Finite Group Databasebeta

← C11×#13332 #14590525

Subgroups — C11×#13332 #14590525

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#510C211yesmaximal, characteristic, complemented
2C2×C11×#509C211yesmaximal, characteristic
3C2×C11×#495C211yesmaximal, characteristic, complemented
4C2×C11×#362C211yesmaximal, characteristic, complemented
5C2×C11×#361C211yesmaximal, characteristic, complemented
6C11×#1974C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10C22×C11×SD16—21no—
11C22×C11×D8C2211yescharacteristic
12C2×C11×#124—21no—
13C11×#510—22no—
14C11×#510—22no—
15C11×#509—22no—
16C11×#509—22no—
17C2×C11×Q32—21no—
18C2×C11×SD32—21no—
19C2×C11×SD32—21no—
20C2×C11×D16—21no—
21C2×C11×M32C2211yescharacteristic
22C2×C11×M32C2211yescharacteristic
23C11×#495—22no—
24C11×#495—22no—
25C2×C11×#108C2211yescharacteristic
26C2×C11×#104—21no—
27C11×#408—21no—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#362—22no—
30C11×#361—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D4×C11—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135—21no—
37C11×#135—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16D412yes—
44C2×C11×Q16D411yescharacteristic
45C2×C11×SD16—24no—
46C2×C11×SD16—21no—
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8—21no—
54C2×C11×D8D412yes—
55C2×C11×D8D411yescharacteristic
56C2×C11×M16—21no—
57C22×C8×C11D411yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#124—24no—
60C11×#124—42no—
61C2×C11×C22⋊C4—42no—
62C2×C42×C11D411yescharacteristic
63C11×Q32—24no—
64C11×SD32—24no—
65C11×SD32—24no—
66C11×D16—24no—
67C11×M32—21no—
68C11×M32—21no—
69C11×M32D412yes—
70C11×M32D412yes—
71C2×C11×C16—21no—
72C2×C11×C16—21no—
73C11×#108—21no—
74C11×#108—21no—
75C11×#104—42no—
76C11×C22⋊C8—42no—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79#13332C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—21no—
105C11×Q16—22no—
106C11×Q16—21no—
107C11×Q16—22no—
108C11×Q16—41no—
109C11×Q16—41no—
110C11×SD16—48no—
111C11×SD16—41no—
112C11×SD16—41no—
113C11×D8—21no—
114C11×D8—22no—
115C11×D8—21no—
116C11×D8—22no—
117C11×D8—41no—
118C11×D8—41no—
119C11×M16—41no—
120C11×M16—41no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—41no—
124C2×C8×C11D812yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11#4111yescharacteristic
131C11×C22⋊C4—48no—
132C42×C11—21no—
133C42×C11D812yes—
134C11×C16—22no—
135C11×C16—22no—
136C2×#510C2×C1111yescharacteristic, complemented
137C2×#509C2×C1111yescharacteristic
138C2×#495C2×C1111yescharacteristic, complemented
139C2×#362C2×C1111yescharacteristic, complemented
140C2×#361C2×C1111yescharacteristic, complemented
141#1974C2×C1111yescharacteristic, complemented
142#1376C2×C1111yescharacteristic, complemented
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—84no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11AGL(1,ℤ/8)11yescharacteristic
149Q8×C11—41no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—41no—
153Q8×C11—81no—
154Q8×C11—81no—
155D4×C11—42no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C8×C11—22no—
178C8×C11—81no—
179C8×C11#12011yescharacteristic
180C8×C11#12011yescharacteristic
181C8×C11#12111yescharacteristic
182C8×C11#12111yescharacteristic
183C2×#135C22×C1111yescharacteristic
184C22×Q16C22×C1111yescharacteristic
185C22×SD16—21no—
186C22×D8C22×C1111yescharacteristic
187C2×#124—21no—
188#510—22no—
189#510—22no—
190#509—22no—
191#509—22no—
192C2×Q32—21no—
193C2×SD32—21no—
194C2×SD32—21no—
195C2×D16—21no—
196C2×M32C22×C1111yescharacteristic
197C2×M32C22×C1111yescharacteristic
198#495—22no—
199#495—22no—
200C2×#108C22×C1111yescharacteristic
201C2×#104—21no—
202#408—21no—
203C2×C4×C8C22×C1111yescharacteristic
204#362—22no—
205#361—22no—
206C22×C11—22no—
