Finite Group Databasebeta

← C22⋊C8×Dic22 #14770288

Subgroups — C22⋊C8×Dic22 #14770288

Order 2816.

1356 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×C8×Dic22C212yesmaximal, complemented
3#13069552C212yesmaximal, complemented
4#13069550C214yesmaximal, complemented
5#13068596C211yesmaximal, characteristic
6#13068594C212yesmaximal
7C22⋊C8×Dic11C212yesmaximal
8C4×C11×C22⋊C8C211yesmaximal, characteristic
9C23×Dic22C411yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C411yescharacteristic
12C22×Dic11⋊C4C412yes—
13C22×C4×Dic11C2212yes—
14C2×C4×Dic22—28no—
15C2×C4×Dic22C411yescharacteristic
16C2×C4×Dic22C411yescharacteristic
17C2×C4×Dic22C412yes—
18C2×C4×Dic22C2212yes—
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2212yes—
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×Dic11⋊C8C2214yes—
26C2×C8×Dic11C2214yes—
27C2×C4⋊(C11⋊C8)C2212yes—
28C8×Dic22—28no—
29C11×#336C2212yes—
30#10622188C2214yes—
31#10622188C2214yes—
32#10622162C2212yes—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C412yes—
37C23×Dic11C2×C412yes—
38C22×Dic22—24no—
39C22×Dic22—24no—
40C22×Dic22C818yescomplemented
41C22×Dic22C2×C412yes—
42C22×Dic22C2×C411yescharacteristic
43C22×Dic22C2×C411yescharacteristic
44C22×C8×C11C2312yes—
45C22×C8×C11C2312yes—
46C2×C42×C11—24no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11C2×C412yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×Dic11⋊C4—28no—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C412yes—
60C2×C4×Dic11—28no—
61C2×C4×Dic11C2×C412yes—
62C2×C4×Dic11C2×C412yes—
63C2×C4×Dic11C2312yes—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2314yes—
66C4×Dic22—24no—
67C4×Dic22—24no—
68C4×Dic22—24no—
69C4×Dic22—28no—
70C4×Dic22—28no—
71C4×Dic22D418yes—
72C11×C22⋊C8—22no—
73C11×C22⋊C8Q814yescomplemented
74C4×C8×C11—24no—
75C22⋊(C11⋊C8)—24no—
76Dic11⋊C8—28no—
77C8×Dic11—28no—
78C4⋊(C11⋊C8)—24no—
79Q8×C22⋊C8—111nomaximal, Sylow
80C24×C11C22×C411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11C2×C814yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×Q812yes—
95C22×C4×C11#4112yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—42no—
102C22×Dic11C2×C818yes—
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C22×Dic11C22×C412yes—
106C22×Dic11C22×C412yes—
107C2×Dic22—24no—
108C2×Dic22—24no—
109C2×Dic22—232no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22C22⋊C414yes—
113C2×Dic22C2×C818yes—
114C2×Dic22C2×C814yes—
115C2×Dic22C2×C814yes—
116C2×Dic22M1614yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C2×Q814yescomplemented
123C42×C11—22no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11C2×D414yes—
127C4⋊Dic11—24no—
128C4⋊Dic11—22no—
129C4⋊Dic11C22⋊C414yes—
130Dic11⋊C4—24no—
131Dic11⋊C4—24no—
132Dic11⋊C4—24no—
133Dic11⋊C4C22⋊C418yes—
134C4×Dic11—24no—
135C4×Dic11—24no—
136C4×Dic11—24no—
137C4×Dic11C2×D418yes—
138C2×C11⋊C8—24no—
139C2×C11⋊C8—24no—
140C2×C11⋊C8—24no—
141C22×C4×Q8—111no—
142C2×C8×Q8—112no—
143#1984—112no—
144#1984—114no—
145#1797—111no—
146#1797—112no—
147C4×C22⋊C8—112no—
148C4×C22⋊C8D1111yescharacteristic
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11C4×Q812yes—
