Finite Group Databasebeta

← #14642829

Subgroups — #14642829

Order 2816.

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

normal subgroups only

This group has 462 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#13074987C211yesmaximal, characteristic
2#13070093C211yesmaximal, characteristic, complemented
3#13070020C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#2099C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×#66949—21no—
10C11×#389C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622607—21no—
13#10622607—21no—
14C2×#66873—21no—
15C2×#66872—21no—
16#10622552C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622278—21no—
19#10622269—21no—
20C11×#340—21no—
21C11×#340—21no—
22C11×#336C2211yescharacteristic
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
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⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66950—42no—
52#66950—42no—
53#66949—42no—
54#66949—42no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66873—42no—
59#66872—42no—
60#7791—111nomaximal, Sylow
61C23×D11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44SD1612yes—
75C2×C4×D11—42no—
76C2×C4×D11—42no—
77C2×C4×D11—81no—
78C2×Dic22—42no—
79C2×Dic22—42no—
80C2×Dic22—81no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4SD1612yes—
94C42×C11—41no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—81no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—42no—
106C4⋊Dic11D812yes—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2683—111no—
117#2099D1111yescharacteristic, complemented
118#2084—111no—
119#2071—111no—
120#1271—111no—
121#1271—111no—
122#1270—111no—
123C23×C11#12011yescharacteristic
124C22×D11—22no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—42no—
162D44—81no—
163C4×D11—84no—
164Dic22—84no—
165C8×C11—81no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168C2×C22⋊Q8—221no—
169C2×C22⋊Q8—221no—
170C2×#106—221no—
171C2×#102—221no—
172#396—221no—
173#396—221no—
174#395—221no—
175#390—111no—
176#389—111no—
177#389C2×D1111yescharacteristic
178#386—221no—
179#384C2×D1111yescharacteristic
180#340—21no—
181#340—21no—
182#340—221no—
183#340—221no—
184#336—111no—
185#336—111no—
186#336C2×D1111yescharacteristic
187C22×C11#44711yescharacteristic
188C22×C11#44811yescharacteristic
189C22×C11#45011yescharacteristic
190C22×C11#45411yescharacteristic
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—42no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8—221no—
214C22×D4—111no—
215C23×C4—221no—
216C22×C8—21no—
217C22×C8—221no—
218C22×C8—221no—
219C22⋊Q8—442no—
220C22⋊Q8—442no—
221C22⋊Q8—442no—
222C22⋊Q8—442no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4C22⋊D1111yescharacteristic
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C42C22×D1111yescharacteristic
241#106—442no—
242#102—442no—
243#95—21no—
244#95—221no—
245#95—221no—
246C2×C11#160811yescharacteristic
247C2×C11#161011yescharacteristic
248C2×C11#161611yescharacteristic
249C2×C11#162711yescharacteristic
250C2×C11#163911yescharacteristic
251C2×C11#165111yescharacteristic
252C2×C11#166411yescharacteristic
253D11—82no—
254C24—221no—
255C2×Q8—442no—
256C2×Q8—442no—
257C2×Q8—881no—
258C2×D4—112no—
259C2×D4—221no—
260C2×D4—441no—
261C2×D4—441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—442no—
269C22×C4—442no—
270C22×C4—881no—
271C22×C4D4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—222no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—112no—
293C4⋊C4—221no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—442no—
297C4⋊C4—442no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4#432512yes—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—881no—
308C42—41no—
309C11#779111yescharacteristic, complemented, Sylow
310C23—222no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23#6699011yescharacteristic
318Q8—884no—
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—222no—
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×C4D8×D1111yescharacteristic
347C2×C4#6696411yescharacteristic
348C2×C4SD16×D1111yescharacteristic
349C2×C4#6696811yescharacteristic
350C2×C4C2×#432511yescharacteristic
351C2×C4#6700211yescharacteristic
352C8—81no—
353C8—442no—
354C8—881no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062265911yescharacteristic
363C22#1062266611yescharacteristic
364C22#1062267511yescharacteristic
365C22#1062276911yescharacteristic
366C22#1062278311yescharacteristic
367C22#1062281511yescharacteristic
368C22#1062281811yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—161no—
378C4—442no—
379C4—881no—
380C4—881no—
381C2—882no—
382C2#1306760511yescharacteristic
383C2#1306761711yescharacteristic
384C2#1306765211yescharacteristic
385C2#1306771611yescharacteristic
386C2#1306779411yescharacteristic
387C2#1306787811yescharacteristic
388C2#1306794711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2099C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#2099D11
hypocenterC11#7791
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
2. #13070093C2semidirect
4. #13066440C2semidirect
5. #13066439C2semidirect
7. C11×#2099C2semidirect
117. #2099D11semidirect
309. C11#7791semidirect

Maximal subgroups

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

subgroupindex
#130749872
#130700932
#130700202
#130664402
#130664392
#130664362
C11×#20992
#779111