Finite Group Databasebeta

← C11×#24989 #14602182

Subgroups — C11×#24989 #14602182

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#473C211yesmaximal, characteristic
2C11×#2950C211yesmaximal, characteristic, complemented
3C11×#2082C212yesmaximal, complemented
4C11×#2049C212yesmaximal
5C11×#1979C211yesmaximal, characteristic, complemented
6C11×#1953C211yesmaximal, characteristic, complemented
7C11×#1905C212yesmaximal
8C11×#1833C211yesmaximal, characteristic, complemented
9C11×#1830C212yesmaximal, complemented
10C11×#1814C211yesmaximal, characteristic
11C11×#1757C211yesmaximal, characteristic
12C2×C11×#137C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15C11×#519C2212yes—
16C11×#473—22no—
17C11×#473—22no—
18C11×#441—22no—
19C4×C11×Q16—22no—
20C11×#430C2212yes—
21C2×C11×#108C2211yescharacteristic
22C2×C11×#108C2211yescharacteristic
23C11×#427C2211yescharacteristic
24C11×#421C2212yes—
25C11×#419C2212yes—
26C11×#419C2212yes—
27C11×#413C2211yescharacteristic
28C2×C11×#101C2212yes—
29C2×C11×#101C2212yes—
30C11×#410C2211yescharacteristic
31C11×#405C2211yescharacteristic
32C11×#405C2211yescharacteristic
33C11×#344C2212yes—
34C11×#344C2211yescharacteristic
35C11×#344C2211yescharacteristic
36C11×#344C2212yes—
37C11×#344C2212yes—
38C11×H(3,ℤ/4)C2212yes—
39C2×C11×#41C2311yescharacteristic
40C22×Q8×C11C2312yes—
41C11×#137—24no—
42C11×#137—42no—
43C2×C11×Q16—22no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—21no—
48C2×C11×Q16D412yes—
49C2×C11×Q16D412yes—
50C2×C11×SD16—22no—
51C11×#131—21no—
52C11×#131—21no—
53C11×#131—21no—
54C11×#131—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2312yes—
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2311yescharacteristic
59C2×C11×M16C2312yes—
60C2×C11×M16C2311yescharacteristic
61C22×C8×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C4×Q8×C11—24no—
64C4×Q8×C11—42no—
65C11×#117—24no—
66C11×#117C2311yescharacteristic
67C11×#117C2312yes—
68C11×#117C2311yescharacteristic
69C11×#108—21no—
70C11×#108—21no—
71C11×#108—21no—
72C11×#108—21no—
73C11×#108—42no—
74C11×#107—21no—
75C11×#106—21no—
76C11×#104—42no—
77C11×#103—24no—
78C11×#103—42no—
79C11×#101—24no—
80C11×#101—21no—
81C11×#101—42no—
82C11×#100—21no—
83C11×#99—22no—
84C11×#97—21no—
85C11×#97—21no—
86C4×C8×C11—21no—
87C4×C8×C11—21no—
88#24989C1111yesmaximal, characteristic, direct product factor, Sylow
89C11×#41—21no—
90C11×#41—21no—
91C11×#41—21no—
92C11×#41—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C2×D414yes—
99C2×Q8×C11#4111yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11#4111yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11C2411yescharacteristic
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×Q16—44no—
110C11×SD16—44no—
111C11×M16—21no—
112C11×M16—22no—
113C11×M16—21no—
114C11×M16—21no—
115C11×M16—22no—
116C11×M16—21no—
117C11×M16—21no—
118C11×M16—22no—
119C11×M16—21no—
120C11×M16—22no—
121C11×M16—41no—
122C11×M16—41no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11#4111yescharacteristic
133C2×C8×C11#4111yescharacteristic
134C2×C8×C11#4111yescharacteristic
135C2×C8×C11#4111yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—44no—
140C11×C22⋊C4—21no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4#4112yes—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11—22no—
146C42×C11—44no—
147C2×#473C2×C1111yescharacteristic
148#2950C2×C1111yescharacteristic, complemented
149#2082C2×C1112yescomplemented
150#2049C2×C1112yes—
151#1979C2×C1111yescharacteristic, complemented
152#1953C2×C1111yescharacteristic, complemented
153#1905C2×C1112yes—
154#1833C2×C1111yescharacteristic, complemented
155#1830C2×C1112yescomplemented
156#1814C2×C1111yescharacteristic
157#1757C2×C1111yescharacteristic
158C23×C11—21no—
159C23×C11C2×#4111yescharacteristic
160Q8×C11—24no—
161Q8×C11—24no—
162Q8×C11—21no—
163Q8×C11—21no—
164Q8×C11—42no—
165Q8×C11—42no—
166D4×C11—21no—
167D4×C11—21no—
168D4×C11—41no—
169D4×C11—41no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C11H(5,𝔽2)11yescharacteristic
185C8×C11—41no—
186C8×C11—42no—
187C8×C11—41no—
188C8×C11—42no—
189C8×C11—41no—
190C8×C11#12311yescharacteristic
191C8×C11#12311yescharacteristic
192C8×C11#12311yescharacteristic
193C8×C11#12311yescharacteristic
194C2×#137C22×C1112yes—
195C22×Q16C22×C1111yescharacteristic
196C2×#131C22×C1111yescharacteristic
197#519C22×C1112yes—
198#473—22no—
199#473—22no—
200#441—22no—
201C4×Q16—22no—
202#430C22×C1112yes—
203C2×#108C22×C1111yescharacteristic
