Finite Group Databasebeta

← C11×#12262 #14589455

Subgroups — C11×#12262 #14589455

Order 2816.

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

normal subgroups only

This group has 596 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×#2668C211yesmaximal, characteristic
2C11×#2029C211yesmaximal, characteristic, complemented
3C11×#1614C211yesmaximal, characteristic, complemented
4C11×#1596C211yesmaximal, characteristic, complemented
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1316C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#120—21no—
11C11×#484—21no—
12C11×#450—21no—
13C11×#399C2211yescharacteristic
14C11×#397—21no—
15C11×#394—21no—
16C11×#392C2211yescharacteristic
17C11×#386—21no—
18C11×#386—21no—
19C11×#379—21no—
20C11×#379C2211yescharacteristic
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23C11×#328—21no—
24C11×#328—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C25×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×SD16—41no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—41no—
37C11×C22⋊Q8—41no—
38C11×#121—44no—
39C11×#120—44no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
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—41no—
52C2×C11×C22⋊C4—41no—
53C2×C11×C22⋊C4D411yescharacteristic
54C2×C11×C22⋊C4C2311yescharacteristic
55C11×#107—41no—
56C11×#103—41no—
57C11×#102—41no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#12262C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—41no—
70C24×C11—42no—
71C24×C11—41no—
72C24×C11—81no—
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×D4×C11—24no—
77C2×D4×C11—41no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—81no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C2×D4×C11—81no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—81no—
97C22×C4×C11—81no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C11×SD16—82no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—81no—
121C11×C22⋊C4—81no—
122C11×C22⋊C4—82no—
123C11×C22⋊C4—82no—
124#2668C2×C1111yescharacteristic
125#2029C2×C1111yescharacteristic, complemented
126#1614C2×C1111yescharacteristic, complemented
127#1596C2×C1111yescharacteristic, complemented
128#1352C2×C1111yescharacteristic, complemented
129#1343C2×C1111yescharacteristic, complemented
130#1316C2×C1111yescharacteristic, complemented
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—22no—
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—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—82no—
154C23×C11—81no—
155C23×C11—82no—
156C23×C11—84no—
157C23×C11—81no—
158C23×C11#12011yescharacteristic
159C23×C11#13511yescharacteristic
160C23×C11#13711yescharacteristic
161Q8×C11—81no—
162Q8×C11—81no—
163D4×C11—42no—
164D4×C11—84no—
165D4×C11—81no—
166D4×C11—82no—
167D4×C11—82no—
168D4×C11—84no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
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—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—84no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C8×C11—81no—
194C8×C11—81no—
195#543C22×C1111yescharacteristic
196C2×#121—21no—
197C2×#120—21no—
198#484—21no—
199#450—21no—
200#399C22×C1111yescharacteristic
201#397—21no—
202#394—21no—
203#392C22×C1111yescharacteristic
204#386—21no—
205#386—21no—
206#379—21no—
207#379C22×C1111yescharacteristic
208#342—21no—
209#342C22×C1111yescharacteristic
210#328—21no—
211#328—21no—
212#323C22×C1111yescharacteristic
213#323C22×C1111yescharacteristic
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#45211yescharacteristic
242C22×C11#45511yescharacteristic
243C22×C11B(4,𝔽2)11yescharacteristic
244C4×C11—42no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—161no—
253C25D4×C1111yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4D4×C1111yescharacteristic
258C23×C4—21no—
259C2×SD16—41no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—41no—
263C22⋊Q8—41no—
264#121—44no—
265#120—44no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4×C1111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4D4×C1111yescharacteristic
280C2×C22⋊C4C23×C1111yescharacteristic
281#107—41no—
282#103—41no—
283#102—41no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286#95—21no—
287#95—21no—
288#95D4×C1111yescharacteristic
289#95D4×C1111yescharacteristic
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11—82no—
295C2×C11—82no—
296C2×C11#160611yescharacteristic
297C2×C11#219611yescharacteristic
298C2×C11#220011yescharacteristic
299C24—21no—
300C24—21no—
301C24—21no—
302C24—21no—
303C24—41no—
304C24—42no—
305C24—41no—
306C24—81no—
307C24C2×D4×C1111yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×D4—24no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1111yescharacteristic
334SD16—82no—
335C2×C8—41no—
336C2×C8—41no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C22⋊C4—81no—
356C22⋊C4—82no—
357C22⋊C4—82no—
358C11#1226211yescharacteristic, direct product factor, Sylow
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—82no—
382C23—81no—
383C23—82no—
384C23—84no—
385C23—81no—
386C23C11×#12011yescharacteristic
387C23C11×#13511yescharacteristic
388C23C11×#13711yescharacteristic
389Q8—81no—
390Q8—81no—
391D4—42no—
392D4—84no—
393D4—81no—
394D4—82no—
395D4—82no—
396D4—84no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—84no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C8—81no—
422C8—81no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—41no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—44no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C11×#45211yescharacteristic
451C22C11×#45511yescharacteristic
452C22C11×B(4,𝔽2)11yescharacteristic
453C4—42no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—161no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—82no—
467C2—82no—
468C2C11×#160611yescharacteristic
469C2C11×#219611yescharacteristic
470C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#2668C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2029C2semidirect
3. C11×#1614C2semidirect
4. C11×#1596C2semidirect
5. C11×#1352C2semidirect
6. C11×#1343C2semidirect
7. C11×#1316C2semidirect
64. #12262C11direct (N × H)
125. #2029C2×C11semidirect
126. #1614C2×C11semidirect
127. #1596C2×C11semidirect
128. #1352C2×C11semidirect
129. #1343C2×C11semidirect
130. #1316C2×C11semidirect
358. C11#12262direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26682
C11×#20292
C11×#16142
C11×#15962
C11×#13522
C11×#13432
C11×#13162
#1226211