Finite Group Databasebeta

← #15623465

Subgroups — #15623465

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic
2#13079163C213yesmaximal, complemented
3#13079158C213yesmaximal, complemented
4#13079150C2112yesmaximal, complemented
5#13079126C213yesmaximal, complemented
6C2×#10622691C213yesmaximal, complemented
7#13077214C214yesmaximal
8C4×#67001C211yesmaximal, characteristic
9C11×#3503C211yesmaximal, characteristic
10Q82×C11—21no—
11C11×#557—21no—
12C11×#554—23no—
13D4×Q8×C11—23no—
14C11×#544C2216yes—
15C11×#533C2213yes—
16C2×C11×C4⋊Q8C2213yes—
17C11×#520C2212yes—
18C4×C11×#41C2211yescharacteristic
19#10623358C2212yes—
20C2×#67001C2212yes—
21#10623101—21no—
22Q8×Dic22—21no—
23#10623074—23no—
24D4×Dic22—23no—
25#10623050C2216yes—
26#10623001C2213yes—
27C2×#66922C2213yes—
28#10622693C22112yes—
29#10622692C2213yes—
30#10622692C2213yes—
31#10622691C2213yes—
32#10622691C22112yes—
33#10622691C2216yes—
34#10622691C2211yescharacteristic
35#10622678C22112yes—
36#10622677C22112yes—
37#10622611C22112yes—
38#10622610C2216yes—
39#10622608C22112yes—
40#10622577C22112yes—
41C2×#66871C22112yes—
42C4×#4318C2213yes—
43C2×C4×C11⋊C8C2213yes—
44C2×C11×#41C2311yescharacteristic
45C22×Q8×C11—23no—
46C22×Dic22—23no—
47C11×C4⋊Q8—26no—
48C11×C4⋊Q8—23no—
49C11×C4⋊Q8—23no—
50C11×C4⋊Q8C2313yes—
51C11×C4⋊Q8C2316yes—
52C11×C4⋊Q8C2311yescharacteristic
53C11×#125—26no—
54C11×#125C2316yes—
55C11×C22⋊Q8—23no—
56C11×C22⋊Q8—23no—
57C11×C22⋊Q8—212no—
58C4×Q8×C11—22no—
59C4×Q8×C11—23no—
60C4×Q8×C11—23no—
61C4×Q8×C11D411yescharacteristic
62C4×Q8×C11D411yescharacteristic
63C4×D4×C11—26no—
64C4×D4×C11D413yes—
65C4×D4×C11D413yes—
66C11×#117C2316yes—
67C11×#117C2313yes—
68C2×C11×C4⋊C4—23no—
69C2×C11×C4⋊C4C2316yes—
70C2×C42×C11C2313yes—
71#67001Q8116yescomplemented
72Q8×Dic11—22no—
73D4×Dic11—26no—
74#66979C2316yes—
75C2×C4⋊Dic11—23no—
76C2×C4⋊Dic11C2316yes—
77#66977—23no—
78#66977—23no—
79C2×#4318C2316yes—
80C22×C11⋊C8C2316yes—
81#66943—26no—
82#66941—26no—
83#66931—212no—
84#66923C2316yes—
85#66922—23no—
86#66922—23no—
87#66922C2313yes—
88#66922C2316yes—
89#66922C2311yescharacteristic
90C4×Dic22—23no—
91C4×Dic22—23no—
92#66872C23112yes—
93#66872C23112yes—
94#66871C23112yes—
95#66871C23124yes—
96#66871C2314yes—
97#66867C2316yes—
98C4×C11⋊C8C2311yescharacteristic
99C4×C11⋊C8C2313yes—
100C4×C11⋊C8C2316yes—
101#60667—111nomaximal, Sylow
102C11×#41C2×Q818yes—
103C2×Q8×C11—21no—
104C2×Q8×C11—23no—
105C2×Q8×C11—26no—
106C2×Q8×C11—86no—
107C2×Q8×C11C2×D411yescharacteristic
108C2×D4×C11C2×D413yes—
109C22×C4×C11—26no—
110C22×C4×C11C2×D413yes—
111C22×C4×C11C2×D413yes—
112C22×C4×C11C2413yes—
113C22×Dic11—26no—
114C2×Dic22—21no—
115C2×Dic22—23no—
116C2×Dic22—26no—
117C2×Dic22—86no—
118C11×C4⋊C4—23no—
119C11×C4⋊C4—26no—
120C11×C4⋊C4—26no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—26no—
123C11×C4⋊C4—26no—
