Finite Group Databasebeta

← C2×#10593635 #11922987

Subgroups — C2×#10593635 #11922987

Order 1152.

738 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 99 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×C4⋊(C3⋊S4)C211yesmaximal, characteristic
2C2×#64259C211yesmaximal, characteristic, complemented
3C2×C3×C8×A4C211yesmaximal, characteristic, complemented
4#10593635C214yesmaximal, direct product factor
5C2×#5401—33nomaximal
6C2×#5114—31nomaximal
7C22×C3⋊S4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3⋊SL(2,ℤ/4)—21no—
10C4⋊(C3⋊S4)—21no—
11C4⋊(C3⋊S4)C2212yes—
12#64259—21no—
13#64259C2212yescomplemented
14C2×#3744—41nomaximal
15C3×C8×A4C2212yescomplemented
16C2×C4⋊S4—33no—
17C2×A4⋊Q8—33no—
18C23×C3×C8D311yescharacteristic, complemented
19C2×#930—31no—
20C2×#924—31no—
21C22×#204—31no—
22C2×C8×A4D313yescomplemented
23#5401—312no—
24#5114—34no—
25#5114—34no—
26C2×#821—31no—
27C2×#817—31no—
28C2×#816—31no—
29C22×C3×A4D411yescharacteristic
30C2×C3⋊S4—22no—
31C2×C3⋊S4—42no—
32C2×C4⋊(C3⋊D3)—41no—
33C2×#634—41no—
34C3×C4×A4D411yescharacteristic
35C3×C4×A4C2311yescharacteristic
36C3⋊SL(2,ℤ/4)—22no—
37C2×C32×C8—41no—
38#3744—44no—
39C2×#465—91noSylow
40C22×S4—63no—
41C23×C3×C4C2×D311yescharacteristic
42C22×#67—61no—
43C22×D12—31no—
44C22×Dic6—31no—
45C2×C4×A4C2×D313yes—
46C2×SL(2,ℤ/4)—63no—
47C4⋊S4—36no—
48C4⋊S4—63no—
49A4⋊Q8—36no—
50A4⋊Q8—63no—
51C22×C3×C8—31no—
52C22×C3×C8—31no—
53C22×C3×C8—32no—
54C22×C3×C8C2×D312yescomplemented
55C2×#217—61no—
56#930—32no—
57#930—32no—
58#930—61no—
59#930—61no—
60C2×(C2×D3)⋊C4—61no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—31no—
63#924—32no—
64#924—32no—
65#924—61no—
66#924—61no—
67C2×Dic3⋊C4—61no—
68C2×#204—34no—
69C2×#204—61no—
70C2×#204—62no—
71C2×#204—61no—
72C2×#204—123no—
73C8×A4C2×D316yescomplemented
74#821—34no—
75#817—34no—
76#816—34no—
77C22×C3⋊D3—81no—
78C2×C3×A4SD1612yescomplemented
79C2×C3×A4C2×D411yescharacteristic
80C3⋊S4—42no—
81C2×C32×C4—41no—
82C2×C3⋊Dic3—81no—
83C4⋊(C3⋊D3)—42no—
84C4⋊(C3⋊D3)—81no—
85#634—42no—
86#634—81no—
87C32×C8—42no—
88C22×SD16—91no—
89C23×C8C3⋊D311yescharacteristic, complemented
90C2×C22⋊Q8—91no—
91C2×#121—91no—
92#465—94no—
93#465—94no—
94C2×#106—91no—
95C2×#103—91no—
96C2×#102—91no—
97C24×C3D1211yescharacteristic
98C23×D3—61no—
99C22×A4D1213yes—
100C2×S4—66no—
101C2×S4—126no—
102C22×C3×C4—31no—
103C22×C3×C4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—31no—
106C22×C3×C4D1211yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C2×#67—62no—
109C2×#67—62no—
110C2×#67—122no—
111C2×#67—122no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C2×D12—32no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—61no—
120C2×D12—61no—
121C2×D12—123no—
