Finite Group Databasebeta

← C11×#22192 #14599385

Subgroups — C11×#22192 #14599385

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C11×#2323C212yesmaximal
3C11×#1927C212yesmaximal, complemented
4C11×#1921C212yesmaximal, complemented
5C11×#1894C212yesmaximal
6C11×#1878C212yesmaximal, complemented
7C11×#1865C212yesmaximal, complemented
8C11×#1807C211yesmaximal, characteristic
9C11×#1729C211yesmaximal, characteristic
10C22×C11×Q16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C4×Q8×C11C2212yes—
15C2×C11×#117C2211yescharacteristic
16C11×#467C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C11×#391C2212yes—
24C11×#389—22no—
25C11×#389C2212yes—
26C11×#388—22no—
27C11×#388—22no—
28C11×#387—22no—
29C11×#380C2212yes—
30C4×C11×C4⋊C4C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C2×C11×Q16—41no—
39C2×C11×Q16—41no—
40C2×C11×Q16C2×C414yes—
41C2×C11×M16—22no—
42C2×C11×M16—41no—
43C2×C11×M16—41no—
44C22×C8×C11—41no—
45C22×C8×C11—41no—
46C22×C8×C11C2×C414yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8C2×C418yes—
52C4×Q8×C11—42no—
53C4×Q8×C11—42no—
54C11×#117—41no—
55C11×#117—41no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4D411yescharacteristic
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11C2312yes—
70C11×#107C2×C414yes—
71C11×#106—41no—
72C11×#106—41no—
73C11×#103—42no—
74C11×#103—42no—
75C11×#103C2×C418yes—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#22192C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11C22×C414yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C11×Q16—44no—
104C11×M16—44no—
105C2×C8×C11—22no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—44no—
113C2×C8×C11C22×C412yes—
114C2×C8×C11C22×C412yes—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—44no—
123C11×C4⋊C4—82no—
124C11×C4⋊C4C22×C414yes—
125C11×C22⋊C4—28no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—82no—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—44no—
132C42×C11—82no—
133C2×#467C2×C1111yescharacteristic
134#2323C2×C1112yes—
135#1927C2×C1112yescomplemented
136#1921C2×C1112yescomplemented
137#1894C2×C1112yes—
138#1878C2×C1112yescomplemented
139#1865C2×C1112yescomplemented
140#1807C2×C1111yescharacteristic
141#1729C2×C1111yescharacteristic
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11C4×D412yes—
147C23×C11C22×D411yescharacteristic
148Q8×C11—24no—
149Q8×C11—24no—
150Q8×C11—42no—
151Q8×C11—42no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11H(5,𝔽2)11yescharacteristic
180C2×C4×C11H(5,𝔽2)11yescharacteristic
181C2×C4×C11H(5,𝔽2)11yescharacteristic
182C2×C4×C112−1+411yescharacteristic
183C8×C11—22no—
184C8×C11—22no—
185C8×C11—42no—
186C22×Q16C22×C1111yescharacteristic
187C22×M16C22×C1111yescharacteristic
188C23×C8C22×C1111yescharacteristic
189C2×C22⋊Q8C22×C1112yes—
190C2×C4×Q8C22×C1112yes—
191C2×#117C22×C1111yescharacteristic
192#467C4×C1118yescomplemented
193C2×#107C22×C1111yescharacteristic
194C2×#106C22×C1111yescharacteristic
195C2×#106C22×C1111yescharacteristic
196C2×#103C22×C1112yes—
197C2×#103C22×C1112yes—
198C2×#103C22×C1112yes—
199#391C22×C1112yes—
200#389—22no—
201#389C22×C1112yes—
202#388—22no—
203#388—22no—
204#387—22no—
205#380C22×C1112yes—
206C4×C4⋊C4C22×C1112yes—
207#340C22×C1112yes—
208#340C22×C1112yes—
209#340C22×C1112yes—
210#336C22×C1112yes—
211#336C22×C1112yes—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11C2×C4×D411yescharacteristic
218C22×C11#53411yescharacteristic
219C22×C11#53711yescharacteristic
220C22×C11#57712yes—
221C22×C11#57812yes—
222C4×C11—22no—
223C4×C11—44no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11—44no—
