Finite Group Databasebeta

← #14654594

Subgroups — #14654594

Order 2816.

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

normal subgroups only

This group has 528 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#13079822C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic
3#13069559C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067059C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic, complemented
7C11×#2562C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#400—21no—
12C11×#394—21no—
13C11×#388—22no—
14C11×#380—21no—
15C11×#380—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622831—21no—
18#10622682—21no—
19#10622678—21no—
20#10622676—22no—
21#10622632—21no—
22#10622631—22no—
23#10622620—21no—
24#10622584—21no—
25#10622583—21no—
26#10622583—21no—
27#10622539C2211yescharacteristic
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622181—22no—
31D4⋊(C11⋊C8)—22no—
32#10622161—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—22no—
52C2×C42×C11D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×#4324—22no—
55#66979—21no—
56#66977—21no—
57#66977—21no—
58C2×#4318—21no—
59#66923—21no—
60#66922D411yescharacteristic
61#66922D411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—21no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66874—22no—
71#66874—22no—
72#66874—22no—
73#66872—22no—
74#66871—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80#66867D412yes—
81C4×C11⋊C8—21no—
82#10009—111nomaximal, Sylow
83C24×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×Dic22—21no—
99C2×Dic22—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—44no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—82no—
115C42×C11—42no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C22⋊Dic11—41no—
121#4324—44no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3236—111no—
135#3110—111no—
136#2562D1111yescharacteristic
137#1986—111no—
138#1528—111no—
139#1490—111no—
140#1285—111no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11#12011yescharacteristic
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—41no—
152D4×C11—41no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×Dic11—41no—
177C2×Dic11—41no—
178Dic22—42no—
179Dic22—42no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183#533—111no—
184C2×#125C2×D1111yescharacteristic
185C2×C4×D4C2×D1111yescharacteristic
186#501—221no—
187#491—221no—
188#484—221no—
189#484—221no—
190#483—221no—
191#479—222no—
192#474—221no—
193#461—221no—
194#450—221no—
195#440—222no—
196#432—111no—
197#432—111no—
198C4×M16—111no—
199#400—21no—
200#394—21no—
201#388—22no—
202#380—21no—
203#380—21no—
204C4×C4⋊C4C2×D1111yescharacteristic
205#339—222no—
206#330—222no—
207D4⋊C8—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#39211yescharacteristic
218C22×C11#45511yescharacteristic
219C22×C11#45611yescharacteristic
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#45412yes—
230Dic11—81no—
231Dic11—81no—
232C22×D4C22⋊D1111yescharacteristic
233C23×C4—21no—
234C2×SD16—222no—
235C2×M16—221no—
236C4⋊Q8—111no—
237C4⋊Q8—111no—
238#125—21no—
239#125—21no—
240#125—21no—
241#125—21no—
242#125—221no—
243C22⋊Q8—221no—
244C22⋊Q8—221no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251#117—221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C4⋊C4C22⋊D1111yescharacteristic
257C2×C4⋊C4C22⋊D1111yescharacteristic
258C2×C22⋊C4—22no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C42C22⋊D1112yes—
262C2×C42C22×D1111yescharacteristic
263#107—222no—
264#107—222no—
265#106—222no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268#103—222no—
269#103—222no—
270#103—222no—
271#102—222no—
272C22⋊C8—221no—
273C22⋊C8—221no—
274#97—112no—
275#97—221no—
276#97—221no—
277C4×C8—221no—
278#95—22no—
279#95—22no—
280#95—21no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—82no—
284C2×C11#200311yescharacteristic
285C2×C11#200711yescharacteristic
286C2×C11#201011yescharacteristic
287C24—21no—
288C2×Q8—221no—
289C2×Q8—221no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×C22⋊D1111yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304SD16—444no—
305M16—222no—
306M16—441no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C22⋊C4—44no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—82no—
331C22⋊C4—441no—
332C42—42no—
333C42—441no—
334C42D4×D1111yescharacteristic
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C11#1000911yescharacteristic, complemented, Sylow
339C23—22no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23#6700611yescharacteristic
347Q8—442no—
348Q8—442no—
349D4—22no—
350D4—22no—
351D4—41no—
352D4—41no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4#6699011yescharacteristic
373C2×C4#6699011yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6699211yescharacteristic
377C2×C4#6699311yescharacteristic
378C8—442no—
379C8—442no—
380C8—442no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22#1062283611yescharacteristic
391C22#1062285511yescharacteristic
392C22#1062285911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—881no—
403C4—881no—
404C4#1062267512yes—
405C2—21no—
406C2—21no—
407C2—82no—
408C2#1306963811yescharacteristic
409C2#1306966311yescharacteristic
410C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2562C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#2562D11
hypocenterC11#10009
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. #13079822C2semidirect
3. #13069559C2semidirect
4. #13067218C2semidirect
6. #13066472C2semidirect
338. C11#10009semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130787152
#130695592
#130672182
#130670592
#130664722
C11×#25622
#1000911