Finite Group Databasebeta

← C2×#10593175 #11921865

Subgroups — C2×#10593175 #11921865

Order 1152.

624 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×S4C211yesmaximal, characteristic
2C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
4#10593175C214yesmaximal, direct product factor
5C2×#5400—31nomaximal
6C2×#5011—31nomaximal
7C22×C3×S4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3×SL(2,ℤ/4)C411yescharacteristic
10C3×C4×S4C412yes—
11C3×C4×S4C2212yes—
12C2×#3711—41nomaximal
13A4×C3⋊C8C2212yescomplemented
14C3⋊(A4⋊C8)C2212yescomplemented
15C2×C4×S4D311yescharacteristic
16C2×C3×C4×D4—31no—
17C22×#208—31no—
18C23×C3⋊C8D311yescharacteristic, complemented
19C2×C8×A4—31no—
20C2×A4⋊C8—31no—
21C2×A4⋊C8—61no—
22#5400—34no—
23C2×#830—31no—
24C2×#830—31no—
25#5011—34no—
26#5011—34no—
27C2×C4⋊(C3⋊C8)—31no—
28C2×#803—31no—
29C22×C3×A4C2×C411yescharacteristic
30C2×C3×S4—22no—
31C2×C3×S4C2×C412yes—
32C2×C3×C4×D3—41no—
33C3×C4×A4C2×C411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35C3×SL(2,ℤ/4)C2×C412yes—
36C2×C3⋊(C3⋊C8)—41no—
37C2×C3×C3⋊C8—41no—
38#3711—44no—
39C2×#435—91noSylow
40C22×S4Dic311yescharacteristic
41C22×C3×D4—31no—
42C23×C3×C4—31no—
43C23×C3×C4C2×D311yescharacteristic
44C2×C4×A4—21no—
45C2×C4×A4C2×D311yescharacteristic
46C2×SL(2,ℤ/4)Dic311yescharacteristic
47C4×S4Dic312yes—
48C4×S4C2×D312yes—
49C3×C4×D4—32no—
50C3×C4×D4—32no—
51C3×C4×D4—32no—
52C3×C4×D4—32no—
53C2×C3×C4⋊C4—31no—
54C2×C3×C22⋊C4—31no—
55C2×C3×C22⋊C4—31no—
56C2×C3×C42—31no—
57C2×#208—34no—
58C2×#208—61no—
59C2×#208—62no—
60C2×#208—61no—
61C22×C3⋊C8—31no—
62C22×C3⋊C8—31no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—31no—
65C22×C3⋊C8—31no—
66C22×C3⋊C8C2×D312yescomplemented
67C2×ΓL(1,𝔽25)—121no—
68C8×A4—32no—
69A4⋊C8—32no—
70A4⋊C8—62no—
71#830—34no—
72#830—32no—
73#830—32no—
74C4⋊(C3⋊C8)—34no—
75#803—34no—
76C22×C3×D3—41no—
77C2×C3×A4M1612yescomplemented
78C2×C3×A4C22×C411yescharacteristic
79C3×S4—22no—
80C2×C32×C4—41no—
81C2×C3×Dic3—41no—
82C3×C4×D3—42no—
83C3×C4×D3—42no—
84C3⋊(C3⋊C8)—42no—
85C3×C3⋊C8—42no—
86C22×M16—91no—
87C23×C8—31no—
88C2×C4×D4—31no—
89#435—94no—
90#435—94no—
91C2×C4⋊C8—91no—
92C2×C22⋊C8—91no—
93C2×C22⋊C8—91no—
94C2×#97—91no—
95C24×C3—31no—
96C24×C3C4×D311yescharacteristic
97C22×A4—21no—
98C22×A4C2×Dic311yescharacteristic
99C2×S4—22no—
100C2×S4C2×Dic312yes—
101C2×C3×D4—32no—
102C2×C3×D4—32no—
103C2×C3×D4—62no—
104C2×C3×D4—62no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—32no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—32no—
114C22×C3×C4—61no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4C4×D311yescharacteristic
119C22×C3×C4C22×D311yescharacteristic
120C2×C4×D3—41no—
121C4×A4—21no—
122C4×A4—21no—
123C4×A4C2×Dic311yescharacteristic