227C4×C11—82no—
228C4×C11—82no—
229C4×C11#51811yescharacteristic
230C4×C11#52011yescharacteristic
231C4×C11#53811yescharacteristic
232C4×C11#53911yescharacteristic
233C22×Q8C23×C1112yes—
234C23×C4C23×C1111yescharacteristic
235C2×Q16—41no—
236C2×Q16—41no—
237C2×Q16C2×C4×C1114yes—
238C2×M16—22no—
239C2×M16—41no—
240C2×M16—41no—
241C22×C8—41no—
242C22×C8—41no—
243C22×C8C2×C4×C1114yes—
244C22×C8C23×C1112yes—
245C22×C8C23×C1111yescharacteristic
246C22×C8C23×C1111yescharacteristic
247C22⋊Q8—24no—
248C22⋊Q8C2×C4×C1118yes—
249C4×Q8—42no—
250C4×Q8—42no—
251#117—41no—
252#117—41no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4D4×C1112yes—
257C2×C4⋊C4C23×C1112yes—
258C2×C4⋊C4C23×C1112yes—
259C2×C4⋊C4C23×C1112yes—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4D4×C1111yescharacteristic
263C2×C22⋊C4D4×C1111yescharacteristic
264C2×C42—22no—
265C2×C42—22no—
266C2×C42C23×C1112yes—
267#107C2×C4×C1114yes—
268#106—41no—
269#106—41no—
270#103—42no—
271#103—42no—
272#103C2×C4×C1118yes—
273#95—22no—
274#95—22no—
275#95—22no—
276#95—22no—
277#95—22no—
278C2×C11—42no—
279C2×C11#232511yescharacteristic
280C2×C11#295011yescharacteristic
281C2×C11#295211yescharacteristic
282C2×C11#320112yes—
283C2×C11#325812yes—
284C24C2×D4×C1111yescharacteristic
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—22no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8C22×C4×C1114yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4C22×C4×C1112yes—
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C11×#4112yes—
304C22×C4C24×C1111yescharacteristic
305Q16—44no—
306M16—44no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—44no—
315C2×C8C22×C4×C1112yes—
316C2×C8C22×C4×C1112yes—
317C4⋊C4—28no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—42no—
324C4⋊C4—44no—
325C4⋊C4—82no—
326C4⋊C4C22×C4×C1114yes—
327C22⋊C4—28no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—82no—
331C42—22no—
332C42—22no—
333C42—44no—
334C42—82no—
335C11#2219211yescharacteristic, direct product factor, Sylow
336C23—21no—
337C23—21no—
338C23—22no—
339C23—22no—
340C23C4×D4×C1112yes—
341C23C22×D4×C1111yescharacteristic
342Q8—24no—
343Q8—24no—
344Q8—42no—
345Q8—42no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4C4×D4×C1112yes—
371C2×C4C23×C4×C1111yescharacteristic
372C2×C4C2×C11×#4111yescharacteristic
373C2×C4C11×H(5,𝔽2)11yescharacteristic
374C2×C4C11×H(5,𝔽2)11yescharacteristic
375C2×C4C11×H(5,𝔽2)11yescharacteristic
376C2×C4C11×2−1+411yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—42no—
384C22—42no—
385C22C2×C4×D4×C1111yescharacteristic
386C22C11×#53411yescharacteristic
387C22C11×#53711yescharacteristic
388C22C11×#57712yes—
389C22C11×#57812yes—
390C4—22no—
391C4—42no—
392C4—42no—
393C4—44no—
394C4—44no—
395C4—82no—
396C4—82no—
397C4C11×#51811yescharacteristic
398C4C11×#52011yescharacteristic
399C4C11×#53811yescharacteristic
400C4C11×#53911yescharacteristic
401C2—42no—
402C2C11×#232511yescharacteristic
403C2C11×#295011yescharacteristic
404C2C11×#295211yescharacteristic
405C2C11×#320112yes—
406C2C11×#325812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1927C2semidirect
4. C11×#1921C2semidirect
6. C11×#1878C2semidirect
7. C11×#1865C2semidirect
16. C11×#467C4semidirect
81. #22192C11direct (N × H)
135. #1927C2×C11semidirect
136. #1921C2×C11semidirect
138. #1878C2×C11semidirect
139. #1865C2×C11semidirect
192. #467C4×C11semidirect
335. C11#22192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C11×#23232
C11×#19272
C11×#19212
C11×#18942
C11×#18782
C11×#18652
C11×#18072
C11×#17292
#2219211