Finite Group Databasebeta

← C11×#10180 #14587373

Subgroups — C11×#10180 #14587373

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic
4C11×#1549C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#487—21no—
14C11×#476—22no—
15C11×#476—22no—
16C11×#463—22no—
17C11×#461—22no—
18C11×#461—21no—
19C11×#459—21no—
20C11×#448—22no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C2×C11×#106—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#102—21no—
28C11×#332—22no—
29C11×D4⋊C8—22no—
30C11×#323—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×SD16—24no—
39C2×C11×D8—22no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8D411yescharacteristic
47C11×#127D411yescharacteristic
48C11×#124—21no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#103—24no—
71C11×#102—24no—
72C11×#102—22no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10180C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C2×D4×C11SD1612yescomplemented
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×SD16—44no—
107C11×SD16—84no—
108C11×D8—44no—
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—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133#3206C2×C1111yescharacteristic, complemented
134C2×#476C2×C1111yescharacteristic, complemented
135#3036C2×C1111yescharacteristic
136#1549C2×C1111yescharacteristic, complemented
137#1480C2×C1111yescharacteristic, complemented
138#1460C2×C1111yescharacteristic, complemented
139#1301C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11#12111yescharacteristic
147Q8×C11—44no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—22no—
153D4×C11—42no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—82no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11C2×SD1611yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11#13711yescharacteristic
182C8×C11—42no—
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—81no—
186C2×AGL(1,ℤ/8)—21no—
187#532C22×C1111yescharacteristic
188C2×C4⋊Q8C22×C1111yescharacteristic
189C2×C4×D4C22×C1111yescharacteristic
190#492—21no—
191#487—21no—
192#476—22no—
193#476—22no—
194#463—22no—
195#461—22no—
196#461—21no—
197#459—21no—
198#448—22no—
199#431C22×C1111yescharacteristic
200#431C22×C1111yescharacteristic
201C2×#106—21no—
202#423C22×C1111yescharacteristic
203C2×C4⋊C8C22×C1111yescharacteristic
204#417—21no—
205C2×#102—21no—
206#332—22no—
207D4⋊C8—22no—
208#323—22no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#39211yescharacteristic
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11—81no—
228C4×C11#44811yescharacteristic
229C4×C11#44911yescharacteristic
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#47112yes—
233C2×#41—21no—
234C22×Q8—21no—
235C22×D4D4×C1111yescharacteristic
236C23×C4—21no—
237AGL(1,ℤ/8)—42no—
238AGL(1,ℤ/8)—42no—
239C2×SD16—22no—
240C2×SD16—24no—
241C2×D8—22no—
242C2×M16—21no—
243C22×C8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C1112yes—
248C4⋊Q8D4×C1111yescharacteristic
249#127D4×C1111yescharacteristic
250#124—21no—
251#121—21no—
252#121—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C1111yescharacteristic
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C1112yes—
270C4⋊C8D4×C1112yes—
271#103—22no—
272#103—24no—
273#102—24no—
274#102—22no—
275C22⋊C8—21no—
276C22⋊C8D4×C1112yes—
277C4×C8—21no—
278C4×C8—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—82no—
282C2×C11—161no—
283C2×C11#200011yescharacteristic
284C2×C11#200811yescharacteristic
285C2×C11#201911yescharacteristic
286C24—21no—
287#41—41no—
288#41—41no—
289#41—41no—
290#41—41no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—82no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4C11×SD1612yescomplemented
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—82no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C11×#4111yescharacteristic
314SD16—44no—
315SD16—84no—
316D8—44no—
317M16—41no—
318M16—41no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C42C2×D4×C1111yescharacteristic
341C11#1018011yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—81no—
347C23—81no—
348C23C11×#12111yescharacteristic
349Q8—44no—
350Q8—41no—
351Q8—41no—
352Q8—82no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—41no—
360D4—42no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4C11×#12011yescharacteristic
375C2×C4C11×#12011yescharacteristic
376C2×C4C11×#12011yescharacteristic
377C2×C4C11×#12111yescharacteristic
378C2×C4C11×#12111yescharacteristic
379C2×C4C11×#12711yescharacteristic
380C2×C4C2×C11×SD1611yescharacteristic
381C2×C4C11×#13511yescharacteristic
382C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
383C2×C4C11×#13711yescharacteristic
384C8—42no—
385C8—42no—
386C8—42no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22C11×#39211yescharacteristic
399C22C11×#46511yescharacteristic
400C22C11×#46811yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4C11×#44811yescharacteristic
408C4C11×#44911yescharacteristic
409C4C11×#45011yescharacteristic
410C4C11×#45211yescharacteristic
411C4C11×#47112yes—
412C2—21no—
413C2—21no—
414C2—82no—
415C2—161no—
416C2C11×#200011yescharacteristic
417C2C11×#200811yescharacteristic
418C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
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×#3206C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#1549C2semidirect
5. C11×#1480C2semidirect
6. C11×#1460C2semidirect
7. C11×#1301C2semidirect
77. #10180C11direct (N × H)
96. C2×D4×C11SD16semidirect
133. #3206C2×C11semidirect
134. C2×#476C2×C11semidirect
136. #1549C2×C11semidirect
137. #1480C2×C11semidirect
138. #1460C2×C11semidirect
139. #1301C2×C11semidirect
304. C2×D4C11×SD16semidirect
341. C11#10180direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C2×C11×#4762
C11×#30362
C11×#15492
C11×#14802
C11×#14602
C11×#13012
#1018011