Finite Group Databasebeta

← C11×#13357 #14590550

Subgroups — C11×#13357 #14590550

Order 2816.

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

normal subgroups only

This group has 772 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
1C2×C11×#454C212yesmaximal, complemented
2C11×#2733C211yesmaximal, characteristic, complemented
3C2×C11×#355C212yesmaximal, complemented
4C11×#1793C211yesmaximal, characteristic, complemented
5C11×#1394C211yesmaximal, characteristic, complemented
6C2×C11×2−1+4C2211yescharacteristic
7C2×C11×AGL(1,ℤ/8)—22no—
8C2×C11×#124C2212yes—
9C11×#454—24no—
10C11×#454—24no—
11C2×C11×#104—22no—
12C2×C11×#104—21no—
13C11×#417—21no—
14C2×C11×#101C2211yescharacteristic
15C2×C11×#101C2212yes—
16C11×#394—21no—
17C11×#392—22no—
18C11×#391C2211yescharacteristic
19C11×#390—21no—
20C11×#388—22no—
21C11×#355—24no—
22C11×2−1+4—22no—
23C11×2−1+4—21no—
24C11×2−1+4—42no—
25C11×2−1+4D412yescomplemented
26C2×C11×#41—21no—
27C2×C11×#41—22no—
28C2×C11×#41—41no—
29C22×Q8×C11—41no—
30C22×Q8×C11C2311yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C11×AGL(1,ℤ/8)—28no—
35C11×AGL(1,ℤ/8)—44no—
36C2×C11×SD16—42no—
37C2×C11×D8—42no—
38C2×C11×M16—22no—
39C2×C11×M16—21no—
40C11×#124—22no—
41C11×#124—22no—
42C11×#124—22no—
43C11×#124—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C42×C11D412yes—
51C2×C42×C11D411yescharacteristic
52C11×#104—28no—
53C11×#104—42no—
54C11×#103—41no—
55C11×#102—41no—
56C11×#101—22no—
57C11×#101—22no—
58C11×#101D414yescomplemented
59C11×#95—21no—
60C11×#95—22no—
61#13357C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11—22no—
63C11×#41—22no—
64C11×#41—24no—
65C11×#41—24no—
66C11×#41—22no—
67C11×#41—41no—
68C11×#41—42no—
69C11×#41—42no—
70C11×#41—44no—
71C11×#41—42no—
72C11×#41—42no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—42no—
79C2×Q8×C11—44no—
80C2×Q8×C11—42no—
81C2×Q8×C11C2×D411yescharacteristic
82C2×Q8×C11C2×D412yes—
83C2×Q8×C11#4111yescharacteristic
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—42no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11—81no—
93C2×D4×C11—81no—
94C2×D4×C11—82no—
95C2×D4×C11—81no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C11×SD16—48no—
104C11×D8—48no—
105C11×M16—24no—
106C11×M16—42no—
107C11×M16—41no—
108C11×M16—41no—
109C2×C8×C11—42no—
110C2×C8×C11—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—81no—
113C11×C22⋊C4—44no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—82no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—41no—
122C2×#454C2×C1112yescomplemented
123#2733C2×C1111yescharacteristic, complemented
124C2×#355C2×C1112yescomplemented
125#1793C2×C1111yescharacteristic, complemented
126#1394C2×C1111yescharacteristic, complemented
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11#12011yescharacteristic
136Q8×C11—24no—
137Q8×C11—22no—
138Q8×C11—41no—
139Q8×C11—42no—
140Q8×C11—41no—
141Q8×C11—42no—
142Q8×C11—41no—
143D4×C11—24no—
144D4×C11—22no—
145D4×C11—42no—
146D4×C11—41no—
147D4×C11—44no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—82no—
151D4×C11—84no—
152D4×C11—84no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11#12012yes—
171C2×C4×C11#12112yes—
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C8×C11—44no—
175C8×C11—81no—
176C2×2−1+4C22×C1111yescharacteristic
177C2×AGL(1,ℤ/8)—22no—
178C2×#124C22×C1112yes—
179#454—24no—
180#454—24no—
181C2×#104—22no—
182C2×#104—21no—
183#417—21no—
184C2×#101C22×C1111yescharacteristic
185C2×#101C22×C1112yes—
186#394—21no—
187#392—22no—
188#391C22×C1111yescharacteristic
