Finite Group Databasebeta

← C2×#10595394 #11900104

Subgroups — C2×#10595394 #11900104

Order 1152.

3429 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595394C2116yesmaximal, direct product factor
5C2×#63898C213yesmaximal, complemented
6C2×Dic3×D12C213yesmaximal, complemented
7C2×D3×C4⋊Dic3C213yesmaximal, complemented
8C2×#63855C213yesmaximal, complemented
9C2×#5827—31nomaximal
10C2×#5574—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239C4116yescomplemented
13C2×C3×#239C2218yes—
14C22×C3×D12C2213yes—
15C22×C3×C4×D3C2213yes—
16C22×D3×Dic3C2216yes—
17Q8×C3⋊Dic3C2218yescomplemented
18C2×C4⋊(C3⋊Dic3)C2213yes—
19C2×C4×C3⋊Dic3C2213yes—
20C3×Q8×Dic3C2218yescomplemented
21C2×C3×C4⋊Dic3C2213yes—
22C2×C3×C4×Dic3C2213yes—
23C2×Dic3⋊Dic3C2211yescharacteristic
24C2×Dic3⋊Dic3C2213yes—
25C2×(C2×D3)⋊Dic3C2213yes—
26C2×(C2×D3)⋊Dic3C2213yes—
27#63898C22124yescomplemented
28Dic3×D12C22124yescomplemented
29D3×C4⋊Dic3C22124yescomplemented
30#63855C22124yescomplemented
31C22×C3×#41—31no—
32C22×#239D311yescharacteristic
33C2×C3×C4×Q8—31no—
34#5827—316no—
35C2×Q8×Dic3—31no—
36C2×Q8×Dic3—31no—
37C2×Q8×Dic3—61no—
38C2×Q8×Dic3D311yescharacteristic, complemented
39C2×D4×Dic3—33no—
40C2×D4×Dic3—33no—
41C2×#926—33no—
42C22×C4⋊Dic3—33no—
43#5574—316no—
44C2×#893—33no—
45C2×D3×C4⋊C4—33no—
46C2×C4×D12—33no—
47C2×#872—33no—
48C23×C3×D3C2313yes—
49C2×C32×Q8C2×C418yescomplemented
50C2×C32×Q8C2314yes—
51C22×C32×C4C2313yes—
52C22×C3⋊Dic3C2313yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3×Dic3C2311yescharacteristic
55C22×C3×Dic3C2313yes—
56C22×C3×Dic3C2311yescharacteristic
57C3×#239C2×C4164yescomplemented
58C2×C3×D12C2×C4124yescomplemented
59C2×C3×D12C23112yes—
60C2×C3×C4×D3C2×C4124yescomplemented
61C2×C3×C4×D3C23112yes—
62C2×D3×Dic3—412no—
63C2×D3×Dic3C23124yes—
64C4⋊(C3⋊Dic3)C23112yes—
65C4×C3⋊Dic3C23112yes—
66C3×C4⋊Dic3C23112yes—
67C3×C4×Dic3C23112yes—
68Dic3⋊Dic3C2314yes—
69Dic3⋊Dic3C23112yes—
70(C2×D3)⋊Dic3C23112yes—
71(C2×D3)⋊Dic3C23112yes—
72C2×#520—91noSylow
73C2×C3×#41—316no—
74C2×C3×#41—38no—
75C22×C3×Q8—21no—
76C22×C3×Q8C2×D311yescharacteristic
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×D4—33no—
79C23×C3×C4—33no—
80C23×Dic3—36no—
81C2×#239Dic3116yescomplemented
82C2×#239C2×D318yes—
83C22×D12C2×D313yes—
84C22×C4×D3—36no—
85C22×C4×D3C2×D313yes—
86C3×C4×Q8—38no—
87C2×C3×C4⋊C4—33no—
88C2×C3×C42—33no—
89C2×#217—33no—
90C2×#217—33no—
91Q8×Dic3—38no—
92Q8×Dic3—38no—
93Q8×Dic3—68no—
94Q8×Dic3C2×D318yescomplemented
95D4×Dic3—324no—
96D4×Dic3—324no—
97C2×(C2×D3)⋊C4—33no—
98C2×(C2×D3)⋊C4—33no—
99#926—324no—
100C2×C4⋊Dic3—33no—
101C2×C4⋊Dic3—33no—
