Finite Group Databasebeta

← C11×#10184 #14587377

Subgroups — C11×#10184 #14587377

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C11×#1546C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C22×C11×SD16—21no—
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#500—21no—
14C11×#486—21no—
15C11×#480—22no—
16C11×#474—22no—
17C11×#463—22no—
18C11×#461—22no—
19C11×#461—21no—
20C11×#461—22no—
21C11×#459—21no—
22C11×#431C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#103—21no—
28C11×#332—22no—
29C11×D4⋊C8—22no—
30C11×#323—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—24no—
38C2×C11×SD16—22no—
39C2×C11×SD16—42no—
40C2×C11×SD16—42no—
41C2×C11×D8—22no—
42C2×C11×M16—21no—
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D411yescharacteristic
48C11×C4⋊Q8D412yes—
49C11×#127D411yescharacteristic
50C11×#124—21no—
51C11×#121—21no—
52C11×#121—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—24no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8D412yes—
71C11×#103—24no—
72C11×#103—22no—
73C11×#102—22no—
74C11×#102—24no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8D412yes—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79#10184C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C2×D4×C11D812yes—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C11×SD16—48no—
112C11×SD16—44no—
113C11×D8—44no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138#3226C2×C1111yescharacteristic, complemented
139#3036C2×C1111yescharacteristic
140C2×#461C2×C1111yescharacteristic, complemented
141#1546C2×C1111yescharacteristic, complemented
142#1480C2×C1111yescharacteristic, complemented
143#1460C2×C1111yescharacteristic, complemented
144#1301C2×C1111yescharacteristic, complemented
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11#12111yescharacteristic
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—42no—
155Q8×C11—41no—
156Q8×C11—81no—
157Q8×C11—81no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—42no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—82no—
179C2×C4×C11—81no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12711yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C8×C11—42no—
191C8×C11—42no—
192C8×C11—42no—
193C8×C11—81no—
194C2×AGL(1,ℤ/8)—21no—
195C22×SD16—21no—
196#532C22×C1111yescharacteristic
197C2×C4⋊Q8C22×C1111yescharacteristic
198C2×C4×D4C22×C1111yescharacteristic
199#500—21no—
200#486—21no—
201#480—22no—
202#474—22no—
203#463—22no—
204#461—22no—
205#461—21no—
206#461—22no—
207#459—21no—
208#431C22×C1111yescharacteristic
209#431C22×C1111yescharacteristic
210#423C22×C1111yescharacteristic
211C2×C4⋊C8C22×C1111yescharacteristic
212#417—21no—
213C2×#103—21no—
214#332—22no—
215D4⋊C8—22no—
216#323—22no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39211yescharacteristic
228C22×C11#46611yescharacteristic
229C22×C11#46911yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11—82no—
235C4×C11—81no—
236C4×C11#44711yescharacteristic
237C4×C11#44711yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#47112yes—
241C2×#41—21no—
242C22×Q8—21no—
243C22×D4D4×C1111yescharacteristic
244C23×C4—21no—
245AGL(1,ℤ/8)—42no—
246AGL(1,ℤ/8)—42no—
247C2×SD16—24no—
248C2×SD16—22no—
249C2×SD16—42no—
250C2×SD16—42no—
251C2×D8—22no—
252C2×M16—21no—
253C22×C8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8D4×C1112yes—
258C4⋊Q8D4×C1111yescharacteristic
259#127D4×C1111yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C23×C1111yescharacteristic
274#107—24no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8D4×C1112yes—
280C4⋊C8D4×C1112yes—
281#103—24no—
282#103—22no—
283#102—22no—
284#102—24no—
285C22⋊C8—21no—
286C22⋊C8D4×C1112yes—
287C4×C8—21no—
288C4×C8—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11—161no—
293C2×C11#199911yescharacteristic
294C2×C11#200911yescharacteristic
295C2×C11#201911yescharacteristic
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4C11×D812yes—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—82no—
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1111yescharacteristic
326C22×C4C11×#4111yescharacteristic
327SD16—48no—
328SD16—44no—
329D8—44no—
330M16—41no—
331M16—41no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42C2×D4×C1111yescharacteristic
351C42C2×D4×C1111yescharacteristic
352C42C2×D4×C1111yescharacteristic
353C42C2×D4×C1111yescharacteristic
354C11#1018411yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23C11×#12111yescharacteristic
362Q8—42no—
363Q8—41no—
364Q8—42no—
365Q8—41no—
366Q8—81no—
367Q8—81no—
368D4—22no—
369D4—22no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—42no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—82no—
389C2×C4—81no—
390C2×C4C11×#12011yescharacteristic
391C2×C4C11×#12011yescharacteristic
392C2×C4C11×#12011yescharacteristic
393C2×C4C11×#12111yescharacteristic
394C2×C4C11×#12111yescharacteristic
395C2×C4C11×#12711yescharacteristic
396C2×C4C2×C11×D811yescharacteristic
397C2×C4C11×#13511yescharacteristic
398C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
399C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
400C8—42no—
401C8—42no—
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—82no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22C11×#39211yescharacteristic
415C22C11×#46611yescharacteristic
416C22C11×#46911yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—81no—
421C4—82no—
422C4—81no—
423C4C11×#44711yescharacteristic
424C4C11×#44711yescharacteristic
425C4C11×#44911yescharacteristic
426C4C11×#44911yescharacteristic
427C4C11×#47112yes—
428C2—21no—
429C2—21no—
430C2—82no—
431C2—161no—
432C2C11×#199911yescharacteristic
433C2C11×#200911yescharacteristic
434C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
LCSG ▷ C2×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×#3226C2semidirect
3. C2×C11×#461C2semidirect
4. C11×#1546C2semidirect
5. C11×#1480C2semidirect
6. C11×#1460C2semidirect
7. C11×#1301C2semidirect
79. #10184C11direct (N × H)
138. #3226C2×C11semidirect
140. C2×#461C2×C11semidirect
141. #1546C2×C11semidirect
142. #1480C2×C11semidirect
143. #1460C2×C11semidirect
144. #1301C2×C11semidirect
354. C11#10184direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#30362
C2×C11×#4612
C11×#15462
C11×#14802
C11×#14602
C11×#13012
#1018411