Finite Group Databasebeta

← C11×#8458 #14585651

Subgroups — C11×#8458 #14585651

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#1955C211yesmaximal, characteristic, complemented
3C11×#1552C211yesmaximal, characteristic, complemented
4C11×#1551C211yesmaximal, characteristic, complemented
5C11×#1531C211yesmaximal, characteristic, complemented
6C11×#1530C211yesmaximal, characteristic, complemented
7C11×#1466C211yesmaximal, characteristic, complemented
8C11×#559—22no—
9C11×#556—21no—
10C11×#555—21no—
11C11×#553—22no—
12C11×#550—21no—
13C11×#547—21no—
14C11×#538—22no—
15C11×#535C412yes—
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#525—22no—
19C11×#520C412yes—
20C2×C4×D4×C11C2211yescharacteristic
21C11×#432C2211yescharacteristic
22C11×#432C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8—22no—
25C2×C11×#97C2211yescharacteristic
26C11×#333—21no—
27C11×#332—21no—
28C11×#332—21no—
29C11×#331—21no—
30C11×#330—22no—
31C11×#329—22no—
32C11×#323—22no—
33C2×C11×#41—22no—
34C2×C11×#41C2×C412yes—
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11D412yes—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—22no—
43C11×#127D411yescharacteristic
44C11×#126—24no—
45C11×#125D412yes—
46C11×#124—24no—
47C11×#124—22no—
48C11×#124D412yes—
49C11×#123—24no—
50C11×#123—24no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C11×#121—22no—
55C11×#121—24no—
56C11×#121—21no—
57C11×#121—21no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#120—24no—
61C4×Q8×C11—22no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117C2×C412yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11C2311yescharacteristic
80C11×C4⋊C8—21no—
81C11×C4⋊C8—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C22⋊C8—21no—
85C11×C22⋊C8—21no—
86C11×C22⋊C8—44no—
87C11×#97—21no—
88C11×#97—21no—
89C11×#97—21no—
90C11×#97—21no—
91#8458C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C22⋊C412yes—
93C11×#41—44no—
94C11×#41—82no—
95C11×#41—82no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22⋊C412yes—
99C2×D4×C11—22no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—42no—
107C2×D4×C11C22⋊C412yes—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C22⋊C412yes—
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C2×C8×C11—42no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C22⋊C412yes—
135C11×C4⋊C4C22⋊C412yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C42×C11—24no—
145C42×C11—22no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150#3506C2×C1111yescharacteristic
151#1955C2×C1111yescharacteristic, complemented
152#1552C2×C1111yescharacteristic, complemented
153#1551C2×C1111yescharacteristic, complemented
154#1531C2×C1111yescharacteristic, complemented
155#1530C2×C1111yescharacteristic, complemented
156#1466C2×C1111yescharacteristic, complemented
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11C2×C22⋊C411yescharacteristic
164Q8×C11—42no—
165Q8×C11—41no—
166Q8×C11—41no—
167Q8×C11—81no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—44no—
172D4×C11—41no—
173D4×C11—41no—
174D4×C11—81no—
175D4×C11—84no—
176D4×C11—84no—
177C2×C4×C11—22no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—44no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11—84no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C8×C11—42no—
198C8×C11—81no—
199C8×C11—81no—
200C8×C11—81no—
201#559—22no—
202#556—21no—
203#555—21no—
204#553—22no—
205#550—21no—
206#547—21no—
207#538—22no—
208#535C4×C1112yes—
209#533C22×C1111yescharacteristic
210#532C22×C1111yescharacteristic
211#525—22no—
212#520C4×C1112yes—
213C2×C4×D4C22×C1111yescharacteristic
214#432C22×C1111yescharacteristic
215#432C22×C1111yescharacteristic
216C2×C4⋊C8C22×C1111yescharacteristic
217C2×C22⋊C8—22no—
218C2×#97C22×C1111yescharacteristic
219#333—21no—
220#332—21no—
221#332—21no—
222#331—21no—
223#330—22no—
224#329—22no—