124C4×A4C22×D311yescharacteristic
125SL(2,ℤ/4)C2×Dic312yes—
126C2×C3×C8—121no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4—32no—
129C3×C22⋊C4—32no—
130C3×C22⋊C4—32no—
131C3×C22⋊C4—32no—
132C3×C22⋊C4—32no—
133C3×C42—32no—
134C3×C42—32no—
135#208—64no—
136#208—64no—
137C2×C3⋊C8—31no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—32no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—32no—
143C2×C3⋊C8—61no—
144C2×C3⋊C8—61no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—121no—
149C2×C3⋊C8—241no—
150C2×C3⋊C8S411yescharacteristic, complemented
151ΓL(1,𝔽25)—124no—
152C22×C32—41no—
153C2×C3×D3—42no—
154C2×C3×D3—82no—
155C3×A4C2×M1611yescharacteristic, complemented
156C32×C4—41no—
157C32×C4—41no—
158C3×Dic3—42no—
159C22×D4—31no—
160C23×C4—31no—
161C23×C4D3211yescharacteristic
162C2×M16—94no—
163C2×M16—181no—
164C2×M16—182no—
165C2×M16—181no—
166C22×C8—32no—
167C22×C8—91no—
168C22×C8—91no—
169C22×C8—92no—
170C22×C8—91no—
171C22×C8—91no—
172C4×D4—32no—
173C4×D4—32no—
174C4×D4—32no—
175C4×D4—32no—
176C2×C4⋊C4—31no—
177C2×C22⋊C4—31no—
178C2×C22⋊C4—31no—
179C2×C42—31no—
180C4⋊C8—94no—
181C22⋊C8—94no—
182C22⋊C8—92no—
183C22⋊C8—92no—
184#97—94no—
185C23×C3—31no—
186C23×C3—31no—
187C23×C3—32no—
188C23×C3—32no—
189C23×C3—61no—
190C23×C3—62no—
191C23×C3—62no—
192C23×C3—61no—
193C23×C3ΓL(1,𝔽25)12yescomplemented
194C23×C3C2×C4×D311yescharacteristic
195C22×D3—41no—
196C2×A4—22no—
197C2×A4—21no—
198C2×A4#20812yescomplemented
199C2×A4C22×Dic311yescharacteristic
200S4—22no—
201C3×D4—64no—
202C3×D4—62no—
203C3×D4—62no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—32no—
212C2×C3×C4—32no—
213C2×C3×C4—32no—
214C2×C3×C4—41no—
215C2×C3×C4—61no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—61no—
220C2×C3×C4—62no—
221C2×C3×C4—61no—
222C2×C3×C4—62no—
223C2×C3×C4—62no—
224C2×C3×C4—81no—
225C2×C3×C4C2×S411yescharacteristic
226C2×Dic3—41no—
227C4×D3—42no—
228C4×D3—42no—
229C3×C8—122no—
230C3⋊C8—32no—
231C3⋊C8—62no—
232C3⋊C8—62no—
233C3⋊C8—122no—
234C3⋊C8—242no—
235C3⋊C8C2×S412yescomplemented
236C2×C32—41no—
237C2×C32—42no—
238C3×D3—82no—
239C24—31no—
240C24D3×Dic311yescharacteristic
241C2×D4—32no—
242C2×D4—32no—
243C2×D4—62no—
244C2×D4—62no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—32no—
254C22×C4—61no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4D3×Dic311yescharacteristic
259C22×C4C2×D3211yescharacteristic
260M16—184no—
261M16—184no—
262C2×C8—31no—
263C2×C8—92no—
264C2×C8—92no—
265C2×C8—91no—
266C2×C8—92no—
267C2×C8—92no—
268C2×C8—92no—
269C2×C8—181no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8—181no—
273C2×C8—181no—
274C4⋊C4—32no—
275C4⋊C4—32no—
276C22⋊C4—32no—
277C22⋊C4—32no—
278C22⋊C4—32no—
279C22⋊C4—32no—
280C42—32no—
281C42—32no—
