Finite Group Databasebeta

← Q8×C11×#137 #14638561

Subgroups — Q8×C11×#137 #14638561

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C11×#41C211yesmaximal, characteristic
2C2×Q82×C11C211yesmaximal, characteristic, complemented
3C11×#3387C216yesmaximal, complemented
4C11×#3385C216yesmaximal, complemented
5Q8×C11×Q16C212yesmaximal, complemented
6Q8×C11×SD16C212yesmaximal, complemented
7C11×#3165C213yesmaximal, complemented
8C11×#3079C213yesmaximal
9C11×#3078C213yesmaximal, complemented
10Q8×C11×M16C211yesmaximal, characteristic, complemented
11C4×C11×#137C213yesmaximal
12C2×C11×#137C2211yescharacteristic
13Q82×C11—21no—
14Q82×C11—23no—
15Q82×C11C2212yes—
16Q82×C11C2216yes—
17Q82×C11C2211yescharacteristic
18C11×#557C2213yes—
19C11×#554—23no—
20C11×#554C2213yes—
21D4×Q8×C11—21no—
22D4×Q8×C11C2211yescharacteristic
23C11×#533—23no—
24C11×#533C2213yes—
25C2×C11×C4⋊Q8—23no—
26C2×C11×C4⋊Q8C2213yes—
27C4×C11×#41C2213yes—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11—21no—
30C2×C4×Q8×C11C2213yes—
31C2×C4×Q8×C11C2211yescharacteristic
32C11×#501C22112yes—
33C11×#500C2216yes—
34C11×#498C2216yes—
35C11×#479C22112yes—
36C11×#477C2216yes—
37C11×#477C2216yes—
38C11×#476C2216yes—
39C11×#475C2216yes—
40C11×#475C2216yes—
41C11×#474C2216yes—
42C11×#446C2216yes—
43C8×Q8×C11C2212yes—
44C11×#441C2216yes—
45C11×#440C2216yes—
46C4×C11×Q16C2216yes—
47C4×C11×SD16C2216yes—
48C11×#428C2213yes—
49C11×#428C2216yes—
50C11×#423C2213yes—
51C11×#419C2213yes—
52C11×#417C2213yes—
53C4×C11×M16C2213yes—
54C2×C11×#41C2311yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11—23no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C11×#137Q818yesdirect product factor
60C2×C11×Q16C2312yes—
61C2×C11×SD16C2312yes—
62C2×C11×M16C2313yes—
63C2×C11×M16C2311yescharacteristic
64C11×C4⋊Q8—23no—
65C11×C4⋊Q8—26no—
66C11×C4⋊Q8—212no—
67C11×C4⋊Q8—26no—
68C11×C4⋊Q8—23no—
69C11×C4⋊Q8—23no—
70C11×C4⋊Q8—23no—
71C11×C4⋊Q8C2313yes—
72C11×C4⋊Q8C2316yes—
73C11×C4⋊Q8C2313yes—
74C11×C4⋊Q8C2316yes—
75C11×#125—26no—
76C11×#125C2316yes—
77C11×C22⋊Q8—23no—
78C11×C22⋊Q8—23no—
79C11×C22⋊Q8—23no—
80C11×C22⋊Q8—23no—
81C11×C22⋊Q8—26no—
82C4×Q8×C11—21no—
83C4×Q8×C11—26no—
84C4×Q8×C11—22no—
85C4×Q8×C11—23no—
86C4×Q8×C11—23no—
87C4×Q8×C11—23no—
88C4×Q8×C11—23no—
89C4×Q8×C11—23no—
90C4×Q8×C11D411yescharacteristic
91C4×Q8×C11D413yes—
92C4×Q8×C11C2316yes—
93C4×Q8×C11C2316yes—
94C4×Q8×C11C2313yes—
95C4×Q8×C11C2313yes—
96C4×Q8×C11C2311yescharacteristic
97C4×Q8×C11C2313yes—
98C4×D4×C11—23no—
99C4×D4×C11—23no—
100C4×D4×C11C2313yes—
101C4×D4×C11C2313yes—
102C11×#117—23no—
103C11×#117C2313yes—
104C2×C11×C4⋊C4—23no—
105C2×C11×C4⋊C4—23no—
106C2×C11×C4⋊C4—23no—
107C2×C11×C4⋊C4D413yes—
108C2×C11×C4⋊C4C2313yes—
109C2×C42×C11—23no—
110C2×C42×C11—23no—
111C2×C42×C11C2313yes—
112C11×#107C2316yes—
113C11×#107C23112yes—
114C11×#106C2316yes—
115C11×#106C23112yes—
116C11×C4⋊C8C2316yes—
117C11×C4⋊C8C2316yes—
118C11×#103C2316yes—
119C11×#103C2316yes—
120C11×#103C2316yes—
121C11×#102C2316yes—
122C11×#97C2316yes—
