Finite Group Databasebeta

← #14663405

Subgroups — #14663405

Order 2816.

494 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073590C211yesmaximal, characteristic
2#13066953C211yesmaximal, characteristic, complemented
3#13066933C211yesmaximal, characteristic, complemented
4#13066549C211yesmaximal, characteristic, complemented
5#13066549C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×#66993C411yescharacteristic
9C2×#66989C411yescharacteristic
10C2×#66946C2211yescharacteristic
11C2×#66928C411yescharacteristic
12C11×#390C2211yescharacteristic
13#10622587C2211yescharacteristic
14#10622572—21no—
15#10622572—21no—
16#10622569—21no—
17#10622569—21no—
18C4×Dic11⋊C4C411yescharacteristic
19#10622339—21no—
20D11×C22⋊C8—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40#66993—42no—
41#66989—41no—
42#66989—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4D411yescharacteristic
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11C2×C411yescharacteristic
50C2×#4313—41no—
51C2×C8×D11—41no—
52#66946—41no—
53#66946—41no—
54#66928—42no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62(C2×D11)⋊C8—41no—
63(C2×D11)⋊C8—41no—
64#11566—111nomaximal, Sylow
65C24×C11—21no—
66C23×D11C22⋊C411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×D44—22no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—41no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—81no—
95C2×C4×D11—81no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C42×C11—41no—
106C22⋊Dic11—42no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113Dic11⋊C4—42no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#4313—82no—
120C8×D11—82no—
121#2544—111no—
122#1465—111no—
123#1459—111no—
124#1319—111no—
125#1319—111no—
126#1318—111no—
127#1318D1111yescharacteristic, complemented
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11C2×C22⋊C411yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11#10012yes—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11#13111yescharacteristic
158C2×C4×C11#13111yescharacteristic
159C22⋊D11—84no—
160C22⋊D11—84no—
161C2×Dic11—22no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11#9911yescharacteristic
171C2×Dic11#9911yescharacteristic
172D44—42no—
173D44—42no—
174C4×D11—42no—
175C4×D11—42no—
176C4×D11—81no—
177C4×D11—81no—
178Dic22—81no—
179Dic22—81no—
180C8×C11—81no—
181C8×C11—81no—
182C11⋊C8—81no—
183C11⋊C8—81no—
184C2×#127—111no—
185C2×#124—111no—
186C2×#124—111no—
187C2×C4×D4—111no—
188#407—221no—
189C2×C22⋊C8—221no—
190#394—221no—
191#394—221no—
192#391—111no—
193#390C2×D1111yescharacteristic
194#386—221no—
195#386—221no—
196C4×C4⋊C4—111no—
197#324—111no—
198#324—111no—
199#324C2×D1111yescharacteristic
200#324C2×D1111yescharacteristic
201#323—221no—
202#323—221no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#40811yescharacteristic
213C22×C11C2×#9911yescharacteristic
214C22×C11C2×#10011yescharacteristic
215C2×D11—22no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—81no—
230Dic11—21no—
231Dic11—21no—
232Dic11—42no—
233Dic11—41no—
234Dic11—81no—
235C22×Q8—111no—
236C22×D4—111no—
237C22×D4—221no—
238C22×D4—221no—
239C22×D4C4×D1111yescharacteristic
240C23×C4—111no—
241C23×C4—111no—
242C2×M16—441no—
243C22×C8—441no—
244#127—442no—
245#124—442no—
246#124—441no—
247#124—441no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4C22×D1111yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—111no—
261C2×C42—111no—
262C2×C42C4×D1111yescharacteristic
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267C22⋊C8—441no—
268C22⋊C8—441no—
269#95—221no—
270#95—221no—
271#95—221no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—161no—
275C2×C11#147111yescharacteristic
276C2×C11#212711yescharacteristic
277C2×C11#213211yescharacteristic
278D11—42no—
279D11—81no—
280C24—21no—
281C24—111no—
282C24—111no—
283C2×Q8—221no—
284C2×Q8—221no—
285C2×Q8—441no—
286C2×Q8—441no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—222no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—441no—
295C2×D4—442no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—881no—
300C2×D4—881no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—881no—
311C22×C4—881no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315M16—882no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—882no—
321C4⋊C4—41no—
322C4⋊C4—442no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—442no—
332C42—41no—
333C42—221no—
334C42—221no—
335C42—441no—
336C11#1156611yescharacteristic, complemented, Sylow
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—112no—
345C23—221no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23C22⋊C4×D1111yescharacteristic
355Q8—881no—
356Q8—881no—
357D4—81no—
358D4—81no—
359D4—442no—
360D4—442no—
361D4—884no—
362D4—884no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—111no—
373C2×C4—111no—
374C2×C4—222no—
375C2×C4—221no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4#6695411yescharacteristic
388C2×C4#6696011yescharacteristic
389C8—81no—
390C8—81no—
391C8—881no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—222no—
403C22—442no—
404C22—442no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—441no—
410C22—881no—
411C22—881no—
412C22#1062234011yescharacteristic
413C22D11×#9911yescharacteristic
414C22D11×#10011yescharacteristic
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—221no—
421C4—221no—
422C4—442no—
423C4—441no—
424C4—881no—
425C2—21no—
426C2—21no—
427C2—161no—
428C2—442no—
429C2—881no—
430C2#1306697411yescharacteristic
431C2#1307028211yescharacteristic
432C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11566
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066953C2semidirect
3. #13066933C2semidirect
4. #13066549C2semidirect
5. #13066549C2semidirect
6. #13066548C2semidirect
7. C11×#1318C2semidirect
127. #1318D11semidirect
336. C11#11566semidirect

Maximal subgroups

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

subgroupindex
#130735902
#130669532
#130669332
#130665492
#130665482
C11×#13182
#1156611