Finite Group Databasebeta

← Q8×C11×#123 #14613736

Subgroups — Q8×C11×#123 #14613736

Order 2816.

2418 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
3C11×#2855C213yesmaximal, complemented
4C11×#2502C213yesmaximal, complemented
5C11×#2487C213yesmaximal
6C11×#2446C216yesmaximal, complemented
7C11×#2423C216yesmaximal, complemented
8Q8×C11×C4⋊C4C212yesmaximal, complemented
9Q8×C11×C22⋊C4C212yesmaximal, complemented
10Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#123C213yesmaximal
12C23×Q8×C11C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14D4×Q8×C11—28no—
15C2×C11×C4⋊Q8C2213yes—
16C2×C11×#123C2211yescharacteristic
17C2×C11×C22⋊Q8C2213yes—
18C2×C11×C22⋊Q8C2213yes—
19C2×C4×Q8×C11—28no—
20C2×C4×Q8×C11C2216yes—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2212yes—
24C2×C4×D4×C11C2213yes—
25C22×C11×C4⋊C4C2213yes—
26C22×C42×C11C2213yes—
27C11×#400C2216yes—
28C11×#399C2216yes—
29C11×#398C22112yes—
30C11×#391C2216yes—
31C11×#391C2216yes—
32C11×#391C2216yes—
33C11×#389C2216yes—
34C11×#389C2216yes—
35C11×#388C2216yes—
36C11×#387C22112yes—
37C11×#387C2216yes—
38C11×#386C2213yes—
39C11×#385C2216yes—
40C11×#385C2213yes—
41C11×#384C2216yes—
42C11×#381C2213yes—
43C11×#380C2216yes—
44C11×#380C2213yes—
45C4×C11×C4⋊C4C2216yes—
46C4×C11×C22⋊C4C2216yes—
47C4×C11×C22⋊C4C2213yes—
48C22×Q8×C11—28no—
49C22×Q8×C11—24no—
50C22×Q8×C11—28no—
51C22×Q8×C11D418yes—
52C22×Q8×C11C2313yes—
53C22×Q8×C11C2313yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11C2313yes—
57C23×C4×C11C2313yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2313yes—
60C11×C4⋊Q8—212no—
61C11×#123Q818yesdirect product factor
62C11×C22⋊Q8—212no—
63C11×C22⋊Q8—212no—
64C4×Q8×C11—224no—
65C4×Q8×C11—28no—
66C4×Q8×C11—24no—
67C4×Q8×C11—28no—
68C4×D4×C11—212no—
69C2×C11×C4⋊C4—212no—
70C2×C11×C4⋊C4C2316yes—
71C2×C11×C4⋊C4C2316yes—
72C2×C11×C4⋊C4C2313yes—
73C2×C11×C4⋊C4C2316yes—
74C2×C11×C4⋊C4C2313yes—
75C2×C11×C4⋊C4C2316yes—
76C2×C11×C4⋊C4C2316yes—
77C2×C11×C4⋊C4C23112yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4C2313yes—
80C2×C11×C22⋊C4C2313yes—
81C2×C11×C22⋊C4C2313yes—
82C2×C11×C22⋊C4C2316yes—
83C2×C11×C22⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4C2312yes—
85C2×C42×C11—212no—
86C2×C42×C11C2316yes—
87C2×C42×C11C2316yes—
88C2×C42×C11C2316yes—
89C2×C42×C11C2313yes—
90C11×#95C2316yes—
91C11×#95C2316yes—
92C11×#95C2316yes—
93C11×#95C2316yes—
94C11×#95C2316yes—
95C11×#95C23112yes—
96C11×#95C2316yes—
97Q8×#123C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2411yescharacteristic
99C24×C11C2411yescharacteristic
100C2×Q8×C11—232no—
101C2×Q8×C11—26no—
102C2×Q8×C11—212no—
103C2×Q8×C11—212no—
104C2×Q8×C11—416no—
105C2×Q8×C11C2×D4112yes—
106C2×Q8×C11C2×D414yes—
