Finite Group Databasebeta

← D11×#2507 #14923013

Subgroups — D11×#2507 #14923013

Order 2816.

2054 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073146C211yesmaximal, characteristic, complemented
2#13073145C211yesmaximal, characteristic, complemented
3#13073144C211yesmaximal, characteristic, complemented
4#13073143C211yesmaximal, characteristic, complemented
5#13073142C212yesmaximal, complemented
6#13073141C211yesmaximal, characteristic, complemented
7#13073140C212yesmaximal, complemented
8#13073139C211yesmaximal, characteristic, complemented
9#13073138C212yesmaximal, complemented
10#13073137C211yesmaximal, characteristic, complemented
11#13073136C212yesmaximal, complemented
12D11×#398C212yesmaximal
13D11×#398C212yesmaximal
14D11×#389C211yesmaximal, characteristic
15D11×#389C211yesmaximal, characteristic
16D11×#389C211yesmaximal, characteristic
17D11×#389C211yesmaximal, characteristic
18D11×#389C212yesmaximal
19D11×#387C212yesmaximal
20D11×#384C211yesmaximal, characteristic
21C4×C4⋊C4×D11C211yesmaximal, characteristic
22C4×C4⋊C4×D11C211yesmaximal, characteristic
23C11×#2507C211yesmaximal, characteristic, complemented
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2212yes—
40C11×#398C2212yes—
41C11×#398C2212yes—
42C11×#389C2212yes—
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#387C2212yes—
48C11×#384C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51#10622598C2212yes—
52#10622598C2211yescharacteristic
53#10622598C2211yescharacteristic
54#10622598C2211yescharacteristic
55#10622598C2211yescharacteristic
56#10622597C2212yes—
57#10622597C2212yes—
58#10622597C2212yes—
59#10622597C2212yes—
60#10622596C2212yes—
61#10622596C2212yes—
62#10622594C2212yes—
63#10622593C2212yes—
64#10622593C2212yes—
65#10622591C2212yes—
66#10622589C2212yes—
67#10622589C2211yescharacteristic
68#10622589C2212yes—
69#10622589C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71C4⋊C4×Dic11C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2211yescharacteristic
74#10622586C2211yescharacteristic
75#10622586C2212yes—
76#10622586C2211yescharacteristic
77#10622586C2211yescharacteristic
78#10622586C2211yescharacteristic
79#10622585C2212yes—
80#10622585C2212yes—
81#10622585C2212yes—
82#10622585C2212yes—
83#10622585C2212yes—
84#10622585C2212yes—
85#10622548C2211yescharacteristic
86C4×C4⋊Dic11C2211yescharacteristic
87C4×C4⋊Dic11C2211yescharacteristic
88#10622546C2212yes—
89C4×Dic11⋊C4C2211yescharacteristic
90C4×Dic11⋊C4C2211yescharacteristic
91C4×Dic11⋊C4C2212yes—
92#10622541C2212yes—
93#10622541C2211yescharacteristic
94#10622541C2211yescharacteristic
95#10622541C2211yescharacteristic
96#10622541C2211yescharacteristic
97D11×#95C2211yescharacteristic
98D11×#95C2212yes—
99D11×#95C2211yescharacteristic
100D11×#95C2212yes—
101D11×#95C2212yes—
102D11×#95C2212yes—
103D11×#95C2212yes—
104#10622274C2212yes—
105#10622274C2212yes—
106#10622270C2212yes—
107#10622270C2212yes—
108#10622270C2212yes—
109#10622270C2212yes—
110#10622268C2212yes—
111#10622267C2212yes—
112#10622266C2212yes—
113#10622265C2212yes—
114#10622262C2212yes—
115#10622262C2211yescharacteristic
116#10622262C2211yescharacteristic
117#10622260C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622260C2212yes—
123C22×C4×D11C2311yescharacteristic
124C22×C4×D11C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2312yes—
