Finite Group Databasebeta

← #14642818

Subgroups — #14642818

Order 2816.

446 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 83 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#13075632C211yesmaximal, characteristic
2#13070143C211yesmaximal, characteristic
3#13070087C211yesmaximal, characteristic, complemented
4#13070026C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic, complemented
8C2×#66949—21no—
9C11×#389C2211yescharacteristic
10C2×#66885—21no—
11C2×#66882—21no—
12C2×#66880—21no—
13#10622607—21no—
14#10622605—21no—
15#10622602—21no—
16C2×#66871—21no—
17#10622552C2211yescharacteristic
18#10622548C2211yescharacteristic
19#10622542C2211yescharacteristic
20#10622278—21no—
21#10622270—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
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⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50#66949—42no—
51#66949—42no—
52C11×#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66885—42no—
57#66882—42no—
58#66880—42no—
59#66871—42no—
60#7789—111nomaximal, Sylow
61C23×D11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—41no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44Q1612yes—
75C2×C4×D11—42no—
76C2×C4×D11—81no—
77C2×C4×D11—81no—
78C2×Dic22—21no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22D812yes—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11—41no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4—81no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2732—111no—
116#2093—111no—
117#2083—111no—
118#2072—111no—
119#1272—111no—
120#1271D1111yescharacteristic, complemented
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—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×Q1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160D44—42no—
161D44—81no—
162C4×D11—84no—
163Dic22—42no—
164Dic22—81no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—42no—
168C2×C22⋊Q8—221no—
169C2×#107—221no—
170C2×#107—221no—
171C2×#103—221no—
172C2×#102—221no—
173#399—221no—
174#398—221no—
175#396—221no—
176#391—111no—
177#390—111no—
178#389C2×D1111yescharacteristic
179#386—221no—
180#385—221no—
181#384—111no—
182#340—221no—
183#340—221no—
184#336—111no—
185#336C2×D1111yescharacteristic
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—81no—
208C4×C11—81no—
209Dic11—42no—
210Dic11—81no—
211Dic11—81no—
212Dic11—161no—
213C22×Q8—111no—
214C22×D4—111no—
215C23×C4—221no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—221no—
219C22⋊Q8—442no—
220C22⋊Q8—442no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4D4411yescharacteristic
231C2×C4⋊C4D4411yescharacteristic
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—442no—
241#102—442no—
242#95—21no—
243#95—221no—
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—112no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×D4—112no—
260C2×D4—221no—
261C2×D4—441no—
262C2×D4—441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—442no—
269C22×C4—441no—
270C22×C4—881no—
271C22×C4—881no—
272C22×C4C2×D4411yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C4⋊C4—441no—
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#6693511yescharacteristic
317Q8—442no—
318Q8—881no—
319D4—442no—
320D4—881no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—884no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6695711yescharacteristic
347C2×C4#6696111yescharacteristic
348C2×C4D8×D1111yescharacteristic
349C2×C4#6696711yescharacteristic
350C2×C4#6696811yescharacteristic
351C2×C4Q16×D1111yescharacteristic
352C8—42no—
353C8—81no—
354C8—442no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062234711yescharacteristic
363C22#1062235511yescharacteristic
364C22#1062236511yescharacteristic
365C22#1062238611yescharacteristic
366C22#1062242111yescharacteristic
367C22#1062243511yescharacteristic
368C22#1062243811yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—81no—
377C4—442no—
378C4—881no—
379C4—881no—
380C4—1761no—
381C2—882no—
382C2#1306760311yescharacteristic
383C2#1306761511yescharacteristic
384C2#1306764211yescharacteristic
385C2#1306768411yescharacteristic
386C2#1306783211yescharacteristic
387C2#1306786611yescharacteristic
388C2#1306793511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1271D11
hypocenterC11#7789
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
3. #13070087C2semidirect
4. #13070026C2semidirect
5. #13066441C2semidirect
7. C11×#1271C2semidirect
120. #1271D11semidirect
308. C11#7789semidirect

Maximal subgroups

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

subgroupindex
#130756322
#130701432
#130700872
#130700262
#130664412
#130664362
C11×#12712
#778911