Finite Group Databasebeta

← C11×#12138 #14589331

Subgroups — C11×#12138 #14589331

Order 2816.

394 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C11×#2834C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic
3C11×#1613C211yesmaximal, characteristic
4C11×#1607C211yesmaximal, characteristic
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1344C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C11×#481—21no—
10C11×#480—21no—
11C2×C11×#99—21no—
12C11×#401—21no—
13C11×#399C2211yescharacteristic
14C11×#398—21no—
15C11×#398—21no—
16C11×#398—21no—
17C11×#397—21no—
18C11×#397C2211yescharacteristic
19C11×#386—21no—
20C11×#385—21no—
21C11×#385C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×D4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C11×#123—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#120—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—41no—
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4C2311yescharacteristic
46C11×#107—41no—
47C11×#106—41no—
48C11×#102—41no—
49C11×#102—41no—
50C11×#99—42no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—41no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12138C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—81no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
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—81no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—82no—
108#2834C2×C1111yescharacteristic, complemented
109#2044C2×C1111yescharacteristic
110#1613C2×C1111yescharacteristic
111#1607C2×C1111yescharacteristic
112#1352C2×C1111yescharacteristic, complemented
113#1344C2×C1111yescharacteristic, complemented
114#1326C2×C1111yescharacteristic, complemented
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—81no—
123C23×C11—81no—
124C23×C11#12011yescharacteristic
125C23×C11#13511yescharacteristic
126C23×C11AGL(1,ℤ/8)11yescharacteristic
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130D4×C11—81no—
131D4×C11—81no—
132D4×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
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×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—42no—
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—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C8×C11—81no—
164C8×C11—81no—
165#534C22×C1111yescharacteristic
166#481—21no—
167#480—21no—
168C2×#99—21no—
169#401—21no—
170#399C22×C1111yescharacteristic
171#398—21no—
172#398—21no—
173#398—21no—
174#397—21no—
175#397C22×C1111yescharacteristic
176#386—21no—
177#385—21no—
178#385C22×C1111yescharacteristic
179#342C22×C1111yescharacteristic
180#327—21no—
181#327—21no—
182#323C22×C1111yescharacteristic
183#323C22×C1111yescharacteristic
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—81no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—161no—
198C22×C11#44911yescharacteristic
199C22×C11#45411yescharacteristic
200C22×C11B(4,𝔽2)11yescharacteristic
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—161no—
211C22×D4—21no—
212C23×C4D4×C1111yescharacteristic
213#123—41no—
214#121—21no—
215#121—21no—
216#120—41no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4D4×C1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—41no—
228C2×C22⋊C4D4×C1111yescharacteristic
229C2×C22⋊C4C23×C1111yescharacteristic
230#107—41no—
231#106—41no—
232#102—41no—
233#102—41no—
234#99—42no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—41no—
245#95D4×C1111yescharacteristic
246#95D4×C1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11—161no—
252C2×C11#159711yescharacteristic
253C2×C11#220011yescharacteristic
254C2×C11#220111yescharacteristic
255C24—21no—
256C24C2×D4×C1111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—81no—
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C22⋊C4—82no—
299C11#1213811yescharacteristic, direct product factor, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—81no—
308C23—81no—
309C23C11×#12011yescharacteristic
310C23C11×#13511yescharacteristic
311C23C11×AGL(1,ℤ/8)11yescharacteristic
312D4—81no—
313D4—81no—
314D4—81no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C8—81no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—82no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—161no—
364C22C11×#44911yescharacteristic
365C22C11×#45411yescharacteristic
366C22C11×B(4,𝔽2)11yescharacteristic
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—161no—
377C2—21no—
378C2—21no—
379C2—41no—
380C2—41no—
381C2—161no—
382C2C11×#159711yescharacteristic
383C2C11×#220011yescharacteristic
384C2C11×#220111yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2834C2semidirect
5. C11×#1352C2semidirect
6. C11×#1344C2semidirect
7. C11×#1326C2semidirect
63. #12138C11direct (N × H)
108. #2834C2×C11semidirect
112. #1352C2×C11semidirect
113. #1344C2×C11semidirect
114. #1326C2×C11semidirect
299. C11#12138direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28342
C11×#20442
C11×#16132
C11×#16072
C11×#13522
C11×#13442
C11×#13262
#1213811