124C11×C4⋊C4C2×D413yes—
125C11×C4⋊C4C2×D413yes—
126C11×C4⋊C4C2416yes—
127C11×C4⋊C4C2412yes—
128C11×C22⋊C4—26no—
129C11×C22⋊C4C2×D416yes—
130C42×C11—26no—
131C42×C11C2×D413yes—
132C42×C11C2×D413yes—
133C42×C11C2411yescharacteristic
134C42×C11C2413yes—
135C22⋊Dic11—26no—
136C4⋊Dic11—21no—
137C4⋊Dic11—23no—
138C4⋊Dic11—26no—
139C4⋊Dic11—26no—
140C4⋊Dic11C2416yes—
141C4⋊Dic11C2412yes—
142Dic11⋊C4—26no—
143Dic11⋊C4—26no—
144C4×Dic11—26no—
145#4318C2×Q8124yescomplemented
146C2×C11⋊C8C2×Q8124yescomplemented
147C2×C11⋊C8C2412yes—
148C2×C11⋊C8C2416yes—
149#3503—111no—
150#3503D1111yescharacteristic
151#3165—113no—
152#3165—113no—
153#3164—1112no—
154#3160—113no—
155C2×#500—113no—
156#2913—114no—
157C4×#131—111no—
158C23×C11C22×D413yes—
159Q8×C11—46no—
160Q8×C11—42no—
161Q8×C11—86no—
162Q8×C11C4⋊Q814yes—
163D4×C11C4⋊Q8112yes—
164C2×C4×C11—26no—
165C2×C4×C11—26no—
166C2×C4×C11—22no—
167C2×C4×C11—26no—
168C2×C4×C11—86no—
169C2×C4×C11C22×D413yes—
170C2×C4×C11C22×D413yes—
171C2×C4×C11C22×D413yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×Q8112yes—
175C2×C4×C11C2511yescharacteristic
176C2×Dic11—22no—
177C2×Dic11—26no—
178C2×Dic11—86no—
179Dic22—46no—
180Dic22—42no—
181Dic22—86no—
182C11⋊C8C22×Q814yes—
183C11⋊C8C22×Q8112yes—
184C2×#131—112no—
185Q82—21no—
186Q82—221no—
187#557—21no—
188#557—221no—
189#554—23no—
190#554—223no—
191D4×Q8—23no—
192D4×Q8—223no—
193#544—116no—
194#544C2×D1116yes—
195#533—113no—
196#533C2×D1113yes—
197C2×C4⋊Q8—113no—
198C2×C4⋊Q8C2×D1113yes—
199#520—112no—
200#520C2×D1112yes—
201C4×#41C2×D1111yescharacteristic
202#501—1112no—
203#501—1112no—
204#500—113no—
205#500—1112no—
206#500—116no—
207#500—111no—
208#499—1112no—
209#498—113no—
210#498—113no—
211#428—1112no—
212#428—1112no—
213#427—1112no—
214C2×#107—1112no—
215#405—116no—
216C4×M16—113no—
217C2×C4×C8—113no—
218C22×C11—23no—
219C22×C11—23no—
220C22×C11C2×C4⋊Q816yes—
221C22×C11C23×D411yescharacteristic
222C4×C11—23no—
223C4×C11—23no—
224C4×C11—46no—
225C4×C11—42no—
226C4×C11C2×C4⋊Q816yes—
227C4×C11#57612yes—
228C4×C11#57812yes—
229C4×C11C23×Q812yes—
230Dic11—46no—
231Dic11—42no—
232C2×#41C22×D1111yescharacteristic
233C22×Q8—23no—
234C22×Q8—223no—
235#131—1116no—
236C2×M16—116no—
237C22×C8—116no—
238C4⋊Q8—26no—
239C4⋊Q8—23no—
240C4⋊Q8—23no—
241C4⋊Q8—113no—
242C4⋊Q8—116no—
243C4⋊Q8—111no—
244C4⋊Q8—226no—
245C4⋊Q8—223no—
246C4⋊Q8—223no—
247C4⋊Q8C22×D1113yes—
248C4⋊Q8C22×D1116yes—
249C4⋊Q8C22×D1111yescharacteristic
250#125—26no—
251#125—116no—
252#125—226no—
253#125C22×D1116yes—
254C22⋊Q8—23no—
255C22⋊Q8—23no—
256C22⋊Q8—212no—
257C22⋊Q8—223no—
258C22⋊Q8—223no—
259C22⋊Q8—2212no—
260C4×Q8—22no—
261C4×Q8—23no—
262C4×Q8—23no—
263C4×Q8—222no—
264C4×Q8—223no—
265C4×Q8—223no—
266C4×Q8C22⋊D1111yescharacteristic
267C4×Q8C22⋊D1111yescharacteristic
268C4×D4—26no—
269C4×D4—226no—
270C4×D4C22⋊D1113yes—
