Finite Group Databasebeta

← C2×#10593651 #11923047

Subgroups — C2×#10593651 #11923047

Order 1152.

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

normal subgroups only

This group has 806 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×C3×Q8×A4C211yesmaximal, characteristic, complemented
2C2×C4⋊(C3⋊S4)C211yesmaximal, characteristic
3#10593651C214yesmaximal, direct product factor
4C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
5C2×#5417—33nomaximal
6C2×#5227—31nomaximal
7C22×C3⋊S4—21no—
8C3×Q8×A4—21no—
9C3×Q8×A4C2212yescomplemented
10C2×C3×C4×A4—21no—
11C2×C3×C4×A4C2211yescharacteristic
12C4⋊(C3⋊S4)—21no—
13C4⋊(C3⋊S4)C2212yes—
14C2×#3755—41nomaximal
15C3⋊(A4⋊C8)C2212yescomplemented
16C23×C3×Q8D311yescharacteristic, complemented
17C2×Q8×A4D313yescomplemented
18C2×C4⋊S4—33no—
19C22×#215—31no—
20C22×#215—31no—
21C2×#930—31no—
22#5417—312no—
23C2×A4⋊C8—33no—
24#5227—34no—
25#5227—34no—
26C2×#835—31no—
27C2×#835—31no—
28C2×#830—31no—
29C22×C3×A4D411yescharacteristic
30C2×C3⋊S4—22no—
31C2×C3⋊S4—42no—
32C2×C32×Q8—41no—
33C2×C4⋊(C3⋊D3)—41no—
34C3×C4×A4—22no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37#3755—44no—
38C2×C3⋊(C3⋊C8)—41no—
39C2×#448—91noSylow
40C22×S4—63no—
41C22×C3×Q8—21no—
42C22×C3×Q8—31no—
43C22×C3×Q8—31no—
44C22×C3×Q8—32no—
45C22×C3×Q8—61no—
46C22×C3×Q8—61no—
47C22×C3×Q8C2×D312yescomplemented
48C23×C3×C4—21no—
49C23×C3×C4C2×D311yescharacteristic
50C22×#67—61no—
51C22×D12—31no—
52Q8×A4—23no—
53Q8×A4C2×D316yescomplemented
54C2×C4×A4—23no—
55C2×C4×A4C2×D313yes—
56C4⋊S4—36no—
57C4⋊S4—63no—
58C2×#215—34no—
59C2×#215—34no—
60C2×#215—62no—
61C2×#215—62no—
62C2×#215—62no—
63C2×#215—61no—
64C2×#215—61no—
65C2×#215—123no—
66#930—32no—
67#930—32no—
68#930—61no—
69#930—61no—
70C2×(C2×D3)⋊C4—61no—
71C2×C4⋊Dic3—31no—
72C22×C3⋊C8—31no—
73C22×C3⋊C8—31no—
74A4⋊C8—36no—
75#835—34no—
76#835—34no—
77#830—32no—
78#830—32no—
79C22×C3⋊D3—81no—
80C2×C3×A4SD1612yescomplemented
81C2×C3×A4C2×D411yescharacteristic
82C3⋊S4—42no—
83C32×Q8—42no—
84C32×Q8—81no—
85C2×C32×C4—41no—
86C2×C32×C4—81no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—81no—
89C3⋊(C3⋊C8)—42no—
90C23×Q8C3⋊D311yescharacteristic, complemented
91C22×SD16—91no—
92C22×SD16—91no—
93C2×#121—91no—
94#448—94no—
95#448—94no—
96C2×#103—91no—
97C2×#103—91no—
98C2×C22⋊C8—91no—
99C24×C3#6711yescharacteristic
100C23×D3—61no—
101C22×A4#6713yes—
102C2×S4—66no—
103C2×S4—126no—
104C2×C3×Q8—32no—
105C2×C3×Q8—32no—
106C2×C3×Q8—32no—
107C2×C3×Q8—32no—
108C2×C3×Q8—32no—
109C2×C3×Q8—31no—
110C2×C3×Q8—43no—
111C2×C3×Q8—61no—
112C2×C3×Q8—61no—
113C2×C3×Q8—61no—
114C2×C3×Q8—62no—
115C2×C3×Q8—61no—
116C2×C3×Q8—61no—
117C2×C3×Q8—62no—
118C2×C3×Q8—64no—
119C2×C3×Q8S411yescharacteristic, complemented
120C22×C3×C4—22no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—31no—
125C22×C3×C4—61no—
126C22×C3×C4—62no—
127C22×C3×C4—61no—
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C2×#67—62no—
