Finite Group Databasebeta

← C11×#19199 #14596392

Subgroups — C11×#19199 #14596392

Order 2816.

650 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
1C11×#3227C211yesmaximal, characteristic
2C11×#3226C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic, complemented
4C11×#2931C211yesmaximal, characteristic
5C11×#1703C214yesmaximal, complemented
6C11×#1683C214yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic, complemented
8C11×#1548C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×#131—21no—
11C11×#532C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C11×#500—21no—
15C11×#498—21no—
16C11×#487—21no—
17C11×#487—21no—
18C11×#487C2212yes—
19C11×#487C2212yes—
20C11×#486—21no—
21C11×#486—21no—
22C11×#481—22no—
23C11×#480—22no—
24C11×#476C2214yes—
25C11×#474C2214yes—
26C11×#436—21no—
27C11×#436C2212yes—
28C8×D4×C11—21no—
29C8×D4×C11C2212yes—
30C11×#431C2211yescharacteristic
31C11×#431C2211yescharacteristic
32C11×#423C2211yescharacteristic
33C2×C11×#103—21no—
34C2×C11×#103—21no—
35C11×#408—21no—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#335C2212yes—
38C11×#334C2212yes—
39C11×#333C2214yes—
40C11×#332C2214yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C11×#131—44no—
45C2×C11×M16—21no—
46C2×C11×M16—22no—
47C22×C8×C11—22no—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2312yes—
59C11×#127D411yescharacteristic
60C11×#124—21no—
61C11×#121—21no—
62C11×#121D412yes—
63C4×D4×C11—21no—
64C4×D4×C11C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C11×#107—24no—
71C11×#106—24no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#103—22no—
80C11×#102—24no—
81C11×#102—24no—
82C11×C22⋊C8—21no—
83C11×C22⋊C8—21no—
84C11×C22⋊C8—22no—
85C11×C22⋊C8—22no—
86C4×C8×C11—21no—
87C4×C8×C11—21no—
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#19199C1111yesmaximal, characteristic, direct product factor, Sylow
93C11×#41—42no—
94C11×#41—42no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—82no—
103C2×D4×C11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C2×D412yes—
107C22×C4×C11—22no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C11×M16—44no—
114C11×M16—42no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—44no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#3227C2×C1111yescharacteristic
142#3226C2×C1111yescharacteristic
143C2×#487C2×C1111yescharacteristic, complemented
144#2931C2×C1111yescharacteristic
145#1703C2×C1114yescomplemented
146#1683C2×C1114yescomplemented
147#1564C2×C1111yescharacteristic, complemented
148#1548C2×C1111yescharacteristic, complemented
149#1546C2×C1111yescharacteristic, complemented
150C23×C11—22no—
151C23×C11#12111yescharacteristic
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—42no—
155Q8×C11—82no—
156Q8×C11—82no—
157Q8×C11—82no—
158D4×C11—24no—
159D4×C11—44no—
160D4×C11—42no—
161D4×C11—42no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—42no—
186C2×#131—21no—
187#532C22×C1111yescharacteristic
188C2×C4⋊Q8C22×C1111yescharacteristic
189C2×C4⋊Q8C22×C1111yescharacteristic
190#500—21no—
191#498—21no—
192#487—21no—
193#487—21no—
194#487C22×C1112yes—
195#487C22×C1112yes—
196#486—21no—
197#486—21no—
198#481—22no—
199#480—22no—
200#476C22×C1114yes—
201#474C22×C1114yes—
202#436—21no—
203#436C22×C1112yes—
204C8×D4—21no—
205C8×D4C22×C1112yes—
206#431C22×C1111yescharacteristic
207#431C22×C1111yescharacteristic
208#423C22×C1111yescharacteristic
209C2×#103—21no—
210C2×#103—21no—
211#408—21no—
212C2×C4×C8C22×C1111yescharacteristic
213#335C22×C1112yes—
214#334C22×C1112yes—
215#333C22×C1114yes—
216#332C22×C1114yes—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11#46312yes—