107C2×Q8×C11#4118yes—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11C2×Q814yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—212no—
114C22×C4×C11—26no—
115C22×C4×C11—26no—
116C22×C4×C11—212no—
117C22×C4×C11—46no—
118C22×C4×C11C2×D4112yes—
119C22×C4×C11C2×Q814yescomplemented
120C22×C4×C11C2416yes—
121C22×C4×C11C2413yes—
122C22×C4×C11C2416yes—
123C22×C4×C11C2413yes—
124C22×C4×C11C2413yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2411yescharacteristic
128C22×C4×C11C2413yes—
129C11×C4⋊C4—212no—
130C11×C4⋊C4—212no—
131C11×C4⋊C4—26no—
132C11×C4⋊C4—26no—
133C11×C4⋊C4—212no—
134C11×C4⋊C4—212no—
135C11×C4⋊C4—46no—
136C11×C4⋊C4—412no—
137C11×C4⋊C4C2×Q818yescomplemented
138C11×C22⋊C4—26no—
139C11×C22⋊C4—26no—
140C11×C22⋊C4—26no—
141C11×C22⋊C4—46no—
142C11×C22⋊C4C2×Q814yescomplemented
143C11×C22⋊C4C2×Q818yescomplemented
144C42×C11—212no—
145C42×C11—212no—
146C42×C11—26no—
147C42×C11—212no—
148C2×D4×Q8C2×C1111yescharacteristic
149C22×C4×Q8C2×C1111yescharacteristic, complemented
150#2855C2×C1113yescomplemented
151#2502C2×C1113yescomplemented
152#2487C2×C1113yes—
153#2446C2×C1116yescomplemented
154#2423C2×C1116yescomplemented
155Q8×C4⋊C4C2×C1112yescomplemented
156Q8×C22⋊C4C2×C1111yescharacteristic, complemented
157Q8×C22⋊C4C2×C1112yescomplemented
158C4×#123C2×C1113yes—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—21no—
162C23×C11—22no—
163C23×C11—21no—
164C23×C11—22no—
165C23×C11C22×D412yes—
166C23×C11C22×Q812yes—
167C23×C11C22×Q812yes—
168C23×C112−1+412yes—
169C23×C11C2511yescharacteristic
170Q8×C11—224no—
171Q8×C11—412no—
172Q8×C11#123116yesdirect product factor
173D4×C11—28no—
174C2×C4×C11—28no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—26no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—224no—
183C2×C4×C11—26no—
184C2×C4×C11—23no—
185C2×C4×C11—23no—
186C2×C4×C11—26no—
187C2×C4×C11—26no—
188C2×C4×C11—26no—
189C2×C4×C11—26no—
190C2×C4×C11—26no—
191C2×C4×C11—26no—
192C2×C4×C11—26no—
193C2×C4×C11—412no—
194C2×C4×C11—412no—
195C2×C4×C11C22×D416yes—
196C2×C4×C11C22×D416yes—
197C2×C4×C11C22×Q814yes—
198C2×C4×C11C22×Q814yes—
199C2×C4×C11C22×Q812yes—
200C2×C4×C11C2×#41112yes—
201C23×Q8C22×C1111yescharacteristic
202C23×Q8C22×C1111yescharacteristic
203D4×Q8—28no—
204C2×C4⋊Q8C22×C1113yes—
205C2×#123C22×C1111yescharacteristic
206C2×C22⋊Q8C22×C1113yes—
207C2×C22⋊Q8C22×C1113yes—
208C2×C4×Q8—28no—
209C2×C4×Q8C22×C1112yes—
210C2×C4×Q8C22×C1112yes—
211C2×C4×Q8C22×C1111yescharacteristic
212C2×C4×Q8C22×C1116yes—
213C2×C4×D4C22×C1113yes—
214C22×C4⋊C4C22×C1113yes—
215C22×C42C22×C1113yes—
216#400C22×C1116yes—
217#399C22×C1116yes—
218#398C22×C11112yes—
219#391C22×C1116yes—
220#391C22×C1116yes—
221#391C22×C1116yes—
222#389C22×C1116yes—
223#389C22×C1116yes—
224#388C22×C1116yes—
225#387C22×C11112yes—
226#387C22×C1116yes—
227#386C22×C1113yes—
228#385C22×C1116yes—
