Finite Group Databasebeta

← C11×#19220 #14596413

Subgroups — C11×#19220 #14596413

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3233C212yesmaximal
2C11×#3170C211yesmaximal, characteristic, complemented
3C11×#2966C211yesmaximal, characteristic
4C11×#1704C212yesmaximal, complemented
5C11×#1703C212yesmaximal, complemented
6C11×#1676C211yesmaximal, characteristic, complemented
7C11×#1675C211yesmaximal, characteristic, complemented
8C11×#1670C211yesmaximal, characteristic, complemented
9C11×#1669C211yesmaximal, characteristic, complemented
10C11×#1564C211yesmaximal, characteristic, complemented
11C11×#1554C212yesmaximal, complemented
12C11×#533C2212yes—
13C11×#529C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#499—22no—
16C11×#494C2211yescharacteristic
17C11×#488—22no—
18C11×#487C2212yes—
19C11×#485—22no—
20C11×#482—22no—
21C11×#477C2212yes—
22C11×#476C2212yes—
23C11×#475C2212yes—
24C11×#474C2212yes—
25C11×#467—21no—
26C11×#467—21no—
27C11×#446C2211yescharacteristic
28C8×Q8×C11C2211yescharacteristic
29C4×C11×Q16—21no—
30C4×C11×Q16—21no—
31C11×#436C2211yescharacteristic
32C11×#435—21no—
33C8×D4×C11—21no—
34C8×D4×C11C2211yescharacteristic
35C11×#433—21no—
36C11×#432C2211yescharacteristic
37C11×#431C2212yes—
38C11×#405—21no—
39C2×C4×C8×C11C2211yescharacteristic
40C11×#335C2211yescharacteristic
41C11×#335C2211yescharacteristic
42C11×#334C2212yes—
43C11×#333C2212yes—
44C11×#333C2212yes—
45C11×#332C2212yes—
46C11×#332C2212yes—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×M16—21no—
50C22×C8×C11—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8C2312yes—
54C11×C4⋊Q8C2312yes—
55C11×#126—21no—
56C11×#125—22no—
57C11×#125D411yescharacteristic
58C11×#124D411yescharacteristic
59C11×#123—21no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8D411yescharacteristic
63C11×#121D411yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11C2311yescharacteristic
67C4×D4×C11—21no—
68C4×D4×C11C2311yescharacteristic
69C11×#117—21no—
70C11×#117—22no—
71C2×C42×C11C2311yescharacteristic
72C11×#107—21no—
73C11×#107—21no—
74C11×#107—22no—
75C11×#107—22no—
76C11×#106—22no—
77C11×#106—22no—
78C11×C4⋊C8—21no—
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2312yes—
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#103—22no—
86C11×#103—22no—
87C11×#103—22no—
88C11×#102—22no—
89C11×#102—22no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—21no—
92C11×C22⋊C8—21no—
93C11×C22⋊C8—21no—
94C11×#97—21no—
95C11×#97—21no—
96C4×C8×C11—21no—
97C4×C8×C11—22no—
98C4×C8×C11D411yescharacteristic
99C4×C8×C11D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101C4×C8×C11C2311yescharacteristic
102#19220C1111yesmaximal, characteristic, direct product factor, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11C2×D411yescharacteristic
106C2×D4×C11—21no—
107C2×D4×C11C2×D411yescharacteristic
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C11×Q16—42no—
113C11×Q16—42no—
114C11×M16—42no—
115C2×C8×C11—22no—
116C2×C8×C11—21no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—41no—
121C2×C8×C11—42no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4C2×D411yescharacteristic
137C11×C4⋊C4C2×D411yescharacteristic
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C11×C22⋊C4—21no—
142C11×C22⋊C4—21no—
143C11×C22⋊C4—42no—
144C42×C11—21no—
145C42×C11—42no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150#3233C2×C1112yes—
151#3170C2×C1111yescharacteristic, complemented
152#2966C2×C1111yescharacteristic
153#1704C2×C1112yescomplemented
154#1703C2×C1112yescomplemented
155#1676C2×C1111yescharacteristic, complemented
156#1675C2×C1111yescharacteristic, complemented
157#1670C2×C1111yescharacteristic, complemented
158#1669C2×C1111yescharacteristic, complemented
159#1564C2×C1111yescharacteristic, complemented
160#1554C2×C1112yescomplemented
161C23×C11—21no—
162C23×C11#12111yescharacteristic
163Q8×C11—21no—
164Q8×C11—21no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—82no—
168D4×C11—21no—
169D4×C11—21no—
170D4×C11—42no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—41no—
193C8×C11—41no—
194C8×C11—42no—
195C8×C11—42no—
196C8×C11#13512yes—
197#533C22×C1112yes—
198#529C22×C1111yescharacteristic
199#500C22×C1111yescharacteristic
200#499—22no—
201#494C22×C1111yescharacteristic
202#488—22no—
203#487C22×C1112yes—
204#485—22no—
205#482—22no—
206#477C22×C1112yes—
207#476C22×C1112yes—
208#475C22×C1112yes—
209#474C22×C1112yes—
210#467—21no—
211#467—21no—
212#446C22×C1111yescharacteristic
213C8×Q8C22×C1111yescharacteristic
