Finite Group Databasebeta

← C2×#10592761 #11864853

Subgroups — C2×#10592761 #11864853

Order 1152.

2184 conjugacy classes of subgroups; only the 313 normal subgroups are shown.

normal subgroups only

This group has 2184 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×#64364C211yesmaximal, characteristic, complemented
2C2×C32×#124C211yesmaximal, characteristic, complemented
3C2×#64141C212yesmaximal, complemented
4C2×#63663C211yesmaximal, characteristic, complemented
5#10592761C218yesmaximal, direct product factor
6C2×#63632C212yesmaximal, complemented
7C2×#5062—34nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C32×D4C2211yescharacteristic
10#64364—22no—
11#64364—24no—
12#64364C2214yescomplemented
13C2×#3832—22no—
14C2×Q8×C3⋊D3—22no—
15C2×#3828—22no—
16C2×#3828C2212yes—
17C32×#124—22no—
18C32×#124C2214yescomplemented
19C2×C32×C22⋊C4—22no—
20C2×C32×C42C2211yescharacteristic
21C2×#3754—22no—
22#64141—24no—
23#64141C2218yescomplemented
24C2×#3753—22no—
25C2×#3748C2212yes—
26#63663C2214yescomplemented
27#63632C2218yescomplemented
28C2×#1007—34no—
29C2×C3×#124D314yescomplemented
30C2×#932—38no—
31C2×#836—34no—
32#5062—332no—
33C2×#805—38no—
34C24×C32—21no—
35C2×C32×Q8—22no—
36C2×C32×Q8—22no—
37C2×C32×Q8D412yes—
38C2×C32×Q8C2312yes—
39C2×C32×D4—22no—
40C2×C32×D4—22no—
41C2×C32×D4—21no—
42C2×C32×D4C2312yes—
43C22×C32×C4—21no—
44C22×C32×C4D412yes—
45C22×C32×C4C2311yescharacteristic
46C2×#638—22no—
47#3832—28no—
48#3832—28no—
49Q8×C3⋊D3—28no—
50Q8×C3⋊D3—28no—
51#3828—28no—
52#3828—28no—
53#3828—22no—
54#3828—22no—
55#3828D414yes—
56#3828C2314yes—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D412yes—
59C2×C4×C3⋊D3—24no—
60C2×C4×C3⋊D3—22no—
61C2×#634—22no—
62C2×#634D412yes—
63C32×C22⋊C4—28no—
64C32×C42—21no—
65C32×C42C2312yes—
66#3754—28no—
67#3753—28no—
68#3748—22no—
69#3748C2314yes—
70C2×C3⋊(C3⋊C8)—22no—
71C2×#454—91noSylow
72C22×C3×Q8C2×D314yes—
73C22×C3×D4C2×D314yes—
74#1007—316no—
75#1007—616no—
76#1007—68no—
77C2×#239—68no—
78C2×D3×Q8—68no—
79C2×#235—38no—
80C2×#235—68no—
81C3×#124—28no—
82C3×#124C2×D3116yescomplemented
83C2×C3×C22⋊C4—28no—
84C2×C3×C42C2×D314yes—
85C2×#214—68no—
86#932—332no—
87#932—616no—
88C2×#213—68no—
89C2×#208—38no—
90#836—316no—
91#805—332no—
92C23×C32—22no—
93C23×C32—44no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C32×Q8—24no—
99C32×Q8—24no—
100C32×D4—24no—
101C32×D4—42no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—42no—
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D414yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2411yescharacteristic
111#638—24no—
112#638—24no—
113C2×C3⋊Dic3—22no—
114C4⋊(C3⋊D3)—28no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)C2×D414yes—
117C4×C3⋊D3—216no—
118C4×C3⋊D3—24no—
119C4×C3⋊D3—24no—
120#634—28no—
121#634—22no—
122#634C2×D414yes—
123C3⋊(C3⋊C8)—24no—
124C2×2−1+4—91no—
125C2×AGL(1,ℤ/8)—92no—
126C2×#124C3⋊D311yescharacteristic, complemented
127#454—98no—
128C2×#104—92no—
129C2×#101—91no—
130C24×C3—24no—
131C2×C3×Q8—28no—
132C2×C3×Q8—28no—
133C2×C3×Q8#6718yes—
134C2×C3×Q8C22×D318yes—
135C2×C3×D4—28no—
136C2×C3×D4—28no—
137C2×C3×D4—24no—
138C2×C3×D4C22×D318yes—
139C22×C3×C4—24no—
140C22×C3×C4#6718yes—
141C22×C3×C4C22×D314yes—
142C2×#67—68no—
143#239—632no—
144#239—632no—
145D3×Q8—632no—
146D3×Q8—632no—
147#235—316no—
148#235—316no—
149#235—632no—
150#235—68no—
151#235—68no—
152#235—632no—
153C2×D12—38no—
154C2×D12—68no—
155C2×C4×D3—616no—
156C2×C4×D3—68no—
157C2×Dic6—38no—
158C2×Dic6—68no—
159C3×C22⋊C4—232no—
160C3×C42—24no—
161C3×C42C22×D318yes—
162#214—632no—
163#213—632no—
164#208—316no—
165#208—68no—
166C2×C3⋊C8—68no—
167C22×C32—22no—
168C22×C32—44no—
169C22×C32—42no—
170C22×C32—82no—
171C22×C32—82no—
172C22×C32#12011yescharacteristic
173C22×C32#12011yescharacteristic
174C22×C32C22×D411yescharacteristic
175C2×C3⋊D3—24no—
176C2×C3⋊D3—44no—
177C32×C4—24no—
178C32×C4—42no—
179C32×C4#12012yes—
180C32×C4C22×D412yes—
181C3⋊Dic3—24no—