229#385C22×C1113yes—
230#384C22×C1116yes—
231#381C22×C1113yes—
232#380C22×C1113yes—
233#380C22×C1116yes—
234C4×C4⋊C4C22×C1116yes—
235C4×C22⋊C4C22×C1116yes—
236C4×C22⋊C4C22×C1113yes—
237C22×C11—22no—
238C22×C11—24no—
239C22×C11—22no—
240C22×C11—24no—
241C22×C11—22no—
242C22×C11—24no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11D4×Q814yes—
247C22×C11C23×D411yescharacteristic
248C22×C11C23×Q811yescharacteristic
249C22×C11C22×#4112yes—
250C22×C11C2×2−1+411yescharacteristic
251C22×C11#58512yes—
252C4×C11—26no—
253C4×C11—24no—
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—43no—
257C4×C11—43no—
258C4×C11—46no—
259C4×C11—46no—
260C4×C11C2×#123112yes—
261C22×Q8—28no—
262C22×Q8—24no—
263C22×Q8—28no—
264C22×Q8D4×C1118yes—
265C22×Q8C23×C1113yes—
266C22×Q8C23×C1113yes—
267C22×Q8C23×C1111yescharacteristic
268C22×D4C23×C1111yescharacteristic
269C23×C4C23×C1113yes—
270C23×C4C23×C1113yes—
271C23×C4C23×C1111yescharacteristic
272C23×C4C23×C1113yes—
273C4⋊Q8—212no—
274#123Q8×C1118yesdirect product factor
275C22⋊Q8—212no—
276C22⋊Q8—212no—
277C4×Q8—224no—
278C4×Q8—28no—
279C4×Q8—24no—
280C4×Q8—28no—
281C4×D4—212no—
282C2×C4⋊C4—212no—
283C2×C4⋊C4C23×C1116yes—
284C2×C4⋊C4C23×C1116yes—
285C2×C4⋊C4C23×C1113yes—
286C2×C4⋊C4C23×C1113yes—
287C2×C4⋊C4C23×C1116yes—
288C2×C4⋊C4C23×C1116yes—
289C2×C4⋊C4C23×C1116yes—
290C2×C4⋊C4C23×C11112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C22⋊C4C23×C1113yes—
293C2×C22⋊C4C23×C1113yes—
294C2×C22⋊C4C23×C1113yes—
295C2×C22⋊C4C23×C1116yes—
296C2×C22⋊C4C23×C1111yescharacteristic
297C2×C22⋊C4C23×C1112yes—
298C2×C42—212no—
299C2×C42C23×C1113yes—
300C2×C42C23×C1116yes—
301C2×C42C23×C1116yes—
302C2×C42C23×C1116yes—
303#95C23×C1116yes—
304#95C23×C1116yes—
305#95C23×C1116yes—
306#95C23×C1116yes—
307#95C23×C1116yes—
308#95C23×C11112yes—
309#95C23×C1116yes—
310C2×C11—24no—
311C2×C11—42no—
312C2×C11C22×#12311yescharacteristic
313C2×C11C2×D4×Q811yescharacteristic
314C2×C11Q8×#4112yes—
315C2×C11#348711yescharacteristic
316C2×C11#351612yes—
317C24C24×C1111yescharacteristic
318C24C24×C1111yescharacteristic
319C2×Q8—232no—
320C2×Q8—26no—
321C2×Q8—212no—
322C2×Q8—212no—
323C2×Q8—416no—
324C2×Q8C2×D4×C11112yes—
325C2×Q8C2×D4×C1114yes—
326C2×Q8C11×#4118yes—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4C2×Q8×C1114yes—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—212no—
333C22×C4—26no—
334C22×C4—26no—
335C22×C4—212no—
336C22×C4—46no—
337C22×C4C2×D4×C11112yes—
338C22×C4C2×Q8×C1114yescomplemented
339C22×C4C24×C1116yes—
340C22×C4C24×C1113yes—
341C22×C4C24×C1116yes—
342C22×C4C24×C1113yes—
343C22×C4C24×C1113yes—
344C22×C4C24×C1112yes—
345C22×C4C24×C1112yes—
346C22×C4C24×C1111yescharacteristic
347C22×C4C24×C1113yes—
348C4⋊C4—212no—
349C4⋊C4—212no—
350C4⋊C4—26no—
351C4⋊C4—26no—
