Finite Group Databasebeta

← #14647308

Subgroups — #14647308

Order 2816.

438 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071233C211yesmaximal, characteristic
2#13066945C211yesmaximal, characteristic
3#13066945C211yesmaximal, characteristic
4#13066523C211yesmaximal, characteristic
5#13066522C211yesmaximal, characteristic
6#13066521C211yesmaximal, characteristic
7C11×#1305C211yesmaximal, characteristic
8C22×Dic11⋊C4C2211yescharacteristic
9C2×#66930C411yescharacteristic
10C2×#66930C411yescharacteristic
11C11×#407C2211yescharacteristic
12C11×#407C2211yescharacteristic
13C11×#380C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622585—21no—
18#10622585—21no—
19#10622555C411yescharacteristic
20#10622555C411yescharacteristic
21#10622260—21no—
22#10622260—21no—
23#10622107—21no—
24#10622107—21no—
25#10622107—21no—
26#10622107—21no—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
36C2×C22⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×Dic11⋊C4D411yescharacteristic
48C2×Dic11⋊C4D411yescharacteristic
49C2×Dic11⋊C4D411yescharacteristic
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53C2×#4318—21no—
54#66930—42no—
55#66930—42no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#8757—111nomaximal, Sylow
69C24×C11C22×C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—81no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C22×Dic11—22no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—81no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C11×M16—81no—
93C11×M16—81no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—81no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C4⋊Dic11—81no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4—81no—
113Dic11⋊C4—81no—
114C4×Dic11—42no—
115C4×Dic11—42no—
116#4318—81no—
117#4318—81no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2316—111no—
121#1463—111no—
122#1463—111no—
123#1305—111no—
124#1305—111no—
125#1305—111no—
126#1305D1111yescharacteristic
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11#11711yescharacteristic
133C23×C11#11711yescharacteristic
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×Dic11—24no—
151C2×Dic11—24no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11#10012yes—
169C2×Dic11#10112yes—
170C8×C11—81no—
171C8×C11—81no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174C2×#117—111no—
175C2×#117—111no—
176C22×C4⋊C4—111no—
177#407—111no—
178#407—111no—
179#407C2×D1111yescharacteristic
180#407C2×D1111yescharacteristic
181#389—221no—
182#389—221no—
183#389—221no—
184#389—221no—
185#380—111no—
186#380—111no—
187#380—111no—
188#380C2×D1111yescharacteristic
189#324—221no—
190#324—221no—
191#324—221no—
192#324—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11#38111yescharacteristic
204C22×C11C2×#10011yescharacteristic
205C22×C11C2×#10111yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—22no—
213Dic11—22no—
214Dic11—41no—
215Dic11—41no—
216Dic11—81no—
217Dic11—81no—
218C23×C4—111no—
219C23×C4—111no—
220C23×C4C22×D1111yescharacteristic
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—221no—
224C2×M16—221no—
225#117—442no—
226#117—442no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4C4×D1111yescharacteristic
244C2×C22⋊C4C4×D1111yescharacteristic
245C2×C42—221no—
246C2×C42—221no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255#95—21no—
256#95—221no—
257#95—221no—
258#95—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—41no—
262C2×C11—41no—
263C2×C11#182111yescharacteristic
264C2×C11#182811yescharacteristic
265C2×C11#183011yescharacteristic
266C24C2×C4×D1111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—81no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—222no—
275C22×C4—222no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—881no—
283C22×C4#433911yescharacteristic
284C22×C4#433911yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4#434111yescharacteristic
288C22×C4#434311yescharacteristic
289M16—81no—
290M16—81no—
291M16—881no—
292M16—881no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—441no—
296C2×C8—441no—
297C4⋊C4—81no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4—881no—
309C4⋊C4—881no—
310C4⋊C4—881no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—442no—
316C42—442no—
317C11#875711yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23#6692511yescharacteristic
323C23C22⋊C4×D1111yescharacteristic
324C23#6694511yescharacteristic
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—112no—
338C2×C4—112no—
339C2×C4—224no—
340C2×C4—224no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4#6693611yescharacteristic
358C2×C4#6693611yescharacteristic
359C2×C4#6694711yescharacteristic
360C2×C4#6694711yescharacteristic
361C8—81no—
362C8—81no—
363C8—881no—
364C8—881no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22#1062227711yescharacteristic
376C22D11×#10011yescharacteristic
377C22D11×#10111yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—222no—
385C4—222no—
386C4—441no—
387C4—441no—
388C4—881no—
389C4—881no—
390C2—21no—
391C2—21no—
392C2—41no—
393C2—41no—
394C2#1306869511yescharacteristic
395C2#1306872311yescharacteristic
396C2#1306872911yescharacteristic
subgroupG/H
centerC22#10622277
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1305C2
socleC22×C11#381
cosocleC23×C4×C11C23
hypercenter#1305D11
hypocenterC11#8757
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
317. C11#8757semidirect

Maximal subgroups

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

subgroupindex
#130712332
#130669452
#130665232
#130665222
#130665212
C11×#13052
#875711