Finite Group Databasebeta

← C22×#63815 #11918472

Subgroups — C22×#63815 #11918472

Order 1152.

3177 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C22×#3711C212yesmaximal, complemented
5C2×#63815C2124yesmaximal, direct product factor
6C22×D3×C3⋊C8C212yesmaximal, complemented
7C22×#948—31nomaximal
8C22×#907—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67C412yes—
11C2×C3×#235C4112yes—
12C2×C3×#235C22112yes—
13C22×C3×D12C411yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C411yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C22112yescomplemented
19C2×C3×#208C22112yescomplemented
20C22×C3×C3⋊C8C2212yes—
21C2×#3711C22124yescomplemented
22#63815C22164yesdirect product factor
23C2×D3×C3⋊C8C22124yescomplemented
24C22×C3×#41—31no—
25C22×#235D311yescharacteristic
26C22×C3×M16—31no—
27C2×#948—324no—
28C22×#208—32no—
29C22×#208D311yescharacteristic, complemented
30C23×C3⋊C8—31no—
31C23×C3⋊C8—31no—
32C23×C3⋊C8—32no—
33C23×C3⋊C8—61no—
34C2×#907—324no—
35C22×ΓL(1,𝔽25)—32no—
36C22×D3×C8—32no—
37C24×C32C2×C411yescharacteristic
38C23×C3×D3C2×C412yes—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C416yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2316yes—
43C2×C3×#67C2×C4124yes—
44C22×C3×Dic3C2×C412yes—
45C3×#235C2×C4148yes—
46C3×#235C23116yes—
47C2×C3×D12C2×C4112yes—
48C2×C3×C4×D3C2×C4112yes—
49C2×C3×C4×D3C23112yes—
50C2×C3×Dic6C2×C4112yes—
51C2×C3⋊(C3⋊C8)C2316yes—
52C2×C3⋊(C3⋊C8)C2316yes—
53C2×C3⋊(C3⋊C8)C23116yescomplemented
54C3×#208C23116yescomplemented
55C2×C3×C3⋊C8C23112yes—
56#3711C23132yescomplemented
57D3×C3⋊C8C23132yescomplemented
58C22×#131—91noSylow
59C2×C3×#41—312no—
60C2×C3×#41—312no—
61C22×C3×Q8—31no—
62C22×C3×D4—32no—
63C22×C3×D4—31no—
64C23×C3×C4—21no—
65C23×C3×C4—32no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C22×#67Dic312yes—
69C2×#235Dic3112yes—
70C2×#235C2×D3112yes—
71C22×D12Dic311yescharacteristic
72C22×C4×D3C2×D312yes—
73C22×Dic6Dic311yescharacteristic
74C2×C3×M16—312no—
75C22×C3×C8—32no—
76#948—364no—
77C2×#208—324no—
78C2×#208C2×D3112yescomplemented
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—312no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—312no—
85C22×C3⋊C8—324no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8—61no—
88C22×C3⋊C8—612no—
89C22×C3⋊C8C2×D312yes—
90#907—364no—
91C2×ΓL(1,𝔽25)—324no—
92C2×D3×C8—324no—
93C23×C32—24no—
94C23×C32C22×C416yes—
95C23×C32C22×C411yescharacteristic
96C22×C3×D3—28no—
97C22×C3×D3C22×C4112yes—
98C2×C32×C4C22×C416yes—
99C2×C32×C4C22×C413yes—
100C2×C32×C4C22×C4112yes—
101C2×C32×C4C2413yes—
102C2×C32×C4C2414yes—
103C3×#67C22×C4132yes—
104C2×C3×Dic3C22×C4112yes—
105C3×D12C22×C4116yes—
106C3×C4×D3C22×C4124yes—
107C3×C4×D3C2418yes—
108C3×Dic6C22×C4116yes—
109C3⋊(C3⋊C8)C2414yes—
110C3⋊(C3⋊C8)C2414yes—
111C3×C3⋊C8C2418yes—
112C22×#41—31no—
113C2×#131—924no—
114C22×M16—31no—
115C22×M16—92no—
116C23×C8—92no—
117C23×C8—91no—
