Finite Group Databasebeta

← C22×#63833 #11918713

Subgroups — C22×#63833 #11918713

Order 1152.

3373 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C22×#3719C212yesmaximal, complemented
5C2×#63833C2124yesmaximal, direct product factor
6C22×#3717C212yesmaximal, complemented
7C22×#942—31nomaximal
8C22×#909—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×#638—21no—
11C2×#3828—26no—
12C2×#3828C22112yes—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C22×#634C2211yescharacteristic
16C23×C3×Dic3—21no—
17C22×C3×Dic6—26no—
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2212yes—
20C22×C3×Dic6C22112yescomplemented
21C2×C3×#208C22112yescomplemented
22C22×C3×C3⋊C8C2212yes—
23C2×#3719C22124yescomplemented
24#63833C22164yesdirect product factor
25C2×#3717C22124yescomplemented
26C23×C3×Q8—31no—
27C22×#235—31no—
28C22×#235—31no—
29C22×#235—61no—
30C23×Dic6D311yescharacteristic, complemented
31C22×C3×M16—31no—
32C22×#216—32no—
33C2×#942—324no—
34C22×#215—32no—
35C22×#208D311yescharacteristic, complemented
36C2×#909—324no—
37C22×Dic12—32no—
38C22×#204—32no—
39C24×C32D411yescharacteristic
40C23×C3⋊D3—21no—
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D416yes—
43C22×C32×C4C2311yescharacteristic
44C22×C32×C4C2316yes—
45C2×#638—212no—
46C22×C3⋊Dic3—21no—
47#3828—224no—
48#3828C23116yes—
49C2×C4⋊(C3⋊D3)—23no—
50C2×C4⋊(C3⋊D3)C2316yes—
51C2×C4×C3⋊D3—212no—
52C2×#634—23no—
53C2×#634C2316yes—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—212no—
56C2×C3×Dic6—26no—
57C2×C3×Dic6—224no—
58C2×C3×Dic6—212no—
59C2×C3×Dic6C23112yes—
60C2×C3×Dic6C23116yescomplemented
61C3×#208C23116yescomplemented
62C2×C3×C3⋊C8C23112yes—
63#3719C23132yescomplemented
64#3717C23132yescomplemented
65C22×#137—91noSylow
66C22×C3×Q8—32no—
67C22×C3×Q8—312no—
68C22×C3×Q8—61no—
69C22×C3×Q8—66no—
70C23×C3×C4—21no—
71C23×C3×C4—61no—
72C23×C3×C4C2×D311yescharacteristic
73C23×C3×C4C2×D311yescharacteristic
74C22×#67—62no—
75C22×#67—61no—
76C22×#67—61no—
77C23×Dic3—21no—
78C2×#235—312no—
79C2×#235—312no—
80C2×#235—612no—
81C2×#235—612no—
82C2×#235—66no—
83C2×#235—66no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×C4×D3—62no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×Dic6—26no—
91C22×Dic6—21no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×Dic6C2×D312yes—
96C22×Dic6C2×D3112yescomplemented
97C2×C3×M16—312no—
98C22×C3×C8—32no—
99C2×#216—324no—
100#942—364no—
101C2×#215—324no—
102C2×#208C2×D3112yescomplemented
103C22×C3⋊C8C2×D312yes—
104#909—364no—
105C2×Dic12—324no—
106C2×#204—324no—
107C23×C32—24no—
108C23×C32C2×D416yes—
109C23×C32C2×D411yescharacteristic
110C22×C3⋊D3—26no—
111C22×C3⋊D3—44no—
112C2×C32×C4C2×D413yes—
113C2×C32×C4C2×D416yes—
114C2×C32×C4C2×D4112yes—
115C2×C32×C4C2413yes—
116C2×C32×C4C2414yes—
117#638—216no—
118C2×C3⋊Dic3—26no—
119C4⋊(C3⋊D3)—26no—
120C4⋊(C3⋊D3)C2414yes—
121C4×C3⋊D3—216no—
122#634—26no—
123#634C2414yes—
124C2×C3×Dic3—212no—
125C2×C3×Dic3—216no—
126C3×Dic6—212no—
127C3×Dic6—216no—
128C3×Dic6C2418yes—
129C3×C3⋊C8C2418yes—
130C22×#41—91no—
131C23×Q8—31no—
132C2×#137—924no—
133C22×Q16—92no—
134C22×SD16—92no—
135C22×M16—31no—
136C24×C3—21no—
137C24×C3D1211yescharacteristic