127C22×C4×D11C2312yes—
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2312yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2312yes—
150C2×C4⋊Dic11C2312yes—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2312yes—
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2311yescharacteristic
162C2×Dic11⋊C4C2312yes—
163C2×Dic11⋊C4C2312yes—
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2311yescharacteristic
168C2×Dic11⋊C4C2311yescharacteristic
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C4⋊C4×D11—24no—
195C4⋊C4×D11—24no—
196C4⋊C4×D11—24no—
197C4⋊C4×D11—24no—
198C4⋊C4×D11—28no—
199C4⋊C4×D11—44no—
200C4⋊C4×D11—44no—
201C4⋊C4×D11—44no—
202C4⋊C4×D11—44no—
203C4⋊C4×D11—44no—
204C4⋊C4×D11Q818yes—
205C4⋊C4×D11Q818yes—
206C42×D11—24no—
207C42×D11—24no—
208C42×D11—24no—
209C42×D11—44no—
210C11×#95C2311yescharacteristic
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2311yescharacteristic
217C11⋊#95C2311yescharacteristic
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C2×#2507—111nomaximal, Sylow
239C23×D11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2412yes—
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×Dic11C2411yescharacteristic
252C22×Dic11C2412yes—
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2411yescharacteristic
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2412yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2411yescharacteristic
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—22no—
267C2×C4×D11—24no—
268C2×C4×D11—22no—
269C2×C4×D11—22no—
270C2×C4×D11—24no—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×C4×D11—24no—
275C2×C4×D11—22no—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—24no—
280C2×C4×D11—22no—
281C2×C4×D11—24no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—24no—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11C2×Q818yes—
288C2×C4×D11C2×Q814yes—
289C2×C4×D11C2×Q814yes—
290C2×C4×D11C2×Q814yes—
291C2×C4×D11C2×Q814yes—
292C2×C4×D11#4114yes—
293C2×C4×D11#4114yes—
294C2×C4×D11#4114yes—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—42no—
301C11×C4⋊C4—42no—
302C11×C4⋊C4—42no—
303C11×C4⋊C4—42no—
304C11×C4⋊C4—42no—
305C11×C4⋊C4C2×Q814yes—
306C11×C4⋊C4C2×Q814yes—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—42no—
311C4⋊Dic11—24no—
312C4⋊Dic11—22no—
313C4⋊Dic11—22no—
314C4⋊Dic11—22no—
315C4⋊Dic11—22no—
316C4⋊Dic11—42no—
317C4⋊Dic11—42no—
318C4⋊Dic11—42no—
319C4⋊Dic11—42no—
320C4⋊Dic11—42no—
321C4⋊Dic11C2×Q814yes—
322C4⋊Dic11C2×Q814yes—
323Dic11⋊C4—24no—
324Dic11⋊C4—22no—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—22no—
330Dic11⋊C4—42no—
331Dic11⋊C4—42no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4C2×Q814yes—
341Dic11⋊C4C2×Q814yes—
342Dic11⋊C4C2×Q818yes—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—42no—
353C4×Dic11—42no—
354C4×Dic11—42no—
355#2507—112no—
356#2507—112no—
357#2507—112no—
358#2507—111no—
359#2507—111no—
360#2507—111no—
361#2507—111no—
362#2507—112no—
363#2507—111no—
364#2507—111no—
365#2507—111no—
366#2507D1111yescharacteristic, direct product factor
367C2×#398—112no—
368C2×#398—112no—
369C2×#389—111no—
370C2×#389—111no—
371C2×#389—112no—
372C2×#389—111no—
373C2×#389—111no—
374C2×#387—112no—
375C2×#384—111no—
376C2×C4×C4⋊C4—111no—
377C2×C4×C4⋊C4—111no—
