Finite Group Databasebeta

← C11×#34274 #14611467

Subgroups — C11×#34274 #14611467

Order 2816.

3154 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#520C212yesmaximal, complemented
3C11×#2363C214yesmaximal, complemented
4C11×#2362C214yesmaximal, complemented
5C11×#2361C214yesmaximal, complemented
6C11×#2360C214yesmaximal, complemented
7C11×#2325C214yesmaximal, complemented
8C11×#2316C211yesmaximal, characteristic, complemented
9C4×C11×#121C214yesmaximal, complemented
10C11×#2297C212yesmaximal, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C11×#537C4116yescomplemented
14C2×C11×C22⋊Q8C2214yes—
15C2×C11×#121C2214yes—
16C2×C11×#121C2214yes—
17C11×#520—216no—
18C2×C4×Q8×C11C2214yes—
19C2×C4×D4×C11C2218yes—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C2×C11×#117C2212yes—
23C2×C11×#117C2214yes—
24C22×C11×C4⋊C4C2214yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2212yes—
29C11×#391C2212yes—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C11×#390C2214yes—
34C11×#389C2214yes—
35C11×#389C2214yes—
36C11×#389C2214yes—
37C11×#388C2218yes—
38C11×#388C2218yes—
39C11×#387C2218yes—
40C11×#386C2214yes—
41C11×#386C2214yes—
42C11×#386C2218yes—
43C11×#385C2218yes—
44C11×#380C2214yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C22⋊C4C2214yes—
49C4×C11×C22⋊C4C2214yes—
50C4×C11×C22⋊C4C2218yes—
51C2×C11×#95C2212yes—
52C2×C11×#41—28no—
53C2×C11×#41—28no—
54C2×C11×#41C2×C4116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2314yes—
57C22×D4×C11C2312yes—
58C22×D4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2318yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C11×C22⋊Q8C2×C4132yescomplemented
67C11×#121C2×C4132yescomplemented
68C11×#121C2×C4132yescomplemented
69C4×Q8×C11—216no—
70C4×D4×C11—232no—
71C4×D4×C11—216no—
72C4×D4×C11—48no—
73C11×#117—28no—
74C11×#117—216no—
75C2×C11×C4⋊C4—216no—
76C2×C11×C4⋊C4C2×C418yescomplemented
77C2×C11×C4⋊C4D418yescomplemented
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2318yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2318yes—
93C2×C42×C11—24no—
94C2×C42×C11—44no—
95C2×C42×C11C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2314yes—
98C2×C42×C11C2314yes—
99C2×C42×C11C2318yes—
100C2×C42×C11C2314yes—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107#34274C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11C2414yes—
109C24×C11C2411yescharacteristic
110C11×#41—264no—
111C2×Q8×C11—24no—
112C2×Q8×C11—24no—
113C2×Q8×C11C22×C418yes—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11C22×C4116yes—
121C2×D4×C11C22×C418yes—
122C2×D4×C11C22×C4116yes—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—28no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—216no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11—48no—
137C22×C4×C11—48no—
138C22×C4×C11C22×C4116yes—
