Finite Group Databasebeta

← #14655815

Subgroups — #14655815

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#13079741C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13067298C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#463—22no—
13C11×#461—21no—
14C11×#459—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17C2×#66896—21no—
18#10622692—21no—
19#10622683—21no—
20#10622647—22no—
21#10622621—22no—
22#10622620—22no—
23#10622620—22no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622119—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C22×C11⋊C8—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922D412yes—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#103—22no—
64C11×#102—22no—
65#66896—24no—
66#66896—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10188—111nomaximal, Sylow
78C24×C11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C2×D4×C11SD1612yes—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—41no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C11×SD16—44no—
107C11×D8—44no—
108C11×M16—41no—
109C11×M16—41no—
110C2×C8×C11—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3227—111no—
133C2×#474—111no—
134#3036D1111yescharacteristic
135#1548—111no—
136#1480—111no—
137#1460—111no—
138#1301—111no—
139C23×C11—22no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146Q8×C11—41no—
147Q8×C11—41no—
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—42no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—42no—
156D4×C11—81no—
157D4×C11—81no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—82no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×SD1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—82no—
179Dic22—82no—
180Dic22—82no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8—81no—
185C2×AGL(1,ℤ/8)—21no—
186#532C2×D1111yescharacteristic
187C2×C4⋊Q8—111no—
188C2×C4×D4C2×D1111yescharacteristic
189#498—221no—
190#486—221no—
191#481—222no—
192#476—222no—
193#474—222no—
194#474—222no—
195#463—22no—
196#461—21no—
197#459—21no—
198#431—111no—
199#431—111no—
200C2×#107—221no—
201#423C2×D1111yescharacteristic
202C2×C4⋊C8—111no—
203#417—21no—
204C2×#102—221no—
205#333—222no—
206D4⋊C8—222no—
207#323—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—42no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#39211yescharacteristic
219C22×C11#46511yescharacteristic
220C22×C11#46811yescharacteristic
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45011yescharacteristic
229C4×C11#45211yescharacteristic
230C4×C11#47212yes—
231Dic11—82no—
232C2×#41—21no—
233C22×Q8—221no—
234C22×D4C22⋊D1111yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—42no—
237AGL(1,ℤ/8)—42no—
238C2×SD16—22no—
239C2×D8—22no—
240C2×M16—21no—
241C22×C8—221no—
242C4⋊Q8—112no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8C22⋊D1111yescharacteristic
247#127C22⋊D1111yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C42C22×D1111yescharacteristic
262#107—224no—
263#106—224no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—22no—
271#102—22no—
272#102—224no—
273#102—224no—
274C22⋊C8—112no—
275C22⋊C8—221no—
276C4×C8—221no—
277C4×C8—221no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—82no—
281C2×C11—161no—
282C2×C11#200011yescharacteristic
283C2×C11#200911yescharacteristic
284C2×C11#201811yescharacteristic
285C24—21no—
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—222no—
292C2×Q8—441no—
293C2×Q8—882no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4#432412yes—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311C22×C4#434111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313SD16—44no—
314D8—44no—
315M16—41no—
316M16—41no—
317C2×C8—22no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#1018811yescharacteristic, complemented, Sylow
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23#6699211yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—882no—
350Q8—882no—
351D4—22no—
352D4—22no—
353D4—42no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—442no—
371C2×C4—882no—
372C2×C4#6698511yescharacteristic
373C2×C4C2×#432411yescharacteristic
374C2×C4#6699011yescharacteristic
375C2×C4#6699011yescharacteristic
376C2×C4#6699111yescharacteristic
377C2×C4#6699211yescharacteristic
378C2×C4#6699311yescharacteristic
379C2×C4#6700311yescharacteristic
380C2×C4#6700411yescharacteristic
381C2×C4#6700611yescharacteristic
382C8—42no—
383C8—442no—
384C8—442no—
385C8—881no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—82no—
390C22—82no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#1062265411yescharacteristic
397C22#1062265511yescharacteristic
398C22#1062283611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—882no—
405C4#1062265011yescharacteristic
406C4#1062265311yescharacteristic
407C4#1062281212yes—
408C4#1062283111yescharacteristic
409C4#1062285211yescharacteristic
410C2—21no—
411C2—21no—
412C2—82no—
413C2—161no—
414C2#1306961911yescharacteristic
415C2#1306967311yescharacteristic
416C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10188
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622620C2semidirect
3. #13067298C2semidirect
4. #13067015C2semidirect
5. #13066937C2semidirect
6. #13066511C2semidirect
339. C11#10188semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226202
#130672982
#130670152
#130669372
#130665112
C11×#30362
#1018811