Finite Group Databasebeta

← C11×#9941 #14587134

Subgroups — C11×#9941 #14587134

Order 2816.

600 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3094C211yesmaximal, characteristic
2C11×#2591C211yesmaximal, characteristic
3C11×#2484C211yesmaximal, characteristic, complemented
4C11×#1826C211yesmaximal, characteristic, complemented
5C11×#1510C211yesmaximal, characteristic
6C11×#1463C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#482—22no—
12C11×#481—21no—
13C11×#480—21no—
14C11×#428—21no—
15C11×#418—21no—
16C11×#407C2211yescharacteristic
17C11×#407C2211yescharacteristic
18C11×#400—21no—
19C11×#400—21no—
20C11×#398—21no—
21C11×#394—21no—
22C11×#388—22no—
23C11×#387—22no—
24C11×#386—21no—
25C11×#386—21no—
26C11×#385—21no—
27C11×#381—21no—
28C11×#381C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C11×#339—22no—
31C11×#327—22no—
32C11×#324—22no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C2×C11×M16—21no—
39C2×C11×M16—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#117—21no—
45C11×#117—21no—
46C11×#117—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—21no—
65C2×C42×C11D412yes—
66C11×#107—22no—
67C11×#106—22no—
68C11×#102—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8D412yes—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95D412yes—
82#9941C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—44no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C11×M16—42no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—82no—
134C42×C11—42no—
135C42×C11—41no—
136C42×C11—41no—
137#3094C2×C1111yescharacteristic
138#2591C2×C1111yescharacteristic
139#2484C2×C1111yescharacteristic, complemented
140#1826C2×C1111yescharacteristic, complemented
141#1510C2×C1111yescharacteristic
142#1463C2×C1111yescharacteristic, complemented
143#1284C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11#12111yescharacteristic
154D4×C11—42no—
155D4×C11—81no—
156D4×C11—82no—
157D4×C11—82no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
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—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—81no—
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12711yescharacteristic
191C8×C11—42no—
192C8×C11—81no—
193C2×#121C22×C1111yescharacteristic
194C2×#117C22×C1111yescharacteristic
195C22×C4⋊C4C22×C1111yescharacteristic
196#482—22no—
197#481—21no—
198#480—21no—
199#428—21no—
200#418—21no—
201#407C22×C1111yescharacteristic
202#407C22×C1111yescharacteristic
203#400—21no—
204#400—21no—
205#398—21no—
206#394—21no—
207#388—22no—
208#387—22no—
209#386—21no—
210#386—21no—
211#385—21no—
212#381—21no—
213#381C22×C1111yescharacteristic
214C4×C22⋊C4C22×C1111yescharacteristic
215#339—22no—
216#327—22no—
217#324—22no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—44no—
226C22×C11—84no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#39211yescharacteristic
231C22×C11#45412yes—
232C22×C11#45812yes—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—82no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—81no—
244C22×D4—21no—
245C22×D4D4×C1111yescharacteristic
246C23×C4D4×C1111yescharacteristic
247C23×C4D4×C1111yescharacteristic
248C23×C4C23×C1111yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255#117—21no—
256#117—21no—
257#117—21no—
258#117—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C1111yescharacteristic
267C2×C4⋊C4D4×C1111yescharacteristic
268C2×C4⋊C4D4×C1111yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C42—21no—
276C2×C42D4×C1112yes—
277#107—22no—
278#106—22no—
279#102—22no—
280#102—22no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8D4×C1112yes—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95—22no—
290#95—21no—
291#95—21no—
292#95D4×C1112yes—
293C2×C11—22no—
294C2×C11—22no—
295C2×C11—41no—
296C2×C11—161no—
297C2×C11#200311yescharacteristic
298C2×C11#201011yescharacteristic
299C2×C11#202211yescharacteristic
300C24—21no—
301C24C2×D4×C1111yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—42no—
305C2×D4—44no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C2×D4×C1111yescharacteristic
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1111yescharacteristic
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C11×#4111yescharacteristic
328M16—42no—
329M16—42no—
330C2×C8—22no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—44no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—44no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—82no—
351C42—42no—
352C42—41no—
353C42—41no—
354C11#994111yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23C11×#12011yescharacteristic
363C23C11×#12011yescharacteristic
364C23C11×#12111yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
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—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4C11×#12011yescharacteristic
399C2×C4C11×#12111yescharacteristic
400C2×C4C11×#12111yescharacteristic
401C2×C4C11×#12711yescharacteristic
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C11×#39211yescharacteristic
417C22C11×#45412yes—
418C22C11×#45812yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4—81no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2C11×#200311yescharacteristic
435C2C11×#201011yescharacteristic
436C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2484C2semidirect
4. C11×#1826C2semidirect
6. C11×#1463C2semidirect
7. C11×#1284C2semidirect
82. #9941C11direct (N × H)
139. #2484C2×C11semidirect
140. #1826C2×C11semidirect
142. #1463C2×C11semidirect
143. #1284C2×C11semidirect
354. C11#9941direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C11×#25912
C11×#24842
C11×#18262
C11×#15102
C11×#14632
C11×#12842
#994111