Finite Group Databasebeta

← #14664833

Subgroups — #14664833

Order 2816.

510 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 77 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#13073579C211yesmaximal, characteristic
2#13068607C211yesmaximal, characteristic, complemented
3#13066933C211yesmaximal, characteristic, complemented
4#13066623C211yesmaximal, characteristic, complemented
5#13066621C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×#66946C2211yescharacteristic
10C2×#66937—21no—
11C11×#394C2211yescharacteristic
12#10622836C411yescharacteristic
13C2×#66887—21no—
14#10622731—21no—
15#10622596C2211yescharacteristic
16#10622569—21no—
17#10622569—21no—
18#10622558—21no—
19D11×C22⋊C8—21no—
20#10622287C411yescharacteristic
21D11×#95C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C4×D11C2×C411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40#66991—41no—
41#66991—41no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×C8×D11—41no—
50#66946—41no—
51#66946—41no—
52#66937—42no—
53#66937—42no—
54C11×C22⋊C8—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66887—42no—
62(C2×D11)⋊C8—41no—
63Dic11⋊C8—41no—
64Dic11⋊C8—41no—
65#11884—111nomaximal, Sylow
66C24×C11—21no—
67C23×D11C22⋊C411yescharacteristic
68C23×D11C22⋊C411yescharacteristic
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—81no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×D44—41no—
86C2×D44—41no—
87C2×D44D812yes—
88C2×D44SD1612yes—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—81no—
96C2×C4×D11—81no—
97C2×C4×D11—81no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—81no—
106C22⋊Dic11—42no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C8×D11—82no—
122#2543—111no—
123#1800—111no—
124#1459—111no—
125#1346—111no—
126#1346—111no—
127#1345—111no—
128#1345D1111yescharacteristic, complemented
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11C2×C22⋊C411yescharacteristic
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#10212yes—
146C22×D11#10212yes—
147D4×C11—82no—
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×C11C2×D811yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
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—81no—
176C4×D11—81no—
177C4×D11—81no—
178C4×D11—84no—
179C8×C11—81no—
180C8×C11—81no—
181C11⋊C8—81no—
182C11⋊C8—81no—
183C2×#121—111no—
184C2×#121—221no—
185C2×C4×D4—111no—
186#423—221no—
187C2×#100—221no—
188C2×C22⋊C8—221no—
189#398—111no—
190#397—111no—
191#394C2×D1111yescharacteristic
192#392—111no—
193#388—221no—
194#386—221no—
195#386—221no—
196C2×#95—111no—
197#343—111no—
198#343C2×D1111yescharacteristic
199#324—111no—
200#324C2×D1111yescharacteristic
201#323—221no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11C2×#9911yescharacteristic
212C22×C11C2×#10211yescharacteristic
213C22×C11#42111yescharacteristic
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—42no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—81no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—81no—
229Dic11—21no—
230Dic11—21no—
231Dic11—42no—
232Dic11—41no—
233Dic11—81no—
234C22×D4—111no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4C4×D1111yescharacteristic
238C23×C4—111no—
239C23×C4—111no—
240C23×C4—221no—
241C2×M16—21no—
242C2×M16—221no—
243C22×C8—441no—
244#121—442no—
245#121—442no—
246#121—441no—
247#121—441no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4C22×D1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—111no—
261C4⋊C8—441no—
262C4⋊C8—441no—
263#100—442no—
264C22⋊C8—21no—
265C22⋊C8—221no—
266C22⋊C8—441no—
267#95—111no—
268#95—221no—
269#95—221no—
270#95—221no—
271#95C4×D1111yescharacteristic
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—161no—
275C2×C11#151911yescharacteristic
276C2×C11#212111yescharacteristic
277C2×C11#213211yescharacteristic
278D11—42no—
279D11—42no—
280C24—21no—
281C24—111no—
282C24—111no—
283C2×D4—41no—
284C2×D4—81no—
285C2×D4—112no—
286C2×D4—112no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—442no—
294C2×D4—881no—
295C22×C4—21no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—442no—
305C22×C4—442no—
306C22×C4—881no—
307C22×C4—881no—
308C22×C4—881no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312M16—41no—
313M16—41no—
314M16—441no—
315M16—441no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—882no—
321C4⋊C4—41no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—81no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—442no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—442no—
334C42—221no—
335C42—221no—
336C11#1188411yescharacteristic, complemented, Sylow
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—112no—
345C23—112no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23C22⋊C4×D1111yescharacteristic
355D4—82no—
356D4—442no—
357D4—442no—
358D4—884no—
359D4—884no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—111no—
370C2×C4—111no—
371C2×C4—222no—
372C2×C4—221no—
373C2×C4—442no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—884no—
385C2×C4D8×D1111yescharacteristic
386C2×C4SD16×D1111yescharacteristic
387C8—81no—
388C8—81no—
389C8—881no—
390C8—881no—
391C22—21no—
392C22—21no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—222no—
401C22—222no—
402C22—442no—
403C22—442no—
404C22—442no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—881no—
410C22D11×#9911yescharacteristic
411C22D11×#10211yescharacteristic
412C22#1062243411yescharacteristic
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—81no—
418C4—221no—
419C4—221no—
420C4—442no—
421C4—441no—
422C4—881no—
423C2—21no—
424C2—21no—
425C2—161no—
426C2—442no—
427C2—442no—
428C2#1306718211yescharacteristic
429C2#1307025911yescharacteristic
430C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radical#13073579C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11884
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068607C2semidirect
3. #13066933C2semidirect
4. #13066623C2semidirect
5. #13066621C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
128. #1345D11semidirect
336. C11#11884semidirect

Maximal subgroups

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

subgroupindex
#130735792
#130686072
#130669332
#130666232
#130666212
#130666192
C11×#13452
#1188411