Finite Group Databasebeta

← C2×#10593634 #11922985

Subgroups — C2×#10593634 #11922985

Order 1152.

738 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊S4C211yesmaximal, characteristic
2C2×C3×C8×A4C211yesmaximal, characteristic, complemented
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
4#10593634C214yesmaximal, direct product factor
5C2×#5400—33nomaximal
6C2×#5111—31nomaximal
7C22×C3⋊S4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3⋊SL(2,ℤ/4)C411yescharacteristic
10C4×C3⋊S4C412yes—
11C4×C3⋊S4C2212yes—
12C2×#3743—41nomaximal
13C3×C8×A4C2212yescomplemented
14C3⋊(A4⋊C8)C2212yescomplemented
15C2×C4×S4—33no—
16C23×C3×C8D311yescharacteristic, complemented
17C2×C4×#67—31no—
18C22×ΓL(1,𝔽25)—31no—
19C2×C8×A4D313yescomplemented
20C2×A4⋊C8—33no—
21#5400—312no—
22C2×#830—31no—
23#5111—34no—
24#5111—34no—
25C2×(C2×D3)⋊C8—31no—
26C2×#815—31no—
27C2×Dic3⋊C8—31no—
28C22×C3×A4C2×C411yescharacteristic
29C2×C3⋊S4—22no—
30C2×C3⋊S4C2×C412yes—
31C2×C4×C3⋊D3—41no—
32C3×C4×A4C2×C411yescharacteristic
33C3×C4×A4C2311yescharacteristic
34C3⋊SL(2,ℤ/4)C2×C412yes—
35C2×C32×C8—41no—
36C2×C3⋊(C3⋊C8)—41no—
37#3743—44no—
38C2×#435—91noSylow
39C22×S4—33no—
40C23×C3×C4C2×D311yescharacteristic
41C22×#67—31no—
42C22×C4×D3—31no—
43C2×C4×A4C2×D313yes—
44C2×SL(2,ℤ/4)—33no—
45C4×S4—36no—
46C4×S4—36no—
47C22×C3×C8—31no—
48C22×C3×C8—31no—
49C22×C3×C8—32no—
50C22×C3×C8C2×D312yescomplemented
51C2×#217—31no—
52C4×#67—32no—
53C4×#67—32no—
54C4×#67—32no—
55C4×#67—32no—
56C2×(C2×D3)⋊C4—31no—
57C2×Dic3⋊C4—31no—
58C2×C4×Dic3—31no—
59C22×C3⋊C8—31no—
60C22×C3⋊C8—31no—
61C2×ΓL(1,𝔽25)—34no—
62C2×ΓL(1,𝔽25)—61no—
63C2×ΓL(1,𝔽25)—62no—
64C2×ΓL(1,𝔽25)—61no—
65C2×ΓL(1,𝔽25)—123no—
66C8×A4C2×D316yescomplemented
67A4⋊C8—36no—
68#830—32no—
69#830—32no—
70(C2×D3)⋊C8—34no—
71#815—34no—
72Dic3⋊C8—34no—
73C22×C3⋊D3—41no—
74C2×C3×A4M1612yescomplemented
75C2×C3×A4C22×C411yescharacteristic
76C3⋊S4—22no—
77C2×C32×C4—41no—
78C2×C3⋊Dic3—41no—
79C4×C3⋊D3—42no—
80C4×C3⋊D3—42no—
81C32×C8—42no—
82C3⋊(C3⋊C8)—42no—
83C22×M16—91no—
84C23×C8C3⋊D311yescharacteristic, complemented
85C2×C4×D4—91no—
86#435—94no—
87#435—94no—
88C2×C4⋊C8—91no—
89C2×C22⋊C8—91no—
90C2×C22⋊C8—91no—
91C2×#97—91no—
92C24×C3C4×D311yescharacteristic
93C23×D3—31no—
94C22×A4C4×D313yes—
95C2×S4—36no—
96C2×S4—66no—
97C22×C3×C4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4C4×D311yescharacteristic
102C22×C3×C4C22×D311yescharacteristic
103C2×#67—32no—
104C2×#67—32no—
105C2×#67—62no—
106C2×#67—62no—
107C22×Dic3—31no—
108C22×Dic3—31no—
109C22×Dic3—31no—
110C2×C4×D3—32no—
111C2×C4×D3—32no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—123no—
117C4×A4C4×D313yes—
118C4×A4C22×D313yes—
119SL(2,ℤ/4)—36no—
120C2×C3×C8—31no—
121C2×C3×C8—32no—
122C2×C3×C8—32no—
