Finite Group Databasebeta

← #14666800

Subgroups — #14666800

Order 2816.

452 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 57 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#13074932C211yesmaximal, characteristic
2#13069968C211yesmaximal, characteristic
3#13067573C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic
5#13066638C211yesmaximal, characteristic
6#13066565C211yesmaximal, characteristic
7C11×#1614C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C2×#66941—21no—
10C2×#66931—21no—
11C11×#484—21no—
12C11×#399C2211yescharacteristic
13#10622663—21no—
14#10622593—21no—
15#10622592—21no—
16#10622560C2211yescharacteristic
17#10622559—21no—
18#10622559C2211yescharacteristic
19#10622557—21no—
20#10622266—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×Dic11D411yescharacteristic
28C22×Dic22—21no—
29C22×Dic22D411yescharacteristic
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—41no—
33C11×C22⋊Q8—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×#4326—41no—
43C2×C4⋊Dic11—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—41no—
49C2×C4×Dic11—21no—
50#66941—44no—
51#66931—44no—
52C11×#107—41no—
53C11×#103—41no—
54C11×C22⋊C8—21no—
55C11×#95D411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—41no—
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63#66874—41no—
64#12252—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—42no—
81C2×Dic22—41no—
82C2×Dic22—42no—
83C2×Dic22—42no—
84C2×Dic22—42no—
85C2×Dic22—81no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C22⋊Dic11—22no—
98C22⋊Dic11—21no—
99C22⋊Dic11—42no—
100C22⋊Dic11—41no—
101C22⋊Dic11Q1612yescomplemented
102#4326—82no—
103C4⋊Dic11—24no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—82no—
109C4×Dic11—42no—
110C2×C11⋊C8—41no—
111#2677—111no—
112#2062—111no—
113#1614D1111yescharacteristic
114#1602—111no—
115#1352—111no—
116#1351—111no—
117#1326—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C23×C11C2×Q1611yescharacteristic
124C23×C11#13711yescharacteristic
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158Dic22—42no—
159Dic22—81no—
160Dic22—84no—
161C8×C11—81no—
162C11⋊C8—81no—
163#543C2×D1111yescharacteristic
164C2×C4⋊Q8—221no—
165C2×C22⋊Q8—221no—
166#484—21no—
167#451—221no—
168#399C2×D1111yescharacteristic
169#398—221no—
170#395—221no—
171#393—111no—
172#388—221no—
173#387—221no—
174#385—111no—
175#385—221no—
176#342—111no—
177#342—221no—
178#328—21no—
179#328—221no—
180#323—111no—
181#323C2×D1111yescharacteristic
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—81no—
191C22×C11#45111yescharacteristic
192C22×C11#45611yescharacteristic
193C22×C11B(4,𝔽2)11yescharacteristic
194C4×C11—42no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200Dic11—42no—
201Dic11—42no—
202Dic11—42no—
203Dic11—81no—
204Dic11—82no—
205C22×Q8—111no—
206C22×Q8—221no—
207C23×C4—111no—
208C2×Q16—441no—
209C4⋊Q8—444no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—41no—
213C22⋊Q8—41no—
214C22⋊Q8—444no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—441no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4C22×D1111yescharacteristic
229C2×C42—221no—
230#107—41no—
231#103—41no—
232#103—441no—
233C22⋊C8—21no—
234C22⋊C8—221no—
235#95—111no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—441no—
241#95C22⋊D1111yescharacteristic
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—41no—
245C2×C11—41no—
246C2×C11#160511yescharacteristic
247C2×C11#219611yescharacteristic
248C2×C11#220111yescharacteristic
249C24D4×D1111yescharacteristic
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—441no—
253C2×Q8—442no—
254C2×Q8—442no—
255C2×Q8—442no—
256C2×Q8—881no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—442no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4D4×D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270Q16—882no—
271C2×C8—41no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—224no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—882no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—112no—
290C22⋊C4—221no—
291C22⋊C4—222no—
292C22⋊C4—442no—
293C22⋊C4—441no—
294C42—442no—
295C11#1225211yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23Q16×D1111yescharacteristic
301C23#6697111yescharacteristic
302C23#6699011yescharacteristic
303Q8—81no—
304Q8—81no—
305Q8—442no—
306Q8—881no—
307Q8—884no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4—881no—
339C8—81no—
340C8—881no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22#1062264511yescharacteristic
351C22#1062279911yescharacteristic
352C22#1062281811yescharacteristic
353C4—42no—
354C4—41no—
355C4—41no—
356C4—81no—
357C4—81no—
358C4—81no—
359C4—442no—
360C4—442no—
361C4—442no—
362C4—881no—
363C4—882no—
364C2—21no—
365C2—21no—
366C2—41no—
367C2—41no—
368C2#1306758811yescharacteristic
369C2#1307059911yescharacteristic
370C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1614C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#1614D11
hypocenterC11#12252
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1614

Complements

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

NH ≅ G/Ntype
101. C22⋊Dic11Q16semidirect
295. C11#12252semidirect

Maximal subgroups

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

subgroupindex
#130749322
#130699682
#130675732
#130666402
#130666382
#130665652
C11×#16142
#1225211