378C23×C11C2511yescharacteristic
379C22×D11C22×Q812yes—
380C22×D11C22×Q812yes—
381C22×D11C2×#4112yes—
382C22×D11C2×#4112yes—
383C22×D11C2×#4112yes—
384C22×D11H(5,𝔽2)12yes—
385C22×D11H(5,𝔽2)12yes—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—21no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11C22×Q814yes—
412C2×C4×C11C22×Q812yes—
413C2×C4×C11C22×Q812yes—
414C2×C4×C11C22×Q812yes—
415C2×C4×C11C22×Q812yes—
416C2×C4×C11C2×#4112yes—
417C2×C4×C11C2×#4112yes—
418C2×C4×C11C2×#4112yes—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—22no—
425C2×Dic11—21no—
426C2×Dic11—22no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—21no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—21no—
442C2×Dic11—22no—
443C2×Dic11—21no—
444C2×Dic11C22×Q812yes—
445C2×Dic11C22×Q814yes—
446C2×Dic11C22×Q812yes—
447C2×Dic11C22×Q812yes—
448C2×Dic11C22×Q812yes—
449C2×Dic11C2×#4112yes—
450C2×Dic11C2×#4112yes—
451C2×Dic11C2×#4112yes—
452C4×D11—28no—
453C4×D11—28no—
454C4×D11—28no—
455C4×D11—28no—
456C4×D11—216no—
457C4×D11—44no—
458C4×D11—48no—
459C4×D11—48no—
460C4×D11—44no—
461C4×D11—48no—
462C4×D11#125116yes—
463C22×C4⋊C4—111no—
464C22×C4⋊C4—111no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4—112no—
467C22×C4⋊C4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4—112no—
471C22×C4⋊C4—112no—
472C22×C4⋊C4—112no—
473C22×C4⋊C4—112no—
474C22×C4⋊C4—112no—
475C22×C42—111no—
476C22×C42—111no—
477C22×C42—111no—
478C22×C42—112no—
479#398—112no—
480#398—112no—
481#398—112no—
482#398—112no—
483#398—112no—
484#398—112no—
485#398—112no—
486#398—112no—
487#398—112no—
488#398—112no—
489#398—112no—
490#398—112no—
491#398—112no—
492#398—112no—
493#398C2×D1112yes—
494#398C2×D1112yes—
495#389—112no—
496#389—112no—
497#389—112no—
498#389—112no—
499#389—112no—
500#389—112no—
501#389—112no—
502#389—111no—
503#389—111no—
504#389—111no—
505#389—111no—
506#389—112no—
507#389—111no—
508#389—111no—
509#389—111no—
510#389—111no—
511#389—112no—
512#389—111no—
513#389—111no—
514#389—111no—
515#389—111no—
516#389—112no—
517#389—112no—
518#389—112no—
519#389—112no—
520#389—112no—
521#389—112no—
522#389C2×D1112yes—
523#389C2×D1111yescharacteristic
524#389C2×D1111yescharacteristic
525#389C2×D1111yescharacteristic
526#389C2×D1111yescharacteristic
527#387—112no—
528#387—112no—
529#387—112no—
530#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387C2×D1112yes—
535#384—112no—
536#384—112no—
537#384—111no—
538#384—111no—
539#384—111no—
540#384C2×D1111yescharacteristic
541C4×C4⋊C4—111no—
542C4×C4⋊C4—111no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—111no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4C2×D1111yescharacteristic
554C4×C4⋊C4C2×D1111yescharacteristic
555C2×#95—111no—
556C2×#95—112no—
557C2×#95—112no—
558C2×#95—112no—
559C2×#95—112no—
560C2×#95—111no—
561C2×#95—112no—
562C22×C11C23×Q811yescharacteristic
563C22×C11C23×Q811yescharacteristic
564C22×C11C22×#4111yescharacteristic
565C22×C11C22×#4111yescharacteristic
566C22×C11C22×#4111yescharacteristic
567C22×C11C2×H(5,𝔽2)11yescharacteristic
568C22×C11C2×H(5,𝔽2)11yescharacteristic
569C2×D11C2×#12514yes—
570C2×D11#53314yes—
571C2×D11#54014yes—
572C2×D11#55314yes—
573C2×D11#55414yes—
574C2×D11#55414yes—
575C2×D11Q8214yes—
576C4×C11—22no—
577C4×C11—22no—
578C4×C11—22no—
579C4×C11—22no—
580C4×C11—24no—
581C4×C11—41no—
