Finite Group Databasebeta

← #14657343

Subgroups — #14657343

Order 2816.

492 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 101 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#13068608C211yesmaximal, characteristic, complemented
2#13067386C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#459—22no—
12C11×#459—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C2×#66897—21no—
16#10622538C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20#10622182—22no—
21#10622182—22no—
22D4⋊(C11⋊C8)—22no—
23#10622168—21no—
24#10622118—22no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C2×C11×D8—24no—
31C2×C11×D8—42no—
32C2×C11×D8—42no—
33C22×C8×C11—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127D412yes—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D412yes—
49C11×#102—24no—
50#66897—42no—
51C22⋊(C11⋊C8)—21no—
52C22⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#10441—111nomaximal, Sylow
62C24×C11—21no—
63C24×C11—41no—
64C2×D4×C11—21no—
65C2×D4×C11—22no—
66C2×D4×C11—21no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—82no—
80C2×D4×C11—82no—
81C2×D4×C11SD1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—82no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C11×D8—48no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101#4318—41no—
102#4318—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×#459D1111yescharacteristic
110#1800—111no—
111#1570—111no—
112#1545—111no—
113#1545—111no—
114#1478—111no—
115#1301—111no—
116C23×C11—22no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—42no—
120C23×C11—81no—
121C23×C11—81no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11#12311yescharacteristic
127D4×C11—22no—
128D4×C11—22no—
129D4×C11—41no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—41no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—82no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159C11⋊C8—81no—
160C22×D8—21no—
161C2×#127C2×D1111yescharacteristic
162C2×C4×D4C2×D1111yescharacteristic
163#459—22no—
164#459—22no—
165#431—111no—
166#431—111no—
167#423—111no—
168#423—111no—
169C2×C4⋊C8C2×D1111yescharacteristic
170C2×#102—21no—
171C2×#100—221no—
172#343—221no—
173#334—222no—
174#331—222no—
175#331—222no—
176D4⋊C8—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—42no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—162no—
188C22×C11—162no—
189C22×C11#39411yescharacteristic
190C22×C11#48111yescharacteristic
191C22×C11#48211yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11#44911yescharacteristic
197C4×C11#45011yescharacteristic
198C4×C11#46511yescharacteristic
199C4×C11#46911yescharacteristic
200C4×C11#47212yes—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4C22⋊D1111yescharacteristic
205C23×C4—21no—
206C2×D8—24no—
207C2×D8—42no—
208C2×D8—42no—
209C2×M16—221no—
210C2×M16—221no—
211C22×C8—21no—
212#127—21no—
213#127—21no—
214#127—21no—
215#127C22⋊D1112yes—
216C4×D4—21no—
217C4×D4—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C4⋊C4C22⋊D1111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—112no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8C22⋊D1112yes—
231#102—24no—
232#100—442no—
233C22⋊C8—221no—
234C22⋊C8—221no—
235C4×C8—221no—
236C4×C8—221no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—82no—
240C2×C11—162no—
241C2×C11#203411yescharacteristic
242C2×C11#204511yescharacteristic
243C2×C11#204811yescharacteristic
244C24—21no—
245C24—41no—
246C2×D4—21no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—82no—
262C2×D4—82no—
263C2×D4#432412yes—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—82no—
268C22×C4#434111yescharacteristic
269C22×C4#434111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271D8—48no—
272M16—441no—
273M16—441no—
274M16—441no—
275M16—441no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—222no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42D4×D1111yescharacteristic
288C42#434111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1044111yescharacteristic, complemented, Sylow
292C23—22no—
293C23—41no—
294C23—41no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—82no—
299C23—82no—
300C23—81no—
301C23—81no—
302C23#6698811yescharacteristic
303D4—22no—
304D4—22no—
305D4—42no—
306D4—41no—
307D4—42no—
308D4—41no—
309D4—82no—
310D4—82no—
311D4—82no—
312D4—82no—
313D4—81no—
314D4—81no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4#6698511yescharacteristic
322C2×C4C2×#432411yescharacteristic
323C2×C4#6698811yescharacteristic
324C2×C4#6698911yescharacteristic
325C2×C4#6699111yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6700211yescharacteristic
329C2×C4#6700311yescharacteristic
330C2×C4#6700611yescharacteristic
331C8—42no—
332C8—442no—
333C8—881no—
334C8—881no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—162no—
347C22—162no—
348C22#1062264711yescharacteristic
349C22#1062264811yescharacteristic
350C22#1062283511yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—81no—
355C4#1062265211yescharacteristic
356C4#1062265411yescharacteristic
357C4#1062277312yes—
358C4#1062283111yescharacteristic
359C4#1062285111yescharacteristic
360C2—21no—
361C2—21no—
362C2—82no—
363C2—162no—
364C2#1306980211yescharacteristic
365C2#1306986911yescharacteristic
366C2#1306988611yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#459C2
socleC22×C11#394
hypercenterC2×#459D11
hypocenterC11#10441
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13068608C2semidirect
2. #13067386C2semidirect
3. #13067284C2semidirect
4. #13067284C2semidirect
5. #13067007C2semidirect
6. #13066513C2semidirect
291. C11#10441semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130673862
#130672842
#130670072
#130665132
C2×C11×#4592
#1044111