Finite Group Databasebeta

← #14729987

Subgroups — #14729987

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079158C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic
3#13078746C211yesmaximal, characteristic
4#13067893C214yesmaximal, complemented
5#13067858C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic
7#13067063C211yesmaximal, characteristic
8#13067063C211yesmaximal, characteristic
9C2×C11×#557C211yesmaximal, characteristic
10C11×#557—22no—
11C11×#557—22no—
12C11×#557—22no—
13C11×#557C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—22no—
17C2×C11×#125—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22#10623001C2211yescharacteristic
23#10622841—21no—
24#10622841—21no—
25#10622693—22no—
26#10622692C2212yes—
27#10622691C2212yes—
28#10622644C2212yes—
29#10622644C2212yes—
30#10622643—22no—
31#10622643—22no—
32#10622633C2212yes—
33#10622633C2212yes—
34#10622584—21no—
35#10622584—21no—
36#10622577—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yes—
41Q8⋊(C11⋊C8)C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11D411yescharacteristic
46C11×C4⋊Q8—24no—
47C11×C4⋊Q8—24no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8C2312yes—
52C11×#125—28no—
53C11×#125—24no—
54C11×#125—28no—
55C11×#125—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D412yes—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×Q8×C11C2312yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4326—22no—
83#66979—21no—
84#66977—21no—
85#66977—21no—
86C2×#4318—21no—
87#66923—21no—
88#66922C2311yescharacteristic
89#66922C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92#66899—22no—
93#66899—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66874—22no—
97#66874—22no—
98#66872—24no—
99#66872—22no—
100#66872—22no—
101#66871—24no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108#18541—111nomaximal, Sylow
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—42no—
115C2×Q8×C11—44no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×D412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—21no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2×D414yes—
141C11×C4⋊C4C2×D412yes—
142C11×C4⋊C4C2×D412yes—
143C42×C11—28no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2411yescharacteristic
152C22⋊Dic11—41no—
153#4326—44no—
154#4326—44no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162#4318—24no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×#557D1111yescharacteristic
167#3165—111no—
168#3113—111no—
169#3113—111no—
170#1653—114no—
171#1648—114no—
172#1556—111no—
173#1491—111no—
174#1491—111no—
175C23×C11#12011yescharacteristic
176Q8×C11—24no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—42no—
181Q8×C11—44no—
182Q8×C11—44no—
183Q8×C11#13714yes—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×Dic11—41no—
204C2×Dic11—41no—
205Dic22—42no—
206Dic22—42no—
207C11⋊C8—24no—
208C11⋊C8—42no—
209C11⋊C8—42no—
210#557—22no—
211#557—22no—
212#557—22no—
213#557C2×D1114yes—
214#533—111no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×#125—22no—
218C2×#125—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8C2×D1111yescharacteristic
222C2×C4×Q8C2×D1111yescharacteristic
223#501—222no—
224#500—112no—
225#498—112no—
226#483—221no—
227#483—221no—
228#475—112no—
229#475—112no—
230#462—112no—
231#462—112no—
232#451—221no—
233#451—221no—
234#441—222no—
235#441—222no—
236#432—111no—
237#432—111no—
238#428—222no—
239C4×M16—111no—
240#332—114no—
241Q8⋊C8—114no—
242Q8⋊C8—114no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#45612yes—
246C22×C11C2×#12011yescharacteristic
247C4×C11—24no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—42no—
253C4×C11—44no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11C2×#13712yes—
257C4×C11#57512yes—
258Dic11—81no—
259Dic11—81no—
260C22×Q8—21no—
261C22×Q8C22⋊D1111yescharacteristic
262C22×Q8C22⋊D1111yescharacteristic
263C2×Q16—222no—
264C2×Q16—222no—
265C2×M16—221no—
266C4⋊Q8—24no—
267C4⋊Q8—24no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—111no—
271C4⋊Q8—111no—
272C4⋊Q8C22⋊D1112yes—
273C4⋊Q8C22×D1112yes—
274#125—28no—
275#125—24no—
276#125—28no—
277#125—24no—
278#125—221no—
279C22⋊Q8—221no—
280C22⋊Q8—221no—
281C4×Q8—24no—
282C4×Q8—24no—
283C4×Q8—24no—
284C4×Q8—24no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—221no—
290C4×Q8—221no—
291C4×Q8C22⋊D1112yes—
292C4×Q8C22⋊D1112yes—
293C4×Q8C22×D1112yes—
294C4×Q8C22×D1112yes—
295#117—221no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C4⋊C4C22⋊D1111yescharacteristic
304C2×C4⋊C4C22⋊D1112yes—
305C2×C42—22no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42C22×D1111yescharacteristic
309#107—224no—
310#106—224no—
311#106—222no—
312#106—222no—
313C4⋊C8—112no—
314C4⋊C8—112no—
315#103—222no—
316#103—222no—
317#103—222no—
318#103—222no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#97—221no—
322#97—221no—
323#97—221no—
324C4×C8—112no—
325C2×C11—22no—
326C2×C11#300411yescharacteristic
327C2×C11#300511yescharacteristic
328C2×C11C2×#45611yescharacteristic
329C2×Q8—24no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—221no—
337C2×Q8—221no—
338C2×Q8C2×C22⋊D1112yes—
339C2×Q8C2×C22⋊D1112yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348Q16—444no—
349Q16—444no—
350M16—224no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—222no—
354C4⋊C4—28no—
355C4⋊C4—28no—
356C4⋊C4—28no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4C2×C22⋊D1112yes—
373C4⋊C4C2×C22⋊D1112yes—
374C4⋊C4C2×C22⋊D1114yes—
375C22⋊C4—441no—
376C42—28no—
377C42—22no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—441no—
382C42C2×C22⋊D1111yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C42C23×D1111yescharacteristic
386C11#1854111yescharacteristic, complemented, Sylow
387C23#6700611yescharacteristic
388Q8—24no—
389Q8—22no—
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—44no—
394Q8—44no—
395Q8—442no—
396Q8—442no—
397Q8#6699514yes—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4#6700611yescharacteristic
414C2×C4#6700611yescharacteristic
415C2×C4#6700611yescharacteristic
416C2×C4C22×C22⋊D1111yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C2×C4C22×C22⋊D1111yescharacteristic
419C8—224no—
420C8—442no—
421C8—442no—
422C22—21no—
423C22—21no—
424C22#1062285912yes—
425C22C2×#6700611yescharacteristic
426C4—24no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—44no—
433C4—42no—
434C4—42no—
435C4—881no—
436C4—881no—
437C4C2×#6699512yes—
438C4#1062335312yes—
439C2—22no—
440C2#1307785011yescharacteristic
441C2#1307785811yescharacteristic
442C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#557C2
socleC22×C11C2×#120
prime radicalC23×C11#120
hypercenterC2×#557D11
hypocenterC11#18541
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13067893C2semidirect
5. #13067858C2semidirect
386. C11#18541semidirect

Maximal subgroups

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

subgroupindex
#130791582
#130787462
#130678932
#130678582
#130673332
#130670632
C2×C11×#5572
#1854111