102C2×C4⋊Dic3—33no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—324no—
105C2×C4⋊Dic3—63no—
106C2×C4⋊Dic3C2×D313yes—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—33no—
109C2×C4×Dic3—33no—
110C2×C4×Dic3—33no—
111C2×C4×Dic3—63no—
112C2×C4×Dic3C2×D313yes—
113#893—324no—
114D3×C4⋊C4—324no—
115C4×D12—324no—
116#872—324no—
117C23×C32C2411yescharacteristic
118C22×C3×D3—26no—
119C22×C3×D3—26no—
120C22×C3×D3C22×C4112yes—
121C22×C3×D3C2416yes—
122C32×Q8C22×C4116yescomplemented
123C2×C32×C4C22×C4112yes—
124C2×C32×C4C2416yes—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—26no—
127C2×C3⋊Dic3C2412yes—
128C2×C3⋊Dic3C2416yes—
129C2×C3×Dic3—26no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C22×C414yes—
132C2×C3×Dic3C2412yes—
133C2×C3×Dic3C2416yes—
134C2×C3×Dic3C2412yes—
135C3×D12C22×C4148yescomplemented
136C3×C4×D3C22×C4148yescomplemented
137D3×Dic3—424no—
138C22×#41—31no—
139#520—916no—
140C2×C4×Q8—31no—
141C2×C4×Q8—91no—
142C2×C4×D4—93no—
143C2×C4×D4—93no—
144C2×#117—93no—
145C22×C4⋊C4—93no—
146C24×C3—33no—
147C23×D3C22×D313yes—
148C3×#41—364no—
149C2×C3×Q8—28no—
150C2×C3×Q8—24no—
151C2×C3×Q8C4×D318yescomplemented
152C2×C3×Q8C2×Dic318yescomplemented
153C2×C3×Q8C22×D314yes—
154C2×C3×Q8C22×D314yes—
155C2×C3×D4—324no—
156C2×C3×D4—312no—
157C22×C3×C4—23no—
158C22×C3×C4—31no—
159C22×C3×C4—324no—
160C22×C3×C4—312no—
161C22×C3×C4—31no—
162C22×C3×C4—33no—
163C22×C3×C4C22×D313yes—
164C22×C3×C4C22×D313yes—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—33no—
168C22×Dic3—33no—
169C22×Dic3—324no—
170C22×Dic3—61no—
171C22×Dic3—63no—
172C22×Dic3—1212no—
173C22×Dic3C22×D311yescharacteristic
174C22×Dic3C22×D313yes—
175C22×Dic3C22×D311yescharacteristic
176#239C2×Dic3164yescomplemented
177C2×D12C2×Dic3124yescomplemented
178C2×D12C22×D3112yes—
179C2×C4×D3—324no—
180C2×C4×D3—1212no—
181C2×C4×D3C2×Dic3124yescomplemented
182C2×C4×D3C22×D3112yes—
183C3×C4⋊C4—312no—
184C3×C42—312no—
185#217—312no—
186#217—312no—
187(C2×D3)⋊C4—312no—
188(C2×D3)⋊C4—312no—
189C4⋊Dic3—312no—
190C4⋊Dic3—312no—
191C4⋊Dic3—312no—
192C4⋊Dic3—34no—
193C4⋊Dic3—612no—
194C4⋊Dic3C22×D3112yes—
195Dic3⋊C4—34no—
196Dic3⋊C4—312no—
197C4×Dic3—312no—
198C4×Dic3—312no—
199C4×Dic3—612no—
200C4×Dic3C22×D3112yes—
201C22×C32C23×C412yes—
202C22×C32H(5,𝔽2)12yes—
203C22×C322−1+412yes—
204C22×C32C2511yescharacteristic
205C2×C3×D3—224no—
206C2×C3×D3—26no—
207C2×C3×D3—26no—
208C2×C3×D3C23×C4112yes—
209C32×C4C23×C4112yes—
210C3⋊Dic3—22no—
211C3⋊Dic3—26no—
212C3×Dic3—26no—
213C3×Dic3—22no—
214C3×Dic3C23×C414yes—
215C2×#41—316no—
216C2×#41—38no—
217C22×Q8D3211yescharacteristic
218C22×D4—33no—
219C23×C4—33no—
220C23×C4—96no—
221C4×Q8—38no—
