Finite Group Databasebeta

← #14649823

Subgroups — #14649823

Order 2816.

612 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074423C211yesmaximal, characteristic
2#13071213C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic, complemented
4C2×#10622106C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12#10622844C412yescomplemented
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622607—22no—
17#10622605C412yescomplemented
18#10622603—22no—
19#10622568—21no—
20#10622568—21no—
21#10622559—21no—
22C22⋊C4×Dic11—21no—
23#10622283—22no—
24C11×#328—22no—
25#10622176—22no—
26#10622106—22no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×C8×C11—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4D412yes—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×Dic11⋊C4—22no—
56C2×C4×Dic11—22no—
57C22×C11⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95D412yes—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95C2×C412yes—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9201—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—21no—
74C23×D11—21no—
75C23×D11—81no—
76C23×D11—81no—
77C23×D11C22⋊C412yes—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—81no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—81no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—21no—
95C22×Dic11—81no—
96C22×Dic11C22⋊C412yes—
97C2×C8×C11—41no—
98C2×C8×C11—81no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—81no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—82no—
117(C2×D11)⋊C4—82no—
118(C2×D11)⋊C4—82no—
119(C2×D11)⋊C4—82no—
120C4⋊Dic11—81no—
121C4⋊Dic11—81no—
122Dic11⋊C4—82no—
123C4×Dic11—82no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—81no—
126#2626—111no—
127#2312—111no—
128#1520—111no—
129#1520D1111yescharacteristic, complemented
130C2×#323—111no—
131#1289—111no—
132#1289—111no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11#12011yescharacteristic
137C23×C11#12311yescharacteristic
138C23×C11#13511yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13711yescharacteristic
141C23×C11#13711yescharacteristic
142C22×D11—22no—
143C22×D11—22no—
144C22×D11—22no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—82no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159Q8×C11—81no—
160Q8×C11—81no—
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—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—81no—
188C8×C11—81no—
189C11⋊C8—81no—
190C2×C22⋊Q8C2×D1111yescharacteristic
191C22×C22⋊C4—111no—
192C2×C22⋊C8—111no—
193C2×C22⋊C8C2×D1111yescharacteristic
194#399—112no—
195#396—222no—
196#393—112no—
197#388—222no—
198#388—222no—
199#385—221no—
200#380—111no—
201#380—111no—
202#380C2×D1111yescharacteristic
203#379—221no—
204#379—221no—
205C4×C22⋊C4—221no—
206#328—22no—
207#328—222no—
208#323—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11#38611yescharacteristic
220C22×C11#41611yescharacteristic
221C22×C11#41911yescharacteristic
222C22×C11#45211yescharacteristic
223C22×C11#45211yescharacteristic
224C22×C11#48511yescharacteristic
225C22×C11#48511yescharacteristic
226C2×D11—44no—
227C2×D11—42no—
228C2×D11—42no—
229C2×D11—42no—
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—82no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11—81no—
242Dic11—42no—
243Dic11—82no—
244Dic11—82no—
245C25—111no—
246C22×Q8C4×D1111yescharacteristic
247C23×C4—111no—
248C23×C4C22×D1111yescharacteristic
249C22×C8—21no—
250C22×C8—221no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4C4×D1111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—112no—
264C2×C22⋊C4—112no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4—222no—
274C2×C22⋊C4—222no—
275C2×C42—222no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280#95—112no—
281#95—112no—
282#95—222no—
283#95—222no—
284#95C22⋊D1112yes—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11#187311yescharacteristic
292C2×C11#191111yescharacteristic
293C2×C11#191311yescharacteristic
294D11—82no—
295C24—112no—
296C24—221no—
297C24—221no—
298C24—221no—
299C24—221no—
300C24—221no—
301C24—221no—
302C24—881no—
303C24—881no—
304C24D4×D1111yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—81no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—81no—
312C22×C4—112no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—881no—
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4#433911yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4#434111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324C2×C8—41no—
325C2×C8—81no—
326C2×C8—441no—
327C2×C8—881no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4—882no—
334C4⋊C4—881no—
335C4⋊C4—881no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—882no—
349C22⋊C4—882no—
350C22⋊C4—882no—
351C22⋊C4—882no—
352C42—882no—
353C11#920111yescharacteristic, complemented, Sylow
354C23—41no—
355C23—41no—
356C23—222no—
357C23—222no—
358C23—222no—
359C23—442no—
360C23—442no—
361C23—442no—
362C23—442no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—881no—
368C23—881no—
369C23—882no—
370C23—882no—
371C23—882no—
372C23—882no—
373C23C22⋊C4×D1111yescharacteristic
374C23#6693611yescharacteristic
375C23#6696811yescharacteristic
376C23#6696911yescharacteristic
377C23#6697111yescharacteristic
378C23#6697211yescharacteristic
379C23#6699011yescharacteristic
380Q8—81no—
381Q8—81no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—222no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—881no—
405C2×C4(C22⋊D11)⋊C411yescharacteristic
406C2×C4#6693711yescharacteristic
407C2×C4C4×C22⋊D1111yescharacteristic
408C2×C4#6699111yescharacteristic
409C8—81no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—444no—
422C22—442no—
423C22—442no—
424C22—442no—
425C22—882no—
426C22—882no—
427C22—882no—
428C22—882no—
429C22—882no—
430C22#1062241511yescharacteristic
431C22#1062241711yescharacteristic
432C22#1062242711yescharacteristic
433C22#1062242811yescharacteristic
434C22#1062256911yescharacteristic
435C22#1062278611yescharacteristic
436C22#1062280011yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—442no—
445C4—882no—
446C4—882no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—882no—
454C2#1306892511yescharacteristic
455C2#1306914511yescharacteristic
456C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#386
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9201
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
3. #13067188C2semidirect
5. #13066484C2semidirect
6. #13066483C2semidirect
7. C11×#1520C2semidirect
12. #10622844C4semidirect
17. #10622605C4semidirect
129. #1520D11semidirect
353. C11#9201semidirect

Maximal subgroups

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

subgroupindex
#130744232
#130712132
#130671882
C2×#106221062
#130664842
#130664832
C11×#15202
#920111