Finite Group Databasebeta

← C2×#10593650 #11923046

Subgroups — C2×#10593650 #11923046

Order 1152.

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

normal subgroups only

This group has 722 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
2C2×#64259C211yesmaximal, characteristic
3#10593650C214yesmaximal, direct product factor
4C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
5C2×#5416—33nomaximal
6C2×#5228—31nomaximal
7C3×Q8×A4—21no—
8C3×Q8×A4C2212yes—
9C2×C3×C4×A4—21no—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)—21no—
12#64259—21no—
13#64259C2212yes—
14C2×#3756—41nomaximal
15C3⋊(A4⋊C8)C2212yes—
16C23×C3×Q8D311yescharacteristic
17C2×Q8×A4D313yes—
18C2×A4⋊Q8—33no—
19C22×#216—31no—
20C22×#216—31no—
21C2×#924—31no—
22#5416—312no—
23C2×A4⋊C8—33no—
24#5228—34no—
25#5228—34no—
26C2×#835—31no—
27C2×#835—31no—
28C2×#830—31no—
29C22×C3×A4D411yescharacteristic
30C2×C32×Q8—41no—
31C2×#634—41no—
32C3×C4×A4—22no—
33C3×C4×A4D411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35C3⋊SL(2,ℤ/4)—22no—
36#3756—44no—
37C2×C3⋊(C3⋊C8)—41no—
38C2×#451—91noSylow
39C22×C3×Q8—21no—
40C22×C3×Q8—31no—
41C22×C3×Q8—31no—
42C22×C3×Q8—32no—
43C22×C3×Q8—61no—
44C22×C3×Q8—61no—
45C22×C3×Q8C2×D312yes—
46C23×C3×C4—21no—
47C23×C3×C4C2×D311yescharacteristic
48C22×Dic6—31no—
49Q8×A4—23no—
50Q8×A4C2×D316yes—
51C2×C4×A4—23no—
52C2×C4×A4C2×D313yes—
53C2×SL(2,ℤ/4)—63no—
54A4⋊Q8—36no—
55A4⋊Q8—63no—
56C2×#217—61no—
57C2×#216—34no—
58C2×#216—34no—
59C2×#216—62no—
60C2×#216—62no—
61C2×#216—62no—
62C2×#216—61no—
63C2×#216—61no—
64C2×#216—123no—
65C2×C4⋊Dic3—31no—
66#924—32no—
67#924—32no—
68#924—61no—
69#924—61no—
70C2×Dic3⋊C4—61no—
71C22×C3⋊C8—31no—
72C22×C3⋊C8—31no—
73A4⋊C8—36no—
74#835—34no—
75#835—34no—
76#830—32no—
77#830—32no—
78C2×C3×A4Q1612yescomplemented
79C2×C3×A4C2×D411yescharacteristic
80C32×Q8—42no—
81C32×Q8—81no—
82C2×C32×C4—41no—
83C2×C32×C4—81no—
84C2×C3⋊Dic3—81no—
85#634—42no—
86#634—81no—
87C3⋊(C3⋊C8)—42no—
88C23×Q8C3⋊D311yescharacteristic
89C22×Q16—91no—
90C22×Q16—91no—
91C2×C22⋊Q8—91no—
92#451—94no—
93#451—94no—
94C2×#103—91no—
95C2×#103—91no—
96C2×C22⋊C8—91no—
97C24×C3#6711yescharacteristic
98C22×A4#6713yes—
99C2×C3×Q8—32no—
100C2×C3×Q8—32no—
101C2×C3×Q8—32no—
102C2×C3×Q8—32no—
103C2×C3×Q8—32no—
104C2×C3×Q8—31no—
105C2×C3×Q8—43no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8—62no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×C3×Q8—62no—
113C2×C3×Q8—64no—
114C2×C3×Q8S411yescharacteristic
115C22×C3×C4—22no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—61no—
121C22×C3×C4—62no—
122C22×C3×C4—61no—
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—61no—
126C22×Dic3—61no—
127C2×Dic6—32no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—61no—
133C2×Dic6—123no—
134C4×A4—26no—
135C4×A4#6713yes—
136C4×A4C22×D313yes—
137SL(2,ℤ/4)—66no—
138#217—62no—
139#217—62no—
140#216—68no—
141#216—64no—
142#216—64no—
143#216—1212no—
144C4⋊Dic3—32no—
145C4⋊Dic3—61no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148C2×C3⋊C8—32no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—123no—
155C22×C32—41no—
156C3×A4C2×Q1611yescharacteristic, complemented
157C32×C4—41no—
158C32×C4—41no—
159C32×C4—82no—
160C3⋊Dic3—82no—
161C22×Q8—21no—
162C22×Q8—31no—
163C22×Q8—31no—
164C22×Q8—32no—
165C22×Q8—61no—
166C22×Q8—61no—
167C22×Q8—91no—
168C22×Q8C2×C3⋊D312yes—
169C23×C4—21no—
170C23×C4C2×C3⋊D311yescharacteristic
171C2×Q16—94no—
172C2×Q16—94no—
173C2×Q16—182no—
174C2×Q16—182no—
175C2×Q16—182no—
176C2×Q16—181no—
177C2×Q16—181no—
178C22×C8—91no—
179C22×C8—91no—
180C22⋊Q8—92no—
181C22⋊Q8—92no—
182C22⋊Q8—181no—
183C22⋊Q8—181no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—181no—
186C2×C22⋊C4—181no—
187#103—94no—
188#103—94no—
189C22⋊C8—92no—
190C22⋊C8—92no—
191C23×C3—31no—
192C23×C3—31no—
193C23×C3—32no—