582C4×C11—42no—
583C4×C11—42no—
584C4×C11—41no—
585C4×C11—42no—
586C4×C11C2×#12514yes—
587Dic11—22no—
588Dic11—22no—
589Dic11—22no—
590Dic11—22no—
591Dic11—24no—
592Dic11—41no—
593Dic11—42no—
594Dic11—42no—
595Dic11—41no—
596Dic11—42no—
597Dic11C2×#12514yes—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4—112no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—112no—
605C23×C4—112no—
606C23×C4—111no—
607C23×C4—112no—
608C23×C4—111no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—118no—
615C2×C4⋊C4—118no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—224no—
644C2×C4⋊C4—224no—
645C2×C4⋊C4—224no—
646C2×C4⋊C4—224no—
647C2×C4⋊C4—228no—
648C2×C4⋊C4—444no—
649C2×C4⋊C4—444no—
650C2×C4⋊C4—444no—
651C2×C4⋊C4—444no—
652C2×C4⋊C4—444no—
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C4⋊C4C22×D1111yescharacteristic
656C2×C4⋊C4C22×D1111yescharacteristic
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1112yes—
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1112yes—
662C2×C4⋊C4C22×D1112yes—
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—111no—
671C2×C42—111no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—112no—
675C2×C42—112no—
676C2×C42—112no—
677C2×C42—224no—
678C2×C42—224no—
679C2×C42—224no—
680C2×C42—444no—
681C2×C42C22×D1111yescharacteristic
682C2×C42C22×D1111yescharacteristic
683C2×C42C22×D1111yescharacteristic
684C2×C42C22×D1112yes—
685#95—111no—
686#95—111no—
687#95—111no—
688#95—111no—
689#95—112no—
690#95—112no—
691#95—111no—
692#95—111no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95C22×D1111yescharacteristic
707#95C22×D1111yescharacteristic
708#95C22×D1112yes—
709#95C22×D1112yes—
710#95C22×D1112yes—
711#95C22×D1112yes—
712#95C22×D1112yes—
713C2×C11C22×#12511yescharacteristic
714C2×C11C2×#53311yescharacteristic
715C2×C11C2×#54011yescharacteristic
716C2×C11C2×#55311yescharacteristic
717C2×C11C2×#55411yescharacteristic
718C2×C11C2×#55411yescharacteristic
719C2×C11C2×Q8211yescharacteristic
720D11#250718yesdirect product factor
721C24—111no—
722C22×C4—111no—
723C22×C4—114no—
724C22×C4—114no—
725C22×C4—114no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—112no—
730C22×C4—111no—
731C22×C4—118no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—111no—
737C22×C4—112no—
738C22×C4—111no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—224no—
747C22×C4—224no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—224no—
754C22×C4—224no—
755C22×C4—224no—
756C22×C4—224no—
757C22×C4—224no—
758C22×C4—222no—
759C22×C4—224no—
760C22×C4—224no—
761C22×C4—224no—
762C22×C4—222no—
763C22×C4—224no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1112yes—
768C22×C4C23×D1111yescharacteristic
769C22×C4C23×D1112yes—
770C22×C4C23×D1112yes—
771C22×C4C23×D1111yescharacteristic
772C22×C4C23×D1111yescharacteristic
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1112yes—
775C22×C4C23×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C4⋊C4—22no—
778C4⋊C4—24no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—42no—
783C4⋊C4—42no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4—118no—
788C4⋊C4—114no—
789C4⋊C4—114no—
790C4⋊C4—114no—
791C4⋊C4—114no—
792C4⋊C4—224no—
793C4⋊C4—224no—
794C4⋊C4—224no—
795C4⋊C4—222no—
796C4⋊C4—224no—
797C4⋊C4—222no—
798C4⋊C4—224no—
799C4⋊C4—222no—
800C4⋊C4—224no—
801C4⋊C4—222no—