139C22×C4×C11C22×C418yes—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C2×D418yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11#4114yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2412yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—216no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—44no—
158C11×C4⋊C4C22×C4116yes—
159C11×C4⋊C4C22×C4116yes—
160C11×C4⋊C4C2×D4116yes—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—216no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—44no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4C22×C4132yes—
168C42×C11—216no—
169C42×C11—28no—
170C42×C11—24no—
171C42×C11—24no—
172C42×C11—28no—
173C42×C11—44no—
174C2×#537C2×C1111yescharacteristic
175C2×#520C2×C1112yescomplemented
176#2363C2×C1114yescomplemented
177#2362C2×C1114yescomplemented
178#2361C2×C1114yescomplemented
179#2360C2×C1114yescomplemented
180#2325C2×C1114yescomplemented
181#2316C2×C1111yescharacteristic, complemented
182C4×#121C2×C1114yescomplemented
183#2297C2×C1112yescomplemented
184C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11C23×C418yes—
196C23×C11C23×C412yes—
197C23×C11C22×D412yes—
198C23×C11C2×#4112yes—
199C23×C11C2511yescharacteristic
200Q8×C11—216no—
201D4×C11—232no—
202D4×C11—216no—
203D4×C11—416no—
204C2×C4×C11—28no—
205C2×C4×C11—24no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—232no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—48no—
226C2×C4×C11—48no—
227C2×C4×C11—44no—
228C2×C4×C11—816no—
229C2×C4×C11C4×D4116yescomplemented
230C2×C4×C11C23×C418yes—
231C2×C4×C11C23×C418yes—
232C2×C4×C11C23×C414yes—
233C2×C4×C11C22×D418yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C2×#4114yes—
236C2×C4×C11H(5,𝔽2)12yes—
237C2×C4×C112−1+412yes—
238C22×#41C22×C1112yes—
239#537C4×C11116yescomplemented
240C2×C22⋊Q8C22×C1114yes—
241C2×#121C22×C1114yes—
242C2×#121C22×C1114yes—
243#520—216no—
244C2×C4×Q8C22×C1114yes—
245C2×C4×D4C22×C1118yes—
246C2×C4×D4C22×C1114yes—
247C2×C4×D4C22×C1114yes—
248C2×#117C22×C1112yes—
249C2×#117C22×C1114yes—
250C22×C4⋊C4C22×C1114yes—
251C22×C4⋊C4C22×C1111yescharacteristic
252C22×C4⋊C4C22×C1111yescharacteristic
253C22×C42C22×C1111yescharacteristic
254C22×C42C22×C1112yes—
255#391C22×C1112yes—
256#391C22×C1112yes—
257#390C22×C1112yes—
258#390C22×C1112yes—
259#390C22×C1114yes—
260#389C22×C1114yes—
261#389C22×C1114yes—
262#389C22×C1114yes—
263#388C22×C1118yes—
264#388C22×C1118yes—
265#387C22×C1118yes—
266#386C22×C1114yes—
267#386C22×C1118yes—
268#386C22×C1114yes—
269#385C22×C1118yes—
270#380C22×C1114yes—
271C4×C4⋊C4C22×C1114yes—
272C4×C4⋊C4C22×C1114yes—
273C4×C4⋊C4C22×C1114yes—
274C4×C22⋊C4C22×C1114yes—
275C4×C22⋊C4C22×C1118yes—
276C4×C22⋊C4C22×C1114yes—
277C2×#95C22×C1112yes—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—28no—
285C22×C11—28no—
286C22×C11—28no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11C2×C4×D414yes—
292C22×C11C24×C411yescharacteristic
293C22×C11C23×D411yescharacteristic
294C22×C11C22×#4111yescharacteristic
295C22×C11C2×H(5,𝔽2)11yescharacteristic
296C22×C11C2×2−1+411yescharacteristic
297C22×C11#58511yescharacteristic