282C22×C3—32no—
283C22×C3—31no—
284C22×C3—31no—
285C22×C3—31no—
286C22×C3—32no—
287C22×C3—32no—
288C22×C3—41no—
289C22×C3—61no—
290C22×C3—62no—
291C22×C3—62no—
292C22×C3—62no—
293C22×C3—81no—
294C22×C3—122no—
295C22×C3—122no—
296C22×C3C2×ΓL(1,𝔽25)11yescharacteristic, complemented
297C22×C3C4×S411yescharacteristic
298C2×D3—42no—
299C2×D3—82no—
300A4—21no—
301A4C2×#20811yescharacteristic, complemented
302C3×C4—31no—
303C3×C4—31no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—62no—
307C3×C4—62no—
308C3×C4—62no—
309C3×C4—81no—
310C3×C4—81no—
311C3×C4C4×S411yescharacteristic
312C3×C4C22×S411yescharacteristic
313Dic3—42no—
314C32—41noSylow
315C23—31no—
316C23—31no—
317C23—32no—
318C23—32no—
319C23—61no—
320C23—62no—
321C23—62no—
322C23—61no—
323C23#371112yescomplemented
324C23C2×D3×Dic311yescharacteristic
325D4—64no—
326D4—62no—
327D4—62no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—61no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—61no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4D3×S411yescharacteristic
348C8—32no—
349C8—92no—
350C8—182no—
351C8—182no—
352C2×C3—31no—
353C2×C3—31no—
354C2×C3—32no—
355C2×C3—41no—
356C2×C3—42no—
357C2×C3—81no—
358C2×C3—82no—
359C2×C3—122no—
360C2×C3#540012yescomplemented
361C2×C3C2×C4×S411yescharacteristic
362D3—82no—
363C22—32no—
364C22—31no—
365C22—31no—
366C22—31no—
367C22—32no—
368C22—32no—
369C22—61no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—122no—
374C22—122no—
375C22C2×#371111yescharacteristic, complemented
376C22Dic3×S411yescharacteristic
377C4—31no—
378C4—31no—
379C4—62no—
380C4—62no—
381C4—62no—
382C4Dic3×S411yescharacteristic
383C4C2×D3×S411yescharacteristic
384C3—41no—
385C3—81no—
386C3C2×#540011yescharacteristic, complemented
387C2—31no—
388C2—31no—
389C2—32no—
390C2—122no—
391C2#1059317512yesdirect product factor
392C2C2×Dic3×S411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutatorC2×C3×A4C22×C4
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3C4×D3
prime radicalC22×C3×S4C4
cosocleC3×C4×A4C23
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×C3⋊C8C2semidirect
3. C2×C3⋊(A4⋊C8)C2semidirect
4. #10593175C2direct (N × H)
13. A4×C3⋊C8C22semidirect
14. C3⋊(A4⋊C8)C22semidirect
18. C23×C3⋊C8D3semidirect
66. C22×C3⋊C8C2×D3semidirect
77. C2×C3×A4M16semidirect
150. C2×C3⋊C8S4semidirect
155. C3×A4C2×M16semidirect
193. C23×C3ΓL(1,𝔽25)semidirect
198. C2×A4#208semidirect
235. C3⋊C8C2×S4semidirect
296. C22×C3C2×ΓL(1,𝔽25)semidirect
301. A4C2×#208semidirect
323. C23#3711semidirect
360. C2×C3#5400semidirect
375. C22C2×#3711semidirect
386. C3C2×#5400semidirect
391. C2#10593175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×S42
C2×A4×C3⋊C82
C2×C3⋊(A4⋊C8)2
#105931752
C2×#54003
C2×#50113
C2×#37114