225#323—22no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—44no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—82no—
236C22×C11#37911yescharacteristic
237C22×C11#41312yes—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—42no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11#45311yescharacteristic
248C4×C11#45511yescharacteristic
249C2×#41—22no—
250C2×#41C2×C4×C1112yes—
251C22×D4C2×C4×C1111yescharacteristic
252C23×C4D4×C1112yes—
253C22×C8—21no—
254C22×C8—21no—
255C4⋊Q8D4×C1111yescharacteristic
256C4⋊Q8D4×C1111yescharacteristic
257C4⋊Q8D4×C1111yescharacteristic
258#127—22no—
259#127D4×C1111yescharacteristic
260#126—24no—
261#125D4×C1112yes—
262#124—24no—
263#124—22no—
264#124D4×C1112yes—
265#123—24no—
266#123—24no—
267C22⋊Q8—22no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270#121—22no—
271#121—24no—
272#121—21no—
273#121—21no—
274#121—22no—
275#121—22no—
276#120—24no—
277C4×Q8—22no—
278C4×Q8—21no—
279C4×Q8—21no—
280C4×D4—24no—
281C4×D4—22no—
282C4×D4—24no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289#117—22no—
290#117—22no—
291#117C2×C4×C1112yes—
292C2×C4⋊C4—22no—
293C2×C4⋊C4C2×C4×C1111yescharacteristic
294C2×C22⋊C4D4×C1112yes—
295C2×C42C23×C1111yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—44no—
303#97—21no—
304#97—21no—
305#97—21no—
306#97—21no—
307C2×C11—22no—
308C2×C11—82no—
309C2×C11—82no—
310C2×C11#178511yescharacteristic
311C2×C11#179211yescharacteristic
312C2×C11#179411yescharacteristic
313C24C11×C22⋊C412yes—
314#41—44no—
315#41—82no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8C11×C22⋊C412yes—
320C2×D4—22no—
321C2×D4—24no—
322C2×D4—24no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—42no—
328C2×D4C11×C22⋊C412yes—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4C11×C22⋊C412yes—
336C22×C4C22×C4×C1111yescharacteristic
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C2×D4×C1111yescharacteristic
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—42no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C4⋊C4—24no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4C11×C22⋊C412yes—
356C4⋊C4C11×C22⋊C412yes—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C42—24no—
366C42—22no—
367C42C2×D4×C1111yescharacteristic
368C42C2×D4×C1111yescharacteristic
369C42C2×D4×C1111yescharacteristic
370C42C2×D4×C1111yescharacteristic
371C11#845811yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—42no—
377C23—42no—
378C23C2×C11×C22⋊C411yescharacteristic
379Q8—42no—
380Q8—41no—
381Q8—41no—
382Q8—81no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—44no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—84no—
391D4—84no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—84no—
406C2×C4C2×C11×C22⋊C411yescharacteristic
407C2×C4C2×C11×C22⋊C411yescharacteristic
408C2×C4C11×#12011yescharacteristic
409C2×C4C11×#12011yescharacteristic
410C2×C4C11×#12011yescharacteristic
411C2×C4C11×#12011yescharacteristic
412C8—42no—
413C8—81no—
414C8—81no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—82no—
426C22C11×#37911yescharacteristic
427C22C11×#41312yes—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4C11×#45311yescharacteristic
438C4C11×#45511yescharacteristic
439C2—22no—
440C2—82no—
441C2—82no—
442C2C11×#178511yescharacteristic
443C2C11×#179211yescharacteristic
444C2C11×#179411yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3506C2
LCSG ▷ C22×C4 ▷ 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×#1955C2semidirect
3. C11×#1552C2semidirect
4. C11×#1551C2semidirect
5. C11×#1531C2semidirect
6. C11×#1530C2semidirect
7. C11×#1466C2semidirect
91. #8458C11direct (N × H)
151. #1955C2×C11semidirect
152. #1552C2×C11semidirect
153. #1551C2×C11semidirect
154. #1531C2×C11semidirect
155. #1530C2×C11semidirect
156. #1466C2×C11semidirect
371. C11#8458direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#19552
C11×#15522
C11×#15512
C11×#15312
C11×#15302
C11×#14662
#845811