118C24×C3—21no—
119C24×C3—32no—
120C24×C3C4×D311yescharacteristic
121C24×C3C2×Dic311yescharacteristic
122C23×D3C2×Dic312yes—
123C3×#41—348no—
124C3×#41—316no—
125C2×C3×Q8—312no—
126C2×C3×D4—324no—
127C2×C3×D4—312no—
128C22×C3×C4—21no—
129C22×C3×C4—26no—
130C22×C3×C4—26no—
131C22×C3×C4—21no—
132C22×C3×C4—32no—
133C22×C3×C4—312no—
134C22×C3×C4—312no—
135C22×C3×C4C4×D311yescharacteristic
136C22×C3×C4C4×D316yes—
137C22×C3×C4C2×Dic311yescharacteristic
138C22×C3×C4C2×Dic316yes—
139C22×C3×C4C22×D316yes—
140C22×C3×C4C22×D316yes—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C2×#67C2×Dic3124yes—
144C22×Dic3C2×Dic312yes—
145#235C2×Dic3148yes—
146#235C22×D3116yes—
147C2×D12C2×Dic3112yes—
148C2×C4×D3C2×Dic3112yes—
149C2×C4×D3C22×D3112yes—
150C2×Dic6C2×Dic3112yes—
151C3×M16—316no—
152C2×C3×C8—312no—
153#208—332no—
154#208C22×D3116yescomplemented
155C2×C3⋊C8—36no—
156C2×C3⋊C8—36no—
157C2×C3⋊C8—316no—
158C2×C3⋊C8—36no—
159C2×C3⋊C8—36no—
160C2×C3⋊C8—316no—
161C2×C3⋊C8—332no—
162C2×C3⋊C8—66no—
163C2×C3⋊C8—66no—
164C2×C3⋊C8—616no—
165C2×C3⋊C8C22×D3112yes—
166ΓL(1,𝔽25)—332no—
167D3×C8—332no—
168C22×C32—212no—
169C22×C32#13114yescomplemented
170C22×C32C23×C414yes—
171C22×C32C23×C413yes—
172C2×C3×D3—224no—
173C2×C3×D3C23×C418yes—
174C32×C4C23×C414yes—
175C32×C4C23×C413yes—
176C32×C4C2511yescharacteristic
177C3×Dic3C23×C418yes—
178C2×#41—312no—
179C2×#41—312no—
180C22×Q8—31no—
181C22×D4—32no—
182C22×D4—31no—
183C23×C4—32no—
184C23×C4D3211yescharacteristic
185#131—964no—
186C2×M16—312no—
187C2×M16—924no—
188C22×C8—32no—
189C22×C8—924no—
190C22×C8—912no—
191C22×C8—91no—
192C22×C8—91no—
193C23×C3—28no—
194C23×C3—24no—
195C23×C3—24no—
196C23×C3—26no—
197C23×C3—21no—
198C23×C3—312no—
199C23×C3—68no—
200C23×C3C2×C4×D316yes—
201C23×C3C2×C4×D311yescharacteristic
202C23×C3C22×Dic316yes—
203C23×C3C22×Dic311yescharacteristic
204C22×D3—28no—
205C22×D3C22×Dic3112yes—
206C3×Q8—316no—
207C3×D4—332no—
208C3×D4—316no—
209C2×C3×C4—23no—
210C2×C3×C4—24no—
211C2×C3×C4—23no—
212C2×C3×C4—26no—
213C2×C3×C4—212no—
214C2×C3×C4—312no—
215C2×C3×C4—324no—
216C2×C3×C4—38no—
217C2×C3×C4C2×C4×D313yes—
218C2×C3×C4C2×C4×D316yes—
219C2×C3×C4C2×C4×D3112yes—
220C2×C3×C4C22×Dic316yes—
221C2×C3×C4C22×Dic313yes—
222C2×C3×C4C22×Dic3112yes—
223C2×C3×C4C23×D313yes—
224C2×C3×C4C23×D314yes—
225C2×C3×C4C23×D313yes—
226C2×C3×C4C23×D314yes—
227#67C22×Dic3132yes—
228C2×Dic3C22×Dic3112yes—
229D12C22×Dic3116yes—
230C4×D3C22×Dic3124yes—
231C4×D3C23×D318yes—
232Dic6C22×Dic3116yes—
233C3×C8—38no—
234C3⋊C8—34no—
235C3⋊C8—34no—
236C3⋊C8—34no—
237C3⋊C8—34no—
238C3⋊C8—64no—
239C3⋊C8—64no—
240C3⋊C8C23×D318yes—
241C2×C32—24no—
242C2×C32C2×#13116yescomplemented
243C2×C32C24×C411yescharacteristic
244C3×D3—28no—
245C24—32no—
246C24D3×Dic311yescharacteristic
247#41—316no—
248#41—348no—
249C2×Q8—312no—
250C2×D4—324no—
251C2×D4—312no—
252C22×C4—32no—
253C22×C4—312no—
254C22×C4—312no—
255C22×C4D3×Dic311yescharacteristic