298C22×C11#58511yescharacteristic
299C4×C11—28no—
300C4×C11—28no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—28no—
304C4×C11—42no—
305C4×C11—44no—
306C4×C11—44no—
307C4×C11C2×C4×D418yes—
308C2×#41—28no—
309C2×#41—28no—
310C2×#41C2×C4×C11116yescomplemented
311C22×Q8C23×C1112yes—
312C22×D4C23×C1114yes—
313C22×D4C23×C1112yes—
314C22×D4C23×C1114yes—
315C23×C4C23×C1111yescharacteristic
316C23×C4C23×C1114yes—
317C23×C4C23×C1118yes—
318C23×C4C23×C1111yescharacteristic
319C23×C4C23×C1112yes—
320C23×C4C23×C1112yes—
321C23×C4C23×C1111yescharacteristic
322C22⋊Q8C2×C4×C11132yescomplemented
323#121C2×C4×C11132yescomplemented
324#121C2×C4×C11132yescomplemented
325C4×Q8—216no—
326C4×D4—232no—
327C4×D4—216no—
328C4×D4—48no—
329#117—28no—
330#117—216no—
331C2×C4⋊C4—216no—
332C2×C4⋊C4C2×C4×C1118yescomplemented
333C2×C4⋊C4D4×C1118yescomplemented
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1118yes—
336C2×C4⋊C4C23×C1112yes—
337C2×C4⋊C4C23×C1114yes—
338C2×C4⋊C4C23×C1114yes—
339C2×C4⋊C4C23×C1114yes—
340C2×C4⋊C4C23×C1114yes—
341C2×C4⋊C4C23×C1114yes—
342C2×C22⋊C4C23×C1114yes—
343C2×C22⋊C4C23×C1118yes—
344C2×C22⋊C4C23×C1114yes—
345C2×C22⋊C4C23×C1114yes—
346C2×C22⋊C4C23×C1114yes—
347C2×C22⋊C4C23×C1114yes—
348C2×C22⋊C4C23×C1118yes—
349C2×C42—24no—
350C2×C42—44no—
351C2×C42C23×C1114yes—
352C2×C42C23×C1118yes—
353C2×C42C23×C1114yes—
354C2×C42C23×C1112yes—
355C2×C42C23×C1112yes—
356C2×C42C23×C1114yes—
357#95C23×C1118yes—
358#95C23×C1114yes—
359#95C23×C1114yes—
360#95C23×C1118yes—
361#95C23×C1114yes—
362#95C23×C1114yes—
363C2×C11—24no—
364C2×C11—48no—
365C2×C11C22×C4×D411yescharacteristic
366C2×C11C4×H(5,𝔽2)11yescharacteristic
367C2×C11C4×2−1+411yescharacteristic
368C2×C11#349211yescharacteristic
369C2×C11#349311yescharacteristic
370C2×C11#349611yescharacteristic
371C2×C11#349711yescharacteristic
372C24C24×C1114yes—
373C24C24×C1111yescharacteristic
374#41—264no—
375C2×Q8—24no—
376C2×Q8—24no—
377C2×Q8C22×C4×C1118yes—
378C2×D4—28no—
379C2×D4—28no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—44no—
383C2×D4—44no—
384C2×D4C22×C4×C11116yes—
385C2×D4C22×C4×C1118yes—
386C2×D4C22×C4×C11116yes—
387C22×C4—22no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—216no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—48no—
401C22×C4—48no—
402C22×C4C22×C4×C11116yes—
403C22×C4C22×C4×C1118yes—
404C22×C4C22×C4×C1114yes—
405C22×C4C2×D4×C1118yes—
406C22×C4C2×D4×C1114yes—
407C22×C4C11×#4114yes—
408C22×C4C24×C1112yes—
409C22×C4C24×C1114yes—
410C22×C4C24×C1114yes—
411C22×C4C24×C1114yes—
412C22×C4C24×C1114yes—
413C22×C4C24×C1114yes—
414C22×C4C24×C1111yescharacteristic
415C22×C4C24×C1111yescharacteristic
416C22×C4C24×C1112yes—
417C4⋊C4—24no—
418C4⋊C4—216no—
419C4⋊C4—24no—
420C4⋊C4—44no—
421C4⋊C4—44no—
422C4⋊C4C22×C4×C11116yes—
423C4⋊C4C22×C4×C11116yes—
424C4⋊C4C2×D4×C11116yes—
425C22⋊C4—28no—
426C22⋊C4—216no—
427C22⋊C4—28no—
428C22⋊C4—28no—
429C22⋊C4—44no—
430C22⋊C4—44no—
431C22⋊C4C22×C4×C11132yes—
432C42—216no—
433C42—28no—
434C42—24no—