123C4×C8×C11C2316yes—
124Q8×#137C1111yesmaximal, characteristic, direct product factor, Sylow
125C11×#41—22no—
126C11×#41C2×Q814yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—23no—
130C2×Q8×C11—23no—
131C2×Q8×C11—26no—
132C2×Q8×C11—26no—
133C2×Q8×C11—22no—
134C2×Q8×C11—44no—
135C2×Q8×C11—86no—
136C2×Q8×C11C2×D413yes—
137C2×Q8×C11C2×D411yescharacteristic
138C2×Q8×C11C2×Q814yescomplemented
139C2×Q8×C11C2412yes—
140C2×Q8×C11C2411yescharacteristic
141C2×D4×C11—21no—
142C2×D4×C11C2411yescharacteristic
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—23no—
146C22×C4×C11—23no—
147C22×C4×C11—23no—
148C22×C4×C11C2×D413yes—
149C22×C4×C11C2×D413yes—
150C22×C4×C11C2411yescharacteristic
151C11×Q16C2×Q818yescomplemented
152C11×SD16C2×Q818yescomplemented
153C11×M16—26no—
154C11×M16C2×Q814yescomplemented
155C2×C8×C11C2416yes—
156C2×C8×C11C2412yes—
157C11×C4⋊C4—26no—
158C11×C4⋊C4—23no—
159C11×C4⋊C4—26no—
160C11×C4⋊C4—26no—
161C11×C4⋊C4—26no—
162C11×C4⋊C4—26no—
163C11×C4⋊C4—23no—
164C11×C4⋊C4—23no—
165C11×C4⋊C4—23no—
166C11×C4⋊C4—23no—
167C11×C4⋊C4—26no—
168C11×C4⋊C4C2×D413yes—
169C11×C4⋊C4C2×D416yes—
170C11×C4⋊C4C2×D413yes—
171C11×C4⋊C4C2416yes—
172C11×C4⋊C4C2413yes—
173C11×C4⋊C4C2413yes—
174C11×C22⋊C4—23no—
175C11×C22⋊C4—23no—
176C11×C22⋊C4—23no—
177C42×C11—23no—
178C42×C11—23no—
179C42×C11—23no—
180C42×C11—26no—
181C42×C11—26no—
182C42×C11C2×D413yes—
183C42×C11C2×D413yes—
184C42×C11C2413yes—
185C42×C11C2413yes—
186Q8×#41C2×C1111yescharacteristic
187C2×Q82C2×C1111yescharacteristic, complemented
188#3387C2×C1116yescomplemented
189#3385C2×C1116yescomplemented
190Q8×Q16C2×C1112yescomplemented
191Q8×SD16C2×C1112yescomplemented
192#3165C2×C1113yescomplemented
193#3079C2×C1113yes—
194#3078C2×C1113yescomplemented
195Q8×M16C2×C1111yescharacteristic, complemented
196C4×#137C2×C1113yes—
197C23×C11—21no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—24no—
200Q8×C11—26no—
201Q8×C11—22no—
202Q8×C11—21no—
203Q8×C11—46no—
204Q8×C11—83no—
205Q8×C11—86no—
206Q8×C11—86no—
207Q8×C11#13714yesdirect product factor
208Q8×C11C22×Q814yes—
209Q8×C11C22×Q812yes—
210D4×C11—24no—
211D4×C11—21no—
212D4×C11C22×Q812yes—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—26no—
218C2×C4×C11—23no—
219C2×C4×C11—23no—
220C2×C4×C11—26no—
221C2×C4×C11—43no—
222C2×C4×C11—46no—
223C2×C4×C11—46no—
224C2×C4×C11—83no—
225C2×C4×C11C22×D413yes—
226C2×C4×C11C22×D413yes—
227C2×C4×C11C22×D413yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D413yes—
230C2×C4×C11C22×Q812yes—
231C2×C4×C112−1+412yes—
232C2×C4×C11C2511yescharacteristic
233C8×C11—26no—
234C8×C11C22×Q814yes—
235C2×#137C22×C1111yescharacteristic
236Q82—21no—
237Q82—23no—
238Q82C22×C1112yes—
239Q82C22×C1111yescharacteristic
240Q82C22×C1116yes—
241#557C22×C1113yes—
242#554—23no—
243#554C22×C1113yes—
244D4×Q8—21no—
245D4×Q8C22×C1111yescharacteristic
246#533—23no—
247#533C22×C1113yes—
248C2×C4⋊Q8—23no—
249C2×C4⋊Q8C22×C1113yes—
250C4×#41C22×C1113yes—
251C2×C4×Q8—21no—
252C2×C4×Q8—21no—
253C2×C4×Q8C22×C1113yes—
