Finite Group Databasebeta

← #14664591

Subgroups — #14664591

Order 2816.

450 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074508C211yesmaximal, characteristic
2#13068607C211yesmaximal, characteristic, complemented
3#13066953C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×#66946C2211yescharacteristic
10C11×#394C2211yescharacteristic
11#10622836C411yescharacteristic
12C2×#66887—21no—
13#10622731—21no—
14#10622599C2211yescharacteristic
15#10622574—21no—
16#10622573—21no—
17#10622569—21no—
18#10622564—21no—
19#10622339—21no—
20#10622290C411yescharacteristic
21#10622277C411yescharacteristic
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×D11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66991—41no—
40#66991—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4313—41no—
50#66946—41no—
51#66946—41no—
52C11×C22⋊C8—21no—
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66887—42no—
60(C2×D11)⋊C8—41no—
61Dic11⋊C8—41no—
62Dic11⋊C8—41no—
63#11832—111nomaximal, Sylow
64C24×C11—21no—
65C23×D11C22⋊C411yescharacteristic
66C23×D11C22⋊C411yescharacteristic
67C2×D4×C11—41no—
68C2×D4×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—81no—
76C2×C22⋊D11—81no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—41no—
86C2×D44—41no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—81no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103C22⋊Dic11—81no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—81no—
107(C2×D11)⋊C4—81no—
108C4⋊Dic11—41no—
109C4⋊Dic11—81no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112#4318—41no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#4313—82no—
117#2635—111no—
118#1800—111no—
119#1465—111no—
120#1353—111no—
121#1353—111no—
122#1345—111no—
123#1345D1111yescharacteristic, complemented
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142D4×C11—82no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C22⋊D11—84no—
155C22⋊D11—84no—
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11#9911yescharacteristic
166C2×Dic11#9911yescharacteristic
167D44—42no—
168D44—42no—
169C4×D11—42no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173C8×C11—81no—
174C8×C11—81no—
175C11⋊C8—81no—
176C11⋊C8—81no—
177C2×#121—111no—
178C2×C4×D4—111no—
179#423—221no—
180C2×#100—221no—
181#407—221no—
182#400—111no—
183#399—111no—
184#394—221no—
185#394C2×D1111yescharacteristic
186#392—111no—
187#392—221no—
188#388—221no—
189#386—221no—
190#381—111no—
191#343—111no—
192#343C2×D1111yescharacteristic
193#324—111no—
194#324C2×D1111yescharacteristic
195#323—221no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11C2×#9911yescharacteristic
206C22×C11#41711yescharacteristic
207C22×C11#42111yescharacteristic
208C2×D11—42no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—81no—
223Dic11—21no—
224Dic11—21no—
225Dic11—41no—
226Dic11—81no—
227Dic11—81no—
228C22×D4—111no—
229C22×D4—221no—
230C22×D4—221no—
231C22×D4C4×D1111yescharacteristic
232C23×C4—111no—
233C23×C4—111no—
234C2×M16—21no—
235C2×M16—221no—
236C2×M16—441no—
237#121—441no—
238#121—441no—
239C4×D4—441no—
240C4×D4—441no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4C22×D1111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C42—111no—
253C4⋊C8—441no—
254C4⋊C8—441no—
255#100—442no—
256C22⋊C8—21no—
257C22⋊C8—221no—
258C22⋊C8—441no—
259#95—111no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95C4×D1111yescharacteristic
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—161no—
267C2×C11#151311yescharacteristic
268C2×C11#212111yescharacteristic
269C2×C11#213411yescharacteristic
270D11—81no—
271D11—81no—
272C24—21no—
273C24—111no—
274C24—111no—
275C2×D4—41no—
276C2×D4—81no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—881no—
284C2×D4—881no—
285C2×D4—881no—
286C2×D4—881no—
287C22×C4—21no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—881no—
297C22×C4—881no—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301M16—41no—
302M16—41no—
303M16—441no—
304M16—441no—
305M16—882no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—41no—
311C4⋊C4—441no—
312C4⋊C4—881no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—81no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—881no—
321C22⋊C4—881no—
322C22⋊C4—881no—
323C42—221no—
324C42—221no—
325C11#1183211yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23C22⋊C4×D1111yescharacteristic
344D4—82no—
345D4—442no—
346D4—442no—
347D4—884no—
348D4—884no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—111no—
359C2×C4—111no—
360C2×C4—221no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6696411yescharacteristic
374C2×C4#6696811yescharacteristic
375C8—81no—
376C8—81no—
377C8—881no—
378C8—881no—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—442no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22D11×#9911yescharacteristic
399C22#1062238411yescharacteristic
400C22#1062243411yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—81no—
406C4—221no—
407C4—221no—
408C4—441no—
409C4—881no—
410C4—881no—
411C2—21no—
412C2—21no—
413C2—161no—
414C2—881no—
415C2—881no—
416C2#1306715611yescharacteristic
417C2#1307025911yescharacteristic
418C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radical#13074508C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11832
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. #13066953C2semidirect
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
123. #1345D11semidirect
325. C11#11832semidirect

Maximal subgroups

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

subgroupindex
#130745082
#130686072
#130669532
#130666442
#130666422
#130666192
C11×#13452
#1183211