138C24×C3#6711yescharacteristic
139C23×D3—62no—
140C23×D3—61no—
141C23×D3—61no—
142C2×C3×Q8—312no—
143C2×C3×Q8—316no—
144C2×C3×Q8—66no—
145C2×C3×Q8—612no—
146C2×C3×Q8—624no—
147C22×C3×C4—21no—
148C22×C3×C4—26no—
149C22×C3×C4—21no—
150C22×C3×C4—26no—
151C22×C3×C4—612no—
152C22×C3×C4—62no—
153C22×C3×C4D1211yescharacteristic
154C22×C3×C4D1216yes—
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4#6716yes—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D316yes—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D316yes—
161C2×#67—624no—
162C2×#67—612no—
163C2×#67—612no—
164C22×Dic3—22no—
165C22×Dic3—212no—
166C22×Dic3—62no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169#235—316no—
170#235—316no—
171#235—616no—
172#235—648no—
173#235—624no—
174#235—624no—
175C2×D12—36no—
176C2×D12—36no—
177C2×D12—66no—
178C2×D12—66no—
179C2×D12—63no—
180C2×D12—63no—
181C2×C4×D3—624no—
182C2×C4×D3—612no—
183C2×C4×D3—612no—
184C2×Dic6—26no—
185C2×Dic6—224no—
186C2×Dic6—212no—
187C2×Dic6—36no—
188C2×Dic6—36no—
189C2×Dic6—66no—
190C2×Dic6—66no—
191C2×Dic6—63no—
192C2×Dic6—63no—
193C2×Dic6C22×D3112yes—
194C2×Dic6C22×D3116yescomplemented
195C3×M16—316no—
196C2×C3×C8—312no—
197#216—332no—
198#215—332no—
199#208C22×D3116yescomplemented
200C2×C3⋊C8C22×D3112yes—
201Dic12—332no—
202#204—332no—
203C22×C32—212no—
204C22×C32#13714yescomplemented
205C22×C32C22×D414yes—
206C22×C32C22×D413yes—
207C2×C3⋊D3—24no—
208C2×C3⋊D3—412no—
209C32×C4C22×D413yes—
210C32×C4C22×D414yes—
211C32×C4C2511yescharacteristic
212C3⋊Dic3—24no—
213C3×Dic3—28no—
214C2×#41—912no—
215C2×#41—186no—
216C22×Q8—32no—
217C22×Q8—312no—
218C22×Q8—66no—
219C22×Q8—61no—
220C22×Q8—91no—
221C22×D4—91no—
222C22×D4—181no—
223C23×C4—61no—
224C23×C4—181no—
225C23×C4D3211yescharacteristic
226#137—964no—
227C2×Q16—924no—
228C2×SD16—924no—
229C2×M16—312no—
230C22×C8—32no—
231C23×C3—24no—
232C23×C3—24no—
233C23×C3—26no—
234C23×C3—21no—
235C23×C3—44no—
236C23×C3C2×D1216yes—
237C23×C3C2×D1211yescharacteristic
238C23×C3C2×#6716yes—
239C23×C3C2×#6711yescharacteristic
240C22×D3—612no—
241C22×D3—66no—
242C22×D3—66no—
243C22×D3—128no—
244C22×D3—124no—
245C22×D3—124no—
246C3×Q8—38no—
247C3×Q8—612no—
248C3×Q8—616no—
249C2×C3×C4—23no—
250C2×C3×C4—24no—
251C2×C3×C4—23no—
252C2×C3×C4—26no—
253C2×C3×C4—212no—
254C2×C3×C4—616no—
255C2×C3×C4—612no—
256C2×C3×C4C2×D1213yes—
257C2×C3×C4C2×D1216yes—
258C2×C3×C4C2×D12112yes—
259C2×C3×C4C2×#6713yes—
260C2×C3×C4C2×#6716yes—
261C2×C3×C4C2×#67112yes—
262C2×C3×C4C23×D313yes—
263C2×C3×C4C23×D314yes—
264C2×C3×C4C23×D313yes—
265C2×C3×C4C23×D314yes—
266#67—632no—
267#67—616no—
268#67—616no—
269C2×Dic3—212no—
270C2×Dic3—216no—
271C2×Dic3—612no—
272C2×Dic3—66no—
273C2×Dic3—66no—
274D12—34no—
275D12—34no—
276D12—64no—
277D12—612no—
278D12—66no—
279D12—66no—
280C4×D3—632no—
281C4×D3—616no—
282C4×D3—616no—
283Dic6—212no—
284Dic6—216no—
285Dic6—34no—
286Dic6—34no—
287Dic6—64no—
288Dic6—612no—
289Dic6—66no—
290Dic6—66no—
291Dic6C23×D318yes—
292C3×C8—38no—
293C3⋊C8C23×D318yes—
294C2×C32—24no—
295C2×C32C2×#13716yescomplemented
296C2×C32C23×D411yescharacteristic
297C3⋊D3—44no—
298C24—181no—
299C24#62611yescharacteristic
