Finite Group Databasebeta

← #14642813

Subgroups — #14642813

Order 2816.

446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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#13075634C211yesmaximal, characteristic
2#13070145C211yesmaximal, characteristic
3#13070088C211yesmaximal, characteristic, complemented
4#13066442C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#2072C211yesmaximal, characteristic, complemented
8C2×#66999—21no—
9C2×C11×#103—21no—
10C11×#391C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622607—21no—
13C2×#66873—21no—
14C2×#66871—21no—
15C2×#66871—21no—
16#10622552C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622290—21no—
19#10622281—21no—
20#10622278—21no—
21#10622274—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36#66999—42no—
37#66999—42no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C11×#103—42no—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66873—42no—
58#66871—42no—
59#66871—42no—
60#7789—111nomaximal, Sylow
61C23×D11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11D812yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44Q1612yes—
79C2×C4×D11—42no—
80C2×C4×D11—81no—
81C2×C4×D11—81no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C42×C11—41no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—81no—
99(C2×D11)⋊C4—81no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—42no—
105C4⋊Dic11—81no—
106Dic11⋊C4—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2732—111no—
116#2093—111no—
117#2083—111no—
118#2072D1111yescharacteristic, complemented
119#1272—111no—
120#1271—111no—
121#1270—111no—
122C23×C11#12011yescharacteristic
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130Q8×C11—42no—
131Q8×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162D44—42no—
163D44—81no—
164C4×D11—84no—
165C8×C11—81no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C2×C22⋊Q8—221no—
169C2×#107—221no—
170C2×#107—221no—
171C2×#103—21no—
172C2×#102—221no—
173#399—221no—
174#398—221no—
175#396—221no—
176#391C2×D1111yescharacteristic
177#390—111no—
178#389—111no—
179#386—221no—
180#385—221no—
181#384C2×D1111yescharacteristic
182#340—21no—
183#340—221no—
184#336—111no—
185#336—111no—
186#336C2×D1111yescharacteristic
187C22×C11#44711yescharacteristic
188C22×C11#44911yescharacteristic
189C22×C11#45111yescharacteristic
190C22×C11#45311yescharacteristic
191C22×C11#45511yescharacteristic
192C22×C11#45611yescharacteristic
193C22×C11#45811yescharacteristic
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11—161no—
210Dic11—81no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8C22⋊D1111yescharacteristic
214C22×D4—111no—
215C23×C4—221no—
216C22×C8—21no—
217C22×C8—221no—
218C22×C8—221no—
219C22⋊Q8—442no—
220C22⋊Q8—442no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4C22⋊D1111yescharacteristic
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42C22×D1111yescharacteristic
238#107—442no—
239#107—442no—
240#103—42no—
241#102—442no—
242#95—21no—
243#95—21no—
244#95—221no—
245#95—221no—
246C2×C11#160711yescharacteristic
247C2×C11#160911yescharacteristic
248C2×C11#161411yescharacteristic
249C2×C11#162111yescharacteristic
250C2×C11#164411yescharacteristic
251C2×C11#164911yescharacteristic
252C2×C11#166111yescharacteristic
253D11—82no—
254C24—221no—
255C2×Q8—21no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8#432312yes—
259C2×D4—112no—
260C2×D4—221no—
261C2×D4—441no—
262C2×D4—441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—442no—
270C22×C4—881no—
271C22×C4—881no—
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—222no—
279C2×C8—222no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—881no—
300C22⋊C4—442no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—881no—
306C22⋊C4—881no—
307C42—41no—
308C11#778911yescharacteristic, complemented, Sylow
309C23—222no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23#6699011yescharacteristic
317Q8—42no—
318Q8—81no—
319D4—442no—
320D4—881no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—884no—
346C2×C4#6696711yescharacteristic
347C2×C4#6696911yescharacteristic
348C2×C4Q16×D1111yescharacteristic
349C2×C4#6697111yescharacteristic
350C2×C4C2×#432311yescharacteristic
351C2×C4#6700211yescharacteristic
352C8—81no—
353C8—442no—
354C8—442no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062264911yescharacteristic
363C22#1062266611yescharacteristic
364C22#1062267411yescharacteristic
365C22#1062278511yescharacteristic
366C22#1062279911yescharacteristic
367C22#1062281111yescharacteristic
368C22#1062281811yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—161no—
378C4—881no—
379C4—881no—
380C4—881no—
381C2—882no—
382C2#1306760111yescharacteristic
383C2#1306761211yescharacteristic
384C2#1306763911yescharacteristic
385C2#1306767911yescharacteristic
386C2#1306782711yescharacteristic
387C2#1306786311yescharacteristic
388C2#1306793211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2072C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#2072D11
hypocenterC11#7789
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #13070088C2semidirect
4. #13066442C2semidirect
5. #13066440C2semidirect
7. C11×#2072C2semidirect
118. #2072D11semidirect
308. C11#7789semidirect

Maximal subgroups

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

subgroupindex
#130756342
#130701452
#130700882
#130664422
#130664402
#130664362
C11×#20722
#778911