194C23×C3#21612yescomplemented
195C23×C3C2×#6711yescharacteristic
196C2×A4#21616yescomplemented
197C2×A4C2×#6713yes—
198C3×Q8—21no—
199C3×Q8—34no—
200C3×Q8—32no—
201C3×Q8—46no—
202C3×Q8—62no—
203C3×Q8—62no—
204C3×Q8—62no—
205C3×Q8—61no—
206C3×Q8—83no—
207C3×Q8C2×S412yes—
208C2×C3×C4—21no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—43no—
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—83no—
224C2×C3×C4C2×S411yescharacteristic
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—121no—
228C2×Dic3—122no—
229C2×Dic3—121no—
230C2×Dic3—243no—
231Dic6—62no—
232Dic6—62no—
233Dic6—126no—
234Dic6—121no—
235Dic6—121no—
236Dic6—243no—
237C3⋊C8—62no—
238C3⋊C8—62no—
239C3⋊C8—126no—
240C2×C32—42no—
241C2×C32—41no—
242C24#63811yescharacteristic
243C2×Q8—32no—
244C2×Q8—32no—
245C2×Q8—32no—
246C2×Q8—32no—
247C2×Q8—32no—
248C2×Q8—31no—
249C2×Q8—61no—
250C2×Q8—61no—
251C2×Q8—61no—
252C2×Q8—62no—
253C2×Q8—61no—
254C2×Q8—61no—
255C2×Q8—62no—
256C2×Q8—64no—
257C2×Q8—92no—
258C2×Q8—181no—
259C2×Q8—181no—
260C2×Q8—181no—
261C2×Q8—181no—
262C2×Q8—181no—
263C2×Q8C3⋊S411yescharacteristic
264C22×C4—22no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—61no—
270C22×C4—62no—
271C22×C4—61no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4#63811yescharacteristic
275C22×C4C22×C3⋊D311yescharacteristic
276Q16—188no—
277Q16—184no—
278Q16—184no—
279C2×C8—92no—
280C2×C8—92no—
281C2×C8—181no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8—181no—
285C4⋊C4—92no—
286C4⋊C4—181no—
287C4⋊C4—182no—
288C4⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22×C3—32no—
292C22×C3—31no—
293C22×C3—32no—
294C22×C3—32no—
295C22×C3—31no—
296C22×C3—31no—
297C22×C3—43no—
298C22×C3—61no—
299C22×C3C2×#21611yescharacteristic, complemented
300C22×C3GL(2,ℤ/4)11yescharacteristic
301A4C2×#21613yescomplemented
302C3×C4—22no—
303C3×C4—31no—
304C3×C4—31no—
305C3×C4—43no—
306C3×C4—43no—
307C3×C4—62no—
308C3×C4—86no—
309C3×C4GL(2,ℤ/4)11yescharacteristic
310C3×C4C22×S411yescharacteristic
311Dic3—122no—
312Dic3—122no—
313Dic3—246no—
314C32—41noSylow
315C23—31no—
316C23—31no—
317C23—32no—
318C23#375612yescomplemented
319C23C2×#63811yescharacteristic
320Q8—21no—
321Q8—34no—
322Q8—32no—
323Q8—62no—
324Q8—62no—
325Q8—62no—
326Q8—61no—
327Q8—182no—
328Q8—182no—
329Q8—361no—
330Q8—361no—
331Q8C2×C3⋊S412yes—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—62no—
341C2×C4—62no—
342C2×C4—61no—
343C2×C4—62no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—361no—
349C2×C4—362no—
350C2×C4—361no—
351C2×C4C2×C3⋊S411yescharacteristic
352C8—182no—
353C8—182no—
354C2×C3—31no—
355C2×C3—31no—
356C2×C3—32no—
357C2×C3—46no—
358C2×C3—43no—
359C2×C3#541612yescomplemented
360C2×C3C2×GL(2,ℤ/4)11yescharacteristic
361C22—32no—
362C22—31no—
363C22—32no—
364C22—32no—
365C22—31no—
366C22—31no—
367C22—61no—
368C22C2×#375611yescharacteristic, complemented
369C22#6426911yescharacteristic
370C4—22no—
371C4—31no—
372C4—31no—
373C4—62no—
374C4—362no—
375C4—362no—
376C4#6426911yescharacteristic
377C4C22×C3⋊S411yescharacteristic
378C3—43no—
379C3C2×#541611yescharacteristic, complemented
380C2—31no—
381C2—31no—
382C2—32no—
383C2#1059365012yesdirect product factor
384C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×Q8D3
socleC24×C3#67
prime radicalC22×C3×A4D4
hypercenterC2×Q8C3⋊S4
hypocenterC3×A4C2×Q16
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
3. #10593650C2direct (N × H)
78. C2×C3×A4Q16semidirect
156. C3×A4C2×Q16semidirect
194. C23×C3#216semidirect
196. C2×A4#216semidirect
299. C22×C3C2×#216semidirect
301. A4C2×#216semidirect
318. C23#3756semidirect
359. C2×C3#5416semidirect
368. C22C2×#3756semidirect
379. C3C2×#5416semidirect
383. C2#10593650direct (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×#642592
#105936502
C2×C3⋊(A4⋊C8)2
C2×#54163
C2×#52283
C2×#37564