222C4×Q8—98no—
223C4×D4—924no—
224C4×D4—924no—
225#117—924no—
226C2×C4⋊C4—33no—
227C2×C4⋊C4—924no—
228C2×C4⋊C4—93no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—93no—
231C2×C22⋊C4—93no—
232C2×C22⋊C4—93no—
233C2×C42—33no—
234C2×C42—93no—
235C23×C3—21no—
236C23×C3—312no—
237C23×C3—36no—
238C23×C3—66no—
239C23×C3—66no—
240C23×C3C23×D311yescharacteristic
241C23×C3C23×D311yescharacteristic
242C22×D3—26no—
243C22×D3—26no—
244C22×D3C22×Dic3112yes—
245C22×D3C23×D316yes—
246C3×Q8—216no—
247C3×Q8C2×C4×D3116yescomplemented
248C3×Q8C22×Dic3116yescomplemented
249C3×D4—348no—
250C2×C3×C4—26no—
251C2×C3×C4—212no—
252C2×C3×C4—34no—
253C2×C3×C4—32no—
254C2×C3×C4—348no—
255C2×C3×C4—32no—
256C2×C3×C4—36no—
257C2×C3×C4—66no—
258C2×C3×C4—62no—
259C2×C3×C4C2×C4×D3112yes—
260C2×C3×C4C22×Dic3112yes—
261C2×C3×C4C23×D316yes—
262C2×C3×C4C23×D316yes—
263C2×Dic3—22no—
264C2×Dic3—26no—
265C2×Dic3—32no—
266C2×Dic3—32no—
267C2×Dic3—36no—
268C2×Dic3—36no—
269C2×Dic3—62no—
270C2×Dic3—66no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—66no—
274C2×Dic3—66no—
275C2×Dic3—62no—
276C2×Dic3—126no—
277C2×Dic3—1224no—
278C2×Dic3C22×Dic314yes—
279C2×Dic3C23×D312yes—
280C2×Dic3C23×D316yes—
281C2×Dic3C23×D312yes—
282D12C22×Dic3148yescomplemented
283C4×D3—1224no—
284C4×D3C22×Dic3148yescomplemented
285C2×C32#52014yescomplemented
286C2×C32C24×C411yescharacteristic
287C2×C32C2×H(5,𝔽2)11yescharacteristic
288C2×C32C2×2−1+411yescharacteristic
289C3×D3—212no—
290C24—33no—
291#41—364no—
292C2×Q8D3×Dic318yescomplemented
293C2×Q8C2×D3214yes—
294C2×D4—312no—
295C2×D4—324no—
296C22×C4—31no—
297C22×C4—312no—
298C22×C4—324no—
299C22×C4—31no—
300C22×C4—33no—
301C22×C4—924no—
302C22×C4—91no—
303C22×C4—93no—
304C22×C4—3612no—
305C22×C4C2×D3213yes—
306C4⋊C4—312no—
307C4⋊C4—912no—
308C4⋊C4—94no—
309C4⋊C4—912no—
310C22⋊C4—912no—
311C22⋊C4—912no—
312C42—312no—
313C42—912no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3—312no—
319C22×C3—66no—
320C22×C3—66no—
321C22×C3—624no—
322C22×C3C22×C4×D312yes—
323C22×C3#100712yes—
324C22×C3#100912yes—
325C22×C3#100912yes—
326C22×C3#101012yes—
327C22×C3C23×Dic312yes—
328C22×C3C24×D311yescharacteristic
329C22×C3C24×D311yescharacteristic
330C2×D3—26no—
331C2×D3—26no—
332C2×D3—224no—
333C2×D3C23×Dic3112yes—
334C3×C4—212no—
335C3×C4—34no—
336C3×C4—66no—
337C3×C4—62no—
338C3×C4C22×C4×D3112yes—
339C3×C4C23×Dic3112yes—
340Dic3—22no—
341Dic3—26no—
342Dic3—64no—
343Dic3—62no—
344Dic3—66no—
345Dic3—66no—
346Dic3—62no—
347Dic3—126no—
348Dic3C23×Dic314yes—
349C32C2×#52011yescharacteristic, complemented, Sylow
350C23—312no—
351C23—36no—
352C23—66no—
353C23—66no—
354C23C22×D3211yescharacteristic
