Finite Group Databasebeta

← C11×#11799 #14588992

Subgroups — C11×#11799 #14588992

Order 2816.

574 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2617C211yesmaximal, characteristic
2C11×#1819C211yesmaximal, characteristic, complemented
3C11×#1462C211yesmaximal, characteristic, complemented
4C11×#1344C212yesmaximal, complemented
5C11×#1343C212yesmaximal, complemented
6C2×C11×#121C411yescharacteristic, complemented
7C2×C11×#120—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C11×#407—21no—
10C11×#397C411yescharacteristic, complemented
11C11×#397C2211yescharacteristic
12C11×#394—21no—
13C11×#394—21no—
14C11×#392C411yescharacteristic, complemented
15C11×#392C2211yescharacteristic
16C11×#386—21no—
17C11×#380C411yescharacteristic, complemented
18C11×#379—21no—
19C11×#342—21no—
20C11×#342C2212yes—
21C11×#323—21no—
22C11×#323C2212yes—
23C25×C11D411yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—41no—
31C11×#121—41no—
32C11×#121—41no—
33C11×#120—44no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—41no—
44C2×C11×C22⋊C4—41no—
45C2×C11×C22⋊C4—41no—
46C2×C11×C22⋊C4—41no—
47C2×C11×C22⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4D411yescharacteristic
50C2×C11×C22⋊C4C2311yescharacteristic
51C11×C22⋊C8—22no—
52C11×C22⋊C8—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11799C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—22no—
61C24×C11—21no—
62C24×C11—41no—
63C24×C11—81no—
64C24×C11—81no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—81no—
76C2×D4×C11—81no—
77C2×D4×C11—81no—
78C2×D4×C11—81no—
79C2×D4×C11—81no—
80C22×C4×C11—21no—
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—42no—
88C22×C4×C11—81no—
89C22×C4×C11—81no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×M16—82no—
95C2×C8×C11—42no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—81no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—82no—
111C11×C22⋊C4—82no—
112#2617C2×C1111yescharacteristic
113#1819C2×C1111yescharacteristic, complemented
114#1462C2×C1111yescharacteristic, complemented
115#1344C2×C1112yescomplemented
116#1343C2×C1112yescomplemented
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11—84no—
144C23×C11—84no—
145C23×C11#9911yescharacteristic
146C23×C11#9911yescharacteristic
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11AGL(1,ℤ/8)12yes—
149D4×C11—82no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—84no—
153D4×C11—84no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—42no—
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—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C8×C11—82no—
179C2×#121C4×C1111yescharacteristic, complemented
180C2×#120—21no—
181C22×C22⋊C4C22×C1111yescharacteristic
182#407—21no—
183#397C4×C1111yescharacteristic, complemented
184#397C22×C1111yescharacteristic
185#394—21no—
186#394—21no—
187#392C4×C1111yescharacteristic, complemented
188#392C22×C1111yescharacteristic
189#386—21no—
190#380C4×C1111yescharacteristic, complemented
191#379—21no—
192#342—21no—
193#342C22×C1112yes—
194#323—21no—
195#323C22×C1112yes—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—22no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—84no—
221C22×C11—84no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C2×#9911yescharacteristic
226C22×C11#41811yescharacteristic
227C22×C11#42111yescharacteristic
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—162no—
236C25D4×C1111yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4C2×C4×C1111yescharacteristic
241C23×C4C2×C4×C1111yescharacteristic
242C23×C4D4×C1111yescharacteristic
243C2×M16—41no—
244#121—41no—
245#121—41no—
246#120—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4—41no—
260C2×C22⋊C4C2×C4×C1111yescharacteristic
261C2×C22⋊C4D4×C1111yescharacteristic
262C2×C22⋊C4D4×C1111yescharacteristic
263C2×C22⋊C4C23×C1111yescharacteristic
264C22⋊C8—22no—
265C22⋊C8—41no—
266#95—21no—
267#95—21no—
268#95C2×C4×C1111yescharacteristic
269#95C2×C4×C1111yescharacteristic
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—42no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11—81no—
276C2×C11—161no—
277C2×C11#151011yescharacteristic
278C2×C11#212111yescharacteristic
279C2×C11#212711yescharacteristic
280C24—21no—
281C24—21no—
282C24—22no—
283C24—21no—
284C24—41no—
285C24—81no—
286C24—81no—
287C24C11×C22⋊C411yescharacteristic
288C24C11×C22⋊C411yescharacteristic
289C24C2×D4×C1111yescharacteristic
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4C11×C22⋊C411yescharacteristic
313C22×C4C11×C22⋊C411yescharacteristic
314C22×C4C22×C4×C1111yescharacteristic
315C22×C4C2×D4×C1111yescharacteristic
316M16—82no—
317C2×C8—42no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—82no—
333C22⋊C4—82no—
334C11#1179911yescharacteristic, direct product factor, Sylow
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23—84no—
362C23—84no—
363C23C11×#9911yescharacteristic
364C23C11×#9911yescharacteristic
365C23C2×C11×C22⋊C411yescharacteristic
366C23C11×AGL(1,ℤ/8)12yes—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—84no—
371D4—84no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C8—82no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22C2×C11×#9911yescharacteristic
427C22C11×#41811yescharacteristic
428C22C11×#42111yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—162no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—41no—
441C2—41no—
442C2—81no—
443C2—161no—
444C2C11×#151011yescharacteristic
445C2C11×#212111yescharacteristic
446C2C11×#212711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#2617C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1819C2semidirect
3. C11×#1462C2semidirect
4. C11×#1344C2semidirect
5. C11×#1343C2semidirect
6. C2×C11×#121C4semidirect
10. C11×#397C4semidirect
14. C11×#392C4semidirect
17. C11×#380C4semidirect
57. #11799C11direct (N × H)
113. #1819C2×C11semidirect
114. #1462C2×C11semidirect
115. #1344C2×C11semidirect
116. #1343C2×C11semidirect
179. C2×#121C4×C11semidirect
183. #397C4×C11semidirect
187. #392C4×C11semidirect
190. #380C4×C11semidirect
334. C11#11799direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26172
C11×#18192
C11×#14622
C11×#13442
C11×#13432
#1179911