Finite Group Databasebeta

← Q8×C11×#135 #14638550

Subgroups — Q8×C11×#135 #14638550

Order 2816.

1786 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C11×#41C212yesmaximal, complemented
2C11×#3383C213yesmaximal, complemented
3Q8×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#3381C216yesmaximal, complemented
5C11×#3380C213yesmaximal, complemented
6Q8×C11×SD16C212yesmaximal, complemented
7Q8×C11×D8C211yesmaximal, characteristic, complemented
8C11×#3160C213yesmaximal, complemented
9C11×#3076C216yesmaximal, complemented
10C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
11C4×C11×#135C213yesmaximal
12C2×C11×#135C2211yescharacteristic
13Q82×C11C2212yes—
14C11×#557C2216yes—
15C11×#554—26no—
16C11×#554C2216yes—
17D4×Q8×C11—22no—
18D4×Q8×C11C2212yes—
19C11×#533—26no—
20C11×#533C2216yes—
21C4×C11×#41C2216yes—
22C2×C4×Q8×C11—22no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#500C2213yes—
25C11×#500C2213yes—
26C11×#499C2216yes—
27C11×#499C2216yes—
28C11×#498C2216yes—
29C11×#479C22112yes—
30C11×#478C22112yes—
31C11×#477C2216yes—
32C11×#476C2216yes—
33C11×#475C2216yes—
34C11×#474C2216yes—
35C8×Q8×C11C2211yescharacteristic
36C8×Q8×C11C2211yescharacteristic
37C8×Q8×C11C2213yes—
38C8×Q8×C11C2213yes—
39C4×C11×Q16C2213yes—
40C4×C11×Q16C2213yes—
41C4×C11×SD16C2216yes—
42C4×C11×SD16C2216yes—
43C4×C11×D8C2213yes—
44C4×C11×D8C2213yes—
45C11×#427C2213yes—
46C11×#427C2216yes—
47C2×C11×C4⋊C8C2213yes—
48C11×#416C2216yes—
49C2×C4×C8×C11C2213yes—
50C2×C11×#41C2312yes—
51C22×Q8×C11—22no—
52C22×Q8×C11D411yescharacteristic
53C11×#135Q818yesdirect product factor
54C2×C11×Q16C2311yescharacteristic
55C2×C11×SD16C2312yes—
56C2×C11×D8C2311yescharacteristic
57C22×C8×C11C2313yes—
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—26no—
60C11×C4⋊Q8—26no—
61C11×C4⋊Q8C2316yes—
62C11×C4⋊Q8C2316yes—
63C11×#125—212no—
64C11×#125C23112yes—
65C11×C22⋊Q8—26no—
66C11×C22⋊Q8—26no—
67C11×C22⋊Q8—26no—
68C11×C22⋊Q8—26no—
69C11×C22⋊Q8—212no—
70C4×Q8×C11—22no—
71C4×Q8×C11—26no—
72C4×Q8×C11—26no—
73C4×Q8×C11—26no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11D413yes—
76C4×Q8×C11C2316yes—
77C4×Q8×C11C2316yes—
78C4×Q8×C11C2311yescharacteristic
79C4×Q8×C11C2313yes—
80C4×D4×C11—26no—
81C4×D4×C11—26no—
82C4×D4×C11C2316yes—
83C4×D4×C11C2316yes—
84C11×#117—26no—
85C11×#117C2316yes—
86C2×C11×C4⋊C4—26no—
87C2×C11×C4⋊C4D413yes—
88C2×C42×C11—26no—
89C2×C42×C11C2313yes—
90C11×#107C2313yes—
91C11×#107C2313yes—
92C11×#107C2316yes—
93C11×#107C2316yes—
94C11×#106C2316yes—
95C11×#106C23112yes—
96C11×C4⋊C8C2313yes—
97C11×C4⋊C8C2313yes—
98C11×C4⋊C8C2316yes—
99C11×#103C2316yes—
100C11×#103C2316yes—
101C11×#102C2316yes—
102C11×#102C2316yes—
103C4×C8×C11C2313yes—
104C4×C8×C11C2313yes—
105C4×C8×C11C2313yes—
106C4×C8×C11C2313yes—
