Finite Group Databasebeta

← #14655792

Subgroups — #14655792

Order 2816.

550 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079737C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#462C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12#10623008C2211yescharacteristic
13C11×#462—22no—
14C11×#462—22no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20#10622644—21no—
21#10622641—22no—
22#10622640—21no—
23#10622580—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622166—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×#4339—21no—
34C2×C11×Q16—24no—
35C2×C11×Q16—42no—
36C2×C11×Q16—42no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yes—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326—22no—
53#66995—42no—
54#66995—42no—
55C2×#4325—22no—
56#66983—21no—
57#66983—21no—
58C2×#4318—21no—
59#66928—21no—
60#66927D411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922D411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—22no—
70#66873—22no—
71#66873—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10185—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11D812yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—41no—
99#4339—41no—
100#4339—41no—
101#4339—41no—
102#4339—41no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C11×Q16—48no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126#4326—44no—
127#4325—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137#3226—111no—
138#3037—111no—
139C2×#462D1111yescharacteristic, complemented
140#1546—111no—
141#1480—111no—
142#1461—111no—
143#1301—111no—
144C23×C11#12111yescharacteristic
145C22×D11—41no—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—81no—
153Q8×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C22⋊D11—81no—
175C22⋊D11—81no—
176C2×Dic11—41no—
177D44—42no—
178D44—41no—
179D44—41no—
180D44—42no—
181C4×D11—81no—
182C4×D11—81no—
183Dic22—41no—
184Dic22—41no—
185C8×C11—42no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C11⋊C8—81no—
189C2×#137—221no—
190C22×Q16—21no—
191#532—111no—
192C2×C4⋊Q8C2×D1111yescharacteristic
193C2×C4×Q8C2×D1111yescharacteristic
194#500—221no—
195#486—221no—
196#480—222no—
197#474—222no—
198#464—222no—
199#462—22no—
200#462—22no—
201#462—221no—
202#460—221no—
203#431—111no—
204#431—111no—
205#423—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207#417—221no—
208C2×#103—21no—
209#332—222no—
210D4⋊C8—222no—
211#324—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#39211yescharacteristic
215C22×C11#46611yescharacteristic
216C22×C11#46911yescharacteristic
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11#44711yescharacteristic
227C4×C11#44711yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#44911yescharacteristic
230C4×C11#47312yes—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—21no—
234C22×Q8C22⋊D1111yescharacteristic
235#137—442no—
236#137—442no—
237C2×Q16—24no—
238C2×Q16—42no—
239C2×Q16—42no—
240C2×Q16—222no—
241C2×SD16—222no—
242C2×M16—221no—
243C22×C8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—111no—
248C4⋊Q8C22⋊D1112yes—
249#127—111no—
250#124—221no—
251#121—221no—
252#121—221no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22⋊D1111yescharacteristic
263C2×C42—21no—
264C2×C42C22×D1111yescharacteristic
265#107—224no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8C22⋊D1112yes—
272#103—24no—
273#103—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—112no—
277C22⋊C8—221no—
278C4×C8—221no—
279C4×C8—221no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11#199911yescharacteristic
283C2×C11#200911yescharacteristic
284C2×C11#202011yescharacteristic
285D11—161no—
286#41—441no—
287#41—441no—
288#41—441no—
289#41—441no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—221no—
302C2×Q8#432312yes—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—441no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314Q16—48no—
315Q16—444no—
316SD16—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—441no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42—41no—
338C42—41no—
339C42D4×D1111yescharacteristic
340C42D4×D1111yescharacteristic
341C42C2×C22⋊D1111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C11#1018511yescharacteristic, complemented, Sylow
344C23—441no—
345C23#6699211yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354Q8—441no—
355Q8—441no—
356D4—442no—
357D4—442no—
358D4—441no—
359D4—441no—
360D4—881no—
361D4—881no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—441no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4C2×#432311yescharacteristic
376C2×C4#6698511yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6699011yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699311yescharacteristic
382C2×C4#6700211yescharacteristic
383C2×C4#6700311yescharacteristic
384C2×C4#6700611yescharacteristic
385C8—42no—
386C8—442no—
387C8—442no—
388C8—881no—
389C22—21no—
390C22—21no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22#1062265111yescharacteristic
395C22#1062265211yescharacteristic
396C22#1062283611yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—82no—
402C4—81no—
403C4—881no—
404C4#1062264911yescharacteristic
405C4#1062265011yescharacteristic
406C4#1062280512yes—
407C4#1062283011yescharacteristic
408C4#1062285111yescharacteristic
409C2—21no—
410C2—21no—
411C2—1761no—
412C2#1306961211yescharacteristic
413C2#1306967411yescharacteristic
414C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#462C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#462D11
hypocenterC11#10185
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13067288C2semidirect
5. #13066940C2semidirect
6. #13066513C2semidirect
7. C2×C11×#462C2semidirect
139. C2×#462D11semidirect
343. C11#10185semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780882
#130672882
#130670142
#130669402
#130665132
C2×C11×#4622
#1018511