131C2×#67—62no—
132C2×#67—122no—
133C2×#67—122no—
134C22×Dic3—61no—
135C2×D12—32no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—123no—
142C4×A4—26no—
143C4×A4#6713yes—
144C4×A4C22×D313yes—
145#215—68no—
146#215—64no—
147#215—64no—
148#215—1212no—
149(C2×D3)⋊C4—62no—
150(C2×D3)⋊C4—62no—
151C4⋊Dic3—32no—
152C4⋊Dic3—61no—
153C2×C3⋊C8—32no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—123no—
160C22×C32—41no—
161C2×C3⋊D3—82no—
162C2×C3⋊D3—162no—
163C3×A4C2×SD1611yescharacteristic, complemented
164C32×C4—41no—
165C32×C4—41no—
166C32×C4—82no—
167C22×Q8—21no—
168C22×Q8—31no—
169C22×Q8—31no—
170C22×Q8—32no—
171C22×Q8—61no—
172C22×Q8—61no—
173C22×Q8C2×C3⋊D312yescomplemented
174C22×D4—91no—
175C22×D4—181no—
176C23×C4—21no—
177C23×C4C2×C3⋊D311yescharacteristic
178C2×SD16—94no—
179C2×SD16—94no—
180C2×SD16—182no—
181C2×SD16—182no—
182C2×SD16—182no—
183C2×SD16—181no—
184C2×SD16—181no—
185C22×C8—91no—
186C22×C8—91no—
187#121—92no—
188#121—92no—
189#121—181no—
190#121—181no—
191C2×C4⋊C4—91no—
192C2×C22⋊C4—181no—
193#103—94no—
194#103—94no—
195C22⋊C8—92no—
196C22⋊C8—92no—
197C23×C3—31no—
198C23×C3—31no—
199C23×C3—32no—
200C23×C3#21512yescomplemented
201C23×C3C2×#6711yescharacteristic
202C22×D3—62no—
203C22×D3—121no—
204C22×D3—122no—
205C22×D3—122no—
206C22×D3—121no—
207C22×D3—243no—
208C2×A4#21516yescomplemented
209C2×A4C2×#6713yes—
210S4—126no—
211C3×Q8—21no—
212C3×Q8—34no—
213C3×Q8—32no—
214C3×Q8—46no—
215C3×Q8—62no—
216C3×Q8—62no—
217C3×Q8—62no—
218C3×Q8—61no—
219C3×Q8—83no—
220C3×Q8C2×S412yescomplemented
221C2×C3×C4—21no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—43no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—61no—
233C2×C3×C4—62no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
236C2×C3×C4—83no—
237C2×C3×C4C2×S411yescharacteristic
238#67—124no—
239#67—122no—
240#67—122no—
241C2×Dic3—62no—
242C2×Dic3—122no—
243D12—62no—
244D12—62no—
245D12—126no—
246D12—121no—
247D12—121no—
248D12—243no—
249C3⋊C8—62no—
250C3⋊C8—62no—
251C3⋊C8—126no—
252C2×C32—42no—
253C2×C32—41no—
254C3⋊D3—162no—
255C24—181no—
256C24#63811yescharacteristic
257C2×Q8—32no—
258C2×Q8—32no—
259C2×Q8—32no—
260C2×Q8—32no—
261C2×Q8—32no—
262C2×Q8—31no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—61no—
266C2×Q8—62no—
267C2×Q8—61no—
268C2×Q8—61no—
269C2×Q8—62no—
270C2×Q8—64no—
271C2×Q8C3⋊S411yescharacteristic, complemented
272C2×D4—92no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4—181no—
277C2×D4—182no—
278C2×D4—182no—
279C2×D4—181no—
280C2×D4—362no—
281C2×D4—362no—
282C22×C4—22no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—61no—
288C22×C4—62no—
289C22×C4—61no—
290C22×C4—181no—
291C22×C4#63811yescharacteristic
292C22×C4C22×C3⋊D311yescharacteristic
293SD16—188no—
294SD16—184no—
295SD16—184no—
296C2×C8—92no—
297C2×C8—92no—
298C2×C8—181no—
299C2×C8—181no—
300C2×C8—181no—
301C2×C8—181no—
302C4⋊C4—92no—
