Finite Group Databasebeta

← C11×#12198 #14589391

Subgroups — C11×#12198 #14589391

Order 2816.

474 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2828C211yesmaximal, characteristic, complemented
2C11×#2006C211yesmaximal, characteristic, complemented
3C11×#1616C211yesmaximal, characteristic, complemented
4C11×#1598C211yesmaximal, characteristic, complemented
5C11×#1353C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#537C2211yescharacteristic
10C11×#481—21no—
11C11×#447—21no—
12C2×C11×#104—21no—
13C11×#400C2211yescharacteristic
14C11×#397—21no—
15C11×#394—21no—
16C11×#394—21no—
17C11×#394C2211yescharacteristic
18C11×#392—21no—
19C11×#392—21no—
20C11×#390C2211yescharacteristic
21C11×#388—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C22×D4×C11D411yescharacteristic
32C11×AGL(1,ℤ/8)—42no—
33C11×AGL(1,ℤ/8)—42no—
34C2×C11×SD16—41no—
35C2×C11×D8—41no—
36C2×C11×D8—41no—
37C2×C11×M16—21no—
38C11×C22⋊Q8—41no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—41no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11D411yescharacteristic
54C11×#106—41no—
55C11×#104—42no—
56C11×#102—41no—
57C11×#102—41no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12198C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C24×C11—21no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—81no—
83C2×D4×C11—81no—
84C2×D4×C11—81no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C11×SD16—44no—
98C11×D8—44no—
99C11×D8—82no—
100C11×M16—22no—
101C11×M16—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—81no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—81no—
115C11×C22⋊C4—81no—
116C11×C22⋊C4—81no—
117C11×C22⋊C4—81no—
118C11×C22⋊C4—81no—
119C11×C22⋊C4—81no—
120C11×C22⋊C4—81no—
121C42×C11—41no—
122#2828C2×C1111yescharacteristic, complemented
123#2006C2×C1111yescharacteristic, complemented
124#1616C2×C1111yescharacteristic, complemented
125#1598C2×C1111yescharacteristic, complemented
126#1353C2×C1111yescharacteristic, complemented
127#1345C2×C1111yescharacteristic, complemented
128#1318C2×C1111yescharacteristic, complemented
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11#12011yescharacteristic
145Q8×C11—41no—
146Q8×C11—41no—
147D4×C11—41no—
148D4×C11—42no—
149D4×C11—41no—
150D4×C11—42no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—84no—
156D4×C11—84no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C8×C11—42no—
183C8×C11—81no—
184C8×C11—81no—
185C2×AGL(1,ℤ/8)—21no—
186#537C22×C1111yescharacteristic
187#481—21no—
188#447—21no—
189C2×#104—21no—
190#400C22×C1111yescharacteristic
191#397—21no—
192#394—21no—
193#394—21no—
194#394C22×C1111yescharacteristic
195#392—21no—
196#392—21no—
197#390C22×C1111yescharacteristic
198#388—21no—
199#343C22×C1111yescharacteristic
200#327—21no—
201#327—21no—
202#324C22×C1111yescharacteristic
203#324C22×C1111yescharacteristic
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#44911yescharacteristic
224C22×C11#45311yescharacteristic
225C22×C11B(4,𝔽2)11yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C2×#41—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4D4×C1111yescharacteristic
239C22×D4D4×C1111yescharacteristic
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—42no—
242C2×SD16—41no—
243C2×D8—41no—
244C2×D8—41no—
245C2×M16—21no—
246C22⋊Q8—41no—
247#121—21no—
248#121—21no—
249#121—41no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C4⋊C4C23×C1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42D4×C1111yescharacteristic
262#106—41no—
263#104—42no—
264#102—41no—
265#102—41no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95D4×C1111yescharacteristic
272#95D4×C1111yescharacteristic
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—161no—
276C2×C11—161no—
277C2×C11—161no—
278C2×C11#160011yescharacteristic
279C2×C11#220011yescharacteristic
280C2×C11#220211yescharacteristic
281C24—21no—
282C24—21no—
283#41—41no—
284#41—41no—
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C2×D4—81no—
303C2×D4—81no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312SD16—44no—
313D8—44no—
314D8—82no—
315M16—22no—
316M16—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—81no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—81no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C42—41no—
337C11#1219811yescharacteristic, direct product factor, Sylow
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23C11×#12011yescharacteristic
354Q8—41no—
355Q8—41no—
356D4—41no—
357D4—42no—
358D4—41no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—84no—
365D4—84no—
366D4—81no—
367D4—81no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C11×#13511yescharacteristic
390C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
391C8—42no—
392C8—81no—
393C8—81no—
394C22—21no—
395C22—21no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C11×#44911yescharacteristic
414C22C11×#45311yescharacteristic
415C22C11×B(4,𝔽2)11yescharacteristic
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C2—21no—
426C2—21no—
427C2—161no—
428C2—161no—
429C2—161no—
430C2C11×#160011yescharacteristic
431C2C11×#220011yescharacteristic
432C2C11×#220211yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2828C2semidirect
2. C11×#2006C2semidirect
3. C11×#1616C2semidirect
4. C11×#1598C2semidirect
5. C11×#1353C2semidirect
6. C11×#1345C2semidirect
7. C11×#1318C2semidirect
65. #12198C11direct (N × H)
122. #2828C2×C11semidirect
123. #2006C2×C11semidirect
124. #1616C2×C11semidirect
125. #1598C2×C11semidirect
126. #1353C2×C11semidirect
127. #1345C2×C11semidirect
128. #1318C2×C11semidirect
337. C11#12198direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28282
C11×#20062
C11×#16162
C11×#15982
C11×#13532
C11×#13452
C11×#13182
#1219811