Finite Group Databasebeta

← #14666947

Subgroups — #14666947

Order 2816.

412 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069772C211yesmaximal, characteristic, complemented
2#13067657C211yesmaximal, characteristic, complemented
3#13067555C211yesmaximal, characteristic, complemented
4#13066643C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#2828C211yesmaximal, characteristic
8#10623031C2211yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#397—21no—
11C11×#394—21no—
12C11×#394—21no—
13C11×#394C2211yescharacteristic
14C11×#392—21no—
15C11×#392—21no—
16C11×#390C2211yescharacteristic
17C11×#388—21no—
18#10622831—21no—
19#10622828—21no—
20#10622583—21no—
21#10622168C2211yescharacteristic
22#10622166C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622161—21no—
25#10622090—21no—
26#10622090—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C42×C11D411yescharacteristic
43C2×#4324—41no—
44#66979—21no—
45#66977—21no—
46#66977—21no—
47C2×#4318—21no—
48#66943—41no—
49#66941—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55#66896—41no—
56#66896—41no—
57#66896—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66871—41no—
62#12274—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C2×D4×C11—81no—
74C2×D4×C11—81no—
75C2×D4×C11—81no—
76C2×D4×C11—81no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×Dic22—21no—
85C2×Dic22—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—81no—
92C11×C22⋊C4—81no—
93C11×C22⋊C4—81no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—41no—
99C22⋊Dic11—41no—
100#4324—82no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2828D1111yescharacteristic
114#2027—111no—
115#1617—111no—
116#1599—111no—
117#1353—111no—
118#1345—111no—
119#1318—111no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11#12011yescharacteristic
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—84no—
140D4×C11—84no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163Dic22—81no—
164Dic22—81no—
165C11⋊C8—81no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168#544—111no—
169#484—221no—
170#450—221no—
171#418—221no—
172#400C2×D1111yescharacteristic
173#397—21no—
174#394—21no—
175#394—21no—
176#394C2×D1111yescharacteristic
177#392—21no—
178#392—21no—
179#390C2×D1111yescharacteristic
180#388—21no—
181#343—111no—
182#339—221no—
183#328—221no—
184#328—221no—
185#324—111no—
186#324—111no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#45211yescharacteristic
204C22×C11#45511yescharacteristic
205C22×C11B(4,𝔽2)11yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214Dic11—81no—
215Dic11—81no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C22⋊D1111yescharacteristic
219C22×D4C22⋊D1111yescharacteristic
220C2×SD16—441no—
221C2×M16—221no—
222C4⋊Q8—441no—
223#125—441no—
224C22⋊Q8—221no—
225C22⋊Q8—221no—
226#117—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C42C22⋊D1111yescharacteristic
239#107—441no—
240#103—441no—
241#102—441no—
242#102—441no—
243#102—441no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95C22⋊D1111yescharacteristic
250#95C22⋊D1111yescharacteristic
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—161no—
254C2×C11—161no—
255C2×C11#160611yescharacteristic
256C2×C11#220011yescharacteristic
257C2×C11#220211yescharacteristic
258C24—21no—
259C24—21no—
260C2×Q8—221no—
261C2×Q8—221no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—81no—
268C2×D4—81no—
269C2×D4—81no—
270C2×D4—81no—
271C2×D4—81no—
272C2×D4—81no—
273C2×D4—81no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—882no—
282M16—441no—
283M16—441no—
284C2×C8—441no—
285C2×C8—441no—
286C2×C8—441no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—441no—
306C42—41no—
307C42—441no—
308C11#1227411yescharacteristic, complemented, Sylow
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#6700611yescharacteristic
324Q8—881no—
325Q8—881no—
326D4—42no—
327D4—42no—
328D4—81no—
329D4—81no—
330D4—84no—
331D4—84no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4#6700311yescharacteristic
353C2×C4#6700411yescharacteristic
354C8—881no—
355C8—881no—
356C8—881no—
357C22—21no—
358C22—21no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22#1062285211yescharacteristic
374C22#1062285511yescharacteristic
375C22#1062285711yescharacteristic
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—881no—
385C4—881no—
386C2—21no—
387C2—21no—
388C2—161no—
389C2—161no—
390C2#1306759611yescharacteristic
391C2#1307062311yescharacteristic
392C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2828C2
socleC22×C11B(4,𝔽2)
hypercenter#2828D11
hypocenterC11#12274
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2828

Complements

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

NH ≅ G/Ntype
1. #13069772C2semidirect
2. #13067657C2semidirect
3. #13067555C2semidirect
4. #13066643C2semidirect
5. #13066619C2semidirect
6. #13066548C2semidirect
308. C11#12274semidirect

Maximal subgroups

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

subgroupindex
#130697722
#130676572
#130675552
#130666432
#130666192
#130665482
C11×#28282
#1227411