Finite Group Databasebeta

← C11×#19196 #14596389

Subgroups — C11×#19196 #14596389

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C11×#3205C211yesmaximal, characteristic
3C2×C11×#486C211yesmaximal, characteristic, complemented
4C11×#2931C211yesmaximal, characteristic, complemented
5C11×#1697C214yesmaximal, complemented
6C11×#1677C214yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic, complemented
8C11×#1548C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#131—21no—
11C11×#532C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C11×#498—21no—
15C11×#493—21no—
16C11×#486—21no—
17C11×#486—21no—
18C11×#486—21no—
19C11×#486—21no—
20C11×#486C2212yes—
21C11×#486C2212yes—
22C11×#481—22no—
23C11×#476C2214yescomplemented
24C11×#459C2214yes—
25C11×#447—22no—
26C11×#436—21no—
27C11×#436C2212yescomplemented
28C8×D4×C11—21no—
29C8×D4×C11C2212yescomplemented
30C11×#431C2211yescharacteristic
31C11×#431C2211yescharacteristic
32C11×#423C2211yescharacteristic
33C2×C11×#102—21no—
34C2×C11×#102—21no—
35C11×#408—21no—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#335C2212yescomplemented
38C11×#334C2212yescomplemented
39C11×#333C2214yescomplemented
40C11×#331C2214yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C2×C11×D8—24no—
47C11×#131—44no—
48C2×C11×M16—21no—
49C2×C11×M16—22no—
50C22×C8×C11—22no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2312yes—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127D411yescharacteristic
62C11×#127C2312yes—
63C11×#124—21no—
64C11×#121—21no—
65C11×#121D412yes—
66C4×D4×C11—21no—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C11×#106—24no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×#102—24no—
77C11×#102—22no—
78C11×#102—22no—
79C11×#102—22no—
80C11×#102—22no—
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#19196C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—41no—
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—41no—
99C2×Q8×C11—82no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—82no—
112C2×D4×C11—82no—
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C11×D8—84no—
120C11×M16—44no—
121C11×M16—42no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—44no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#3227C2×C1111yescharacteristic, complemented
145#3205C2×C1111yescharacteristic
146C2×#486C2×C1111yescharacteristic, complemented
147#2931C2×C1111yescharacteristic, complemented
148#1697C2×C1114yescomplemented
149#1677C2×C1114yescomplemented
150#1564C2×C1111yescharacteristic, complemented
151#1548C2×C1111yescharacteristic, complemented
152#1545C2×C1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—82no—
156C23×C11—82no—
157C23×C11—82no—
158C23×C11#12111yescharacteristic
159Q8×C11—42no—
160Q8×C11—82no—
161Q8×C11—82no—
162D4×C11—24no—
163D4×C11—44no—
164D4×C11—42no—
165D4×C11—42no—
166D4×C11—44no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—82no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#13512yes—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C8×C11—21no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—42no—
193C8×C11—42no—
194C8×C11—42no—
195C2×#131—21no—
196#532C22×C1111yescharacteristic
197C2×C4⋊Q8C22×C1111yescharacteristic
198C2×#127C22×C1111yescharacteristic
199#498—21no—
200#493—21no—
201#486—21no—
202#486—21no—
203#486—21no—
204#486—21no—
205#486C22×C1112yes—
206#486C22×C1112yes—
207#481—22no—
208#476C22×C1114yescomplemented
209#459C22×C1114yes—
210#447—22no—
211#436—21no—
212#436C22×C1112yescomplemented
213C8×D4—21no—
214C8×D4C22×C1112yescomplemented
215#431C22×C1111yescharacteristic
216#431C22×C1111yescharacteristic
217#423C22×C1111yescharacteristic
218C2×#102—21no—
219C2×#102—21no—
220#408—21no—
221C2×C4×C8C22×C1111yescharacteristic
222#335C22×C1112yescomplemented
223#334C22×C1112yescomplemented
224#333C22×C1114yescomplemented
225#331C22×C1114yes—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—82no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—164no—
235C22×C11#46312yes—
236C22×C11C2×#12111yescharacteristic
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11#46312yes—
242C4×C11#47212yes—