300#41—916no—
301#41—1824no—
302C2×Q8—312no—
303C2×Q8—316no—
304C2×Q8—612no—
305C2×Q8—66no—
306C2×Q8—624no—
307C2×Q8—96no—
308C2×Q8—183no—
309C2×D4—96no—
310C2×D4—1812no—
311C2×D4—183no—
312C22×C4—612no—
313C22×C4—62no—
314C22×C4—181no—
315C22×C4—1812no—
316C22×C4#62616yes—
317C22×C4#62611yescharacteristic
318C22×C4C2×D3216yes—
319C22×C4C2×D3211yescharacteristic
320Q16—932no—
321SD16—932no—
322M16—316no—
323C2×C8—312no—
324C22×C3—212no—
325C22×C3—212no—
326C22×C3—23no—
327C22×C3—24no—
328C22×C3—24no—
329C22×C3—412no—
330C22×C3#90914yescomplemented
331C22×C3#94214yescomplemented
332C22×C3C22×D1214yes—
333C22×C3C22×D1213yes—
334C22×C3C22×#6714yes—
335C22×C3C22×#6713yes—
336C2×D3—68no—
337C2×D3—64no—
338C2×D3—64no—
339C2×D3—1224no—
340C2×D3—1212no—
341C2×D3—1212no—
342C3×C4—23no—
343C3×C4—24no—
344C3×C4—21no—
345C3×C4—68no—
346C3×C4C22×D1213yes—
347C3×C4C22×D1214yes—
348C3×C4C22×#6713yes—
349C3×C4C22×#6714yes—
350C3×C4C24×D311yescharacteristic
351C3×C4C24×D311yescharacteristic
352Dic3—28no—
353Dic3—68no—
354Dic3—64no—
355Dic3—64no—
356C32C22×#13711yescharacteristic, complemented, Sylow
357C23—24no—
358C23—186no—
359C23—364no—
360C23C2×#62616yes—
361C23C2×#62611yescharacteristic
362Q8—38no—
363Q8—616no—
364Q8—612no—
365Q8—94no—
366Q8—186no—
367D4—94no—
368D4—1816no—
369D4—186no—
370C2×C4—616no—
371C2×C4—612no—
372C2×C4—186no—
373C2×C4—1816no—
374C2×C4C2×#62616yes—
375C2×C4C2×#62613yes—
376C2×C4C2×#626112yes—
377C2×C4C22×D3213yes—
378C2×C4C22×D3214yes—
379C8—38no—
380C2×C3—24no—
381C2×C3—24no—
382C2×C3—21no—
383C2×C3—26no—
384C2×C3—44no—
385C2×C3C2×#90916yescomplemented
386C2×C3C2×#94216yescomplemented
387C2×C3C23×D1211yescharacteristic
388C2×C3C23×#6711yescharacteristic
389D3—128no—
390D3—124no—
391D3—124no—
392C22—212no—
393C22—184no—
394C22—3612no—
395C22#6383314yesdirect product factor
396C22C22×#62614yes—
397C22C22×#62613yes—
398C4—68no—
399C4—184no—
400C4C22×#62614yes—
401C4C22×#62613yes—
402C4C23×D3211yescharacteristic
403C3—21no—
404C3C22×#90911yescharacteristic, complemented
405C3C22×#94211yescharacteristic, complemented
406C2—24no—
407C2—364no—
408C2C2×#6383316yesdirect product factor
409C2C23×#62611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3×Dic6C2semidirect
3. C22×C3×#208C2semidirect
4. C22×#3719C2semidirect
5. C2×#63833C2direct (N × H)
6. C22×#3717C2semidirect
20. C22×C3×Dic6C22semidirect
21. C2×C3×#208C22semidirect
23. C2×#3719C22semidirect
24. #63833C22direct (N × H)
25. C2×#3717C22semidirect
30. C23×Dic6D3semidirect
35. C22×#208D3semidirect
60. C2×C3×Dic6C23semidirect
61. C3×#208C23semidirect
63. #3719C23semidirect
64. #3717C23semidirect
96. C22×Dic6C2×D3semidirect
102. C2×#208C2×D3semidirect
194. C2×Dic6C22×D3semidirect
199. #208C22×D3semidirect
204. C22×C32#137semidirect
295. C2×C32C2×#137semidirect
330. C22×C3#909semidirect
331. C22×C3#942semidirect
356. C32C22×#137semidirect
385. C2×C3C2×#909semidirect
386. C2×C3C2×#942semidirect
395. C22#63833direct (N × H)
404. C3C22×#909semidirect
405. C3C22×#942semidirect
408. C2C2×#63833direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C23×C3×Dic62
C22×C3×#2082
C22×#37192
C2×#638332
C22×#37172
C22×#9423
C22×#9093