Finite Group Databasebeta

← #14666758

Subgroups — #14666758

Order 2816.

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

normal subgroups only

This group has 458 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#13075384C211yesmaximal, characteristic
2#13067607C211yesmaximal, characteristic, complemented
3#13067539C211yesmaximal, characteristic
4#13066615C211yesmaximal, characteristic, complemented
5#13066612C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2062C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C2×#66938—21no—
10C11×#385—21no—
11C11×#385C2211yescharacteristic
12#10622826—21no—
13#10622659—21no—
14#10622656—21no—
15#10622604—21no—
16#10622587—21no—
17#10622573C2211yescharacteristic
18#10622566C2211yescharacteristic
19#10622286—21no—
20#10622283—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44D411yescharacteristic
30C22×Dic22—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—41no—
34C11×C22⋊Q8—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×#4325—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4×Dic11—21no—
50#66938—42no—
51#66938—42no—
52C11×#95—21no—
53C11×#95—41no—
54#66899—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#12245—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—81no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—41no—
86C2×D44—81no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—81no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—82no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4SD1612yescomplemented
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105#4325—82no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111C4⋊Dic11—41no—
112C4×Dic11—42no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2712—111no—
116#2062D1111yescharacteristic, complemented
117#1608—111no—
118#1596—111no—
119#1344—111no—
120#1343—111no—
121#1326—111no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127C23×C11C2×SD1611yescharacteristic
128C23×C11AGL(1,ℤ/8)11yescharacteristic
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136Q8×C11—81no—
137Q8×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C22⋊D11—82no—
158C22⋊D11—82no—
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168D44—42no—
169D44—81no—
170Dic22—84no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173#543C2×D1111yescharacteristic
174C2×#124—221no—
175#483—221no—
176#450—221no—
177#397—111no—
178#394—221no—
179#393—221no—
180#392—111no—
181#391—221no—
182#388—221no—
183#386—221no—
184#385—21no—
185#385C2×D1111yescharacteristic
186#342—21no—
187#342C2×D1111yescharacteristic
188#328—221no—
189#328—221no—
190#323—111no—
191#323—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11#45011yescharacteristic
202C22×C11#45611yescharacteristic
203C22×C11B(4,𝔽2)11yescharacteristic
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—42no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218Dic11—42no—
219Dic11—81no—
220Dic11—81no—
221C22×Q8—221no—
222C22×D4—111no—
223C22×D4—221no—
224C23×C4C22⋊D1111yescharacteristic
225C2×SD16—441no—
226#124—442no—
227#124—442no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—41no—
231C22⋊Q8—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—111no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4C22⋊D1111yescharacteristic
244C2×C22⋊C4C22×D1111yescharacteristic
245C2×C42—221no—
246#106—441no—
247#103—441no—
248#102—441no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251#95—21no—
252#95—41no—
253#95—111no—
254#95—111no—
255#95—221no—
256#95—221no—
257#95—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—41no—
261C2×C11—41no—
262C2×C11#160411yescharacteristic
263C2×C11#219811yescharacteristic
264C2×C11#219911yescharacteristic
265D11—161no—
266C24—221no—
267C24C2×C22⋊D1111yescharacteristic
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—442no—
271C2×Q8—442no—
272C2×Q8—881no—
273C2×D4—441no—
274C2×D4—442no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—881no—
278C2×D4—881no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—81no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291SD16—882no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C4⋊C4—82no—
300C4⋊C4—441no—
301C22⋊C4—21no—
302C22⋊C4—22no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C22⋊C4—881no—
313C22⋊C4—881no—
314C22⋊C4#432512yescomplemented
315C42—442no—
316C11#1224511yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23#6699011yescharacteristic
329C23C2×#432511yescharacteristic
330C23#6700211yescharacteristic
331Q8—81no—
332Q8—81no—
333Q8—884no—
334D4—442no—
335D4—881no—
336D4—882no—
337D4—882no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—222no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C8—881no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22#1062264511yescharacteristic
385C22#1062265911yescharacteristic
386C22#1062270811yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—442no—
395C4—881no—
396C4—881no—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—1761no—
402C2#1306758411yescharacteristic
403C2#1307061011yescharacteristic
404C2#1307061511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2062C2
socleC22×C11B(4,𝔽2)
prime radical#10622573C22
hypercenter#2062D11
hypocenterC11#12245
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
2. #13067607C2semidirect
4. #13066615C2semidirect
6. #13066564C2semidirect
7. C11×#2062C2semidirect
102. C11×C22⋊C4SD16semidirect
116. #2062D11semidirect
314. C22⋊C4#4325semidirect
316. C11#12245semidirect

Maximal subgroups

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

subgroupindex
#130753842
#130676072
#130675392
#130666152
#130666122
#130665642
C11×#20622
#1224511