Finite Group Databasebeta

← C4×#10622115 #14668952

Subgroups — C4×#10622115 #14668952

Order 2816.

532 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#67000C211yesmaximal, characteristic
2C2×#10622115C212yesmaximal
3C4×#66900C211yesmaximal, characteristic, complemented
4#13066742C212yesmaximal, complemented
5C4×C11×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C2211yescharacteristic
8C2×C4×D44C411yescharacteristic
9C2×C11×#101C2212yes—
10C4×C11×M16—21no—
11#10622843C2211yescharacteristic
12C2×#66900C2212yes—
13#10622603—21no—
14#10622603—21no—
15#10622601C411yescharacteristic
16#10622590C411yescharacteristic
17C4×(C2×D11)⋊C4—21no—
18C4×(C2×D11)⋊C4—21no—
19C42×Dic11C411yescharacteristic
20C4×#4318—21no—
21C11×#343—21no—
22#10622168—21no—
23#10622115C418yesdirect product factor
24C22×Q8×C11C2311yescharacteristic
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C2×C11×M16—22no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36#67000—22no—
37#67000C2×C414yes—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4×Dic11—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×#4318—22no—
49C4×D44—41no—
50C4×D44—41no—
51C11×#101—22no—
52C11×#101C2×C414yescomplemented
53C11×#97—41no—
54C4×C8×C11—41no—
55#66900—22no—
56#66900C2×C414yescomplemented
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61#66867—41no—
62C4×C11⋊C8—41no—
63C4×#355—111nomaximal, Sylow
64C23×D11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11C22×C412yes—
68C2×Q8×C11#4112yes—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×D44—21no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44C4212yes—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C11×M16—24no—
88C11×M16—42no—
89C2×C8×C11—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—21no—
99(C2×D11)⋊C4—24no—
100(C2×D11)⋊C4—24no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—41no—
105C4×Dic11—21no—
106C4×Dic11—41no—
107C4×Dic11—42no—
108C4×Dic11—42no—
109C4×Dic11C4212yes—
110#4318—24no—
111#4318—42no—
112C2×C11⋊C8—42no—
113C4×#124—111no—
114C2×#355—112no—
115C4×#101—111no—
116C4×#101D1111yescharacteristic, complemented
117#1394—112no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—22no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126Q8×C11—42no—
127Q8×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11C2×C4211yescharacteristic
144C2×C4×C11#11711yescharacteristic
145C2×C4×C11C4×D412yes—
146C2×C4×C11C4×D412yes—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156D44—42no—
157D44—42no—
158C4×D11—82no—
159C4×D11—82no—
160C8×C11—44no—
161C11⋊C8—44no—
162C2×#124—111no—
163C2×C4×Q8C2×D1111yescharacteristic
164C2×C4×D4—111no—
165C2×#101—112no—
166C2×#101C2×D1112yes—
167C4×M16—21no—
168C4×M16—221no—
169#391—111no—
170#390—111no—
171#388—221no—
172#388—221no—
173#382—111no—
174C4×C22⋊C4—221no—
175C4×C22⋊C4—221no—
176C43—111no—
177#355—118no—
178#343—21no—
179#343—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11C4×C22⋊C411yescharacteristic
183C22×C11C2×#9911yescharacteristic
184C22×C11#41011yescharacteristic
185C2×D11—42no—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11#35512yescomplemented
201Dic11—42no—
202Dic11—42no—
203Dic11—81no—
204C22×Q8C22×D1111yescharacteristic
205C22×D4—111no—
206C23×C4—221no—
207C2×M16—22no—
208C2×M16—222no—
209#124—114no—
210#124—222no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×D4—441no—
214C4×D4—441no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4C4×D1111yescharacteristic
217C2×C4⋊C4D4411yescharacteristic
218C2×C4⋊C4C22⋊D1111yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—221no—
227C2×C42—221no—
228C2×C42C4×D1111yescharacteristic
229C2×C42D4411yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231#101—22no—
232#101—114no—
233#101—222no—
234#101C4×D1114yescomplemented
235#97—41no—
236#97—441no—
237C4×C8—41no—
238C4×C8—441no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11C4×#9911yescharacteristic
246C2×C11C2×#35511yescharacteristic
247C2×C11#213211yescharacteristic
248D11—82no—
249C24—221no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8C2×C4×D1112yes—
253C2×Q8#433912yes—
254C2×D4—112no—
255C2×D4—221no—
256C2×D4—441no—
257C2×D4—441no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4—442no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4(C2×D11)⋊C411yescharacteristic
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—24no—
273M16—42no—
274M16—224no—
275M16—442no—
276C2×C8—42no—
277C2×C8—442no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—441no—
282C22⋊C4—224no—
283C22⋊C4—224no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—112no—
294C42—221no—
295C42—441no—
296C42—442no—
297C42—442no—
298C11C4×#35511yescharacteristic, complemented, Sylow
299C23—222no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23C2×(C2×D11)⋊C411yescharacteristic
307Q8—42no—
308Q8—42no—
309D4—442no—
310D4—442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4#6687011yescharacteristic
336C2×C4#6687011yescharacteristic
337C2×C4C42×D1111yescharacteristic
338C2×C4#6692511yescharacteristic
339C2×C4C4×D4412yes—
340C2×C4C4×C22⋊D1112yes—
341C8—44no—
342C8—444no—
343C22—21no—
344C22—21no—
345C22—442no—
346C22—442no—
347C22—442no—
348C22—881no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22C4×(C2×D11)⋊C411yescharacteristic
353C22C2×#6687011yescharacteristic
354C22#1062261911yescharacteristic
355C4—22no—
356C4—22no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—442no—
364C4—442no—
365C4—881no—
366C4#1062211512yesdirect product factor
367C2—21no—
368C2—21no—
369C2—882no—
370C2C4×#6687011yescharacteristic
371C2C2×#1062211511yescharacteristic
372C2#1307029911yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC2×C4×C11C2×C42
FrattiniC22×Q8C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC22×Q8×C11C23
hypercenterC4×#101D11
hypocenterC11C4×#355
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
3. C4×#66900C2semidirect
4. #13066742C2semidirect
5. C4×C11×#101C2semidirect
23. #10622115C4direct (N × H)
52. C11×#101C2×C4semidirect
56. #66900C2×C4semidirect
116. C4×#101D11semidirect
200. C4×C11#355semidirect
234. #101C4×D11semidirect
298. C11C4×#355semidirect
366. C4#10622115direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#670002
C2×#106221152
C4×#669002
#130667422
C4×C11×#1012
C4×#35511