Finite Group Databasebeta

← C11×#13335 #14590528

Subgroups — C11×#13335 #14590528

Order 2816.

536 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×#3414C211yesmaximal, characteristic
2C2×C11×#510C211yesmaximal, characteristic, complemented
3C11×#3156C211yesmaximal, characteristic, complemented
4C11×#2145C211yesmaximal, characteristic, complemented
5C11×#2141C211yesmaximal, characteristic, complemented
6C11×#1976C211yesmaximal, characteristic, complemented
7C11×#1378C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C2×C11×#135C2211yescharacteristic
10C2×C11×#135C2211yescharacteristic
11C22×C11×Q16C2211yescharacteristic
12C11×#536—21no—
13C11×#510—22no—
14C11×#510—21no—
15C11×#510—21no—
16C11×#510—22no—
17C11×#509—21no—
18C11×#509—21no—
19C11×#508—22no—
20C2×C11×Q32—21no—
21C2×C11×SD32—21no—
22C2×C11×M32C2211yescharacteristic
23C2×C11×M32C2211yescharacteristic
24C11×#497—22no—
25C11×#495—21no—
26C11×#494—21no—
27C11×#427C2211yescharacteristic
28C11×#421—21no—
29C11×#410—21no—
30C11×#405C2211yescharacteristic
31C11×#360—22no—
32C11×#358—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C22×Q8×C11—21no—
36C11×#137—42no—
37C11×#137—42no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135—21no—
41C11×#135—21no—
42C11×#135—21no—
43C11×#135—21no—
44C11×#135—21no—
45C11×#135—21no—
46C2×C11×Q16—22no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—21no—
51C2×C11×Q16—21no—
52C2×C11×Q16D411yescharacteristic
53C2×C11×Q16D412yes—
54C2×C11×Q16D411yescharacteristic
55C2×C11×SD16—22no—
56C2×C11×SD16—21no—
57C2×C11×SD16—21no—
58C2×C11×D8D411yescharacteristic
59C2×C11×D8D411yescharacteristic
60C2×C11×M16D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×#124—22no—
64C11×#123—42no—
65C11×C22⋊Q8—42no—
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C11×Q32—24no—
69C11×Q32—22no—
70C11×SD32—24no—
71C11×SD32—22no—
72C11×SD32—22no—
73C11×D16—22no—
74C11×M32—21no—
75C11×M32—21no—
76C11×M32—21no—
77C11×M32D412yes—
78C2×C11×C16—21no—
79C2×C11×C16D412yes—
80C11×#107—21no—
81C11×#106—21no—
82C11×#104—42no—
83C11×#99—42no—
84C11×#97—21no—
85C4×C8×C11—21no—
86#13335C1111yesmaximal, characteristic, direct product factor, Sylow
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—22no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C2×Q8×C11—41no—
101C2×Q8×C11—41no—
102C2×Q8×C11—41no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C11×Q16—22no—
112C11×Q16—21no—
113C11×Q16—21no—
114C11×Q16—21no—
115C11×Q16—22no—
116C11×Q16—21no—
117C11×Q16—44no—
118C11×Q16—41no—
119C11×Q16—41no—
120C11×SD16—44no—
121C11×SD16—41no—
122C11×SD16—41no—
123C11×SD16—41no—
124C11×SD16—41no—
125C11×D8—21no—
126C11×D8—21no—
127C11×D8—21no—
128C11×D8—21no—
129C11×M16—21no—
130C11×M16D812yes—
131C2×C8×C11—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11#4111yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4D812yes—
144C42×C11—21no—
145C42×C11—41no—
146C11×C16—22no—
147C11×C16—22no—
148#3414C2×C1111yescharacteristic
149C2×#510C2×C1111yescharacteristic, complemented
150#3156C2×C1111yescharacteristic, complemented
151#2145C2×C1111yescharacteristic, complemented
152#2141C2×C1111yescharacteristic, complemented
153#1976C2×C1111yescharacteristic, complemented
154#1378C2×C1111yescharacteristic, complemented
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C2×D811yescharacteristic
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—81no—
165Q8×C11—81no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173D4×C11—81no—
174C2×C4×C11—22no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12711yescharacteristic
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C8×C11—22no—
192C8×C11#12011yescharacteristic
193C8×C11#12011yescharacteristic
194C8×C11#12111yescharacteristic
195C8×C11#12111yescharacteristic
196C2×#137—21no—
197C2×#135C22×C1111yescharacteristic
198C2×#135C22×C1111yescharacteristic
199C22×Q16C22×C1111yescharacteristic
200#536—21no—
201#510—22no—
202#510—21no—
203#510—21no—
204#510—22no—
205#509—21no—
206#509—21no—
207#508—22no—
208C2×Q32—21no—
209C2×SD32—21no—
210C2×M32C22×C1111yescharacteristic
211C2×M32C22×C1111yescharacteristic
212#497—22no—
213#495—21no—