154C23×C11C22×C812yes—
155C23×C11#13112yes—
156C23×C11C23×C411yescharacteristic
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—28no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—44no—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11C2×C22⋊C412yes—
172C2×C4×C11C4×Q812yes—
173C2×C4×C11C22×C812yes—
174C2×C4×C11C22×C812yes—
175C2×C4×C11C2×M1612yes—
176C2×C4×C11C22×D412yes—
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C112−1+412yes—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—216no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—48no—
189C2×Dic11C2×C22⋊C414yes—
190C2×Dic11C2×C22⋊C414yes—
191C2×Dic11C22×C814yes—
192C2×Dic11C22×C814yes—
193C2×Dic11C2×M1614yes—
194Dic22—28no—
195Dic22—216no—
196Dic22C22⋊C8116yesdirect product factor
197C8×C11—24no—
198C8×C11—42no—
199C11⋊C8—44no—
200C23×Q8—111no—
201C2×C4×Q8—111no—
202C2×C4×Q8—112no—
203C2×C4×Q8—111no—
204C2×C4×Q8—112no—
205C2×C4×Q8—111no—
206C2×C4×Q8—111no—
207C2×C4×Q8—228no—
208C22×C4⋊C4—112no—
209C22×C4⋊C4—111no—
210C22×C42—112no—
211C22×C42C2×D1111yescharacteristic
212C8×Q8—228no—
213C2×C4⋊C8—114no—
214C2×C4⋊C8—112no—
215C2×C22⋊C8—112no—
216C2×C22⋊C8C2×D1111yescharacteristic
217C2×C22⋊C8C2×D1111yescharacteristic
218C2×C4×C8—114no—
219C2×C4×C8C2×D1112yes—
220#336—114no—
221#336—114no—
222#336—112no—
223#336C2×D1112yes—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11C8×Q814yescomplemented
231C22×C11C22×C22⋊C411yescharacteristic
232C22×C11C2×C4×Q811yescharacteristic
233C22×C11#51911yescharacteristic
234C22×C11C23×C811yescharacteristic
235C22×C11C22×M1611yescharacteristic
236C22×C11C2×#13111yescharacteristic
237C22×C11#56811yescharacteristic
238C4×C11—22no—
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—41no—
242C4×C11C2×C22⋊C814yes—
243C4×C11#54812yes—
244C4×C11D4×Q812yes—
245Dic11—24no—
246Dic11—24no—
247Dic11—42no—
248Dic11C2×C22⋊C818yes—
249C22×Q8—118no—
250C22×Q8—111no—
251C22×Q8—112no—
252C22×Q8—111no—
253C22×Q8—224no—
254C22×Q8—224no—
255C23×C4—112no—
256C23×C4—112no—
257C23×C4C4×D1111yescharacteristic
258C23×C4C4×D1111yescharacteristic
259C23×C4C22×D1111yescharacteristic
260C22×C8—114no—
261C22×C8C22×D1112yes—
262C22×C8C22×D1112yes—
263C4×Q8—118no—
264C4×Q8—228no—
265C4×Q8—228no—
266C4×Q8—224no—
267C4×Q8—224no—
268C4×Q8—224no—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—228no—
277C2×C4⋊C4—224no—
278C2×C42—24no—
279C2×C42—112no—
280C2×C42—112no—
281C2×C42—112no—
282C2×C42—112no—
283C2×C42—228no—
284C2×C42C4×D1111yescharacteristic
285C2×C42C4×D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
287C2×C42C22×D1111yescharacteristic
288C4⋊C8—228no—
289C4⋊C8—224no—
290C22⋊C8—22no—
291C22⋊C8—224no—
292C22⋊C8Dic2214yesdirect product factor
293C4×C8—24no—
294C4×C8—228no—
295C2×C11—24no—
296C2×C11Q8×C22⋊C411yescharacteristic
297C2×C11C22×C22⋊C811yescharacteristic
298C2×C11#288011yescharacteristic
299C2×C11C2×C8×Q811yescharacteristic
300C2×C11Q8×M1611yescharacteristic
301C2×C11#298211yescharacteristic
302C2×C11#298411yescharacteristic
303C24C2×C4×D1111yescharacteristic
304C2×Q8—114no—
305C2×Q8—114no—
306C2×Q8—118no—
307C2×Q8—114no—
