Finite Group Databasebeta

← #14663348

Subgroups — #14663348

Order 2816.

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

normal subgroups only

This group has 440 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#13073105C211yesmaximal, characteristic
2#13066944C211yesmaximal, characteristic, complemented
3D11×#324C211yesmaximal, characteristic, complemented
4#13066560C211yesmaximal, characteristic, complemented
5#13066547C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic, complemented
7C11×#1324C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622601C2211yescharacteristic
12#10622590C411yescharacteristic
13#10622552C411yescharacteristic
14C4×(C2×D11)⋊C4C411yescharacteristic
15#10622339—21no—
16D11×C22⋊C8—21no—
17#10622288—21no—
18#10622288—21no—
19#10622278—21no—
20#10622278—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×D44—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4D411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×#4313—41no—
46C2×C8×D11—41no—
47#66948—41no—
48#66948—41no—
49C4⋊C4×D11—41no—
50C4⋊C4×D11—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11553—111nomaximal, Sylow
63C23×D11—21no—
64C23×D11C22⋊C411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—41no—
81C2×D44—41no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—41no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11—21no—
98C42×C11—21no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—81no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#4313—82no—
112C8×D11—82no—
113#2504—111no—
114#1463—111no—
115C2×#324—111no—
116#1324—111no—
117#1324D1111yescharacteristic, complemented
118#1318—111no—
119#1318—111no—
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11#9911yescharacteristic
133C22×D11#9911yescharacteristic
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
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#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158D44—81no—
159D44—81no—
160D44—82no—
161D44—82no—
162C4×D11—41no—
163C4×D11—41no—
164C4×D11—41no—
165C4×D11—41no—
166C4×D11—42no—
167C4×D11—42no—
168C4×D11—81no—
169C4×D11—81no—
170C8×C11—81no—
171C8×C11—81no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174C2×#121—111no—
175C22×C4⋊C4—111no—
176#407—221no—
177C2×C22⋊C8—221no—
178#397—221no—
179#397—221no—
180#390—111no—
181#390—111no—
182#386—221no—
183#386—221no—
184#382—111no—
185#382C2×D1111yescharacteristic
186C4×C22⋊C4—111no—
187#324—111no—
188#324—111no—
189#324—221no—
190#324—221no—
191#324C2×D1111yescharacteristic
192#324C2×D1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#40811yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11#41311yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11#35512yes—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—81no—
218C4×C11—81no—
219Dic11—41no—
220Dic11—41no—
221Dic11—41no—
222Dic11—81no—
223C22×D4—111no—
224C22×D4—221no—
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—111no—
228C2×M16—441no—
229C22×C8—441no—
230#121—441no—
231#121—441no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—441no—
236C2×C4⋊C4—441no—
237C2×C4⋊C4C4×D1111yescharacteristic
238C2×C4⋊C4C22×D1111yescharacteristic
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C42—111no—
246C2×C42C4×D1111yescharacteristic
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251C22⋊C8—441no—
252C22⋊C8—441no—
253#95—21no—
254#95—21no—
255#95—221no—
256#95—221no—
257#95—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11#146811yescharacteristic
261C2×C11#212711yescharacteristic
262C2×C11C2×#35511yescharacteristic
263D11—22no—
264D11—41no—
265D11—161no—
266C24—111no—
267C24—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—442no—
275C2×D4—442no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—441no—
291C22×C4—881no—
292C22×C4—881no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296M16—882no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—441no—
300C2×C8—441no—
301C2×C8—882no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—881no—
310C22⋊C4—881no—
311C22⋊C4—881no—
312C22⋊C4—881no—
313C42—21no—
314C42—21no—
315C42—441no—
316C11#1155311yescharacteristic, complemented, Sylow
317C23—111no—
318C23—111no—
319C23—222no—
320C23—221no—
321C23—221no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23—441no—
330C23C22⋊C4×D1111yescharacteristic
331D4—881no—
332D4—881no—
333D4—882no—
334D4—882no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4#6695411yescharacteristic
366C2×C4#6696011yescharacteristic
367C8—81no—
368C8—81no—
369C8—881no—
370C8—881no—
371C22—21no—
372C22—21no—
373C22—112no—
374C22—221no—
375C22—221no—
376C22—221no—
377C22—221no—
378C22—221no—
379C22—442no—
380C22—442no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22#1062234011yescharacteristic
389C22D11×#9911yescharacteristic
390C22#1062236411yescharacteristic
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—441no—
398C4—441no—
399C4—441no—
400C4—881no—
401C2—21no—
402C2—21no—
403C2—222no—
404C2—441no—
405C2—1761no—
406C2#1306696311yescharacteristic
407C2#1307028411yescharacteristic
408C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC2×#66948C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11553
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #13066944C2semidirect
3. D11×#324C2semidirect
4. #13066560C2semidirect
5. #13066547C2semidirect
6. #13066547C2semidirect
7. C11×#1324C2semidirect
117. #1324D11semidirect
316. C11#11553semidirect

Maximal subgroups

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

subgroupindex
#130731052
#130669442
D11×#3242
#130665602
#130665472
C11×#13242
#1155311