Finite Group Databasebeta

← C11×#9992 #14587185

Subgroups — C11×#9992 #14587185

Order 2816.

562 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3192C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic, complemented
3C2×C11×#480C211yesmaximal, characteristic, complemented
4C11×#1821C211yesmaximal, characteristic, complemented
5C11×#1471C211yesmaximal, characteristic, complemented
6C11×#1471C211yesmaximal, characteristic, complemented
7C11×#1298C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#481—21no—
12C11×#481—21no—
13C11×#481—22no—
14C11×#481—22no—
15C11×#480—22no—
16C11×#480—22no—
17C11×#469—22no—
18C11×#447—21no—
19C11×#447—21no—
20C2×C11×#107—21no—
21C2×C11×#106—21no—
22C2×C11×#102—21no—
23C2×C11×#102—21no—
24C11×#407C2211yescharacteristic
25C11×#407C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#343—22no—
29C11×#323—22no—
30C11×#323—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C2×C11×D8—22no—
38C2×C11×M16—21no—
39C2×C11×M16D412yes—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C11×#121—21no—
48C11×#121—21no—
49C11×#121—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C11×#107—24no—
61C11×#106—24no—
62C11×#106—22no—
63C11×#102—24no—
64C11×#102—24no—
65C11×#102—22no—
66C11×#102—22no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8D412yes—
74C11×C22⋊C8D412yes—
75#9992C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C24×C11—21no—
78C24×C11#4111yescharacteristic
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—82no—
90C2×D4×C11—82no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×D8—82no—
105C11×M16—42no—
106C11×M16—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125#3192C2×C1111yescharacteristic
126C2×#481C2×C1111yescharacteristic, complemented
127C2×#480C2×C1111yescharacteristic, complemented
128#1821C2×C1111yescharacteristic, complemented
129#1471C2×C1111yescharacteristic, complemented
130#1471C2×C1111yescharacteristic, complemented
131#1298C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11#12111yescharacteristic
144C23×C11#12111yescharacteristic
145C23×C11#12111yescharacteristic
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—82no—
153D4×C11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C8×C11—42no—
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—81no—
176C2×#121C22×C1111yescharacteristic
177C2×#121C22×C1111yescharacteristic
178C22×C4⋊C4C22×C1111yescharacteristic
179#481—22no—
180#481—21no—
181#481—21no—
182#481—22no—
183#480—22no—
184#480—22no—
185#469—22no—
186#447—21no—
187#447—21no—
188C2×#107—21no—
189C2×#106—21no—
190C2×#102—21no—
191C2×#102—21no—
192#407C22×C1111yescharacteristic
193#407C22×C1111yescharacteristic
194C2×C22⋊C8C22×C1111yescharacteristic
195C2×C22⋊C8C22×C1111yescharacteristic
196#343—22no—
197#323—22no—
198#323—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—44no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—162no—
214C22×C11—162no—
215C22×C11#39211yescharacteristic
216C22×C11#47112yes—
217C22×C11#47212yes—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11#45812yes—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4D4×C1111yescharacteristic
228C22×D4D4×C1111yescharacteristic
229C23×C4—21no—
230C23×C4C23×C1111yescharacteristic
231C2×D8—22no—
232C2×M16—21no—
233C2×M16D4×C1112yes—
234C22×C8—21no—
235C22×C8—21no—
236#121—21no—
237#121—21no—
238#121—21no—
239#121—21no—
240#121—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1112yes—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254#107—24no—
255#106—24no—
256#106—22no—
257#102—24no—
258#102—24no—
259#102—22no—
260#102—22no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8D4×C1112yes—
268C22⋊C8D4×C1112yes—
269C2×C11—22no—
270C2×C11—22no—
271C2×C11—41no—
272C2×C11—161no—
273C2×C11—161no—
274C2×C11#201811yescharacteristic
275C2×C11#201911yescharacteristic
276C2×C11#202211yescharacteristic
277C24—21no—
278C24—21no—
279C24C11×#4111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—82no—
291C2×D4—82no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—82no—
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1111yescharacteristic
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1111yescharacteristic
305D8—82no—
306M16—42no—
307M16—42no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—41no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C11#999211yescharacteristic, direct product factor, Sylow
327C23—22no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23C11×#12111yescharacteristic
339C23C11×#12111yescharacteristic
340C23C11×#12111yescharacteristic
341D4—42no—
342D4—42no—
343D4—42no—
344D4—42no—
345D4—82no—
346D4—82no—
347D4—82no—
348D4—82no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12711yescharacteristic
367C8—42no—
368C8—42no—
369C8—42no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—162no—
386C22—162no—
387C22C11×#39211yescharacteristic
388C22C11×#47112yes—
389C22C11×#47212yes—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4C11×#45812yes—
397C2—22no—
398C2—22no—
399C2—41no—
400C2—161no—
401C2—161no—
402C2C11×#201811yescharacteristic
403C2C11×#201911yescharacteristic
404C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC11×#3192C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C2×C11×#480C2semidirect
4. C11×#1821C2semidirect
5. C11×#1471C2semidirect
6. C11×#1471C2semidirect
7. C11×#1298C2semidirect
75. #9992C11direct (N × H)
126. C2×#481C2×C11semidirect
127. C2×#480C2×C11semidirect
128. #1821C2×C11semidirect
129. #1471C2×C11semidirect
130. #1471C2×C11semidirect
131. #1298C2×C11semidirect
326. C11#9992direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31922
C2×C11×#4812
C2×C11×#4802
C11×#18212
C11×#14712
C11×#12982
#999211