122C2×Dic6—32no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—123no—
129C4×A4D1213yes—
130C4×A4C22×D313yes—
131SL(2,ℤ/4)—66no—
132C2×C3×C8—31no—
133C2×C3×C8—32no—
134C2×C3×C8—32no—
135C2×C3×C8—32no—
136C2×C3×C8—43no—
137C2×C3×C8—61no—
138C2×C3×C8S411yescharacteristic, complemented
139#217—62no—
140#217—62no—
141(C2×D3)⋊C4—62no—
142(C2×D3)⋊C4—62no—
143C4⋊Dic3—32no—
144C4⋊Dic3—32no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149#204—64no—
150#204—64no—
151#204—1212no—
152C22×C32—41no—
153C2×C3⋊D3—82no—
154C2×C3⋊D3—162no—
155C3×A4C2×SD1611yescharacteristic, complemented
156C32×C4—41no—
157C32×C4—41no—
158C3⋊Dic3—82no—
159C22×Q8—91no—
160C22×D4—91no—
161C22×D4—181no—
162C23×C4C2×C3⋊D311yescharacteristic
163C2×SD16—94no—
164C2×SD16—181no—
165C2×SD16—182no—
166C2×SD16—181no—
167C22×C8—31no—
168C22×C8—31no—
169C22×C8—32no—
170C22×C8C2×C3⋊D312yescomplemented
171C22⋊Q8—92no—
172C22⋊Q8—92no—
173C22⋊Q8—181no—
174C22⋊Q8—181no—
175#121—92no—
176#121—92no—
177#121—181no—
178#121—181no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—91no—
181C2×C4⋊C4—181no—
182C2×C22⋊C4—181no—
183C2×C22⋊C4—181no—
184#106—94no—
185#103—94no—
186#102—94no—
187C23×C3—31no—
188C23×C3—31no—
189C23×C3—32no—
190C23×C3#20412yescomplemented
191C23×C3C2×D1211yescharacteristic
192C22×D3—62no—
193C22×D3—121no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—121no—
197C22×D3—243no—
198C2×A4#20416yescomplemented
199C2×A4C2×D1213yes—
200S4—126no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—43no—
209C2×C3×C4—61no—
210C2×C3×C4C2×S411yescharacteristic
211#67—124no—
212#67—122no—
213#67—122no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—121no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—121no—
221C2×Dic3—243no—
222D12—62no—
223D12—62no—
224D12—126no—
225D12—121no—
226D12—121no—
227D12—243no—
228Dic6—62no—
229Dic6—62no—
230Dic6—126no—
231Dic6—121no—
232Dic6—121no—
233Dic6—243no—
234C3×C8—32no—
235C3×C8—46no—
236C3×C8C2×S412yescomplemented
237C2×C32—41no—
238C2×C32—42no—
239C3⋊D3—162no—
240C24—181no—
241C24C4⋊(C3⋊D3)11yescharacteristic
242C2×Q8—92no—
243C2×Q8—181no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×D4—92no—
249C2×D4—181no—
250C2×D4—181no—
251C2×D4—181no—
252C2×D4—181no—
253C2×D4—182no—
254C2×D4—182no—
255C2×D4—181no—
256C2×D4—362no—
257C2×D4—362no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—181no—
263C22×C4—181no—
264C22×C4—181no—
265C22×C4C4⋊(C3⋊D3)11yescharacteristic
266C22×C4C22×C3⋊D311yescharacteristic
267SD16—184no—
268SD16—184no—
269C2×C8—31no—
270C2×C8—32no—
271C2×C8—32no—
272C2×C8—32no—
273C2×C8—61no—
274C2×C8C3⋊S411yescharacteristic, complemented
275C4⋊C4—92no—
276C4⋊C4—92no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C22×C3—32no—
286C22×C3—31no—
287C22×C3—31no—