308C2×Q8—114no—
309C2×Q8—224no—
310C2×Q8—224no—
311C2×Q8—2232no—
312C2×Q8—222no—
313C2×Q8—222no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—118no—
323C22×C4—112no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—224no—
329C22×C4—224no—
330C22×C4—442no—
331C22×C4C8×D1114yes—
332C22×C4C2×Dic2212yes—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4C2×C4×D1111yescharacteristic
335C22×C4C2×C4×D1111yescharacteristic
336C22×C4C2×C4×D1111yescharacteristic
337C22×C4C2×C4×D1111yescharacteristic
338C22×C4#433912yes—
339C22×C4C23×D1111yescharacteristic
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—224no—
346C2×C8—224no—
347C2×C8—224no—
348C2×C8C2×Dic2214yescomplemented
349C4⋊C4—118no—
350C4⋊C4—114no—
351C4⋊C4—224no—
352C4⋊C4—224no—
353C4⋊C4—224no—
354C4⋊C4—224no—
355C4⋊C4—222no—
356C42—22no—
357C42—22no—
358C42—22no—
359C42—118no—
360C42—224no—
361C42—224no—
362C42—224no—
363C42D4×D1114yes—
364C11Q8×C22⋊C811yescharacteristic, complemented, Sylow
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23C4×Dic2212yes—
370C23C2×C8×D1112yes—
371C23#6695412yes—
372C23C22×C4×D1111yescharacteristic
373Q8—1116no—
374Q8—2216no—
375Q8—228no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—28no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—44no—
389C2×C4—114no—
390C2×C4—114no—
391C2×C4—114no—
392C2×C4—114no—
393C2×C4—114no—
394C2×C4—2216no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—448no—
403C2×C4C4×Dic2212yes—
404C2×C4C22⋊C4×D1112yes—
405C2×C4C22⋊C4×D1112yes—
406C2×C4C2×C8×D1112yes—
407C2×C4C2×C8×D1112yes—
408C2×C4M16×D1112yes—
409C2×C4C22×Dic2211yescharacteristic
410C2×C4C2×#433911yescharacteristic
411C2×C4C2×D4×D1112yes—
412C2×C4#6704312yes—
413C8—24no—
414C8—42no—
415C8—444no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22C8×Dic2214yescomplemented
423C22C2×C4×Dic2211yescharacteristic
424C22C2×C22⋊C4×D1111yescharacteristic
425C22#1062304711yescharacteristic
426C22C22×C8×D1111yescharacteristic
427C22C2×#6695411yescharacteristic
428C22C2×M16×D1111yescharacteristic
429C22#1062327611yescharacteristic
430C4—22no—
431C4—22no—
432C4—22no—
433C4—41no—
434C4—118no—
435C4—224no—
436C4—224no—
437C4—442no—
438C4D11×C22⋊C814yes—
439C4D4×Dic2212yes—
440C4#1062308312yes—
441C2—24no—
442C2C22⋊C4×Dic2211yescharacteristic
443C2C2×D11×C22⋊C811yescharacteristic
444C2#1307706211yescharacteristic
445C2C2×C8×Dic2211yescharacteristic
446C2M16×Dic2211yescharacteristic
447C2#1307769611yescharacteristic
448C2#1307770311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC4×C11×C22⋊C8C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11Q8×C22⋊C8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13069552C2semidirect
4. #13069550C2semidirect
40. C22×Dic22C8semidirect
73. C11×C22⋊C8Q8semidirect
122. C2×C8×C11C2×Q8semidirect
196. Dic22C22⋊C8direct (N × H)
230. C22×C11C8×Q8semidirect
292. C22⋊C8Dic22direct (N × H)
348. C2×C8C2×Dic22semidirect
364. C11Q8×C22⋊C8semidirect
422. C22C8×Dic22semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×C8×Dic222
#130695522
#130695502
#130685962
#130685942
C22⋊C8×Dic112
C4×C11×C22⋊C82
Q8×C22⋊C811