271C4×D4C22⋊D1113yes—
272#117—116no—
273#117C22×D1116yes—
274#117C22×D1113yes—
275C2×C4⋊C4—23no—
276C2×C4⋊C4—116no—
277C2×C4⋊C4—223no—
278C2×C4⋊C4C22×D1116yes—
279C2×C42C22×D1113yes—
280#107—1112no—
281#107—1124no—
282#107—114no—
283#106—1112no—
284#106—1112no—
285#97—116no—
286C4×C8—111no—
287C4×C8—113no—
288C4×C8—116no—
289C2×C11—26no—
290C2×C11C22×C4⋊Q811yescharacteristic
291C2×C11C2×#57611yescharacteristic
292C2×C11C2×#57811yescharacteristic
293#41Q8×D1118yes—
294C2×Q8—21no—
295C2×Q8—23no—
296C2×Q8—26no—
297C2×Q8—86no—
298C2×Q8—221no—
299C2×Q8—223no—
300C2×Q8—226no—
301C2×Q8—886no—
302C2×Q8C2×C22⋊D1111yescharacteristic
303C2×D4C2×C22⋊D1113yes—
304C22×C4—26no—
305C22×C4—226no—
306C22×C4C2×C22⋊D1113yes—
307C22×C4C2×C22⋊D1113yes—
308C22×C4C23×D1113yes—
309M16—1124no—
310C2×C8—1124no—
311C2×C8—112no—
312C2×C8—116no—
313C4⋊C4—23no—
314C4⋊C4—26no—
315C4⋊C4—26no—
316C4⋊C4—21no—
317C4⋊C4—26no—
318C4⋊C4—26no—
319C4⋊C4—112no—
320C4⋊C4—116no—
321C4⋊C4—226no—
322C4⋊C4—223no—
323C4⋊C4—226no—
324C4⋊C4—221no—
325C4⋊C4—226no—
326C4⋊C4—226no—
327C4⋊C4C2×C22⋊D1113yes—
328C4⋊C4C2×C22⋊D1113yes—
329C4⋊C4C23×D1112yes—
330C4⋊C4C23×D1116yes—
331C22⋊C4—26no—
332C22⋊C4—226no—
333C22⋊C4C2×C22⋊D1116yes—
334C42—26no—
335C42—226no—
336C42C2×C22⋊D1113yes—
337C42C2×C22⋊D1113yes—
338C42C23×D1111yescharacteristic
339C42C23×D1113yes—
340C11#6066711yescharacteristic, complemented, Sylow
341C23C22×C22⋊D1113yes—
342Q8—46no—
343Q8—42no—
344Q8—86no—
345Q8—446no—
346Q8—442no—
347Q8—886no—
348Q8#6699714yes—
349D4#66997112yes—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—22no—
353C2×C4—26no—
354C2×C4—86no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—886no—
358C2×C4C2×Q8×D11112yes—
359C2×C4C22×C22⋊D1113yes—
360C2×C4C22×C22⋊D1113yes—
361C2×C4C22×C22⋊D1113yes—
362C2×C4C22×C22⋊D1111yescharacteristic
363C2×C4C22×C22⋊D1111yescharacteristic
364C2×C4C24×D1111yescharacteristic
365C8—114no—
366C8—1112no—
367C22—23no—
368C22—23no—
369C22C2×#6699716yes—
370C22C23×C22⋊D1111yescharacteristic
371C4—23no—
372C4—23no—
373C4—46no—
374C4—42no—
375C4—446no—
376C4—442no—
377C4C2×#6699716yes—
378C4#1062336612yes—
379C4#1062336912yes—
380C4C22×Q8×D1112yes—
381C2—26no—
382C2C22×#6699711yescharacteristic
383C2C2×#1062336611yescharacteristic
384C2C2×#1062336911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3503C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenter#3503D11
hypocenterC11#60667
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #13079163C2semidirect
3. #13079158C2semidirect
4. #13079150C2semidirect
5. #13079126C2semidirect
6. C2×#10622691C2semidirect
71. #67001Q8semidirect
145. #4318C2×Q8semidirect
146. C2×C11⋊C8C2×Q8semidirect
340. C11#60667semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130791632
#130791582
#130791502
#130791262
C2×#106226912
#130772142
C4×#670012
C11×#35032
#6066711