Finite Group Databasebeta

← C11×#12137 #14589330

Subgroups — C11×#12137 #14589330

Order 2816.

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

normal subgroups only

This group has 446 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×#2826C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic, complemented
3C11×#1613C211yesmaximal, characteristic, complemented
4C11×#1595C211yesmaximal, characteristic
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C11×#481—21no—
10C11×#447—21no—
11C2×C11×#99—21no—
12C11×#400—21no—
13C11×#399C2211yescharacteristic
14C11×#397—21no—
15C11×#396—21no—
16C11×#394—21no—
17C11×#394—21no—
18C11×#392C2211yescharacteristic
19C11×#386—21no—
20C11×#386—21no—
21C11×#385C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C2×C11×D8—41no—
32C11×#123—41no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#120—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—41no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C11×#106—41no—
51C11×#102—41no—
52C11×#102—41no—
53C11×#99—42no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—41no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12137C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—81no—
79C2×D4×C11—81no—
80C2×D4×C11—81no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—81no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×D8—82no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—21no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4—82no—
115#2826C2×C1111yescharacteristic, complemented
116#2044C2×C1111yescharacteristic, complemented
117#1613C2×C1111yescharacteristic, complemented
118#1595C2×C1111yescharacteristic
119#1352C2×C1111yescharacteristic, complemented
120#1343C2×C1111yescharacteristic, complemented
121#1326C2×C1111yescharacteristic, complemented
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—81no—
137C23×C11—81no—
138C23×C11#12011yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—81no—
145D4×C11—81no—
146D4×C11—81no—
147D4×C11—82no—
148D4×C11—82no—
149D4×C11—81no—
150D4×C11—81no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
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—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C8×C11—81no—
179C8×C11—81no—
180#534C22×C1111yescharacteristic
181#481—21no—
182#447—21no—
183C2×#99—21no—
184#400—21no—
185#399C22×C1111yescharacteristic
186#397—21no—
187#396—21no—
188#394—21no—
189#394—21no—
190#392C22×C1111yescharacteristic
191#386—21no—
192#386—21no—
193#385C22×C1111yescharacteristic
194#342C22×C1111yescharacteristic
195#327—21no—
196#327—21no—
197#323C22×C1111yescharacteristic
198#323C22×C1111yescharacteristic
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—82no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—161no—
220C22×C11#44911yescharacteristic
221C22×C11#45411yescharacteristic
222C22×C11B(4,𝔽2)11yescharacteristic
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—161no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4D4×C1111yescharacteristic
235C23×C4D4×C1111yescharacteristic
236C2×D8—41no—
237#123—41no—
238#121—21no—
239#121—21no—
240#120—41no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C1111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—41no—
253C2×C22⋊C4D4×C1111yescharacteristic
254C2×C22⋊C4C23×C1111yescharacteristic
255#106—41no—
256#102—41no—
257#102—41no—
258#99—42no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—41no—
266#95D4×C1111yescharacteristic
267#95D4×C1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—41no—
271C2×C11—41no—
272C2×C11—161no—
273C2×C11—161no—
274C2×C11#159711yescharacteristic
275C2×C11#220011yescharacteristic
276C2×C11#220011yescharacteristic
277C24—21no—
278C24—21no—
279C24C2×D4×C1111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—81no—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1111yescharacteristic
305D8—82no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—81no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—81no—
322C22⋊C4—81no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—82no—
328C11#1213711yescharacteristic, direct product factor, Sylow
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—81no—
344C23—81no—
345C23C11×#12011yescharacteristic
346C23C11×#13511yescharacteristic
347C23C11×AGL(1,ℤ/8)11yescharacteristic
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—82no—
355D4—82no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C8—81no—
386C8—81no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—82no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—161no—
408C22C11×#44911yescharacteristic
409C22C11×#45411yescharacteristic
410C22C11×B(4,𝔽2)11yescharacteristic
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—161no—
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2—161no—
425C2—161no—
426C2C11×#159711yescharacteristic
427C2C11×#220011yescharacteristic
428C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#1595C2
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×#2826C2semidirect
2. C11×#2044C2semidirect
3. C11×#1613C2semidirect
5. C11×#1352C2semidirect
6. C11×#1343C2semidirect
7. C11×#1326C2semidirect
63. #12137C11direct (N × H)
115. #2826C2×C11semidirect
116. #2044C2×C11semidirect
117. #1613C2×C11semidirect
119. #1352C2×C11semidirect
120. #1343C2×C11semidirect
121. #1326C2×C11semidirect
328. C11#12137direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28262
C11×#20442
C11×#16132
C11×#15952
C11×#13522
C11×#13432
C11×#13262
#1213711