256C22×C4D3×Dic316yes—
257C22×C4C2×D3216yes—
258C22×C4C2×D3211yescharacteristic
259M16—316no—
260M16—932no—
261C2×C8—312no—
262C2×C8—932no—
263C2×C8—96no—
264C2×C8—96no—
265C2×C8—916no—
266C22×C3—224no—
267C22×C3—212no—
268C22×C3—212no—
269C22×C3—24no—
270C22×C3—23no—
271C22×C3—24no—
272C22×C3—38no—
273C22×C3—624no—
274C22×C3#90714yescomplemented
275C22×C3#94814yescomplemented
276C22×C3C22×C4×D314yes—
277C22×C3C22×C4×D313yes—
278C22×C3C23×Dic314yes—
279C22×C3C23×Dic313yes—
280C2×D3—224no—
281C2×D3C23×Dic318yes—
282C3×C4—23no—
283C3×C4—24no—
284C3×C4—21no—
285C3×C4—38no—
286C3×C4C22×C4×D313yes—
287C3×C4C22×C4×D314yes—
288C3×C4C23×Dic314yes—
289C3×C4C23×Dic313yes—
290C3×C4C24×D311yescharacteristic
291C3×C4C24×D311yescharacteristic
292Dic3C23×Dic318yes—
293C32C22×#13111yescharacteristic, complemented, Sylow
294C23—24no—
295C23—312no—
296C23—68no—
297C23C2×D3×Dic316yes—
298C23C2×D3×Dic311yescharacteristic
299Q8—316no—
300D4—332no—
301D4—316no—
302C2×C4—312no—
303C2×C4—324no—
304C2×C4—38no—
305C2×C4C2×D3×Dic313yes—
306C2×C4C2×D3×Dic316yes—
307C2×C4C2×D3×Dic3112yes—
308C2×C4C22×D3213yes—
309C2×C4C22×D3214yes—
310C8—38no—
311C8—94no—
312C8—94no—
313C2×C3—28no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3—21no—
317C2×C3—26no—
318C2×C3—68no—
319C2×C3C2×#90716yescomplemented
320C2×C3C2×#94816yescomplemented
321C2×C3C23×C4×D311yescharacteristic
322C2×C3C24×Dic311yescharacteristic
323D3—28no—
324C22—212no—
325C22—38no—
326C22—624no—
327C22#6381514yesdirect product factor
328C22C22×D3×Dic314yes—
329C22C22×D3×Dic313yes—
330C4—38no—
331C4C22×D3×Dic313yes—
332C4C22×D3×Dic314yes—
333C4C23×D3211yescharacteristic
334C3—21no—
335C3C22×#90711yescharacteristic, complemented
336C3C22×#94811yescharacteristic, complemented
337C2—24no—
338C2—68no—
339C2C2×#6381516yesdirect product factor
340C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×C3×#235C2
cosocleC32×C4C25
hypercenterC23×C4D32
hypocenterC32C22×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3⋊(C3⋊C8)C2semidirect
3. C22×C3×#208C2semidirect
4. C22×#3711C2semidirect
5. C2×#63815C2direct (N × H)
6. C22×D3×C3⋊C8C2semidirect
18. C22×C3⋊(C3⋊C8)C22semidirect
19. C2×C3×#208C22semidirect
21. C2×#3711C22semidirect
22. #63815C22direct (N × H)
23. C2×D3×C3⋊C8C22semidirect
29. C22×#208D3semidirect
53. C2×C3⋊(C3⋊C8)C23semidirect
54. C3×#208C23semidirect
56. #3711C23semidirect
57. D3×C3⋊C8C23semidirect
78. C2×#208C2×D3semidirect
154. #208C22×D3semidirect
169. C22×C32#131semidirect
242. C2×C32C2×#131semidirect
274. C22×C3#907semidirect
275. C22×C3#948semidirect
293. C32C22×#131semidirect
319. C2×C3C2×#907semidirect
320. C2×C3C2×#948semidirect
327. C22#63815direct (N × H)
335. C3C22×#907semidirect
336. C3C22×#948semidirect
339. C2C2×#63815direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C23×C3⋊(C3⋊C8)2
C22×C3×#2082
C22×#37112
C2×#638152
C22×D3×C3⋊C82
C22×#9483
C22×#9073