254C2×C4×Q8C22×C1111yescharacteristic
255#501C22×C11112yes—
256#500C22×C1116yes—
257#498C22×C1116yes—
258#479C22×C11112yes—
259#477C22×C1116yes—
260#477C22×C1116yes—
261#476C22×C1116yes—
262#475C22×C1116yes—
263#475C22×C1116yes—
264#474C22×C1116yes—
265#446C22×C1116yes—
266C8×Q8C22×C1112yes—
267#441C22×C1116yes—
268#440C22×C1116yes—
269C4×Q16C22×C1116yes—
270C4×SD16C22×C1116yes—
271#428C22×C1116yes—
272#428C22×C1113yes—
273#423C22×C1113yes—
274#419C22×C1113yes—
275#417C22×C1113yes—
276C4×M16C22×C1113yes—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—22no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11D4×Q812yes—
283C22×C11C23×D411yescharacteristic
284C4×C11—23no—
285C4×C11—23no—
286C4×C11—22no—
287C4×C11—24no—
288C4×C11—23no—
289C4×C11—46no—
290C4×C11—43no—
291C4×C11—43no—
292C4×C11D4×Q812yes—
293C4×C11C2×#13716yes—
294C4×C11C23×Q811yescharacteristic
295C4×C11C2×2−1+411yescharacteristic
296C2×#41C23×C1111yescharacteristic
297C22×Q8—21no—
298C22×Q8—23no—
299C22×Q8D4×C1111yescharacteristic
300C22×Q8C23×C1111yescharacteristic
301#137Q8×C1118yesdirect product factor
302C2×Q16C23×C1112yes—
303C2×SD16C23×C1112yes—
304C2×M16C23×C1113yes—
305C2×M16C23×C1111yescharacteristic
306C4⋊Q8—23no—
307C4⋊Q8—26no—
308C4⋊Q8—212no—
309C4⋊Q8—26no—
310C4⋊Q8—23no—
311C4⋊Q8—23no—
312C4⋊Q8—23no—
313C4⋊Q8C23×C1116yes—
314C4⋊Q8C23×C1116yes—
315C4⋊Q8C23×C1113yes—
316C4⋊Q8C23×C1113yes—
317#125—26no—
318#125C23×C1116yes—
319C22⋊Q8—23no—
320C22⋊Q8—23no—
321C22⋊Q8—23no—
322C22⋊Q8—23no—
323C22⋊Q8—26no—
324C4×Q8—21no—
325C4×Q8—26no—
326C4×Q8—22no—
327C4×Q8—23no—
328C4×Q8—23no—
329C4×Q8—23no—
330C4×Q8—23no—
331C4×Q8—23no—
332C4×Q8D4×C1111yescharacteristic
333C4×Q8D4×C1113yes—
334C4×Q8C23×C1116yes—
335C4×Q8C23×C1116yes—
336C4×Q8C23×C1113yes—
337C4×Q8C23×C1113yes—
338C4×Q8C23×C1111yescharacteristic
339C4×Q8C23×C1113yes—
340C4×D4—23no—
341C4×D4—23no—
342C4×D4C23×C1113yes—
343C4×D4C23×C1113yes—
344#117—23no—
345#117C23×C1113yes—
346C2×C4⋊C4—23no—
347C2×C4⋊C4—23no—
348C2×C4⋊C4—23no—
349C2×C4⋊C4D4×C1113yes—
350C2×C4⋊C4C23×C1113yes—
351C2×C42—23no—
352C2×C42—23no—
353C2×C42C23×C1113yes—
354#107C23×C1116yes—
355#107C23×C11112yes—
356#106C23×C1116yes—
357#106C23×C11112yes—
358C4⋊C8C23×C1116yes—
359C4⋊C8C23×C1116yes—
360#103C23×C1116yes—
361#103C23×C1116yes—
362#103C23×C1116yes—
363#102C23×C1116yes—
364#97C23×C1116yes—
365C4×C8C23×C1116yes—
366C2×C11—22no—
367C2×C11—42no—
368C2×C11C2×D4×Q811yescharacteristic
369C2×C11C22×#13711yescharacteristic
370C2×C11#358511yescharacteristic
371#41—22no—
372#41C2×Q8×C1114yes—
373C2×Q8—24no—
374C2×Q8—21no—
375C2×Q8—23no—
376C2×Q8—23no—
377C2×Q8—26no—
378C2×Q8—26no—
379C2×Q8—22no—
380C2×Q8—44no—
381C2×Q8—86no—
382C2×Q8C2×D4×C1113yes—
383C2×Q8C2×D4×C1111yescharacteristic
384C2×Q8C2×Q8×C1114yescomplemented
385C2×Q8C24×C1112yes—
386C2×Q8C24×C1111yescharacteristic
387C2×D4—21no—
388C2×D4C24×C1111yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—23no—
392C22×C4—23no—
393C22×C4—23no—
394C22×C4C2×D4×C1113yes—