107Q8×#135C1111yesmaximal, characteristic, direct product factor, Sylow
108C11×#41—24no—
109C11×#41C2×Q818yescomplemented
110C2×Q8×C11—24no—
111C2×Q8×C11—26no—
112C2×Q8×C11—26no—
113C2×Q8×C11—48no—
114C2×Q8×C11C2×D413yes—
115C2×Q8×C11C2×D411yescharacteristic
116C2×Q8×C11C2412yes—
117C2×D4×C11—22no—
118C2×D4×C11C2412yes—
119C22×C4×C11—22no—
120C22×C4×C11—26no—
121C22×C4×C11—26no—
122C22×C4×C11C2×D413yes—
123C22×C4×C11C2×D413yes—
124C22×C4×C11C2411yescharacteristic
125C11×Q16C2×Q814yescomplemented
126C11×SD16C2×Q818yescomplemented
127C11×D8C2×Q814yescomplemented
128C2×C8×C11—26no—
129C2×C8×C11C2×Q814yescomplemented
130C2×C8×C11C2413yes—
131C2×C8×C11C2413yes—
132C2×C8×C11C2411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—212no—
135C11×C4⋊C4—26no—
136C11×C4⋊C4—26no—
137C11×C4⋊C4—26no—
138C11×C4⋊C4—26no—
139C11×C4⋊C4—212no—
140C11×C4⋊C4C2×D413yes—
141C11×C4⋊C4C2×D416yes—
142C11×C4⋊C4C2×D413yes—
143C11×C4⋊C4C2416yes—
144C11×C4⋊C4C2416yes—
145C11×C22⋊C4—26no—
146C11×C22⋊C4—26no—
147C11×C22⋊C4—26no—
148C42×C11—26no—
149C42×C11—26no—
150C42×C11—26no—
151C42×C11C2×D413yes—
152C42×C11C2×D413yes—
153C42×C11C2413yes—
154C42×C11C2413yes—
155Q8×#41C2×C1112yescomplemented
156#3383C2×C1113yescomplemented
157Q8×Q16C2×C1111yescharacteristic, complemented
158#3381C2×C1116yescomplemented
159#3380C2×C1113yescomplemented
160Q8×SD16C2×C1112yescomplemented
161Q8×D8C2×C1111yescharacteristic, complemented
162#3160C2×C1113yescomplemented
163#3076C2×C1116yescomplemented
164C2×C8×Q8C2×C1111yescharacteristic, complemented
165C4×#135C2×C1113yes—
166C23×C11—22no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—26no—
169Q8×C11—22no—
170Q8×C11—412no—
171Q8×C11—86no—
172Q8×C11#13514yesdirect product factor
173Q8×C11C22×Q814yes—
174D4×C11—28no—
175D4×C11—22no—
176D4×C11C22×Q814yes—
177C2×C4×C11—22no—
178C2×C4×C11—28no—
179C2×C4×C11—26no—
180C2×C4×C11—26no—
181C2×C4×C11—26no—
182C2×C4×C11—43no—
183C2×C4×C11—412no—
184C2×C4×C11—86no—
185C2×C4×C11C22×D413yes—
186C2×C4×C11C22×D413yes—
187C2×C4×C11C22×D413yes—
188C2×C4×C11C22×D413yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q812yes—
191C2×C4×C112−1+412yes—
192C2×C4×C11C2511yescharacteristic
193C8×C11—23no—
194C8×C11—23no—
195C8×C11C22×Q812yes—
196C8×C11C22×Q812yes—
197C2×#135C22×C1111yescharacteristic
198Q82C22×C1112yes—
199#557C22×C1116yes—
200#554—26no—
201#554C22×C1116yes—
202D4×Q8—22no—
203D4×Q8C22×C1112yes—
204#533—26no—
205#533C22×C1116yes—
206C4×#41C22×C1116yes—
207C2×C4×Q8—22no—
208C2×C4×Q8C22×C1111yescharacteristic
209#500C22×C1113yes—
210#500C22×C1113yes—
211#499C22×C1116yes—
212#499C22×C1116yes—
213#498C22×C1116yes—
214#479C22×C11112yes—
215#478C22×C11112yes—
216#477C22×C1116yes—
217#476C22×C1116yes—
218#475C22×C1116yes—
219#474C22×C1116yes—
220C8×Q8C22×C1111yescharacteristic