214C4×Q16—21no—
215C4×Q16—21no—
216#436C22×C1111yescharacteristic
217#435—21no—
218C8×D4—21no—
219C8×D4C22×C1111yescharacteristic
220#433—21no—
221#432C22×C1111yescharacteristic
222#431C22×C1112yes—
223#405—21no—
224C2×C4×C8C22×C1111yescharacteristic
225#335C22×C1111yescharacteristic
226#335C22×C1111yescharacteristic
227#334C22×C1112yes—
228#333C22×C1112yes—
229#333C22×C1112yes—
230#332C22×C1112yes—
231#332C22×C1112yes—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11C2×#12111yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—82no—
247C4×C11—82no—
248C4×C11C2×#13511yescharacteristic
249C4×C11#57511yescharacteristic
250C4×C11#57811yescharacteristic
251C4×C11#57811yescharacteristic
252C2×Q16—21no—
253C2×Q16—21no—
254C2×M16—21no—
255C22×C8—21no—
256C22×C8D4×C1111yescharacteristic
257C22×C8D4×C1111yescharacteristic
258C4⋊Q8C23×C1112yes—
259C4⋊Q8C23×C1112yes—
260#126—21no—
261#125—22no—
262#125D4×C1111yescharacteristic
263#124D4×C1111yescharacteristic
264#123—21no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8D4×C1111yescharacteristic
268#121D4×C1111yescharacteristic
269C4×Q8—22no—
270C4×Q8—22no—
271C4×Q8C23×C1111yescharacteristic
272C4×D4—21no—
273C4×D4C23×C1111yescharacteristic
274#117—21no—
275#117—22no—
276C2×C42C23×C1111yescharacteristic
277#107—21no—
278#107—21no—
279#107—22no—
280#107—22no—
281#106—22no—
282#106—22no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8C23×C1111yescharacteristic
286C4⋊C8C23×C1111yescharacteristic
287C4⋊C8C23×C1112yes—
288C4⋊C8C23×C1112yes—
289#103—22no—
290#103—22no—
291#103—22no—
292#103—22no—
293#102—22no—
294#102—22no—
295C22⋊C8—22no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299#97—21no—
300#97—21no—
301C4×C8—21no—
302C4×C8—22no—
303C4×C8D4×C1111yescharacteristic
304C4×C8D4×C1111yescharacteristic
305C4×C8C23×C1111yescharacteristic
306C4×C8C23×C1111yescharacteristic
307C2×C11—41no—
308C2×C11—81no—
309C2×C11#303511yescharacteristic
310C2×C11#305911yescharacteristic
311C2×C11#306711yescharacteristic
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8C2×D4×C1111yescharacteristic
315C2×D4—21no—
316C2×D4C2×D4×C1111yescharacteristic
317C22×C4—21no—
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C11×#4111yescharacteristic
321Q16—42no—
322Q16—42no—
323M16—42no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8C2×D4×C1111yescharacteristic
332C2×C8C2×D4×C1111yescharacteristic
333C2×C8C2×D4×C1111yescharacteristic
334C2×C8C2×D4×C1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4C2×D4×C1111yescharacteristic
346C4⋊C4C2×D4×C1111yescharacteristic
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—42no—
353C42—21no—
354C42—42no—
355C42C2×D4×C1111yescharacteristic
356C42C2×D4×C1111yescharacteristic
357C42C11×#4111yescharacteristic
358C42C24×C1111yescharacteristic
359C11#1922011yescharacteristic, direct product factor, Sylow
360C23—21no—
361C23C11×#12111yescharacteristic
362Q8—21no—
363Q8—21no—
364Q8—42no—
365Q8—42no—
366Q8—82no—
367D4—21no—
368D4—21no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4C11×#12111yescharacteristic
383C2×C4C11×#12111yescharacteristic
384C2×C4C11×#12111yescharacteristic
385C2×C4C22×D4×C1111yescharacteristic
386C2×C4C22×D4×C1111yescharacteristic
387C2×C4C2×C11×#4111yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—41no—
392C8—41no—
393C8—42no—
394C8—42no—
395C8C11×#13512yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×C11×#12111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—82no—
411C4—82no—
412C4C2×C11×#13511yescharacteristic
413C4C11×#57511yescharacteristic
414C4C11×#57811yescharacteristic
415C4C11×#57811yescharacteristic
416C2—41no—
417C2—81no—
418C2C11×#303511yescharacteristic
419C2C11×#305911yescharacteristic
420C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#121D4
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×#3170C2semidirect
4. C11×#1704C2semidirect
5. C11×#1703C2semidirect
6. C11×#1676C2semidirect
7. C11×#1675C2semidirect
8. C11×#1670C2semidirect
9. C11×#1669C2semidirect
10. C11×#1564C2semidirect
11. C11×#1554C2semidirect
102. #19220C11direct (N × H)
151. #3170C2×C11semidirect
153. #1704C2×C11semidirect
154. #1703C2×C11semidirect
155. #1676C2×C11semidirect
156. #1675C2×C11semidirect
157. #1670C2×C11semidirect
158. #1669C2×C11semidirect
159. #1564C2×C11semidirect
160. #1554C2×C11semidirect
359. C11#19220direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32332
C11×#31702
C11×#29662
C11×#17042
C11×#17032
C11×#16762
C11×#16752
C11×#16702
C11×#16692
C11×#15642
C11×#15542
#1922011