Finite Group Databasebeta

← C11×#9173 #14586366

Subgroups — C11×#9173 #14586366

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3038C211yesmaximal, characteristic
2C11×#2906C211yesmaximal, characteristic, complemented
3C11×#1545C211yesmaximal, characteristic, complemented
4C2×C11×#331C211yesmaximal, characteristic, complemented
5C11×#1477C211yesmaximal, characteristic, complemented
6C11×#1301C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C2×C11×#131—21no—
10C2×C11×#127C2211yescharacteristic
11C4×C11×#41C2211yescharacteristic
12C11×#460—21no—
13C11×#460C412yes—
14C11×#459—21no—
15C11×#459C412yes—
16C11×#431C2211yescharacteristic
17C11×#424—21no—
18C11×#424—22no—
19C11×#423—21no—
20C11×#423C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C2×C11×C4⋊C8—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C11×#418—21no—
26C11×#331—21no—
27C11×#331—21no—
28C11×#331—22no—
29C11×Q8⋊C8—21no—
30C11×D4⋊C8—21no—
31C2×C11×#41D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C11×#131—42no—
40C11×#131—42no—
41C2×C11×M16—22no—
42C2×C11×M16—21no—
43C2×C11×M16—21no—
44C22×C8×C11—22no—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127C2×C412yes—
51C4×Q8×C11C2×C411yescharacteristic
52C4×Q8×C11D411yescharacteristic
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11C2×C411yescharacteristic
56C4×D4×C11D411yescharacteristic
57C11×#117—21no—
58C11×#117D411yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×C4⋊C8—22no—
62C11×C4⋊C8—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2×C412yes—
70C11×C4⋊C8D411yescharacteristic
71C11×C4⋊C8D411yescharacteristic
72C11×C4⋊C8D412yes—
73C11×#102—22no—
74C11×#102—22no—
75C11×C22⋊C8—21no—
76C4×C8×C11—21no—
77#9173C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—41no—
79C11×#41—21no—
80C11×#41—21no—
81C11×#41D812yes—
82C11×#41SD1612yes—
83C2×Q8×C11C22⋊C411yescharacteristic
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—81no—
96C2×D4×C11—81no—
97C2×D4×C11—82no—
98C2×D4×C11C22⋊C411yescharacteristic
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C11×SD16—44no—
106C11×D8—44no—
107C11×M16—44no—
108C11×M16—41no—
109C11×M16—41no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—22no—
113C2×C8×C11—21no—
114C2×C8×C11—22no—
115C2×C8×C11—21no—
116C2×C8×C11—44no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—81no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4C22⋊C411yescharacteristic
125C11×C4⋊C4C22⋊C411yescharacteristic
126C11×C22⋊C4—21no—
127C11×C22⋊C4—21no—
128C11×C22⋊C4—21no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11C22×C411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136#3038C2×C1111yescharacteristic
137#2906C2×C1111yescharacteristic, complemented
138#1545C2×C1111yescharacteristic, complemented
139C2×#331C2×C1111yescharacteristic, complemented
140#1477C2×C1111yescharacteristic, complemented
141#1301C2×C1111yescharacteristic, complemented
142#1292C2×C1111yescharacteristic, complemented
143C23×C11—21no—
144C23×C11—42no—
145C23×C11—82no—
146C23×C11—82no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11#12311yescharacteristic
150Q8×C11—21no—
151Q8×C11#10212yes—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—21no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—82no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11#10212yes—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11C2×C22⋊C411yescharacteristic
177C2×C4×C11C4×D411yescharacteristic
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11#13711yescharacteristic
186C8×C11—42no—
187C8×C11—41no—
188C8×C11—42no—
189C8×C11—41no—
190C8×C11—81no—
191C8×C11—81no—
192C2×AGL(1,ℤ/8)—21no—
193C2×#131—21no—
194C2×#127C22×C1111yescharacteristic
195C4×#41C22×C1111yescharacteristic
196#460—21no—
197#460C4×C1112yes—
198#459—21no—
199#459C4×C1112yes—
200#431C22×C1111yescharacteristic
201#424—21no—
202#424—22no—
203#423—21no—
204#423C22×C1111yescharacteristic
205#423C22×C1111yescharacteristic
206C2×C4⋊C8—21no—
207C2×C4⋊C8C22×C1111yescharacteristic
208C2×C4⋊C8C22×C1111yescharacteristic
209#418—21no—
210#331—21no—
211#331—21no—
212#331—22no—
213Q8⋊C8—21no—
214D4⋊C8—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—22no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—162no—
