Finite Group Databasebeta

← C11×#12132 #14589325

Subgroups — C11×#12132 #14589325

Order 2816.

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

normal subgroups only

This group has 544 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×#2455C211yesmaximal, 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
9C2×C11×#123—21no—
10C2×C4×D4×C11—21no—
11C11×#481—21no—
12C11×#447—21no—
13C2×C11×#99—21no—
14C11×#399C2211yescharacteristic
15C11×#394—21no—
16C11×#392C2211yescharacteristic
17C11×#389—21no—
18C11×#388—21no—
19C11×#386—21no—
20C11×#385—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×C11—21no—
31C23×C4×C11D411yescharacteristic
32C2×C11×D8—41no—
33C11×#123—44no—
34C11×#123—41no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#120—41no—
38C4×D4×C11—44no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C11×C22⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C11×#106—41no—
55C11×#102—41no—
56C11×#102—41no—
57C11×#99—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—41no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12132C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C24×C11—21no—
68C24×C11C2×D411yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—41no—
94C22×C4×C11—81no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C11×D8—82no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—82no—
120C42×C11—42no—
121#2455C2×C1111yescharacteristic, complemented
122#2044C2×C1111yescharacteristic, complemented
123#1613C2×C1111yescharacteristic, complemented
124#1595C2×C1111yescharacteristic
125#1352C2×C1111yescharacteristic, complemented
126#1343C2×C1111yescharacteristic, complemented
127#1326C2×C1111yescharacteristic, complemented
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11#12011yescharacteristic
145C23×C11#13511yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147D4×C11—42no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—84no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C8×C11—81no—
186C8×C11—81no—
187#534C22×C1111yescharacteristic
188C2×#123—21no—
189C2×C4×D4—21no—
190#481—21no—
191#447—21no—
192C2×#99—21no—
193#399C22×C1111yescharacteristic
194#394—21no—
195#392C22×C1111yescharacteristic
196#389—21no—
197#388—21no—
198#386—21no—
199#385—21no—
200#385C22×C1111yescharacteristic
201#342C22×C1111yescharacteristic
202#327—21no—
203#327—21no—
204#323C22×C1111yescharacteristic
205#323C22×C1111yescharacteristic
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—42no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—82no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—161no—
227C22×C11#44911yescharacteristic
228C22×C11#45411yescharacteristic
229C22×C11B(4,𝔽2)11yescharacteristic
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11—161no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4D4×C1111yescharacteristic
242C23×C4—21no—
243C23×C4D4×C1111yescharacteristic
244C2×D8—41no—
245#123—44no—
246#123—41no—
247#121—21no—
248#121—21no—
249#120—41no—
250C4×D4—44no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C1111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4D4×C1111yescharacteristic
264C2×C22⋊C4C23×C1111yescharacteristic
265C2×C42—21no—
266#106—41no—
267#102—41no—
268#102—41no—
269#99—42no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272#95—21no—
273#95—21no—
274#95—41no—
275#95D4×C1111yescharacteristic
276#95D4×C1111yescharacteristic
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11—82no—
282C2×C11—161no—
283C2×C11#159711yescharacteristic
284C2×C11#219611yescharacteristic
285C2×C11#219811yescharacteristic
286C24—21no—
287C24—21no—
288C24C2×D4×C1111yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—81no—
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1111yescharacteristic
317D8—82no—
318C2×C8—41no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C22⋊C4—24no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—82no—
340C42—42no—
341C11#1213211yescharacteristic, direct product factor, Sylow
342C23—21no—
343C23—21no—
344C23—22no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23C11×#12011yescharacteristic
359C23C11×#13511yescharacteristic
360C23C11×AGL(1,ℤ/8)11yescharacteristic
361D4—42no—
362D4—44no—
363D4—44no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—84no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—41no—
406C22—41no—
407C22—42no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—42no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—161no—
422C22C11×#44911yescharacteristic
423C22C11×#45411yescharacteristic
424C22C11×B(4,𝔽2)11yescharacteristic
425C4—42no—
426C4—42no—
427C4—41no—
428C4—42no—
429C4—41no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—161no—
434C2—21no—
435C2—21no—
436C2—41no—
437C2—41no—
438C2—82no—
439C2—161no—
440C2C11×#159711yescharacteristic
441C2C11×#219611yescharacteristic
442C2C11×#219811yescharacteristic
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×#2455C2semidirect
2. C11×#2044C2semidirect
3. C11×#1613C2semidirect
5. C11×#1352C2semidirect
6. C11×#1343C2semidirect
7. C11×#1326C2semidirect
65. #12132C11direct (N × H)
121. #2455C2×C11semidirect
122. #2044C2×C11semidirect
123. #1613C2×C11semidirect
125. #1352C2×C11semidirect
126. #1343C2×C11semidirect
127. #1326C2×C11semidirect
341. C11#12132direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24552
C11×#20442
C11×#16132
C11×#15952
C11×#13522
C11×#13432
C11×#13262
#1213211