802C4⋊C4—222no—
803C4⋊C4—222no—
804C4⋊C4—442no—
805C4⋊C4—442no—
806C4⋊C4—442no—
807C4⋊C4—442no—
808C4⋊C4—442no—
809C4⋊C4—442no—
810C4⋊C4—442no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4—442no—
817C4⋊C4—442no—
818C4⋊C4—442no—
819C4⋊C4Q8×D1114yes—
820C4⋊C4Q8×D1114yes—
821C42—22no—
822C42—22no—
823C42—22no—
824C42—42no—
825C42—222no—
826C42—222no—
827C42—222no—
828C42—222no—
829C42—222no—
830C42—222no—
831C42—222no—
832C42—222no—
833C42—222no—
834C42—442no—
835C42—442no—
836C42—442no—
837C11C2×#250711yescharacteristic, complemented, Sylow
838C23—112no—
839C23—112no—
840C23—112no—
841C23—112no—
842C23—112no—
843C23—112no—
844C23—112no—
845C23C24×D1111yescharacteristic
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—1116no—
875C2×C4—114no—
876C2×C4—112no—
877C2×C4—112no—
878C2×C4—112no—
879C2×C4—112no—
880C2×C4—228no—
881C2×C4—228no—
882C2×C4—228no—
883C2×C4—2216no—
884C2×C4—228no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—222no—
890C2×C4—221no—
891C2×C4—221no—
892C2×C4—222no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—222no—
898C2×C4—221no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—221no—
905C2×C4—222no—
906C2×C4—221no—
907C2×C4—222no—
908C2×C4—221no—
909C2×C4—222no—
910C2×C4—444no—
911C2×C4—448no—
912C2×C4—444no—
913C2×C4—448no—
914C2×C4—448no—
915C2×C4C2×Q8×D1114yes—
916C2×C4C2×Q8×D1112yes—
917C2×C4C2×Q8×D1112yes—
918C2×C4C2×Q8×D1112yes—
919C2×C4C2×Q8×D1112yes—
920C2×C4#41×D1112yes—
921C2×C4#41×D1112yes—
922C2×C4#41×D1112yes—
923C22—114no—
924C22—114no—
925C22—114no—
926C22—114no—
927C22—114no—
928C22—114no—
929C22—114no—
930C22C22×Q8×D1111yescharacteristic
931C22C22×Q8×D1111yescharacteristic
932C22C2×#41×D1111yescharacteristic
933C22C2×#41×D1111yescharacteristic
934C22C2×#41×D1111yescharacteristic
935C22D11×H(5,𝔽2)11yescharacteristic
936C22D11×H(5,𝔽2)11yescharacteristic
937C4—22no—
938C4—22no—
939C4—22no—
940C4—24no—
941C4—22no—
942C4—41no—
943C4—42no—
944C4—41no—
945C4—42no—
946C4—42no—
947C4—114no—
948C4—222no—
949C4—222no—
950C4—222no—
951C4—224no—
952C4—222no—
953C4—441no—
954C4—442no—
955C4—441no—
956C4—442no—
957C4—442no—
958C4D11×#12514yes—
959C2—118no—
960C2C2×D11×#12511yescharacteristic
961C2D11×#53311yescharacteristic
962C2D11×#54011yescharacteristic
963C2D11×#55311yescharacteristic
964C2D11×#55411yescharacteristic
965C2D11×#55411yescharacteristic
966C2Q82×D1111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2507C2
prime radicalC23×D11C24
hypercenter#2507D11
hypocenterC11C2×#2507
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2507

Complements

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

NH ≅ G/Ntype
1. #13073146C2semidirect
2. #13073145C2semidirect
3. #13073144C2semidirect
4. #13073143C2semidirect
5. #13073142C2semidirect
6. #13073141C2semidirect
7. #13073140C2semidirect
8. #13073139C2semidirect
9. #13073138C2semidirect
10. #13073137C2semidirect
11. #13073136C2semidirect
23. C11×#2507C2semidirect
366. #2507D11direct (N × H)
720. D11#2507direct (N × H)
837. C11C2×#2507semidirect

Maximal subgroups

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

subgroupindex
#130731462
#130731452
#130731442
#130731432
#130731422
#130731412
#130731402
#130731392
#130731382
#130731372
#130731362
D11×#3982
D11×#3892
D11×#3872
D11×#3842
C4×C4⋊C4×D112
C11×#25072
C2×#250711