Finite Group Databasebeta

← #14650826

Subgroups — #14650826

Order 2816.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078560C211yesmaximal, characteristic
2#13077270C211yesmaximal, characteristic
3#13068708C211yesmaximal, characteristic
4#13066980C211yesmaximal, characteristic
5#13066522C211yesmaximal, characteristic
6#13066504C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12#10622838C411yescharacteristic, complemented
13#10622838C411yescharacteristic, complemented
14#10622820C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622715—21no—
18#10622714—21no—
19#10622658—21no—
20#10622658—21no—
21#10622657—21no—
22#10622656—21no—
23#10622577C411yescharacteristic, complemented
24#10622577C411yescharacteristic, complemented
25#10622333—22no—
26#10622332—21no—
27#10622331—21no—
28C11×#328—21no—
29C11×#328—21no—
30#10622167—21no—
31#10622167—21no—
32#10622166—22no—
33C22×Q8×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C8×C11—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46#66979—21no—
47#66979—21no—
48#66979C2×C411yescharacteristic
49#66979C2×C411yescharacteristic
50#66979D411yescharacteristic
51#66979D411yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4×Dic11—21no—
55C2×#4318—21no—
56C2×#4318C2×C411yescharacteristic
57C2×#4318C2×C411yescharacteristic
58C22×C11⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8D411yescharacteristic
61C11×C22⋊C8D411yescharacteristic
62C11×#95—21no—
63#66899—21no—
64#66899—21no—
65#66899—21no—
66#66899—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66879—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77#66872—21no—
78#66872—21no—
79#66871—21no—
80#66871—21no—
81#9346—111nomaximal, Sylow
82C24×C11#4111yescharacteristic
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—81no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—21no—
116C22⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22⋊C411yescharacteristic
120C4⋊Dic11C22⋊C411yescharacteristic
121C4⋊Dic11C22⋊C411yescharacteristic
122C4⋊Dic11C22⋊C411yescharacteristic
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127#4318—41no—
128#4318—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#3095—111no—
138#2924—111no—
139#1825—111no—
140#1520D1111yescharacteristic
141#1472—111no—
142#1305—111no—
143#1298—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11C4×D411yescharacteristic
149C23×C11#12111yescharacteristic
150C23×C11#12311yescharacteristic
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—81no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11C2×C22⋊C411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—81no—
181C8×C11—41no—
182C8×C11—41no—
183C11⋊C8—42no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186C11⋊C8—81no—
187C2×C22⋊Q8C2×D1111yescharacteristic
188C2×#117—111no—
189#485—221no—
190#485—221no—
191#484—221no—
192#483—221no—
193#433—222no—
194#432—221no—
195#431—221no—
196#428—111no—
197#428—111no—
198#424—221no—
199#419—111no—
200#419—111no—
201#407—111no—
202#407—111no—
203C2×C22⋊C8—111no—
204C2×C22⋊C8C2×D1111yescharacteristic
205#405—221no—
206#380C2×D1111yescharacteristic
207#340—221no—
208#340—221no—
209#328—21no—
210#328—21no—
211#324—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#38611yescharacteristic
223C22×C11#47111yescharacteristic
224C22×C11#47311yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—161no—
231C4×C11#41011yescharacteristic
232C4×C11#41011yescharacteristic
233Dic11—41no—
234Dic11—41no—
235Dic11—41no—
236Dic11—41no—
237C22×Q8C4×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C2×M16—111no—
240C2×M16—111no—
241C2×M16—221no—
242C22×C8—21no—
243C22×C8—221no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#117—111no—
249#117—111no—
250#117—111no—
251#117—111no—
252#117—221no—
253#117—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—221no—
262C2×C42—221no—
263#107—221no—
264#107—221no—
265#106—221no—
266#106—221no—
267C4⋊C8—222no—
268C4⋊C8—222no—
269#103—221no—
270#103—221no—
271#103—221no—
272#103—221no—
273C22⋊C8—21no—
274C22⋊C8—112no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C22⋊C8C22⋊D1111yescharacteristic
281C22⋊C8C22⋊D1111yescharacteristic
282#97—222no—
283C4×C8—222no—
284#95—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11#188111yescharacteristic
290C2×C11#189911yescharacteristic
291C2×C11#190811yescharacteristic
292C24#434111yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—41no—
296C2×Q8—41no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4C2×C4×D1111yescharacteristic
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310M16—441no—
311M16—441no—
312M16—441no—
313M16—441no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—221no—
319C2×C8—221no—
320C2×C8—222no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—111no—
331C4⋊C4—111no—
332C4⋊C4—111no—
333C4⋊C4—111no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C42—221no—
344C42—221no—
345C42—221no—
346C42—221no—
347C11#934611yescharacteristic, complemented, Sylow
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23(C22⋊D11)⋊C411yescharacteristic
353C23#6693611yescharacteristic
354C23#6699111yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4C22⋊C4×D1111yescharacteristic
382C2×C4#6693711yescharacteristic
383C2×C4C4×C22⋊D1111yescharacteristic
384C2×C4#6699011yescharacteristic
385C8—41no—
386C8—41no—
387C8—442no—
388C8—441no—
389C8—441no—
390C8—881no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—81no—
400C22—81no—
401C22#1062256911yescharacteristic
402C22#1062279011yescharacteristic
403C22#1062280511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—81no—
408C4—81no—
409C4—161no—
410C4—441no—
411C4—441no—
412C4—441no—
413C4—441no—
414C4#1062235311yescharacteristic
415C4#1062235311yescharacteristic
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1306897511yescharacteristic
421C2#1306907111yescharacteristic
422C2#1306913411yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#386
prime radicalC24×C11#41
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9346
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
12. #10622838C4semidirect
13. #10622838C4semidirect
23. #10622577C4semidirect
24. #10622577C4semidirect
347. C11#9346semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130772702
#130687082
#130669802
#130665222
#130665042
C11×#15202
#934611