204C2×#108C22×C1111yescharacteristic
205#427C22×C1111yescharacteristic
206#421C22×C1112yes—
207#419C22×C1112yes—
208#419C22×C1112yes—
209#413C22×C1111yescharacteristic
210C2×#101C22×C1112yes—
211C2×#101C22×C1112yes—
212#410C22×C1111yescharacteristic
213#405C22×C1111yescharacteristic
214#405C22×C1111yescharacteristic
215#344C22×C1112yes—
216#344C22×C1112yes—
217#344C22×C1111yescharacteristic
218#344C22×C1111yescharacteristic
219#344C22×C1112yes—
220H(3,ℤ/4)C22×C1112yes—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—81no—
224C22×C11#52911yescharacteristic
225C22×C11#54611yescharacteristic
226C22×C11#55511yescharacteristic
227C4×C11—42no—
228C4×C11—41no—
229C4×C11—44no—
230C4×C11—82no—
231C4×C11—81no—
232C4×C11C2×#12311yescharacteristic
233C4×C11#54011yescharacteristic
234C4×C11#54611yescharacteristic
235C4×C11#55311yescharacteristic
236C2×#41C23×C1111yescharacteristic
237C22×Q8C23×C1112yes—
238#137—24no—
239#137—42no—
240C2×Q16—22no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16D4×C1112yes—
246C2×Q16D4×C1112yes—
247C2×SD16—22no—
248#131—21no—
249#131—21no—
250#131—21no—
251#131—21no—
252C2×M16—21no—
253C2×M16C23×C1111yescharacteristic
254C2×M16C23×C1112yes—
255C2×M16C23×C1111yescharacteristic
256C2×M16C23×C1112yes—
257C2×M16C23×C1111yescharacteristic
258C22×C8—21no—
259C22×C8C23×C1111yescharacteristic
260C4×Q8—24no—
261C4×Q8—42no—
262#117—24no—
263#117C23×C1112yes—
264#117C23×C1111yescharacteristic
265#117C23×C1111yescharacteristic
266#108—21no—
267#108—21no—
268#108—21no—
269#108—21no—
270#108—42no—
271#107—21no—
272#106—21no—
273#104—42no—
274#103—24no—
275#103—42no—
276#101—24no—
277#101—21no—
278#101—42no—
279#100—21no—
280#99—22no—
281#97—21no—
282#97—21no—
283C4×C8—21no—
284C4×C8—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—81no—
289C2×C11#242011yescharacteristic
290#41—21no—
291#41—21no—
292#41—21no—
293#41—21no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8C2×D4×C1114yes—
300C2×Q8C11×#4111yescharacteristic
301C2×D4—21no—
302C2×D4C11×#4111yescharacteristic
303C22×C4—22no—
304C22×C4—21no—
305C22×C4C24×C1111yescharacteristic
306Q16—22no—
307Q16—22no—
308Q16—22no—
309Q16—22no—
310Q16—44no—
311SD16—44no—
312M16—21no—
313M16—22no—
314M16—21no—
315M16—21no—
316M16—22no—
317M16—21no—
318M16—21no—
319M16—22no—
320M16—21no—
321M16—22no—
322M16—41no—
323M16—41no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8C2×D4×C1111yescharacteristic
332C2×C8C2×D4×C1111yescharacteristic
333C2×C8C11×#4111yescharacteristic
334C2×C8C11×#4111yescharacteristic
335C2×C8C11×#4111yescharacteristic
336C2×C8C11×#4111yescharacteristic
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—44no—
341C22⋊C4—21no—
342C22⋊C4—22no—
343C22⋊C4C11×#4112yes—
344C42—21no—
345C42—21no—
346C42—22no—
347C42—44no—
348C11#2498911yescharacteristic, direct product factor, Sylow
349C23—21no—
350C23C2×C11×#4111yescharacteristic
351Q8—24no—
352Q8—24no—
353Q8—21no—
354Q8—21no—
355Q8—42no—
356Q8—42no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4C22×D4×C1111yescharacteristic
371C2×C4C2×C11×#4111yescharacteristic
372C2×C4C2×C11×#4111yescharacteristic
373C2×C4C2×C11×#4111yescharacteristic
374C2×C4C11×H(5,𝔽2)11yescharacteristic
375C2×C4C11×H(5,𝔽2)11yescharacteristic
376C8—41no—
377C8—42no—
378C8—42no—
379C8—41no—
380C8—41no—
381C8C11×#12311yescharacteristic
382C8C11×#12311yescharacteristic
383C8C11×#12311yescharacteristic
384C8C11×#12311yescharacteristic
385C22—41no—
386C22—41no—
387C22—81no—
388C22C11×#52911yescharacteristic
389C22C11×#54611yescharacteristic
390C22C11×#55511yescharacteristic
391C4—42no—
392C4—41no—
393C4—44no—
394C4—82no—
395C4—81no—
396C4C2×C11×#12311yescharacteristic
397C4C11×#54011yescharacteristic
398C4C11×#54611yescharacteristic
399C4C11×#55311yescharacteristic
400C2—21no—
401C2—21no—
402C2—21no—
403C2—81no—
404C2C11×#242011yescharacteristic
subgroupG/H
center, socleC2×C11#2420
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2950C2semidirect
3. C11×#2082C2semidirect
5. C11×#1979C2semidirect
6. C11×#1953C2semidirect
8. C11×#1833C2semidirect
9. C11×#1830C2semidirect
88. #24989C11direct (N × H)
148. #2950C2×C11semidirect
149. #2082C2×C11semidirect
151. #1979C2×C11semidirect
152. #1953C2×C11semidirect
154. #1833C2×C11semidirect
155. #1830C2×C11semidirect
348. C11#24989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4732
C11×#29502
C11×#20822
C11×#20492
C11×#19792
C11×#19532
C11×#19052
C11×#18332
C11×#18302
C11×#18142
C11×#17572
#2498911