207C22×C11—84no—
208C22×C11—82no—
209C22×C11—81no—
210C22×C11—82no—
211C22×C11—162no—
212C22×C11—162no—
213C22×C11#44711yescharacteristic
214C22×C11#45911yescharacteristic
215C22×C11#49611yescharacteristic
216C4×C11—42no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11#39211yescharacteristic
220C4×C11#44711yescharacteristic
221C4×C11#45911yescharacteristic
222C4×C11#49311yescharacteristic
223C2×#41—21no—
224C22×Q8—21no—
225C22×D4—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16D4×C1112yes—
236C2×Q16D4×C1111yescharacteristic
237C2×SD16—24no—
238C2×SD16—21no—
239C2×SD16—42no—
240C2×SD16—42no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8D4×C1112yes—
247C2×D8D4×C1111yescharacteristic
248C2×M16—21no—
249C22×C8D4×C1111yescharacteristic
250C22×C8C23×C1111yescharacteristic
251#124—24no—
252#124—42no—
253C2×C22⋊C4—42no—
254C2×C42D4×C1111yescharacteristic
255Q32—24no—
256SD32—24no—
257SD32—24no—
258D16—24no—
259M32—21no—
260M32—21no—
261M32D4×C1112yes—
262M32D4×C1112yes—
263C2×C16—21no—
264C2×C16—21no—
265#108—21no—
266#108—21no—
267#104—42no—
268C22⋊C8—42no—
269C4×C8—21no—
270C4×C8—21no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—161no—
274C2×C11—162no—
275C2×C11#201111yescharacteristic
276C2×C11#221212yes—
277C24—41no—
278#41—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C2×D4×C1111yescharacteristic
301Q16—21no—
302Q16—22no—
303Q16—21no—
304Q16—22no—
305Q16—41no—
306Q16—41no—
307SD16—48no—
308SD16—41no—
309SD16—41no—
310D8—21no—
311D8—22no—
312D8—21no—
313D8—22no—
314D8—41no—
315D8—41no—
316M16—41no—
317M16—41no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8C11×D812yes—
322C2×C8C2×D4×C1111yescharacteristic
323C2×C8C2×D4×C1111yescharacteristic
324C2×C8C2×D4×C1111yescharacteristic
325C2×C8C2×D4×C1111yescharacteristic
326C2×C8C2×D4×C1111yescharacteristic
327C2×C8C11×#4111yescharacteristic
328C22⋊C4—48no—
329C42—21no—
330C42C11×D812yes—
331C16—22no—
332C16—22no—
333C11#1333211yescharacteristic, direct product factor, Sylow
334C23—42no—
335C23—41no—
336C23—84no—
337C23—81no—
338C23—81no—
339C23C11×AGL(1,ℤ/8)11yescharacteristic
340Q8—41no—
341Q8—42no—
342Q8—42no—
343Q8—41no—
344Q8—81no—
345Q8—81no—
346D4—42no—
347D4—41no—
348D4—42no—
349D4—41no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C11×#12011yescharacteristic
363C2×C4C11×#12111yescharacteristic
364C2×C4C11×#12711yescharacteristic
365C2×C4C2×C11×D811yescharacteristic
366C2×C4C2×C11×D811yescharacteristic
367C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
368C8—22no—
369C8—81no—
370C8C11×#12011yescharacteristic
371C8C11×#12011yescharacteristic
372C8C11×#12111yescharacteristic
373C8C11×#12111yescharacteristic
374C22—22no—
375C22—84no—
376C22—82no—
377C22—81no—
378C22—82no—
379C22—162no—
380C22—162no—
381C22C11×#44711yescharacteristic
382C22C11×#45911yescharacteristic
383C22C11×#49611yescharacteristic
384C4—42no—
385C4—81no—
386C4—82no—
387C4C11×#39211yescharacteristic
388C4C11×#44711yescharacteristic
389C4C11×#45911yescharacteristic
390C4C11×#49311yescharacteristic
391C2—21no—
392C2—21no—
393C2—162no—
394C2—161no—
395C2C11×#201111yescharacteristic
396C2C11×#221212yes—
subgroupG/H
center, socleC22×C11#459
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#510C2semidirect
3. C2×C11×#495C2semidirect
4. C2×C11×#362C2semidirect
5. C2×C11×#361C2semidirect
6. C11×#1974C2semidirect
7. C11×#1376C2semidirect
79. #13332C11direct (N × H)
136. C2×#510C2×C11semidirect
138. C2×#495C2×C11semidirect
139. C2×#362C2×C11semidirect
140. C2×#361C2×C11semidirect
141. #1974C2×C11semidirect
142. #1376C2×C11semidirect
333. C11#13332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5102
C2×C11×#5092
C2×C11×#4952
C2×C11×#3622
C2×C11×#3612
C11×#19742
C11×#13762
#1333211