221C8×Q8C22×C1111yescharacteristic
222C8×Q8C22×C1113yes—
223C8×Q8C22×C1113yes—
224C4×Q16C22×C1113yes—
225C4×Q16C22×C1113yes—
226C4×SD16C22×C1116yes—
227C4×SD16C22×C1116yes—
228C4×D8C22×C1113yes—
229C4×D8C22×C1113yes—
230#427C22×C1116yes—
231#427C22×C1113yes—
232C2×C4⋊C8C22×C1113yes—
233#416C22×C1116yes—
234C2×C4×C8C22×C1113yes—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—24no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11D4×Q812yes—
241C22×C11C23×D411yescharacteristic
242C4×C11—23no—
243C4×C11—23no—
244C4×C11—24no—
245C4×C11—23no—
246C4×C11—46no—
247C4×C11—46no—
248C4×C11D4×Q812yes—
249C4×C11C2×#13516yes—
250C4×C11C23×Q811yescharacteristic
251C4×C11C2×2−1+411yescharacteristic
252C2×#41C23×C1112yes—
253C22×Q8—22no—
254C22×Q8D4×C1111yescharacteristic
255#135Q8×C1118yesdirect product factor
256C2×Q16C23×C1111yescharacteristic
257C2×SD16C23×C1112yes—
258C2×D8C23×C1111yescharacteristic
259C22×C8C23×C1113yes—
260C22×C8C23×C1111yescharacteristic
261C4⋊Q8—26no—
262C4⋊Q8—26no—
263C4⋊Q8C23×C1116yes—
264C4⋊Q8C23×C1116yes—
265#125—212no—
266#125C23×C11112yes—
267C22⋊Q8—26no—
268C22⋊Q8—26no—
269C22⋊Q8—26no—
270C22⋊Q8—26no—
271C22⋊Q8—212no—
272C4×Q8—22no—
273C4×Q8—26no—
274C4×Q8—26no—
275C4×Q8—26no—
276C4×Q8D4×C1111yescharacteristic
277C4×Q8D4×C1113yes—
278C4×Q8C23×C1116yes—
279C4×Q8C23×C1116yes—
280C4×Q8C23×C1111yescharacteristic
281C4×Q8C23×C1113yes—
282C4×D4—26no—
283C4×D4—26no—
284C4×D4C23×C1116yes—
285C4×D4C23×C1116yes—
286#117—26no—
287#117C23×C1116yes—
288C2×C4⋊C4—26no—
289C2×C4⋊C4D4×C1113yes—
290C2×C42—26no—
291C2×C42C23×C1113yes—
292#107C23×C1113yes—
293#107C23×C1113yes—
294#107C23×C1116yes—
295#107C23×C1116yes—
296#106C23×C1116yes—
297#106C23×C11112yes—
298C4⋊C8C23×C1113yes—
299C4⋊C8C23×C1113yes—
300C4⋊C8C23×C1116yes—
301#103C23×C1116yes—
302#103C23×C1116yes—
303#102C23×C1116yes—
304#102C23×C1116yes—
305C4×C8C23×C1113yes—
306C4×C8C23×C1113yes—
307C4×C8C23×C1113yes—
308C4×C8C23×C1113yes—
309C2×C11—22no—
310C2×C11—44no—
311C2×C11C2×D4×Q811yescharacteristic
312C2×C11C22×#13511yescharacteristic
313C2×C11#358411yescharacteristic
314#41—24no—
315#41C2×Q8×C1118yescomplemented
316C2×Q8—24no—
317C2×Q8—26no—
318C2×Q8—26no—
319C2×Q8—48no—
320C2×Q8C2×D4×C1113yes—
321C2×Q8C2×D4×C1111yescharacteristic
322C2×Q8C24×C1112yes—
323C2×D4—22no—
324C2×D4C24×C1112yes—
325C22×C4—22no—
326C22×C4—26no—
327C22×C4—26no—
328C22×C4C2×D4×C1113yes—
329C22×C4C2×D4×C1113yes—
330C22×C4C24×C1111yescharacteristic
331Q16C2×Q8×C1114yescomplemented
332SD16C2×Q8×C1118yescomplemented
333D8C2×Q8×C1114yescomplemented
334C2×C8—26no—
335C2×C8C2×Q8×C1114yescomplemented
336C2×C8C24×C1113yes—
337C2×C8C24×C1113yes—
338C2×C8C24×C1111yescharacteristic
339C2×C8C24×C1111yescharacteristic
340C4⋊C4—212no—
341C4⋊C4—26no—
342C4⋊C4—26no—
