Finite Group Databasebeta

← #14656259

Subgroups — #14656259

Order 2816.

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

normal subgroups only

This group has 528 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#13079928C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3078C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#479—22no—
13C11×#477—21no—
14C11×#475—21no—
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C11×#419—21no—
18#10622697—21no—
19#10622696—21no—
20#10622661—22no—
21#10622644—21no—
22#10622641—22no—
23#10622640—21no—
24#10622640—21no—
25#10622633—21no—
26#10622579—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31#10622162—22no—
32#10622121—22no—
33C22×Q8×C11D411yescharacteristic
34C2×#4339—21no—
35C2×C11×M16—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—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—
56C2×#4325—22no—
57#66983—21no—
58#66983—21no—
59C2×#4318—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8D412yes—
62#66928—21no—
63#66927D411yescharacteristic
64C4×D44—21no—
65C4×D44—21no—
66#66922D411yescharacteristic
67C11×#107—22no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×#103—22no—
72C11×#103—22no—
73#66899—22no—
74#66874—22no—
75#66873—22no—
76#66873—22no—
77#66872—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—21no—
84#10257—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11SD1612yescomplemented
93C22×C4×C11—21no—
94C22×C4×C11—21no—
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×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×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129#4326—44no—
130#4325—44no—
131#4325—82no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136#4318—41no—
137#4318—41no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144#3246—111no—
145#3078D1111yescharacteristic, complemented
146#3037—111no—
147#1984—111no—
148#1493—111no—
149#1492—111no—
150#1292—111no—
151C23×C11#12111yescharacteristic
152C22×D11—41no—
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—42no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11#13711yescharacteristic
180C22⋊D11—81no—
181C22⋊D11—81no—
182C2×Dic11—41no—
183D44—42no—
184D44—41no—
185D44—41no—
186D44—41no—
187D44—41no—
188C4×D11—81no—
189C4×D11—81no—
190Dic22—41no—
191Dic22—41no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×#137—221no—
197#533C2×D1111yescharacteristic
198#532—111no—
199C2×C4×Q8C2×D1111yescharacteristic
200#479—22no—
201#477—21no—
202#476—221no—
203#475—21no—
204#475—221no—
205#465—222no—
206#464—222no—
207#462—221no—
208#461—221no—
209#460—221no—
210#460—221no—
211#428—21no—
212#423—111no—
213#423C2×D1111yescharacteristic
214C2×C4⋊C8—111no—
215#419—21no—
216#417—221no—
217C2×C4×C8—111no—
218#336—222no—
219Q8⋊C8—222no—
220D4⋊C8—222no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11#39211yescharacteristic
224C22×C11#46511yescharacteristic
225C22×C11#46811yescharacteristic
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11#44811yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#45011yescharacteristic
239C4×C11#45211yescharacteristic
240C4×C11#45511yescharacteristic
241C4×C11#45611yescharacteristic
242Dic11—81no—
243C2×#41—221no—
244C22×Q8C22⋊D1111yescharacteristic
245#137—442no—
246#137—442no—
247C2×Q16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C2×M16—21no—
251C2×M16—221no—
252C22×C8—112no—
253C22×C8—221no—
254C4⋊Q8—111no—
255C4⋊Q8C22⋊D1111yescharacteristic
256C4⋊Q8C22⋊D1111yescharacteristic
257#127—111no—
258#125—21no—
259#124—221no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—221no—
263#121—221no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×D4—221no—
271C4×D4—221no—
272#117—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C42—21no—
276C2×C42C22×D1111yescharacteristic
277#107—22no—
278#106—22no—
279#106—222no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8C22⋊D1112yes—
286#103—22no—
287#103—22no—
288#103—222no—
289#103—222no—
290#102—222no—
291#102—222no—
292C4×C8—221no—
293C4×C8—221no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11#200011yescharacteristic
297C2×C11#200711yescharacteristic
298C2×C11#201711yescharacteristic
299D11—161no—
300#41—441no—
301#41—441no—
302#41—441no—
303#41—441no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—221no—
312C2×Q8#432512yescomplemented
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C2×D4—441no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—441no—
320C22×C4D4×D1111yescharacteristic
321C22×C4#434111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323Q16—444no—
324SD16—444no—
325SD16—882no—
326M16—41no—
327M16—41no—
328M16—441no—
329M16—441no—
330C2×C8—22no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—442no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C22⋊C4—41no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42D4×D1111yescharacteristic
356C42D4×D1111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C11#1025711yescharacteristic, complemented, Sylow
360C23—441no—
361C23#6699211yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—42no—
365Q8—41no—
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—441no—
370Q8—441no—
371D4—442no—
372D4—441no—
373D4—441no—
374D4—441no—
375D4—441no—
376D4—881no—
377D4—881no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—441no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4#6699011yescharacteristic
392C2×C4#6699011yescharacteristic
393C2×C4#6699111yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6699311yescharacteristic
396C2×C4C2×#432511yescharacteristic
397C2×C4#6699511yescharacteristic
398C2×C4#6700211yescharacteristic
399C2×C4#6700311yescharacteristic
400C2×C4#6700611yescharacteristic
401C8—42no—
402C8—442no—
403C8—442no—
404C8—442no—
405C22—21no—
406C22—21no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22#1062266111yescharacteristic
411C22#1062266211yescharacteristic
412C22#1062283611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—881no—
421C4#1062265911yescharacteristic
422C4#1062266011yescharacteristic
423C4#1062281511yescharacteristic
424C4#1062281811yescharacteristic
425C4#1062284011yescharacteristic
426C4#1062285111yescharacteristic
427C2—21no—
428C2—21no—
429C2—1761no—
430C2#1306961711yescharacteristic
431C2#1306966111yescharacteristic
432C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3078D11
hypocenterC11#10257
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #13069553C2semidirect
4. #13067071C2semidirect
6. #13066490C2semidirect
7. C11×#3078C2semidirect
92. C2×Q8×C11SD16semidirect
145. #3078D11semidirect
312. C2×Q8#4325semidirect
359. C11#10257semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130780882
#130695532
#130670712
#130670662
#130664902
C11×#30782
#1025711