Finite Group Databasebeta

← #14650979

Subgroups — #14650979

Order 2816.

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

normal subgroups only

This group has 542 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#13078552C211yesmaximal, characteristic
2#13071503C211yesmaximal, characteristic, complemented
3#13068716C211yesmaximal, characteristic, complemented
4#13067132C211yesmaximal, characteristic
5#13066522C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C2×C11×#99—22no—
11C11×#380C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622828C412yescomplemented
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622648—22no—
18#10622647—21no—
19#10622646—21no—
20C4⋊C4×Dic11—21no—
21#10622586—21no—
22#10622577C412yescomplemented
23#10622558—22no—
24#10622263—21no—
25#10622261—21no—
26#10622175—21no—
27#10622175—21no—
28#10622161—22no—
29C22×D4×C11—21no—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#121—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4D412yes—
41C2×C42×C11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44#66979—21no—
45#66979—21no—
46#66979C2×C412yes—
47#66979D412yes—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—22no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—22no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55C2×#4318C2×C412yes—
56C11×#99—44no—
57C11×#95—21no—
58C11×#95—21no—
59#66896—22no—
60#66896—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66872—22no—
70#66871—22no—
71#9367—111nomaximal, Sylow
72C24×C11—21no—
73C24×C11C2×D411yescharacteristic
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
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—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—42no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C42×C11—42no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11C22⋊C412yes—
110C4⋊Dic11C22⋊C412yes—
111Dic11⋊C4—82no—
112C4×Dic11—22no—
113C4×Dic11—22no—
114C4×Dic11—42no—
115C4×Dic11—44no—
116#4318—42no—
117#4318—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3094—111no—
121#2346—111no—
122#1964D1111yescharacteristic
123#1826—111no—
124#1507—111no—
125#1305—111no—
126#1297—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—81no—
134C23×C11—81no—
135C23×C11C4×D411yescharacteristic
136C23×C11#12011yescharacteristic
137C23×C11#12111yescharacteristic
138D4×C11—42no—
139D4×C11—81no—
140D4×C11—82no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12311yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C11⋊C8—42no—
173C11⋊C8—81no—
174C2×#121C2×D1111yescharacteristic
175C2×#117—111no—
176#482—222no—
177#481—221no—
178#480—221no—
179#428—112no—
180#418—112no—
181C2×#99—22no—
182#407—111no—
183#407—111no—
184#389—221no—
185#388—222no—
186#382—221no—
187#380C2×D1111yescharacteristic
188C4×C4⋊C4—221no—
189C4×C22⋊C4—111no—
190C4×C22⋊C4C2×D1111yescharacteristic
191#376—221no—
192#339—222no—
193#327—221no—
194#327—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—162no—
209C22×C11#38611yescharacteristic
210C22×C11#45311yescharacteristic
211C22×C11#45411yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—82no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#41012yes—
219Dic11—42no—
220Dic11—42no—
221Dic11—42no—
222Dic11—81no—
223C22×D4—21no—
224C22×D4C4×D1111yescharacteristic
225C23×C4C22×D1111yescharacteristic
226C2×M16—112no—
227C2×M16—221no—
228#121—21no—
229#121—21no—
230#121—21no—
231#121—21no—
232#117—112no—
233#117—112no—
234#117—221no—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4C4×D1111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4C22⋊D1112yes—
246C2×C42—21no—
247C2×C42—221no—
248C2×C42—222no—
249C2×C42—221no—
250#107—222no—
251#106—222no—
252#102—222no—
253#102—222no—
254#99—44no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259#95—21no—
260#95—21no—
261#95—111no—
262#95—111no—
263#95—222no—
264#95—222no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—41no—
268C2×C11—41no—
269C2×C11—161no—
270C2×C11#188311yescharacteristic
271C2×C11#189911yescharacteristic
272C2×C11#190611yescharacteristic
273C24—21no—
274C24C2×C22⋊D1111yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4#433911yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4#434111yescharacteristic
296M16—442no—
297M16—442no—
298C2×C8—222no—
299C2×C8—441no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—42no—
303C4⋊C4—112no—
304C4⋊C4—112no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—882no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—442no—
316C42—42no—
317C42—222no—
318C42—222no—
319C42—442no—
320C42—444no—
321C11#936711yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—81no—
329C23—81no—
330C23C4×C22⋊D1111yescharacteristic
331C23#6699011yescharacteristic
332C23#6699111yescharacteristic
333D4—42no—
334D4—81no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—441no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4C22⋊C4×D1111yescharacteristic
364C2×C4(C22⋊D11)⋊C411yescharacteristic
365C2×C4#6693611yescharacteristic
366C2×C4#6693711yescharacteristic
367C8—442no—
368C8—881no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—162no—
383C22#1062256911yescharacteristic
384C22#1062267511yescharacteristic
385C22#1062269011yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—81no—
392C4—442no—
393C4—442no—
394C4—442no—
395C4—881no—
396C4#1062235312yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—161no—
402C2#1306899511yescharacteristic
403C2#1306907111yescharacteristic
404C2#1306911411yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1964D11
hypocenterC11#9367
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13071503C2semidirect
3. #13068716C2semidirect
5. #13066522C2semidirect
6. #13066502C2semidirect
13. #10622828C4semidirect
22. #10622577C4semidirect
321. C11#9367semidirect

Maximal subgroups

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

subgroupindex
#130785522
#130715032
#130687162
#130671322
#130665222
#130665022
C11×#19642
#936711