Finite Group Databasebeta

← C11×#10178 #14587371

Subgroups — C11×#10178 #14587371

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C11×#1545C211yesmaximal, characteristic, complemented
5C11×#1481C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C11×#533C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#486—21no—
14C11×#478—22no—
15C11×#476—21no—
16C11×#474—21no—
17C11×#460—22no—
18C11×#459—22no—
19C11×#459—22no—
20C11×#450—22no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C11×#428—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#418—21no—
27C2×C11×#102—21no—
28C11×#331—22no—
29C11×Q8⋊C8—22no—
30C11×#323—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×D8—42no—
39C2×C11×D8—42no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127D412yes—
48C11×#125—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C11×#117—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—22no—
62C11×#106—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#102—24no—
70C11×#102—22no—
71C11×#102—22no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10178C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11—41no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C2×D4×C11SD1612yescomplemented
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C11×SD16—84no—
108C11×D8—48no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133#3208C2×C1111yescharacteristic, complemented
134#3077C2×C1111yescharacteristic, complemented
135C2×#459C2×C1111yescharacteristic
136#1545C2×C1111yescharacteristic, complemented
137#1481C2×C1111yescharacteristic, complemented
138#1460C2×C1111yescharacteristic, complemented
139#1301C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—82no—
147C23×C11—82no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11#12111yescharacteristic
151Q8×C11—42no—
152Q8×C11—42no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—44no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—82no—
171C2×C4×C11—82no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×SD1611yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—42no—
186C8×C11—81no—
187C22×D8—21no—
188#533C22×C1111yescharacteristic
189C2×#127C22×C1111yescharacteristic
190C2×C4×D4C22×C1111yescharacteristic
191#492—21no—
192#486—21no—
193#478—22no—
194#476—21no—
195#474—21no—
196#460—22no—
197#459—22no—
198#459—22no—
199#450—22no—
200#431C22×C1111yescharacteristic
201#431C22×C1111yescharacteristic
202#428—21no—
203#423C22×C1111yescharacteristic
204C2×C4⋊C8C22×C1111yescharacteristic
205#418—21no—
206C2×#102—21no—
207#331—22no—
208Q8⋊C8—22no—
209#323—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—42no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—162no—
221C22×C11—162no—
222C22×C11#39211yescharacteristic
223C22×C11#46511yescharacteristic
224C22×C11#46811yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11#44811yescharacteristic
232C4×C11#44911yescharacteristic
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#47212yes—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4D4×C1111yescharacteristic
240C23×C4—21no—
241C2×SD16—24no—
242C2×D8—24no—
243C2×D8—42no—
244C2×D8—42no—
245C2×M16—21no—
246C22×C8—21no—
247C4⋊Q8D4×C1111yescharacteristic
248C4⋊Q8D4×C1111yescharacteristic
249#127—21no—
250#127—21no—
251#127—21no—
252#127D4×C1112yes—
253#125—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262#117—21no—
263C2×C4⋊C4D4×C1111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C42C23×C1111yescharacteristic
266#107—22no—
267#106—22no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8D4×C1112yes—
273C4⋊C8D4×C1112yes—
274#102—24no—
275#102—22no—
276#102—22no—
277#102—24no—
278C22⋊C8—21no—
279C22⋊C8D4×C1112yes—
280C4×C8—21no—
281C4×C8—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—82no—
285C2×C11—162no—
286C2×C11#200011yescharacteristic
287C2×C11#200811yescharacteristic
288C2×C11#201811yescharacteristic
289C24—21no—
290C24—41no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—82no—
309C2×D4—82no—
310C2×D4C11×SD1612yescomplemented
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C11×#4111yescharacteristic
318SD16—84no—
319D8—48no—
320M16—41no—
321M16—41no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—41no—
340C42C2×D4×C1111yescharacteristic
341C42C2×D4×C1111yescharacteristic
342C42C2×D4×C1111yescharacteristic
343C42C2×D4×C1111yescharacteristic
344C11#1017811yescharacteristic, direct product factor, Sylow
345C23—22no—
346C23—41no—
347C23—41no—
348C23—42no—
349C23—81no—
350C23—81no—
351C23—82no—
352C23—82no—
353C23—81no—
354C23—81no—
355C23C11×#12111yescharacteristic
356Q8—42no—
357Q8—42no—
358D4—22no—
359D4—22no—
360D4—44no—
361D4—41no—
362D4—42no—
363D4—41no—
364D4—42no—
365D4—82no—
366D4—82no—
367D4—81no—
368D4—81no—
369D4—82no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4C11×#12011yescharacteristic
379C2×C4C11×#12011yescharacteristic
380C2×C4C11×#12011yescharacteristic
381C2×C4C11×#12111yescharacteristic
382C2×C4C11×#12111yescharacteristic
383C2×C4C11×#12711yescharacteristic
384C2×C4C2×C11×SD1611yescharacteristic
385C2×C4C11×#13511yescharacteristic
386C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
387C2×C4C11×#13711yescharacteristic
388C8—42no—
389C8—42no—
390C8—42no—
391C8—81no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—82no—
396C22—82no—
397C22—81no—
398C22—81no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—162no—
403C22—162no—
404C22C11×#39211yescharacteristic
405C22C11×#46511yescharacteristic
406C22C11×#46811yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4C11×#44811yescharacteristic
414C4C11×#44911yescharacteristic
415C4C11×#45011yescharacteristic
416C4C11×#45211yescharacteristic
417C4C11×#47212yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—162no—
422C2C11×#200011yescharacteristic
423C2C11×#200811yescharacteristic
424C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3208C2semidirect
2. C11×#3077C2semidirect
4. C11×#1545C2semidirect
5. C11×#1481C2semidirect
6. C11×#1460C2semidirect
7. C11×#1301C2semidirect
77. #10178C11direct (N × H)
99. C2×D4×C11SD16semidirect
133. #3208C2×C11semidirect
134. #3077C2×C11semidirect
136. #1545C2×C11semidirect
137. #1481C2×C11semidirect
138. #1460C2×C11semidirect
139. #1301C2×C11semidirect
310. C2×D4C11×SD16semidirect
344. C11#10178direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#30772
C2×C11×#4592
C11×#15452
C11×#14812
C11×#14602
C11×#13012
#1017811