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—32no—
291C22×C3—43no—
292C22×C3—61no—
293C22×C3C2×#20411yescharacteristic, complemented
294C22×C3C4⋊S411yescharacteristic
295C2×D3—122no—
296C2×D3—122no—
297C2×D3—122no—
298C2×D3—246no—
299C2×D3—242no—
300C2×D3—242no—
301C2×D3—486no—
302A4C2×#20413yescomplemented
303C3×C4—31no—
304C3×C4—31no—
305C3×C4—43no—
306C3×C4—43no—
307C3×C4C4⋊S411yescharacteristic
308C3×C4C22×S411yescharacteristic
309Dic3—122no—
310Dic3—122no—
311Dic3—122no—
312Dic3—246no—
313C32—41noSylow
314C23—31no—
315C23—31no—
316C23—32no—
317C23—182no—
318C23—361no—
319C23—362no—
320C23—362no—
321C23—361no—
322C23#374412yescomplemented
323C23C2×C4⋊(C3⋊D3)11yescharacteristic
324Q8—182no—
325Q8—182no—
326Q8—361no—
327Q8—361no—
328D4—182no—
329D4—182no—
330D4—361no—
331D4—364no—
332D4—362no—
333D4—362no—
334D4—361no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—61no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—362no—
347C2×C4—361no—
348C2×C4—362no—
349C2×C4—361no—
350C2×C4C2×C3⋊S411yescharacteristic
351C8—32no—
352C8C2×C3⋊S412yescomplemented
353C2×C3—31no—
354C2×C3—31no—
355C2×C3—32no—
356C2×C3—46no—
357C2×C3—43no—
358C2×C3#540112yescomplemented
359C2×C3C2×C4⋊S411yescharacteristic
360D3—242no—
361D3—486no—
362C22—32no—
363C22—31no—
364C22—32no—
365C22—32no—
366C22—31no—
367C22—31no—
368C22—61no—
369C22—362no—
370C22—362no—
371C22—362no—
372C22—722no—
373C22—722no—
374C22C2×#374411yescharacteristic, complemented
375C22C4⋊(C3⋊S4)11yescharacteristic
376C4—31no—
377C4—31no—
378C4—362no—
379C4—362no—
380C4—362no—
381C4C4⋊(C3⋊S4)11yescharacteristic
382C4C22×C3⋊S411yescharacteristic
383C3—43no—
384C3C2×#540111yescharacteristic, complemented
385C2—31no—
386C2—31no—
387C2—32no—
388C2—722no—
389C2#1059363512yesdirect product factor
390C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3D12
prime radicalC2×C4⋊(C3⋊S4)C2
hypercenterC2×C8C3⋊S4
hypocenterC3×A4C2×SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#64259C2semidirect
3. C2×C3×C8×A4C2semidirect
4. #10593635C2direct (N × H)
13. #64259C22semidirect
15. C3×C8×A4C22semidirect
18. C23×C3×C8D3semidirect
22. C2×C8×A4D3semidirect
54. C22×C3×C8C2×D3semidirect
73. C8×A4C2×D3semidirect
78. C2×C3×A4SD16semidirect
89. C23×C8C3⋊D3semidirect
138. C2×C3×C8S4semidirect
155. C3×A4C2×SD16semidirect
170. C22×C8C2×C3⋊D3semidirect
190. C23×C3#204semidirect
198. C2×A4#204semidirect
236. C3×C8C2×S4semidirect
274. C2×C8C3⋊S4semidirect
293. C22×C3C2×#204semidirect
302. A4C2×#204semidirect
322. C23#3744semidirect
352. C8C2×C3⋊S4semidirect
358. C2×C3#5401semidirect
374. C22C2×#3744semidirect
384. C3C2×#5401semidirect
389. C2#10593635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C2×#642592
C2×C3×C8×A42
#105936352
C2×#54013
C2×#51143
C2×#37444