352C4⋊C4—212no—
353C4⋊C4—212no—
354C4⋊C4—46no—
355C4⋊C4—412no—
356C4⋊C4C2×Q8×C1118yescomplemented
357C22⋊C4—26no—
358C22⋊C4—26no—
359C22⋊C4—26no—
360C22⋊C4—46no—
361C22⋊C4C2×Q8×C1114yescomplemented
362C22⋊C4C2×Q8×C1118yescomplemented
363C42—212no—
364C42—212no—
365C42—26no—
366C42—212no—
367C11Q8×#12311yescharacteristic, direct product factor, Sylow
368C23—22no—
369C23—22no—
370C23—21no—
371C23—22no—
372C23—21no—
373C23—22no—
374C23C22×D4×C1112yes—
375C23C22×Q8×C1112yes—
376C23C22×Q8×C1112yes—
377C23C11×2−1+412yes—
378C23C25×C1111yescharacteristic
379Q8—224no—
380Q8—412no—
381Q8C11×#123116yesdirect product factor
382D4—28no—
383C2×C4—28no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—26no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—224no—
392C2×C4—26no—
393C2×C4—23no—
394C2×C4—23no—
395C2×C4—26no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—26no—
400C2×C4—26no—
401C2×C4—26no—
402C2×C4—412no—
403C2×C4—412no—
404C2×C4C22×D4×C1116yes—
405C2×C4C22×D4×C1116yes—
406C2×C4C22×Q8×C1114yes—
407C2×C4C22×Q8×C1114yes—
408C2×C4C22×Q8×C1112yes—
409C2×C4C2×C11×#41112yes—
410C22—22no—
411C22—24no—
412C22—22no—
413C22—24no—
414C22—22no—
415C22—24no—
416C22—41no—
417C22—41no—
418C22—42no—
419C22D4×Q8×C1114yes—
420C22C23×D4×C1111yescharacteristic
421C22C23×Q8×C1111yescharacteristic
422C22C22×C11×#4112yes—
423C22C2×C11×2−1+411yescharacteristic
424C22C11×#58512yes—
425C4—26no—
426C4—24no—
427C4—22no—
428C4—24no—
429C4—43no—
430C4—46no—
431C4—43no—
432C4—46no—
433C4C2×C11×#123112yes—
434C2—24no—
435C2—42no—
436C2C22×C11×#12311yescharacteristic
437C2C2×D4×Q8×C1111yescharacteristic
438C2Q8×C11×#4112yes—
439C2C11×#348711yescharacteristic
440C2C11×#351612yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×Q8×C11C2semidirect
3. C11×#2855C2semidirect
4. C11×#2502C2semidirect
6. C11×#2446C2semidirect
7. C11×#2423C2semidirect
8. Q8×C11×C4⋊C4C2semidirect
9. Q8×C11×C22⋊C4C2semidirect
10. Q8×C11×C22⋊C4C2semidirect
61. C11×#123Q8direct (N × H)
97. Q8×#123C11direct (N × H)
119. C22×C4×C11C2×Q8semidirect
137. C11×C4⋊C4C2×Q8semidirect
142. C11×C22⋊C4C2×Q8semidirect
143. C11×C22⋊C4C2×Q8semidirect
149. C22×C4×Q8C2×C11semidirect
150. #2855C2×C11semidirect
151. #2502C2×C11semidirect
153. #2446C2×C11semidirect
154. #2423C2×C11semidirect
155. Q8×C4⋊C4C2×C11semidirect
156. Q8×C22⋊C4C2×C11semidirect
157. Q8×C22⋊C4C2×C11semidirect
172. Q8×C11#123direct (N × H)
274. #123Q8×C11direct (N × H)
338. C22×C4C2×Q8×C11semidirect
356. C4⋊C4C2×Q8×C11semidirect
361. C22⋊C4C2×Q8×C11semidirect
362. C22⋊C4C2×Q8×C11semidirect
367. C11Q8×#123direct (N × H)
381. Q8C11×#123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C22×C4×Q8×C112
C11×#28552
C11×#25022
C11×#24872
C11×#24462
C11×#24232
Q8×C11×C4⋊C42
Q8×C11×C22⋊C42
C4×C11×#1232
Q8×#12311