355Q8C2×D3×Dic3116yescomplemented
356D4—348no—
357C2×C4—34no—
358C2×C4—32no—
359C2×C4—348no—
360C2×C4—32no—
361C2×C4—36no—
362C2×C4—62no—
363C2×C4—66no—
364C2×C4—92no—
365C2×C4—96no—
366C2×C4—182no—
367C2×C4—186no—
368C2×C4—3624no—
369C2×C4C2×D3×Dic3112yes—
370C2×C4C22×D3216yes—
371C2×C3—24no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—612no—
376C2×C3#557414yescomplemented
377C2×C3#582714yescomplemented
378C2×C3C23×C4×D311yescharacteristic
379C2×C3C2×#100711yescharacteristic
380C2×C3C2×#100911yescharacteristic
381C2×C3C2×#100911yescharacteristic
382C2×C3C2×#101011yescharacteristic
383C2×C3C24×Dic311yescharacteristic
384D3—212no—
385C22—312no—
386C22—624no—
387C22—66no—
388C22—66no—
389C22#6431512yes—
390C22#6432012yes—
391C22C22×D3×Dic312yes—
392C22C23×D3211yescharacteristic
393C4—34no—
394C4—62no—
395C4—66no—
396C4—182no—
397C4—186no—
398C4C22×D3×Dic3112yes—
399C3—21no—
400C3C2×#557411yescharacteristic, complemented
401C3C2×#582711yescharacteristic, complemented
402C2—612no—
403C2#1059539414yesdirect product factor
404C2C2×#6431511yescharacteristic
405C2C2×#6432011yescharacteristic
406C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×C3×#239C2
cosocleC22×C32C25
hypercenterC22×Q8D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C3⋊Dic3C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595394C2direct (N × H)
5. C2×#63898C2semidirect
6. C2×Dic3×D12C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63855C2semidirect
12. C2×C3×#239C4semidirect
17. Q8×C3⋊Dic3C22semidirect
20. C3×Q8×Dic3C22semidirect
27. #63898C22semidirect
28. Dic3×D12C22semidirect
29. D3×C4⋊Dic3C22semidirect
30. #63855C22semidirect
38. C2×Q8×Dic3D3semidirect
49. C2×C32×Q8C2×C4semidirect
57. C3×#239C2×C4semidirect
58. C2×C3×D12C2×C4semidirect
60. C2×C3×C4×D3C2×C4semidirect
81. C2×#239Dic3semidirect
94. Q8×Dic3C2×D3semidirect
122. C32×Q8C22×C4semidirect
135. C3×D12C22×C4semidirect
136. C3×C4×D3C22×C4semidirect
151. C2×C3×Q8C4×D3semidirect
152. C2×C3×Q8C2×Dic3semidirect
176. #239C2×Dic3semidirect
177. C2×D12C2×Dic3semidirect
181. C2×C4×D3C2×Dic3semidirect
247. C3×Q8C2×C4×D3semidirect
248. C3×Q8C22×Dic3semidirect
282. D12C22×Dic3semidirect
284. C4×D3C22×Dic3semidirect
285. C2×C32#520semidirect
292. C2×Q8D3×Dic3semidirect
349. C32C2×#520semidirect
355. Q8C2×D3×Dic3semidirect
376. C2×C3#5574semidirect
377. C2×C3#5827semidirect
400. C3C2×#5574semidirect
401. C3C2×#5827semidirect
403. C2#10595394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×Q8×C3⋊Dic32
C2×C3×Q8×Dic32
#105953942
C2×#638982
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×#638552
C2×#58273
C2×#55743