343C4⋊C4—26no—
344C4⋊C4—26no—
345C4⋊C4—212no—
346C4⋊C4C2×D4×C1113yes—
347C4⋊C4C2×D4×C1116yes—
348C4⋊C4C2×D4×C1113yes—
349C4⋊C4C24×C1116yes—
350C4⋊C4C24×C1116yes—
351C22⋊C4—26no—
352C22⋊C4—26no—
353C22⋊C4—26no—
354C42—26no—
355C42—26no—
356C42—26no—
357C42C2×D4×C1113yes—
358C42C2×D4×C1113yes—
359C42C24×C1113yes—
360C42C24×C1113yes—
361C11Q8×#13511yescharacteristic, direct product factor, Sylow
362C23—22no—
363C23C22×D4×C1111yescharacteristic
364Q8—26no—
365Q8—22no—
366Q8—412no—
367Q8—86no—
368Q8C11×#13514yesdirect product factor
369Q8C22×Q8×C1114yes—
370D4—28no—
371D4—22no—
372D4C22×Q8×C1114yes—
373C2×C4—22no—
374C2×C4—28no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—43no—
379C2×C4—412no—
380C2×C4—86no—
381C2×C4C22×D4×C1113yes—
382C2×C4C22×D4×C1113yes—
383C2×C4C22×D4×C1113yes—
384C2×C4C22×D4×C1111yescharacteristic
385C2×C4C22×D4×C1113yes—
386C2×C4C22×Q8×C1112yes—
387C2×C4C11×2−1+412yes—
388C2×C4C25×C1111yescharacteristic
389C8—23no—
390C8—23no—
391C8C22×Q8×C1112yes—
392C8C22×Q8×C1112yes—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—42no—
397C22—42no—
398C22D4×Q8×C1112yes—
399C22C23×D4×C1111yescharacteristic
400C4—24no—
401C4—23no—
402C4—23no—
403C4—23no—
404C4—46no—
405C4—46no—
406C4D4×Q8×C1112yes—
407C4C2×C11×#13516yes—
408C4C23×Q8×C1111yescharacteristic
409C4C2×C11×2−1+411yescharacteristic
410C2—22no—
411C2—44no—
412C2C2×D4×Q8×C1111yescharacteristic
413C2C22×C11×#13511yescharacteristic
414C2C11×#358411yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
prime radicalC2×C11×#135C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. Q8×C11×#41C2semidirect
2. C11×#3383C2semidirect
3. Q8×C11×Q16C2semidirect
4. C11×#3381C2semidirect
5. C11×#3380C2semidirect
6. Q8×C11×SD16C2semidirect
7. Q8×C11×D8C2semidirect
8. C11×#3160C2semidirect
9. C11×#3076C2semidirect
10. C2×C8×Q8×C11C2semidirect
53. C11×#135Q8direct (N × H)
107. Q8×#135C11direct (N × H)
109. C11×#41C2×Q8semidirect
125. C11×Q16C2×Q8semidirect
126. C11×SD16C2×Q8semidirect
127. C11×D8C2×Q8semidirect
129. C2×C8×C11C2×Q8semidirect
155. Q8×#41C2×C11semidirect
156. #3383C2×C11semidirect
157. Q8×Q16C2×C11semidirect
158. #3381C2×C11semidirect
159. #3380C2×C11semidirect
160. Q8×SD16C2×C11semidirect
161. Q8×D8C2×C11semidirect
162. #3160C2×C11semidirect
163. #3076C2×C11semidirect
164. C2×C8×Q8C2×C11semidirect
172. Q8×C11#135direct (N × H)
255. #135Q8×C11direct (N × H)
315. #41C2×Q8×C11semidirect
331. Q16C2×Q8×C11semidirect
332. SD16C2×Q8×C11semidirect
333. D8C2×Q8×C11semidirect
335. C2×C8C2×Q8×C11semidirect
361. C11Q8×#135direct (N × H)
368. Q8C11×#135direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×C11×#412
C11×#33832
Q8×C11×Q162
C11×#33812
C11×#33802
Q8×C11×SD162
Q8×C11×D82
C11×#31602
C11×#30762
C2×C8×Q8×C112
C4×C11×#1352
Q8×#13511