Finite Group Databasebeta

← #14732389

Subgroups — #14732389

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079760C211yesmaximal, characteristic
2#13078655C211yesmaximal, characteristic
3#13078421C211yesmaximal, characteristic
4#13067893C214yesmaximal, complemented
5#13067774C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic
7#13067045C211yesmaximal, characteristic
8#13067011C211yesmaximal, 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#10622838—21no—
25#10622707—22no—
26#10622706C2212yes—
27#10622692C2212yes—
28#10622644C2212yes—
29C4×#4326—22no—
30#10622635—22no—
31#10622634C2212yes—
32#10622634C2212yes—
33#10622633C2212yes—
34#10622584—22no—
35#10622583—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
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⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D412yes—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82#66979—21no—
83#66977—21no—
84#66977—21no—
85C2×#4318—21no—
86#66923—21no—
87#66922C2311yescharacteristic
88#66922C2311yescharacteristic
89C4×Dic22—21no—
90C4×Dic22—21no—
91#66899—22no—
92#66899—22no—
93#66899—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66874—22no—
97#66874—24no—
98#66872—22no—
99#66872—24no—
100#66871—22no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108#18761—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—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11C2×D412yes—
119C2×Q8×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×Dic22—21no—
129C2×Dic22—21no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D412yes—
143C11×C4⋊C4C2×D412yes—
144C11×C4⋊C4C2×D414yes—
145C42×C11—28no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—41no—
155#4326—44no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×#557D1111yescharacteristic
168#3229—111no—
169#3104—111no—
170#3078—111no—
171#1653—114no—
172#1636—114no—
173#1546—111no—
174#1487—111no—
175#1479—111no—
176C23×C11#12011yescharacteristic
177Q8×C11—24no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—44no—
185Q8×C11#13714yes—
186C2×C4×C11—24no—
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—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—44no—
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#13512yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208Dic22—42no—
209Dic22—42no—
210C11⋊C8—42no—
211C11⋊C8—42no—
212C11⋊C8—42no—
213#557—22no—
214#557—22no—
215#557—22no—
216#557C2×D1114yes—
217#533—111no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2×D1111yescharacteristic
220C2×#125—22no—
221C2×#125—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8C2×D1111yescharacteristic
225C2×C4×Q8C2×D1111yescharacteristic
226#498—112no—
227#487—112no—
228#484—221no—
229#483—222no—
230#479—222no—
231#477—112no—
232#477—112no—
233#475—112no—
234#475—222no—
235#462—112no—
236#451—221no—
237C4×Q16—222no—
238#431—111no—
239#431—111no—
240#428—221no—
241#423—111no—
242#419—221no—
243#332—114no—
244Q8⋊C8—114no—
245Q8⋊C8—114no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11#45212yes—
249C22×C11C2×#12011yescharacteristic
250C4×C11—24no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11—44no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11#45212yes—
259C4×C11C2×#13511yescharacteristic
260C4×C11C2×#13712yes—
261C4×C11C2×#13711yescharacteristic
262Dic11—81no—
263Dic11—81no—
264C22×Q8—21no—
265C22×Q8C22⋊D1111yescharacteristic
266C22×Q8C22⋊D1111yescharacteristic
267C2×Q16—222no—
268C2×M16—221no—
269C4⋊Q8—24no—
270C4⋊Q8—24no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8C22⋊D1112yes—
276C4⋊Q8C22×D1112yes—
277#125—28no—
278#125—24no—
279#125—28no—
280#125—24no—
281#125—221no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284C4×Q8—24no—
285C4×Q8—24no—
286C4×Q8—24no—
287C4×Q8—24no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×Q8C22⋊D1112yes—
295C4×Q8C22⋊D1112yes—
296C4×Q8C22×D1112yes—
297C4×Q8C22×D1112yes—
298#117—221no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C22⋊D1111yescharacteristic
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22⋊D1112yes—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42C22×D1111yescharacteristic
312#107—222no—
313#107—222no—
314#106—222no—
315#106—224no—
316C4⋊C8—112no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320#103—222no—
321#103—222no—
322#103—222no—
323#103—222no—
324#103—224no—
325C22⋊C8—221no—
326C22⋊C8—221no—
327C4×C8—112no—
328C4×C8—221no—
329C2×C11—22no—
330C2×C11C2×#45211yescharacteristic
331C2×C11#300411yescharacteristic
332C2×C11#302011yescharacteristic
333C2×Q8—24no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8C2×C22⋊D1112yes—
345C2×Q8C2×C22⋊D1112yes—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354Q16—444no—
355M16—442no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C4⋊C4—28no—
360C4⋊C4—28no—
361C4⋊C4—28no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4C2×C22⋊D1114yes—
378C4⋊C4C2×C22⋊D1112yes—
379C4⋊C4C2×C22⋊D1112yes—
380C22⋊C4—441no—
381C42—28no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—441no—
387C42C2×C22⋊D1111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1876111yescharacteristic, complemented, Sylow
392C23#6700611yescharacteristic
393Q8—24no—
394Q8—22no—
395Q8—22no—
396Q8—22no—
397Q8—42no—
398Q8—42no—
399Q8—42no—
400Q8—44no—
401Q8—442no—
402Q8—442no—
403Q8#6699514yes—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4#6700312yes—
419C2×C4#6700412yes—
420C2×C4#6700611yescharacteristic
421C2×C4#6700611yescharacteristic
422C2×C4#6700611yescharacteristic
423C2×C4C22×C22⋊D1111yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C2×C4C22×C22⋊D1111yescharacteristic
426C8—442no—
427C8—442no—
428C8—442no—
429C22—21no—
430C22—21no—
431C22#1062285212yes—
432C22C2×#6700611yescharacteristic
433C4—24no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—44no—
439C4—42no—
440C4—42no—
441C4—881no—
442C4—881no—
443C4#1062285212yes—
444C4C2×#6699512yes—
445C4C2×#6700311yescharacteristic
446C4C2×#6700411yescharacteristic
447C2—22no—
448C2C2×#1062285211yescharacteristic
449C2#1307785011yescharacteristic
450C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#557C2
socleC22×C11C2×#120
prime radicalC23×C11#120
hypercenterC2×#557D11
hypocenterC11#18761
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. #13067774C2semidirect
391. C11#18761semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130786552
#130784212
#130678932
#130677742
#130672882
#130670452
#130670112
C2×C11×#5572
#1876111