224C22×C11—162no—
225C22×C11#38611yescharacteristic
226C22×C11#48011yescharacteristic
227C22×C11#48111yescharacteristic
228C4×C11—22no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11C2×#10211yescharacteristic
235C4×C11#41711yescharacteristic
236C4×C11#44711yescharacteristic
237C4×C11#44811yescharacteristic
238C4×C11#47111yescharacteristic
239C4×C11#47211yescharacteristic
240C2×#41D4×C1111yescharacteristic
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244AGL(1,ℤ/8)—42no—
245AGL(1,ℤ/8)—42no—
246C2×SD16—22no—
247C2×D8—22no—
248#131—42no—
249#131—42no—
250C2×M16—22no—
251C2×M16—21no—
252C2×M16—21no—
253C22×C8—22no—
254C22×C8—21no—
255C22×C8—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2×C4×C1112yes—
260C4×Q8C2×C4×C1111yescharacteristic
261C4×Q8D4×C1111yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C2×C4×C1111yescharacteristic
265C4×D4D4×C1111yescharacteristic
266#117—21no—
267#117D4×C1111yescharacteristic
268C2×C42—21no—
269C2×C42C23×C1111yescharacteristic
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8C2×C4×C1112yes—
279C4⋊C8D4×C1111yescharacteristic
280C4⋊C8D4×C1111yescharacteristic
281C4⋊C8D4×C1112yes—
282#102—22no—
283#102—22no—
284C22⋊C8—21no—
285C4×C8—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—42no—
289C2×C11—162no—
290C2×C11#187411yescharacteristic
291C2×C11#190311yescharacteristic
292C2×C11#190711yescharacteristic
293C24—41no—
294#41—21no—
295#41—21no—
296#41C11×D812yes—
297#41C11×SD1612yes—
298C2×Q8C11×C22⋊C411yescharacteristic
299C2×D4—21no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—81no—
311C2×D4—81no—
312C2×D4—82no—
313C2×D4C11×C22⋊C411yescharacteristic
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C11×#4111yescharacteristic
319C22×C4C11×#4111yescharacteristic
320SD16—44no—
321D8—44no—
322M16—44no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—44no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—81no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4C11×C22⋊C411yescharacteristic
340C4⋊C4C11×C22⋊C411yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42C22×C4×C1111yescharacteristic
348C42C2×D4×C1111yescharacteristic
349C42C2×D4×C1111yescharacteristic
350C42C2×D4×C1111yescharacteristic
351C11#917311yescharacteristic, direct product factor, Sylow
352C23—21no—
353C23—42no—
354C23—82no—
355C23—82no—
356C23—81no—
357C23—81no—
358C23C11×#12311yescharacteristic
359Q8—21no—
360Q8C11×#10212yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—82no—
367D4—82no—
368D4—82no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4C11×#10212yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×C11×C22⋊C411yescharacteristic
386C2×C4C4×D4×C1111yescharacteristic
387C2×C4C4×D4×C1111yescharacteristic
388C2×C4C11×#12011yescharacteristic
389C2×C4C11×#12111yescharacteristic
390C2×C4C11×#12111yescharacteristic
391C2×C4C2×C11×D811yescharacteristic
392C2×C4C2×C11×SD1611yescharacteristic
393C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
394C2×C4C11×#13711yescharacteristic
395C8—42no—
396C8—41no—
397C8—42no—
398C8—41no—
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—162no—
410C22—162no—
411C22C11×#38611yescharacteristic
412C22C11×#48011yescharacteristic
413C22C11×#48111yescharacteristic
414C4—22no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4C2×C11×#10211yescharacteristic
421C4C11×#41711yescharacteristic
422C4C11×#44711yescharacteristic
423C4C11×#44811yescharacteristic
424C4C11×#47111yescharacteristic
425C4C11×#47211yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—162no—
430C2C11×#187411yescharacteristic
431C2C11×#190311yescharacteristic
432C2C11×#190711yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3038C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2906C2semidirect
3. C11×#1545C2semidirect
4. C2×C11×#331C2semidirect
5. C11×#1477C2semidirect
6. C11×#1301C2semidirect
7. C11×#1292C2semidirect
77. #9173C11direct (N × H)
137. #2906C2×C11semidirect
138. #1545C2×C11semidirect
139. C2×#331C2×C11semidirect
140. #1477C2×C11semidirect
141. #1301C2×C11semidirect
142. #1292C2×C11semidirect
351. C11#9173direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30382
C11×#29062
C11×#15452
C2×C11×#3312
C11×#14772
C11×#13012
C11×#12922
#917311