1822−1+4—94no—
1832−1+4—184no—
1842−1+4—182no—
185C2×#41—92no—
186C2×#41—182no—
187C2×#41—182no—
188C22×Q8—182no—
189C22×Q8C2×C3⋊D311yescharacteristic
190C22×D4C2×C3⋊D311yescharacteristic
191AGL(1,ℤ/8)—98no—
192AGL(1,ℤ/8)—184no—
193C2×SD16—182no—
194C2×D8—182no—
195C2×M16—92no—
196#124—22no—
197#124C2×C3⋊D314yescomplemented
198C2×C22⋊C4—22no—
199C2×C42C2×C3⋊D311yescharacteristic
200#104—98no—
201#101—94no—
202C23×C3—28no—
203C23×C3—416no—
204C23×C3—44no—
205C23×C3—44no—
206C23×C3C2×#6714yes—
207C22×D3—68no—
208C3×Q8—216no—
209C3×Q8—216no—
210C3×D4—216no—
211C3×D4—48no—
212C2×C3×C4—28no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—48no—
216C2×C3×C4D3×D418yes—
217C2×C3×C4D3×D418yes—
218C2×C3×C4C2×#67116yes—
219C2×C3×C4C2×#6714yes—
220C2×C3×C4C23×D314yes—
221#67—616no—
222#67—616no—
223C2×Dic3—68no—
224D12—316no—
225D12—632no—
226D12—68no—
227C4×D3—664no—
228C4×D3—616no—
229C4×D3—616no—
230Dic6—316no—
231Dic6—632no—
232Dic6—68no—
233C3⋊C8—616no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32—82no—
237C2×C32#45412yescomplemented
238C2×C32C2×#12011yescharacteristic
239C3⋊D3—44no—
240C24—21no—
241#41—94no—
242#41—94no—
243#41—188no—
244#41—188no—
245#41—188no—
246#41—182no—
247#41—182no—
248#41—188no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—92no—
252C2×Q8—182no—
253C2×Q8—188no—
254C2×Q8—188no—
255C2×Q8#63812yes—
256C2×Q8C22×C3⋊D312yes—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—92no—
261C2×D4—182no—
262C2×D4—182no—
263C2×D4C22×C3⋊D312yes—
264C22×C4—21no—
265C22×C4—184no—
266C22×C4—182no—
267C22×C4#63812yes—
268C22×C4C22×C3⋊D311yescharacteristic
269SD16—188no—
270D8—188no—
271M16—94no—
272M16—182no—
273C2×C8—182no—
274C22⋊C4—28no—
275C42—21no—
276C42C22×C3⋊D312yes—
277C22×C3—28no—
278C22×C3—416no—
279C22×C3—48no—
280C22×C3—88no—
281C22×C3—88no—
282C22×C3#93714yes—
283C22×C3#93714yes—
284C22×C3C22×#6714yes—
285C2×D3—616no—
286C2×D3—1216no—
287C3×C4—216no—
288C3×C4—48no—
289C3×C4#93718yes—
290C3×C4C2×D3×D418yes—
291Dic3—616no—
292C32C2×#45411yescharacteristic, complemented, Sylow
293C23—22no—
294C23—44no—
295C23—41no—
296C23—41no—
297C23—182no—
298C23C2×#63811yescharacteristic
299Q8—24no—
300Q8—24no—
301Q8—94no—
302Q8—188no—
303Q8—182no—
304D4—24no—
305D4—42no—
306D4—94no—
307D4—188no—
308D4—184no—
309D4—184no—
310D4—182no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—1816no—
316C2×C4—182no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4D4×C3⋊D312yes—
320C2×C4D4×C3⋊D312yes—
321C2×C4C2×#63814yes—
322C2×C4C2×#63811yescharacteristic
323C2×C4C23×C3⋊D311yescharacteristic
324C8—184no—
325C2×C3—24no—
326C2×C3—24no—
327C2×C3—88no—
328C2×C3#506218yescomplemented
329C2×C3C2×#93714yes—
330D3—1216no—
331C22—22no—
332C22—44no—
333C22—42no—
334C22—82no—
335C22—82no—
336C22—184no—
337C22—364no—
338C22#6414611yescharacteristic
339C22#6414611yescharacteristic
340C22C22×#63811yescharacteristic
341C4—24no—
342C4—42no—
343C4—184no—
344C4#6414612yes—
345C4C2×D4×C3⋊D312yes—
346C3C2×#506214yescomplemented
347C2—21no—
348C2—21no—
349C2—82no—
350C2—364no—
351C2#1059276112yesdirect product factor
352C2C2×#6414611yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#124C2
socleC22×C32#120
hypercenterC2×#124C3⋊D3
hypocenterC32C2×#454
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
1. C2×#64364C2semidirect
2. C2×C32×#124C2semidirect
3. C2×#64141C2semidirect
4. C2×#63663C2semidirect
5. #10592761C2direct (N × H)
6. C2×#63632C2semidirect
12. #64364C22semidirect
18. C32×#124C22semidirect
23. #64141C22semidirect
26. #63663C22semidirect
27. #63632C22semidirect
29. C2×C3×#124D3semidirect
82. C3×#124C2×D3semidirect
126. C2×#124C3⋊D3semidirect
197. #124C2×C3⋊D3semidirect
237. C2×C32#454semidirect
292. C32C2×#454semidirect
328. C2×C3#5062semidirect
346. C3C2×#5062semidirect
351. C2#10592761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643642
C2×C32×#1242
C2×#641412
C2×#636632
#105927612
C2×#636322
C2×#50623