303C4⋊C4—181no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C22×C3—32no—
307C22×C3—31no—
308C22×C3—32no—
309C22×C3—32no—
310C22×C3—31no—
311C22×C3—31no—
312C22×C3—43no—
313C22×C3—61no—
314C22×C3C2×#21511yescharacteristic, complemented
315C22×C3GL(2,ℤ/4)11yescharacteristic
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—246no—
320C2×D3—242no—
321C2×D3—242no—
322C2×D3—486no—
323A4C2×#21513yescomplemented
324C3×C4—22no—
325C3×C4—31no—
326C3×C4—31no—
327C3×C4—43no—
328C3×C4—43no—
329C3×C4—62no—
330C3×C4—86no—
331C3×C4GL(2,ℤ/4)11yescharacteristic
332C3×C4C22×S411yescharacteristic
333Dic3—122no—
334C32—41noSylow
335C23—31no—
336C23—31no—
337C23—32no—
338C23—182no—
339C23—361no—
340C23—362no—
341C23—362no—
342C23—361no—
343C23#375512yescomplemented
344C23C2×#63811yescharacteristic
345Q8—21no—
346Q8—34no—
347Q8—32no—
348Q8—62no—
349Q8—62no—
350Q8—62no—
351Q8—61no—
352Q8C2×C3⋊S412yescomplemented
353D4—182no—
354D4—182no—
355D4—361no—
356D4—364no—
357D4—362no—
358D4—362no—
359D4—361no—
360C2×C4—21no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—61no—
371C2×C4—62no—
372C2×C4—61no—
373C2×C4—62no—
374C2×C4—182no—
375C2×C4—362no—
376C2×C4C2×C3⋊S411yescharacteristic
377C8—182no—
378C8—182no—
379C2×C3—31no—
380C2×C3—31no—
381C2×C3—32no—
382C2×C3—46no—
383C2×C3—43no—
384C2×C3#541712yescomplemented
385C2×C3C2×GL(2,ℤ/4)11yescharacteristic
386D3—242no—
387D3—486no—
388C22—32no—
389C22—31no—
390C22—32no—
391C22—32no—
392C22—31no—
393C22—31no—
394C22—61no—
395C22—362no—
396C22—362no—
397C22—362no—
398C22—722no—
399C22—722no—
400C22C2×#375511yescharacteristic, complemented
401C22#6426911yescharacteristic
402C4—22no—
403C4—31no—
404C4—31no—
405C4—62no—
406C4—362no—
407C4#6426911yescharacteristic
408C4C22×C3⋊S411yescharacteristic
409C3—43no—
410C3C2×#541711yescharacteristic, complemented
411C2—31no—
412C2—31no—
413C2—32no—
414C2—722no—
415C2#1059365112yesdirect product factor
416C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×Q8D3
socleC24×C3#67
prime radicalC2×C4⋊(C3⋊S4)C2
hypercenterC2×Q8C3⋊S4
hypocenterC3×A4C2×SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
3. #10593651C2direct (N × H)
4. C2×C3⋊(A4⋊C8)C2semidirect
9. C3×Q8×A4C22semidirect
15. C3⋊(A4⋊C8)C22semidirect
16. C23×C3×Q8D3semidirect
17. C2×Q8×A4D3semidirect
47. C22×C3×Q8C2×D3semidirect
53. Q8×A4C2×D3semidirect
80. C2×C3×A4SD16semidirect
90. C23×Q8C3⋊D3semidirect
119. C2×C3×Q8S4semidirect
163. C3×A4C2×SD16semidirect
173. C22×Q8C2×C3⋊D3semidirect
200. C23×C3#215semidirect
208. C2×A4#215semidirect
220. C3×Q8C2×S4semidirect
271. C2×Q8C3⋊S4semidirect
314. C22×C3C2×#215semidirect
323. A4C2×#215semidirect
343. C23#3755semidirect
352. Q8C2×C3⋊S4semidirect
384. C2×C3#5417semidirect
400. C22C2×#3755semidirect
410. C3C2×#5417semidirect
415. C2#10593651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C2×C4⋊(C3⋊S4)2
#105936512
C2×C3⋊(A4⋊C8)2
C2×#54173
C2×#52273
C2×#37554