Finite Group Databasebeta

← #14654393

Subgroups — #14654393

Order 2816.

518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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, complemented
2#13078552C211yesmaximal, characteristic
3#13068685C211yesmaximal, characteristic, complemented
4#13066980C211yesmaximal, characteristic, complemented
5#13066976C211yesmaximal, characteristic
6#13066493C211yesmaximal, characteristic, complemented
7C11×#3187C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66979C2211yescharacteristic
11C11×#483—21no—
12C11×#481—21no—
13C11×#465—22no—
14C11×#450—21no—
15C11×#448—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622838—21no—
18#10622828—21no—
19#10622820C2211yescharacteristic
20#10622820C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622658—22no—
23#10622657—21no—
24#10622656—21no—
25#10622648—22no—
26#10622647—21no—
27#10622646—21no—
28#10622577—21no—
29#10622577—21no—
30#10622188—22no—
31#10622166—22no—
32#10622163—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C2×C11×SD16—22no—
38C22×C8×C11D412yes—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53#66979—21no—
54#66979—21no—
55#66979—21no—
56#66979—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4×Dic11—21no—
60C2×#4318—21no—
61C2×#4318—21no—
62C22×C11⋊C8—21no—
63C11×#106—22no—
64C11×#103—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68#66899—22no—
69#66899—22no—
70#66896—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77C22⋊(C11⋊C8)D412yes—
78#66872—22no—
79#66872—22no—
80#66871—22no—
81#66871—22no—
82#9978—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11#4111yescharacteristic
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—42no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—82no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—42no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C11×SD16—82no—
107C2×C8×C11—22no—
108C2×C8×C11—42no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127#4318—42no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—41no—
133#3187D1111yescharacteristic
134#3095—111no—
135#3094—111no—
136#1818—111no—
137#1472—111no—
138#1471—111no—
139#1293—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11#12111yescharacteristic
148C23×C11#12111yescharacteristic
149C23×C11#12111yescharacteristic
150Q8×C11—42no—
151Q8×C11—42no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—82no—
155D4×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C11⋊C8—81no—
180C2×C22⋊Q8C2×D1111yescharacteristic
181C2×#121C2×D1111yescharacteristic
182C2×#117—111no—
183#485—222no—
184#484—221no—
185#483—21no—
186#483—221no—
187#482—222no—
188#481—21no—
189#481—221no—
190#480—221no—
191#465—22no—
192#450—21no—
193#448—21no—
194#428—221no—
195#428—221no—
196#419—221no—
197#418—221no—
198#407—111no—
199#407—111no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#336—222no—
203#324—222no—
204#323—222no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—162no—
218C22×C11#39211yescharacteristic
219C22×C11#47112yes—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#45812yes—
227Dic11—81no—
228Dic11—81no—
229C22×Q8C22⋊D1111yescharacteristic
230C22×D4—21no—
231C22×D4C22⋊D1111yescharacteristic
232C23×C4C22×D1111yescharacteristic
233C2×SD16—22no—
234C2×M16—221no—
235C2×M16—221no—
236C22×C8—221no—
237C22×C8C22⋊D1112yes—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242#121—21no—
243#121—21no—
244#121—21no—
245#121—21no—
246#117—221no—
247#117—221no—
248#117—221no—
249#117—221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—221no—
258C2×C42—221no—
259#107—222no—
260#107—222no—
261#106—22no—
262#106—222no—
263#106—222no—
264#103—22no—
265#103—222no—
266#103—222no—
267#102—22no—
268#102—222no—
269#102—222no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—112no—
273C22⋊C8—112no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C2×C11—22no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11—161no—
282C2×C11#201711yescharacteristic
283C2×C11#201911yescharacteristic
284C2×C11#202211yescharacteristic
285C24—21no—
286C24#434111yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—82no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—82no—
309M16—442no—
310M16—442no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—442no—
316C2×C8—441no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C42—441no—
334C42—441no—
335C11#997811yescharacteristic, complemented, Sylow
336C23—22no—
337C23—41no—
338C23—41no—
339C23—42no—
340C23—41no—
341C23—81no—
342C23—81no—
343C23#6699111yescharacteristic
344C23#6699211yescharacteristic
345C23#6699211yescharacteristic
346Q8—42no—
347Q8—42no—
348D4—42no—
349D4—42no—
350D4—82no—
351D4—82no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4#6699011yescharacteristic
369C2×C4#6699011yescharacteristic
370C2×C4#6699311yescharacteristic
371C2×C4#6700611yescharacteristic
372C8—42no—
373C8—442no—
374C8—442no—
375C8—881no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—82no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—162no—
389C22#1062279012yes—
390C22#1062283611yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—881no—
398C4—881no—
399C4#1062285612yes—
400C2—22no—
401C2—41no—
402C2—41no—
403C2—161no—
404C2#1306971911yescharacteristic
405C2#1306972811yescharacteristic
406C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3187C2
socleC22×C11#392
prime radicalC2×C11×#121C22
hypercenter#3187D11
hypocenterC11#9978
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. #13078560C2semidirect
3. #13068685C2semidirect
4. #13066980C2semidirect
6. #13066493C2semidirect
335. C11#9978semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130785522
#130686852
#130669802
#130669762
#130664932
C11×#31872
#997811