189#390—21no—
190#388—22no—
191#355—24no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11#39211yescharacteristic
205C22×C11B(4,𝔽2)11yescharacteristic
206C22×C11B(4,𝔽2)11yescharacteristic
207C4×C11—22no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—42no—
213C4×C11—82no—
214C4×C11—81no—
2152−1+4—22no—
2162−1+4—21no—
2172−1+4—42no—
2182−1+4D4×C1112yescomplemented
219C2×#41—22no—
220C2×#41—21no—
221C2×#41—41no—
222C22×Q8—41no—
223C22×Q8C23×C1111yescharacteristic
224C22×D4—21no—
225C22×D4—21no—
226C22×D4D4×C1112yes—
227AGL(1,ℤ/8)—28no—
228AGL(1,ℤ/8)—44no—
229C2×SD16—42no—
230C2×D8—42no—
231C2×M16—22no—
232C2×M16—21no—
233#124—22no—
234#124—22no—
235#124—22no—
236#124—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C1111yescharacteristic
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C42D4×C1112yes—
244C2×C42D4×C1111yescharacteristic
245#104—28no—
246#104—42no—
247#103—41no—
248#102—41no—
249#101—22no—
250#101—22no—
251#101D4×C1114yescomplemented
252#95—21no—
253#95—22no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—82no—
257C2×C11—162no—
258C2×C11#202111yescharacteristic
259C2×C11#220211yescharacteristic
260C2×C11#220411yescharacteristic
261C24—22no—
262#41—22no—
263#41—24no—
264#41—24no—
265#41—22no—
266#41—41no—
267#41—42no—
268#41—42no—
269#41—44no—
270#41—42no—
271#41—42no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—44no—
279C2×Q8—42no—
280C2×Q8C2×D4×C1111yescharacteristic
281C2×Q8C2×D4×C1112yes—
282C2×Q8C11×#4111yescharacteristic
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—82no—
294C2×D4—81no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1111yescharacteristic
302SD16—48no—
303D8—48no—
304M16—24no—
305M16—42no—
306M16—41no—
307M16—41no—
308C2×C8—42no—
309C2×C8—41no—
310C4⋊C4—41no—
311C4⋊C4—81no—
312C22⋊C4—44no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—82no—
318C42—22no—
319C42—22no—
320C42—41no—
321C11#1335711yescharacteristic, direct product factor, Sylow
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23C11×#12011yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—41no—
334Q8—42no—
335Q8—41no—
336Q8—41no—
337Q8—42no—
338D4—24no—
339D4—22no—
340D4—41no—
341D4—42no—
342D4—44no—
343D4—42no—
344D4—42no—
345D4—82no—
346D4—84no—
347D4—84no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4C11×#12012yes—
366C2×C4C11×#12112yes—
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12711yescharacteristic
369C8—44no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—82no—
375C22—82no—
376C22—82no—
377C22—82no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22C11×#39211yescharacteristic
384C22C11×B(4,𝔽2)11yescharacteristic
385C22C11×B(4,𝔽2)11yescharacteristic
386C4—22no—
387C4—21no—
388C4—21no—
389C4—22no—
390C4—42no—
391C4—42no—
392C4—82no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—162no—
398C2C11×#202111yescharacteristic
399C2C11×#220211yescharacteristic
400C2C11×#220411yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C11
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#454C2semidirect
2. C11×#2733C2semidirect
3. C2×C11×#355C2semidirect
4. C11×#1793C2semidirect
5. C11×#1394C2semidirect
25. C11×2−1+4D4semidirect
58. C11×#101D4semidirect
61. #13357C11direct (N × H)
122. C2×#454C2×C11semidirect
123. #2733C2×C11semidirect
124. C2×#355C2×C11semidirect
125. #1793C2×C11semidirect
126. #1394C2×C11semidirect
218. 2−1+4D4×C11semidirect
251. #101D4×C11semidirect
321. C11#13357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4542
C11×#27332
C2×C11×#3552
C11×#17932
C11×#13942
#1335711