223C22×C11C2×#12111yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11—82no—
228C4×C11—82no—
229C4×C11#46312yes—
230C4×C11#47112yes—
231C4×C11C2×#13511yescharacteristic
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C11#57812yes—
234C2×#41—21no—
235C22×Q8—21no—
236C22×Q8—21no—
237#131—44no—
238C2×M16—21no—
239C2×M16—22no—
240C22×C8—22no—
241C22×C8D4×C1111yescharacteristic
242C22×C8D4×C1111yescharacteristic
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4×C1111yescharacteristic
250C4⋊Q8C23×C1112yes—
251C4⋊Q8C23×C1112yes—
252#127D4×C1111yescharacteristic
253#124—21no—
254#121—21no—
255#121D4×C1112yes—
256C4×D4—21no—
257C4×D4C23×C1112yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C42C23×C1111yescharacteristic
263#107—24no—
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8C23×C1112yes—
267C4⋊C8C23×C1112yes—
268C4⋊C8C23×C1112yes—
269#103—22no—
270#103—22no—
271#103—22no—
272#103—22no—
273#102—24no—
274#102—24no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C4×C8—21no—
280C4×C8—21no—
281C4×C8D4×C1111yescharacteristic
282C4×C8D4×C1111yescharacteristic
283C4×C8C23×C1111yescharacteristic
284C4×C8C23×C1111yescharacteristic
285C2×C11—22no—
286C2×C11—82no—
287C2×C11C2×#46311yescharacteristic
288C2×C11#305911yescharacteristic
289C2×C11C2×#47111yescharacteristic
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×Q8—82no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4C2×D4×C1112yes—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C11×#4111yescharacteristic
310M16—44no—
311M16—42no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—44no—
318C2×C8C2×D4×C1111yescharacteristic
319C2×C8C2×D4×C1111yescharacteristic
320C2×C8C2×D4×C1111yescharacteristic
321C2×C8C2×D4×C1111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4C2×D4×C1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C42C2×D4×C1111yescharacteristic
335C42C2×D4×C1111yescharacteristic
336C42C11×#4111yescharacteristic
337C42C24×C1111yescharacteristic
338C11#1919911yescharacteristic, direct product factor, Sylow
339C23—22no—
340C23C11×#12111yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—42no—
344Q8—82no—
345Q8—82no—
346Q8—82no—
347D4—24no—
348D4—44no—
349D4—42no—
350D4—42no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4C11×#12111yescharacteristic
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12111yescharacteristic
363C2×C4C11×#13512yes—
364C2×C4C11×AGL(1,ℤ/8)12yes—
365C2×C4C22×D4×C1111yescharacteristic
366C2×C4C22×D4×C1111yescharacteristic
367C2×C4C2×C11×#4111yescharacteristic
368C8—21no—
369C8—21no—
370C8—21no—
371C8—21no—
372C8—42no—
373C8—42no—
374C8—42no—
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22C11×#46312yes—
381C22C2×C11×#12111yescharacteristic
382C4—21no—
383C4—21no—
384C4—42no—
385C4—82no—
386C4—82no—
387C4C11×#46312yes—
388C4C11×#47112yes—
389C4C2×C11×#13511yescharacteristic
390C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
391C4C11×#57812yes—
392C2—22no—
393C2—82no—
394C2C2×C11×#46311yescharacteristic
395C2C11×#305911yescharacteristic
396C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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
3. C2×C11×#487C2semidirect
5. C11×#1703C2semidirect
6. C11×#1683C2semidirect
7. C11×#1564C2semidirect
8. C11×#1548C2semidirect
9. C11×#1546C2semidirect
92. #19199C11direct (N × H)
143. C2×#487C2×C11semidirect
145. #1703C2×C11semidirect
146. #1683C2×C11semidirect
147. #1564C2×C11semidirect
148. #1548C2×C11semidirect
149. #1546C2×C11semidirect
338. C11#19199direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#32262
C2×C11×#4872
C11×#29312
C11×#17032
C11×#16832
C11×#15642
C11×#15482
C11×#15462
#1919911