243C4×C11C2×#13511yescharacteristic
244C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C11#57712yes—
246C2×#41—21no—
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C2×D8—24no—
252#131—44no—
253C2×M16—21no—
254C2×M16—22no—
255C22×C8—22no—
256C22×C8D4×C1111yescharacteristic
257C22×C8D4×C1111yescharacteristic
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8D4×C1111yescharacteristic
262C4⋊Q8C23×C1112yes—
263#127—21no—
264#127—21no—
265#127—21no—
266#127D4×C1111yescharacteristic
267#127C23×C1112yes—
268#124—21no—
269#121—21no—
270#121D4×C1112yes—
271C4×D4—21no—
272C4×D4C23×C1112yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C42C23×C1111yescharacteristic
276#106—24no—
277C4⋊C8—21no—
278C4⋊C8C23×C1112yes—
279C4⋊C8C23×C1112yes—
280C4⋊C8C23×C1112yes—
281#102—24no—
282#102—22no—
283#102—22no—
284#102—22no—
285#102—22no—
286#102—24no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—22no—
290C22⋊C8—22no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8D4×C1111yescharacteristic
294C4×C8D4×C1111yescharacteristic
295C4×C8C23×C1111yescharacteristic
296C4×C8C23×C1111yescharacteristic
297C2×C11—22no—
298C2×C11—82no—
299C2×C11—162no—
300C2×C11C2×#46311yescharacteristic
301C2×C11#305711yescharacteristic
302C2×C11C2×#47211yescharacteristic
303C24—41no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4C2×D4×C1112yes—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C11×#4111yescharacteristic
329D8—84no—
330M16—44no—
331M16—42no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—44no—
338C2×C8C2×D4×C1111yescharacteristic
339C2×C8C2×D4×C1111yescharacteristic
340C2×C8C2×D4×C1111yescharacteristic
341C2×C8C2×D4×C1111yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4C2×D4×C1112yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C42C2×D4×C1111yescharacteristic
351C42C2×D4×C1111yescharacteristic
352C42C11×#4111yescharacteristic
353C42C24×C1111yescharacteristic
354C11#1919611yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—42no—
357C23—82no—
358C23—82no—
359C23—82no—
360C23C11×#12111yescharacteristic
361Q8—42no—
362Q8—82no—
363Q8—82no—
364D4—24no—
365D4—44no—
366D4—42no—
367D4—42no—
368D4—44no—
369D4—42no—
370D4—42no—
371D4—82no—
372D4—82no—
373D4—82no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4C11×#12111yescharacteristic
383C2×C4C11×#12111yescharacteristic
384C2×C4C11×#12111yescharacteristic
385C2×C4C11×#13512yes—
386C2×C4C11×AGL(1,ℤ/8)12yes—
387C2×C4C22×D4×C1111yescharacteristic
388C2×C4C22×D4×C1111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C8—21no—
391C8—21no—
392C8—21no—
393C8—21no—
394C8—42no—
395C8—42no—
396C8—42no—
397C22—21no—
398C22—21no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—164no—
406C22C11×#46312yes—
407C22C2×C11×#12111yescharacteristic
408C4—21no—
409C4—21no—
410C4—42no—
411C4—82no—
412C4C11×#46312yes—
413C4C11×#47212yes—
414C4C2×C11×#13511yescharacteristic
415C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
416C4C11×#57712yes—
417C2—22no—
418C2—82no—
419C2—162no—
420C2C2×C11×#46311yescharacteristic
421C2C11×#305711yescharacteristic
422C2C2×C11×#47211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3205C2
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
1. C11×#3227C2semidirect
3. C2×C11×#486C2semidirect
4. C11×#2931C2semidirect
5. C11×#1697C2semidirect
6. C11×#1677C2semidirect
7. C11×#1564C2semidirect
8. C11×#1548C2semidirect
9. C11×#1545C2semidirect
23. C11×#476C22semidirect
27. C11×#436C22semidirect
29. C8×D4×C11C22semidirect
37. C11×#335C22semidirect
38. C11×#334C22semidirect
39. C11×#333C22semidirect
92. #19196C11direct (N × H)
144. #3227C2×C11semidirect
146. C2×#486C2×C11semidirect
147. #2931C2×C11semidirect
148. #1697C2×C11semidirect
149. #1677C2×C11semidirect
150. #1564C2×C11semidirect
151. #1548C2×C11semidirect
152. #1545C2×C11semidirect
208. #476C22×C11semidirect
212. #436C22×C11semidirect
214. C8×D4C22×C11semidirect
222. #335C22×C11semidirect
223. #334C22×C11semidirect
224. #333C22×C11semidirect
354. C11#19196direct (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×#32052
C2×C11×#4862
C11×#29312
C11×#16972
C11×#16772
C11×#15642
C11×#15482
C11×#15452
#1919611