Finite Group Databasebeta

← C11×#12148 #14589341

Subgroups — C11×#12148 #14589341

Order 2816.

622 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2675C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic, complemented
3C11×#1595C211yesmaximal, characteristic, complemented
4C11×#1595C211yesmaximal, characteristic, complemented
5C11×#1343C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#121—21no—
11C2×C11×#121—21no—
12C11×#447—21no—
13C11×#447—21no—
14C2×C11×#99—21no—
15C11×#396—21no—
16C11×#392—21no—
17C11×#392C2211yescharacteristic
18C11×#392C2211yescharacteristic
19C11×#386—21no—
20C11×#385—21no—
21C11×#385C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C23×C4×C11D411yescharacteristic
36C2×C11×D8—41no—
37C2×C11×D8—41no—
38C11×#123—41no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—44no—
42C11×#121—44no—
43C11×#121—42no—
44C11×#121—42no—
45C11×#120—41no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—41no—
56C2×C11×C22⋊C4D411yescharacteristic
57C2×C11×C22⋊C4C2311yescharacteristic
58C11×#102—41no—
59C11×#102—41no—
60C11×#99—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64C11×#95—41no—
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67#12148C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—21no—
69C24×C11—21no—
70C24×C11—21no—
71C24×C11C2×D411yescharacteristic
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—81no—
94C2×D4×C11—81no—
95C2×D4×C11—81no—
96C2×D4×C11—81no—
97C2×D4×C11—81no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—81no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C11×D8—82no—
112C11×D8—82no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—42no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—21no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—81no—
131C11×C22⋊C4—82no—
132C11×C22⋊C4D812yescomplemented
133#2675C2×C1111yescharacteristic, complemented
134#2044C2×C1111yescharacteristic, complemented
135#1595C2×C1111yescharacteristic, complemented
136#1595C2×C1111yescharacteristic, complemented
137#1343C2×C1111yescharacteristic, complemented
138#1343C2×C1111yescharacteristic, complemented
139#1326C2×C1111yescharacteristic, complemented
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11#12011yescharacteristic
164C23×C11C2×D811yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—82no—
170D4×C11—82no—
171D4×C11—84no—
172D4×C11—84no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—82no—
179D4×C11—82no—
180D4×C11—81no—
181D4×C11—81no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—81no—
203C2×C4×C11—84no—
204C2×C4×C11—81no—
205C2×C4×C11—81no—
206C2×C4×C11—81no—
207C8×C11—81no—
208C8×C11—81no—
209#534C22×C1111yescharacteristic
210C2×#121—21no—
211C2×#121—21no—
212C2×#121—21no—
213#447—21no—
214#447—21no—
215C2×#99—21no—
216#396—21no—
217#392—21no—
218#392C22×C1111yescharacteristic
219#392C22×C1111yescharacteristic
220#386—21no—
221#385—21no—
222#385C22×C1111yescharacteristic
223#342C22×C1111yescharacteristic
224#327—21no—
225#327—21no—
226#323C22×C1111yescharacteristic
227#323C22×C1111yescharacteristic
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—161no—
256C22×C11#44711yescharacteristic
257C22×C11#45411yescharacteristic
258C22×C11B(4,𝔽2)11yescharacteristic
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11—161no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4D4×C1111yescharacteristic
273C22×D4D4×C1111yescharacteristic
274C23×C4—21no—
275C23×C4D4×C1111yescharacteristic
276C2×D8—41no—
277C2×D8—41no—
278#123—41no—
279#121—21no—
280#121—21no—
281#121—44no—
282#121—44no—
283#121—42no—
284#121—42no—
285#120—41no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4D4×C1111yescharacteristic
297C2×C22⋊C4C23×C1111yescharacteristic
298#102—41no—
299#102—41no—
300#99—42no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303#95—21no—
304#95—41no—
305#95D4×C1111yescharacteristic
306#95D4×C1111yescharacteristic
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—41no—
310C2×C11—41no—
311C2×C11—82no—
312C2×C11—161no—
313C2×C11—161no—
314C2×C11#159811yescharacteristic
315C2×C11#219611yescharacteristic
316C2×C11#220011yescharacteristic
317C24—21no—
318C24—21no—
319C24—21no—
320C24C2×D4×C1111yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4—81no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—81no—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C2×D4×C1111yescharacteristic
360D8—82no—
361D8—82no—
362C2×C8—41no—
363C2×C8—41no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C22⋊C4—24no—
370C22⋊C4—21no—
371C22⋊C4—41no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—81no—
380C22⋊C4—82no—
381C22⋊C4C11×D812yescomplemented
382C11#1214811yescharacteristic, direct product factor, Sylow
383C23—21no—
384C23—21no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—81no—
405C23—81no—
406C23C11×#12011yescharacteristic
407C23C2×C11×D811yescharacteristic
408C23C11×AGL(1,ℤ/8)11yescharacteristic
409D4—42no—
410D4—42no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—84no—
415D4—84no—
416D4—81no—
417D4—81no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—82no—
422D4—82no—
423D4—81no—
424D4—81no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—84no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C8—81no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—42no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—82no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—161no—
480C22C11×#44711yescharacteristic
481C22C11×#45411yescharacteristic
482C22C11×B(4,𝔽2)11yescharacteristic
483C4—42no—
484C4—42no—
485C4—41no—
486C4—42no—
487C4—41no—
488C4—81no—
489C4—81no—
490C4—161no—
491C2—21no—
492C2—21no—
493C2—41no—
494C2—41no—
495C2—82no—
496C2—161no—
497C2—161no—
498C2C11×#159811yescharacteristic
499C2C11×#219611yescharacteristic
500C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
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
1. C11×#2675C2semidirect
2. C11×#2044C2semidirect
3. C11×#1595C2semidirect
4. C11×#1595C2semidirect
5. C11×#1343C2semidirect
6. C11×#1343C2semidirect
7. C11×#1326C2semidirect
67. #12148C11direct (N × H)
132. C11×C22⋊C4D8semidirect
133. #2675C2×C11semidirect
134. #2044C2×C11semidirect
135. #1595C2×C11semidirect
136. #1595C2×C11semidirect
137. #1343C2×C11semidirect
138. #1343C2×C11semidirect
139. #1326C2×C11semidirect
381. C22⋊C4C11×D8semidirect
382. C11#12148direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26752
C11×#20442
C11×#15952
C11×#13432
C11×#13262
#1214811