214#494—21no—
215#427C22×C1111yescharacteristic
216#421—21no—
217#410—21no—
218#405C22×C1111yescharacteristic
219#360—22no—
220#358—22no—
221C22×C11—41no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—161no—
226C22×C11#44711yescharacteristic
227C22×C11#45911yescharacteristic
228C22×C11#49311yescharacteristic
229C4×C11—42no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—82no—
233C4×C11—161no—
234C4×C11#39211yescharacteristic
235C4×C11#44711yescharacteristic
236C4×C11#45911yescharacteristic
237C4×C11#49611yescharacteristic
238C2×#41—21no—
239C2×#41—21no—
240C22×Q8—21no—
241#137—42no—
242#137—42no—
243#135—21no—
244#135—21no—
245#135—21no—
246#135—21no—
247#135—21no—
248#135—21no—
249#135—21no—
250#135—21no—
251C2×Q16—22no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16D4×C1112yes—
258C2×Q16D4×C1111yescharacteristic
259C2×Q16D4×C1111yescharacteristic
260C2×SD16—22no—
261C2×SD16—21no—
262C2×SD16—21no—
263C2×D8D4×C1111yescharacteristic
264C2×D8D4×C1111yescharacteristic
265C2×M16D4×C1111yescharacteristic
266C22×C8C23×C1111yescharacteristic
267C4⋊Q8—22no—
268#124—22no—
269#123—42no—
270C22⋊Q8—42no—
271#117—21no—
272#117D4×C1111yescharacteristic
273Q32—24no—
274Q32—22no—
275SD32—24no—
276SD32—22no—
277SD32—22no—
278D16—22no—
279M32—21no—
280M32—21no—
281M32—21no—
282M32D4×C1112yes—
283C2×C16—21no—
284C2×C16D4×C1112yes—
285#107—21no—
286#106—21no—
287#104—42no—
288#99—42no—
289#97—21no—
290C4×C8—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—161no—
295C2×C11—161no—
296C2×C11#201111yescharacteristic
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—22no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C1111yescharacteristic
321Q16—22no—
322Q16—21no—
323Q16—21no—
324Q16—21no—
325Q16—22no—
326Q16—21no—
327Q16—44no—
328Q16—41no—
329Q16—41no—
330SD16—44no—
331SD16—41no—
332SD16—41no—
333SD16—41no—
334SD16—41no—
335D8—21no—
336D8—21no—
337D8—21no—
338D8—21no—
339M16—21no—
340M16C11×D812yes—
341C2×C8—21no—
342C2×C8C2×D4×C1111yescharacteristic
343C2×C8C2×D4×C1111yescharacteristic
344C2×C8C2×D4×C1111yescharacteristic
345C2×C8C2×D4×C1111yescharacteristic
346C2×C8C2×D4×C1111yescharacteristic
347C2×C8C11×#4111yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—44no—
350C4⋊C4—41no—
351C22⋊C4—44no—
352C22⋊C4—41no—
353C22⋊C4C11×D812yes—
354C42—21no—
355C42—41no—
356C16—22no—
357C16—22no—
358C11#1333511yescharacteristic, direct product factor, Sylow
359C23—41no—
360C23—41no—
361C23C2×C11×D811yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—42no—
365Q8—42no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369Q8—81no—
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C11×#12011yescharacteristic
390C2×C4C11×#12111yescharacteristic
391C2×C4C11×#12711yescharacteristic
392C2×C4C2×C11×D811yescharacteristic
393C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
394C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
395C8—22no—
396C8C11×#12011yescharacteristic
397C8C11×#12011yescharacteristic
398C8C11×#12111yescharacteristic
399C8C11×#12111yescharacteristic
400C22—41no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22—161no—
405C22C11×#44711yescharacteristic
406C22C11×#45911yescharacteristic
407C22C11×#49311yescharacteristic
408C4—42no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—161no—
413C4C11×#39211yescharacteristic
414C4C11×#44711yescharacteristic
415C4C11×#45911yescharacteristic
416C4C11×#49611yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—161no—
421C2—161no—
422C2C11×#201111yescharacteristic
subgroupG/H
center, socleC2×C11#2011
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC11×#3414C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#510C2semidirect
3. C11×#3156C2semidirect
4. C11×#2145C2semidirect
5. C11×#2141C2semidirect
6. C11×#1976C2semidirect
7. C11×#1378C2semidirect
86. #13335C11direct (N × H)
149. C2×#510C2×C11semidirect
150. #3156C2×C11semidirect
151. #2145C2×C11semidirect
152. #2141C2×C11semidirect
153. #1976C2×C11semidirect
154. #1378C2×C11semidirect
358. C11#13335direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34142
C2×C11×#5102
C11×#31562
C11×#21452
C11×#21412
C11×#19762
C11×#13782
#1333511