Finite Group Databasebeta

← #14666000

Subgroups — #14666000

Order 2816.

440 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069747C211yesmaximal, characteristic
2#13067635C211yesmaximal, characteristic
3#13067567C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066546C211yesmaximal, characteristic, complemented
7C11×#2841C211yesmaximal, characteristic, complemented
8C2×#66982—21no—
9#10623024C2211yescharacteristic
10C11×#400—21no—
11C11×#399C2211yescharacteristic
12C11×#398—21no—
13C11×#398—21no—
14C11×#396—21no—
15C11×#395—21no—
16C11×#393C2211yescharacteristic
17C11×#381C2211yescharacteristic
18C11×#380—21no—
19#10622840—21no—
20#10622581—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×#4325—41no—
43#66983—21no—
44#66983—21no—
45#66982—42no—
46#66982—42no—
47C2×(C2×D11)⋊C4—41no—
48C2×Dic11⋊C4—41no—
49#66939—41no—
50#66935—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59#66899—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#66870—42no—
65#12125—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—81no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11SD1612yescomplemented
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C2×D44—21no—
91C2×D44—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C22⋊Dic11—22no—
104C22⋊Dic11—41no—
105#4325—82no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—44no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—44no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2841D1111yescharacteristic, complemented
115#2022—111no—
116#1613—111no—
117#1601—111no—
118#1352—111no—
119#1351—111no—
120#1317—111no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126C23×C11C2×SD1611yescharacteristic
127C23×C11#13711yescharacteristic
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—81no—
132C22×D11—81no—
133Q8×C11—42no—
134Q8×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C22⋊D11—81no—
160C22⋊D11—81no—
161C22⋊D11—81no—
162C22⋊D11—81no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169D44—81no—
170D44—81no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173#534—111no—
174C2×#123—221no—
175#481—221no—
176#448—221no—
177C2×#99—221no—
178#400—21no—
179#399C2×D1111yescharacteristic
180#398—21no—
181#398—21no—
182#396—21no—
183#395—21no—
184#393C2×D1111yescharacteristic
185#381C2×D1111yescharacteristic
186#380—21no—
187#342—111no—
188#327—221no—
189#327—221no—
190#323—111no—
191#323—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11#44811yescharacteristic
202C22×C11#45311yescharacteristic
203C22×C11B(4,𝔽2)11yescharacteristic
204C2×D11—82no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—161no—
209C4×C11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217Dic11—82no—
218Dic11—81no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4—221no—
221C23×C4C22⋊D1111yescharacteristic
222C2×SD16—441no—
223#123—441no—
224#123—442no—
225#123—442no—
226#121—221no—
227#121—221no—
228#120—441no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—441no—
236C2×C4⋊C4C22⋊D1111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—441no—
241C2×C22⋊C4C22⋊D1111yescharacteristic
242C2×C22⋊C4C22×D1111yescharacteristic
243#106—441no—
244#103—441no—
245#102—441no—
246#99—442no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95C22⋊D1111yescharacteristic
256#95C22⋊D1111yescharacteristic
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—41no—
260C2×C11—41no—
261C2×C11#159611yescharacteristic
262C2×C11#220011yescharacteristic
263C2×C11#220111yescharacteristic
264D11—161no—
265C24—221no—
266C24C2×C22⋊D1111yescharacteristic
267C2×Q8—41no—
268C2×Q8—81no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4—441no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—441no—
288C22×C4#432512yescomplemented
289C22×C4C2×C22⋊D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291SD16—882no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—81no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—444no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—222no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—444no—
312C22⋊C4—441no—
313C11#1212511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—881no—
322C23—881no—
323C23C2×#432511yescharacteristic
324C23#6699511yescharacteristic
325C23#6700611yescharacteristic
326Q8—42no—
327Q8—81no—
328D4—881no—
329D4—881no—
330D4—881no—
331D4—881no—
332D4—881no—
333D4—881no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—881no—
363C2×C4—881no—
364C8—881no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—882no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22—1761no—
380C22#1062284011yescharacteristic
381C22#1062285411yescharacteristic
382C22#1062285711yescharacteristic
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—882no—
392C4—881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—1761no—
398C2#1306753911yescharacteristic
399C2#1307062311yescharacteristic
400C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2841C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2841D11
hypocenterC11#12125
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2841

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066637C2semidirect
6. #13066546C2semidirect
7. C11×#2841C2semidirect
79. C22×C4×C11SD16semidirect
114. #2841D11semidirect
288. C22×C4#4325semidirect
313. C11#12125semidirect

Maximal subgroups

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

subgroupindex
#130697472
#130676352
#130675672
#130666402
#130666372
#130665462
C11×#28412
#1212511