395C22×C4C2×D4×C1113yes—
396C22×C4C24×C1111yescharacteristic
397Q16C2×Q8×C1118yescomplemented
398SD16C2×Q8×C1118yescomplemented
399M16—26no—
400M16C2×Q8×C1114yescomplemented
401C2×C8C24×C1116yes—
402C2×C8C24×C1112yes—
403C4⋊C4—26no—
404C4⋊C4—23no—
405C4⋊C4—26no—
406C4⋊C4—26no—
407C4⋊C4—26no—
408C4⋊C4—26no—
409C4⋊C4—23no—
410C4⋊C4—23no—
411C4⋊C4—23no—
412C4⋊C4—23no—
413C4⋊C4—26no—
414C4⋊C4C2×D4×C1113yes—
415C4⋊C4C2×D4×C1116yes—
416C4⋊C4C2×D4×C1113yes—
417C4⋊C4C24×C1116yes—
418C4⋊C4C24×C1113yes—
419C4⋊C4C24×C1113yes—
420C22⋊C4—23no—
421C22⋊C4—23no—
422C22⋊C4—23no—
423C42—23no—
424C42—23no—
425C42—23no—
426C42—26no—
427C42—26no—
428C42C2×D4×C1113yes—
429C42C2×D4×C1113yes—
430C42C24×C1113yes—
431C42C24×C1113yes—
432C11Q8×#13711yescharacteristic, direct product factor, Sylow
433C23—21no—
434C23C22×D4×C1111yescharacteristic
435Q8—24no—
436Q8—26no—
437Q8—22no—
438Q8—21no—
439Q8—46no—
440Q8—83no—
441Q8—86no—
442Q8—86no—
443Q8C11×#13714yesdirect product factor
444Q8C22×Q8×C1114yes—
445Q8C22×Q8×C1112yes—
446D4—24no—
447D4—21no—
448D4C22×Q8×C1112yes—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—26no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—26no—
457C2×C4—43no—
458C2×C4—46no—
459C2×C4—46no—
460C2×C4—83no—
461C2×C4C22×D4×C1113yes—
462C2×C4C22×D4×C1113yes—
463C2×C4C22×D4×C1113yes—
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1113yes—
466C2×C4C22×Q8×C1112yes—
467C2×C4C11×2−1+412yes—
468C2×C4C25×C1111yescharacteristic
469C8—26no—
470C8C22×Q8×C1114yes—
471C22—21no—
472C22—21no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22D4×Q8×C1112yes—
477C22C23×D4×C1111yescharacteristic
478C4—22no—
479C4—24no—
480C4—23no—
481C4—23no—
482C4—23no—
483C4—43no—
484C4—46no—
485C4—43no—
486C4D4×Q8×C1112yes—
487C4C2×C11×#13716yes—
488C4C23×Q8×C1111yescharacteristic
489C4C2×C11×2−1+411yescharacteristic
490C2—22no—
491C2—42no—
492C2C2×D4×Q8×C1111yescharacteristic
493C2C22×C11×#13711yescharacteristic
494C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×Q82×C11C2semidirect
3. C11×#3387C2semidirect
4. C11×#3385C2semidirect
5. Q8×C11×Q16C2semidirect
6. Q8×C11×SD16C2semidirect
7. C11×#3165C2semidirect
9. C11×#3078C2semidirect
10. Q8×C11×M16C2semidirect
59. C11×#137Q8direct (N × H)
124. Q8×#137C11direct (N × H)
138. C2×Q8×C11C2×Q8semidirect
151. C11×Q16C2×Q8semidirect
152. C11×SD16C2×Q8semidirect
154. C11×M16C2×Q8semidirect
187. C2×Q82C2×C11semidirect
188. #3387C2×C11semidirect
189. #3385C2×C11semidirect
190. Q8×Q16C2×C11semidirect
191. Q8×SD16C2×C11semidirect
192. #3165C2×C11semidirect
194. #3078C2×C11semidirect
195. Q8×M16C2×C11semidirect
207. Q8×C11#137direct (N × H)
301. #137Q8×C11direct (N × H)
384. C2×Q8C2×Q8×C11semidirect
397. Q16C2×Q8×C11semidirect
398. SD16C2×Q8×C11semidirect
400. M16C2×Q8×C11semidirect
432. C11Q8×#137direct (N × H)
443. Q8C11×#137direct (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
C2×Q82×C112
C11×#33872
C11×#33852
Q8×C11×Q162
Q8×C11×SD162
C11×#31652
C11×#30792
C11×#30782
Q8×C11×M162
C4×C11×#1372
Q8×#13711