123C2×C3×C8—32no—
124C2×C3×C8—43no—
125C2×C3×C8—61no—
126C2×C3×C8S411yescharacteristic, complemented
127#217—32no—
128#217—32no—
129(C2×D3)⋊C4—32no—
130(C2×D3)⋊C4—32no—
131Dic3⋊C4—32no—
132Dic3⋊C4—32no—
133C4×Dic3—32no—
134C4×Dic3—32no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—32no—
137C2×C3⋊C8—61no—
138C2×C3⋊C8—61no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8—123no—
142ΓL(1,𝔽25)—64no—
143ΓL(1,𝔽25)—64no—
144ΓL(1,𝔽25)—1212no—
145C22×C32—41no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3—82no—
148C3×A4C2×M1611yescharacteristic, complemented
149C32×C4—41no—
150C32×C4—41no—
151C3⋊Dic3—42no—
152C22×D4—91no—
153C23×C4—91no—
154C23×C4C2×C3⋊D311yescharacteristic
155C2×M16—94no—
156C2×M16—181no—
157C2×M16—182no—
158C2×M16—181no—
159C22×C8—31no—
160C22×C8—31no—
161C22×C8—32no—
162C22×C8—91no—
163C22×C8—91no—
164C22×C8C2×C3⋊D312yescomplemented
165C4×D4—92no—
166C4×D4—92no—
167C4×D4—92no—
168C4×D4—92no—
169C2×C4⋊C4—91no—
170C2×C22⋊C4—91no—
171C2×C22⋊C4—91no—
172C2×C42—91no—
173C4⋊C8—94no—
174C22⋊C8—94no—
175C22⋊C8—92no—
176C22⋊C8—92no—
177#97—94no—
178C23×C3—31no—
179C23×C3—31no—
180C23×C3—32no—
181C23×C3ΓL(1,𝔽25)12yescomplemented
182C23×C3C2×C4×D311yescharacteristic
183C22×D3—32no—
184C22×D3—61no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—61no—
188C22×D3—123no—
189C2×A4ΓL(1,𝔽25)16yescomplemented
190C2×A4C2×C4×D313yes—
191S4—66no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—31no—
196C2×C3×C4—31no—
197C2×C3×C4—31no—
198C2×C3×C4—31no—
199C2×C3×C4—43no—
200C2×C3×C4—61no—
201C2×C3×C4C2×S411yescharacteristic
202#67—64no—
203#67—62no—
204#67—62no—
205C2×Dic3—32no—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—61no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—61no—
212C2×Dic3—123no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—126no—
218C4×D3—126no—
219C3×C8—32no—
220C3×C8—46no—
221C3×C8C2×S412yescomplemented
222C3⋊C8—62no—
223C3⋊C8—62no—
224C3⋊C8—126no—
225C2×C32—41no—
226C2×C32—42no—
227C3⋊D3—82no—
228C24—91no—
229C24C4×C3⋊D311yescharacteristic
230C2×D4—92no—
231C2×D4—92no—
232C2×D4—182no—
233C2×D4—182no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4—181no—
246C22×C4—181no—
247C22×C4C4×C3⋊D311yescharacteristic
248C22×C4C22×C3⋊D311yescharacteristic
249M16—184no—
250M16—184no—
251C2×C8—31no—
252C2×C8—32no—
253C2×C8—32no—
254C2×C8—32no—
255C2×C8—61no—
256C2×C8—92no—
257C2×C8—92no—
258C2×C8—181no—
259C2×C8—181no—
260C2×C8—181no—
261C2×C8—181no—
262C2×C8C3⋊S411yescharacteristic, complemented
263C4⋊C4—92no—
264C4⋊C4—92no—
265C22⋊C4—92no—
266C22⋊C4—92no—
267C22⋊C4—92no—
268C22⋊C4—92no—
269C42—92no—
270C42—92no—
271C22×C3—32no—
272C22×C3—31no—
273C22×C3—31no—
274C22×C3—31no—
275C22×C3—32no—
276C22×C3—32no—
277C22×C3—43no—
278C22×C3—61no—
