Finite Group Databasebeta

← #14663291

Subgroups — #14663291

Order 2816.

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

normal subgroups only

This group has 460 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#13072887C211yesmaximal, characteristic
2#13066947C211yesmaximal, characteristic, complemented
3#13066927C211yesmaximal, characteristic, complemented
4#13066565C211yesmaximal, characteristic, complemented
5#13066563C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic
7C11×#1316C211yesmaximal, characteristic
8C22×C22⋊Dic11C411yescharacteristic
9C2×#66930C2211yescharacteristic
10C11×#379C2211yescharacteristic
11#10622860C411yescharacteristic
12#10622565—21no—
13#10622564—21no—
14#10622563C411yescharacteristic
15#10622562—21no—
16#10622559C2211yescharacteristic
17#10622558—21no—
18#10622556C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C25×C11C2×C411yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—41no—
39C2×C22⋊Dic11—41no—
40C2×C22⋊Dic11C2×C411yescharacteristic
41C2×C22⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4D411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48#66930—41no—
49#66930—41no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11542—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—41no—
67C24×C11—42no—
68C24×C11—41no—
69C24×C11—81no—
70C24×C11C22×C411yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—81no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—81no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—41no—
96C22⋊Dic11—42no—
97C22⋊Dic11—42no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—81no—
101C4⋊Dic11—81no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—81no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2482—111no—
112#1464—111no—
113#1458—111no—
114#1326—111no—
115#1326—111no—
116#1316—111no—
117#1316D1111yescharacteristic
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—22no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11—84no—
136C23×C11—81no—
137C23×C11—81no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#13111yescharacteristic
140C23×C11#13111yescharacteristic
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—41no—
156C2×Dic11—41no—
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—41no—
166C2×Dic11—41no—
167C2×Dic11—82no—
168C2×Dic11#9911yescharacteristic
169C2×Dic11#9911yescharacteristic
170C8×C11—81no—
171C8×C11—81no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174C2×#117—111no—
175C22×C22⋊C4—111no—
176#432—221no—
177#431—221no—
178#399—221no—
179#397—221no—
180#388—221no—
181#388—221no—
182#385—111no—
183#385—111no—
184#381—111no—
185#379—111no—
186#379C2×D1111yescharacteristic
187#324—221no—
188#324—221no—
189#323—111no—
190#323—111no—
191#323C2×D1111yescharacteristic
192#323C2×D1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—42no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#40811yescharacteristic
214C22×C11C2×#9911yescharacteristic
215C22×C11#41311yescharacteristic
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—81no—
219Dic11—21no—
220Dic11—21no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224Dic11—81no—
225Dic11—81no—
226C25C4×D1111yescharacteristic
227C23×C4—111no—
228C23×C4—111no—
229#117—441no—
230#117—441no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—441no—
244C2×C22⋊C4—441no—
245C2×C22⋊C4C4×D1111yescharacteristic
246C2×C22⋊C4C22×D1111yescharacteristic
247C2×C42—111no—
248C2×C42—111no—
249C4⋊C8—441no—
250C4⋊C8—441no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255#97—441no—
256C4×C8—441no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—41no—
264C2×C11—41no—
265C2×C11—82no—
266C2×C11#146811yescharacteristic
267C2×C11#212011yescharacteristic
268C2×C11#212211yescharacteristic
269C24—21no—
270C24—21no—
271C24—21no—
272C24—41no—
273C24—42no—
274C24—41no—
275C24—81no—
276C24C2×C4×D1111yescharacteristic
277C22×C4—21no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4—881no—
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—441no—
296C2×C8—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—881no—
300C4⋊C4—881no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—881no—
313C42—221no—
314C42—221no—
315C42—221no—
316C42—221no—
317C11#1154211yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23—82no—
334C23—82no—
335C23—84no—
336C23—81no—
337C23—81no—
338C23C22⋊C4×D1111yescharacteristic
339C23#6695411yescharacteristic
340C23#6696011yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—882no—
370C8—81no—
371C8—81no—
372C8—881no—
373C8—881no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1062234011yescharacteristic
395C22D11×#9911yescharacteristic
396C22#1062235811yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—221no—
401C4—221no—
402C4—441no—
403C4—441no—
404C4—441no—
405C4—881no—
406C4—881no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#1306696111yescharacteristic
413C2#1307025411yescharacteristic
414C2#1307026411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1316C2
socleC22×C11C2×#99
prime radicalC25×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1316D11
hypocenterC11#11542
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #13066947C2semidirect
3. #13066927C2semidirect
4. #13066565C2semidirect
5. #13066563C2semidirect
317. C11#11542semidirect

Maximal subgroups

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

subgroupindex
#130728872
#130669472
#130669272
#130665652
#130665632
#130665442
C11×#13162
#1154211