Finite Group Databasebeta

← #14650341

Subgroups — #14650341

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071701C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic
6#13066462C211yesmaximal, characteristic
7C11×#3189C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C11×#484—21no—
11C11×#484C412yescomplemented
12C11×#467—22no—
13C11×#451—21no—
14C11×#451C412yescomplemented
15C2×C11×C22⋊C8C2211yescharacteristic
16#10622843—21no—
17#10622825C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21#10622594—21no—
22#10622594—21no—
23C4⋊C4×Dic11—21no—
24#10622563—21no—
25C22⋊C4×Dic11—21no—
26#10622176—22no—
27#10622176—21no—
28#10622176—21no—
29#10622164—21no—
30#10622164—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C2×C11×Q16—22no—
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8C2×C412yes—
44C11×C22⋊Q8D412yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11D411yescharacteristic
53C2×C22⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11—21no—
60C22×C11⋊C8—21no—
61C11×#107—22no—
62C11×#103—22no—
63C11×#103—22no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8C2×C412yes—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77#9276—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—81no—
83C2×Q8×C11—81no—
84C2×Q8×C11C22⋊C412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—81no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—42no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—81no—
105C11×Q16—82no—
106C2×C8×C11—22no—
107C2×C8×C11—81no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4C22⋊C412yes—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—21no—
121C22⋊Dic11—21no—
122C22⋊Dic11—21no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11Q1612yescomplemented
126C4⋊Dic11—42no—
127C4⋊Dic11—81no—
128C4⋊Dic11—81no—
129C4×Dic11—42no—
130C4×Dic11—81no—
131C4×Dic11—81no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—81no—
134#3189D1111yescharacteristic
135#2368—111no—
136#1996—111no—
137#1520—111no—
138C2×#328—111no—
139#1294—111no—
140#1282—111no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C4×D411yescharacteristic
144C23×C11#12011yescharacteristic
145C23×C11#12111yescharacteristic
146C23×C11C2×Q1611yescharacteristic
147C23×C11#13511yescharacteristic
148C23×C11#13711yescharacteristic
149C23×C11#13711yescharacteristic
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—81no—
153Q8×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11C2×C22⋊C411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12311yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—82no—
187C2×Dic11—82no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C8×C11—42no—
192C11⋊C8—81no—
193C2×C22⋊Q8C2×D1111yescharacteristic
194C2×C22⋊Q8C2×D1111yescharacteristic
195#484—21no—
196#484Dic1112yescomplemented
197#467—22no—
198#451—21no—
199#451Dic1112yescomplemented
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#391—221no—
203#387—221no—
204#387—221no—
205#385—221no—
206#380—111no—
207C4×C4⋊C4—221no—
208C4×C22⋊C4—111no—
209C4×C22⋊C4—221no—
210C2×#95—111no—
211#342—221no—
212#342—221no—
213#328—221no—
214#328—221no—
215#328—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11#38611yescharacteristic
227C22×C11C4×Q1611yescharacteristic
228C22×C11#44111yescharacteristic
229C22×C11#45111yescharacteristic
230C22×C11#45211yescharacteristic
231C22×C11#46211yescharacteristic
232C22×C11#46411yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—81no—
240C4×C11—81no—
241Dic11—42no—
242Dic11—42no—
243Dic11—81no—
244Dic11—81no—
245Dic11—161no—
246C22×Q8C2×Dic1111yescharacteristic
247C22×Q8C22⋊D1111yescharacteristic
248C23×C4—221no—
249C23×C4C22×D1111yescharacteristic
250C2×Q16—22no—
251C22×C8—21no—
252C22×C8—221no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8C2×Dic1112yes—
260C22⋊Q8C22⋊D1112yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4C2×Dic1111yescharacteristic
267C2×C4⋊C4C22⋊D1111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—221no—
273C2×C42—221no—
274C2×C42—221no—
275C2×C42—221no—
276#107—22no—
277#103—22no—
278#103—22no—
279C22⋊C8—21no—
280C22⋊C8—221no—
281C22⋊C8—221no—
282C22⋊C8C2×Dic1112yes—
283#95—111no—
284#95—111no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95—221no—
291#95—221no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11#187811yescharacteristic
299C2×C11#190611yescharacteristic
300C2×C11#191311yescharacteristic
301C24D4×D1111yescharacteristic
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—81no—
306C2×Q8—81no—
307C2×Q8C22⋊Dic1112yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—81no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—881no—
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4#434111yescharacteristic
325C22×C4C22×Dic1111yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327C22×C4C2×C22⋊D1111yescharacteristic
328Q16—82no—
329C2×C8—22no—
330C2×C8—81no—
331C2×C8—441no—
332C2×C8—881no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—442no—
341C4⋊C4—881no—
342C4⋊C4—881no—
343C4⋊C4C22⋊Dic1112yes—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—112no—
349C22⋊C4—221no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—442no—
355C42—881no—
356C42—881no—
357C11#927611yescharacteristic, complemented, Sylow
358C23—41no—
359C23—41no—
360C23Q16×D1111yescharacteristic
361C23#6697111yescharacteristic
362C23#6697111yescharacteristic
363C23#6697211yescharacteristic
364C23D4×Dic1111yescharacteristic
365C23#6699011yescharacteristic
366C23#6699211yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4D4×Dic1111yescharacteristic
405C2×C4#6698811yescharacteristic
406C2×C4#6699211yescharacteristic
407C2×C4C2×C22⋊Dic1111yescharacteristic
408C8—42no—
409C8—881no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1062279511yescharacteristic
421C22Q16×Dic1111yescharacteristic
422C22#1062279711yescharacteristic
423C22#1062279811yescharacteristic
424C22#1062279911yescharacteristic
425C22#1062280011yescharacteristic
426C22#1062283311yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—81no—
434C4—81no—
435C4—442no—
436C4—442no—
437C4—881no—
438C4—881no—
439C4—1761no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#1306895911yescharacteristic
447C2#1306911911yescharacteristic
448C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#3189C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#3189D11
hypocenterC11#9276
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
11. C11×#484C4semidirect
14. C11×#451C4semidirect
125. C22⋊Dic11Q16semidirect
196. #484Dic11semidirect
199. #451Dic11semidirect
357. C11#9276semidirect

Maximal subgroups

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

subgroupindex
#130717012
#130696022
#130671882
C2×#106221762
#130664962
#130664622
C11×#31892
#927611