279C22×C3C2×ΓL(1,𝔽25)11yescharacteristic, complemented
280C22×C3C4×S411yescharacteristic
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—126no—
285C2×D3—122no—
286C2×D3—122no—
287C2×D3—246no—
288A4C2×ΓL(1,𝔽25)13yescomplemented
289C3×C4—31no—
290C3×C4—31no—
291C3×C4—43no—
292C3×C4—43no—
293C3×C4C4×S411yescharacteristic
294C3×C4C22×S411yescharacteristic
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—126no—
299C32—41noSylow
300C23—31no—
301C23—31no—
302C23—32no—
303C23—92no—
304C23—181no—
305C23—182no—
306C23—182no—
307C23—181no—
308C23#374312yescomplemented
309C23C2×C4×C3⋊D311yescharacteristic
310D4—184no—
311D4—182no—
312D4—182no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—31no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—61no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—182no—
325C2×C4—182no—
326C2×C4—181no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4C2×C3⋊S411yescharacteristic
333C8—32no—
334C8—182no—
335C8—182no—
336C8C2×C3⋊S412yescomplemented
337C2×C3—31no—
338C2×C3—31no—
339C2×C3—32no—
340C2×C3—46no—
341C2×C3—43no—
342C2×C3#540012yescomplemented
343C2×C3C2×C4×S411yescharacteristic
344D3—122no—
345D3—246no—
346C22—32no—
347C22—31no—
348C22—32no—
349C22—32no—
350C22—31no—
351C22—31no—
352C22—61no—
353C22—182no—
354C22—182no—
355C22—182no—
356C22—362no—
357C22—362no—
358C22C2×#374311yescharacteristic, complemented
359C22C4×C3⋊S411yescharacteristic
360C4—31no—
361C4—31no—
362C4—182no—
363C4—182no—
364C4—182no—
365C4C4×C3⋊S411yescharacteristic
366C4C22×C3⋊S411yescharacteristic
367C3—43no—
368C3C2×#540011yescharacteristic, complemented
369C2—31no—
370C2—31no—
371C2—32no—
372C2—362no—
373C2#1059363412yesdirect product factor
374C2C2×C4×C3⋊S411yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3C4×D3
prime radicalC22×C3⋊S4C4
cosocleC3×C4×A4C23
hypercenterC2×C8C3⋊S4
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×A4C2semidirect
3. C2×C3⋊(A4⋊C8)C2semidirect
4. #10593634C2direct (N × H)
13. C3×C8×A4C22semidirect
14. C3⋊(A4⋊C8)C22semidirect
16. C23×C3×C8D3semidirect
19. C2×C8×A4D3semidirect
50. C22×C3×C8C2×D3semidirect
66. C8×A4C2×D3semidirect
74. C2×C3×A4M16semidirect
84. C23×C8C3⋊D3semidirect
126. C2×C3×C8S4semidirect
148. C3×A4C2×M16semidirect
164. C22×C8C2×C3⋊D3semidirect
181. C23×C3ΓL(1,𝔽25)semidirect
189. C2×A4ΓL(1,𝔽25)semidirect
221. C3×C8C2×S4semidirect
262. C2×C8C3⋊S4semidirect
279. C22×C3C2×ΓL(1,𝔽25)semidirect
288. A4C2×ΓL(1,𝔽25)semidirect
308. C23#3743semidirect
336. C8C2×C3⋊S4semidirect
342. C2×C3#5400semidirect
358. C22C2×#3743semidirect
368. C3C2×#5400semidirect
373. C2#10593634direct (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⋊S42
C2×C3×C8×A42
C2×C3⋊(A4⋊C8)2
#105936342
C2×#54003
C2×#51113
C2×#37434