613