435C42—24no—
436C42—28no—
437C42—44no—
438C11#3427411yescharacteristic, direct product factor, Sylow
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—24no—
444C23—24no—
445C23—24no—
446C23—24no—
447C23—24no—
448C23—24no—
449C23C23×C4×C1118yes—
450C23C23×C4×C1112yes—
451C23C22×D4×C1112yes—
452C23C2×C11×#4112yes—
453C23C25×C1111yescharacteristic
454Q8—216no—
455D4—232no—
456D4—216no—
457D4—416no—
458C2×C4—28no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—232no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—48no—
480C2×C4—48no—
481C2×C4—44no—
482C2×C4—816no—
483C2×C4C4×D4×C11116yescomplemented
484C2×C4C23×C4×C1118yes—
485C2×C4C23×C4×C1118yes—
486C2×C4C23×C4×C1114yes—
487C2×C4C22×D4×C1118yes—
488C2×C4C22×D4×C1114yes—
489C2×C4C2×C11×#4114yes—
490C2×C4C11×H(5,𝔽2)12yes—
491C2×C4C11×2−1+412yes—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—28no—
499C22—28no—
500C22—28no—
501C22—44no—
502C22—44no—
503C22—44no—
504C22—44no—
505C22C2×C4×D4×C1114yes—
506C22C24×C4×C1111yescharacteristic
507C22C23×D4×C1111yescharacteristic
508C22C22×C11×#4111yescharacteristic
509C22C2×C11×H(5,𝔽2)11yescharacteristic
510C22C2×C11×2−1+411yescharacteristic
511C22C11×#58511yescharacteristic
512C22C11×#58511yescharacteristic
513C4—28no—
514C4—28no—
515C4—22no—
516C4—22no—
517C4—28no—
518C4—42no—
519C4—44no—
520C4—44no—
521C4C2×C4×D4×C1118yes—
522C2—24no—
523C2—48no—
524C2C22×C4×D4×C1111yescharacteristic
525C2C4×C11×H(5,𝔽2)11yescharacteristic
526C2C4×C11×2−1+411yescharacteristic
527C2C11×#349211yescharacteristic
528C2C11×#349311yescharacteristic
529C2C11×#349611yescharacteristic
530C2C11×#349711yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#537C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#520C2semidirect
3. C11×#2363C2semidirect
4. C11×#2362C2semidirect
5. C11×#2361C2semidirect
6. C11×#2360C2semidirect
7. C11×#2325C2semidirect
8. C11×#2316C2semidirect
9. C4×C11×#121C2semidirect
10. C11×#2297C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
13. C11×#537C4semidirect
54. C2×C11×#41C2×C4semidirect
66. C11×C22⋊Q8C2×C4semidirect
67. C11×#121C2×C4semidirect
68. C11×#121C2×C4semidirect
76. C2×C11×C4⋊C4C2×C4semidirect
77. C2×C11×C4⋊C4D4semidirect
107. #34274C11direct (N × H)
175. C2×#520C2×C11semidirect
176. #2363C2×C11semidirect
177. #2362C2×C11semidirect
178. #2361C2×C11semidirect
179. #2360C2×C11semidirect
180. #2325C2×C11semidirect
181. #2316C2×C11semidirect
182. C4×#121C2×C11semidirect
183. #2297C2×C11semidirect
184. C2×C4×C4⋊C4C2×C11semidirect
229. C2×C4×C11C4×D4semidirect
239. #537C4×C11semidirect
310. C2×#41C2×C4×C11semidirect
322. C22⋊Q8C2×C4×C11semidirect
323. #121C2×C4×C11semidirect
324. #121C2×C4×C11semidirect
332. C2×C4⋊C4C2×C4×C11semidirect
333. C2×C4⋊C4D4×C11semidirect
438. C11#34274direct (N × H)
483. C2×C4C4×D4×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#5202
C11×#23632
C11×#23622
C11×#23612
C11×#23602
C11×#23252
C11×#23162
C4×C11×#1212
C11×#22972
C2×C4×C11×C4⋊C42
#3427411