Finite Group Databasebeta

← #14683114

Subgroups — #14683114

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622278C211yesmaximal, characteristic, complemented
7C2×#10622602C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066841C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622602—24no—
52#10622601—24no—
53#10622284C418yescomplemented
54#10622278—24no—
55#10622278—24no—
56#10622278—24no—
57#10622278—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44—22no—
82C22×D44—22no—
83C22×D44—41no—
84C22×D44—41no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44—41no—
90C22×D44—41no—
91C22×D44C2×C414yes—
92C22×D44C2×C414yescomplemented
93C22×D44C2×C414yescomplemented
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—41no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4C2×C414yescomplemented
146C2×(C2×D11)⋊C4C2×C414yescomplemented
147C2×(C2×D11)⋊C4C2×C414yescomplemented
148C2×(C2×D11)⋊C4D414yescomplemented
149C2×(C2×D11)⋊C4D414yescomplemented
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—41no—
152C2×Dic11⋊C4—41no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—41no—
156C11×#95—22no—
157C11×#95—22no—
158C11×#95—22no—
159C11×#95—22no—
160C11×#95—41no—
161C11×#95C2×C414yescomplemented
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95D414yescomplemented
170#14519—111nomaximal, Sylow
171C24×C11C2411yescharacteristic
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11C22×C412yes—
211C23×D11C22×C412yes—
212C23×D11C22×C412yes—
213C23×D11C2×D412yes—
214C23×D11C2×D412yes—
215C23×D11#4112yes—
216C23×D11#4112yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11C22×C412yes—
260C22×C4×C11C22×C412yes—
261C22×C4×C11C22×C412yes—
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11#4112yes—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11C22×C412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C2×D44—28no—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—28no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—44no—
310C2×D44—44no—
311C2×D44—44no—
312C2×D44—44no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44—44no—
316C2×D44—44no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C2×C4×D11—44no—
330C2×C4×D11—44no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C11×C4⋊C4—44no—
337(C2×D11)⋊C4—28no—
338(C2×D11)⋊C4—44no—
339(C2×D11)⋊C4—44no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—44no—
349(C2×D11)⋊C4—44no—
350Dic11⋊C4—44no—
351C4×Dic11—44no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#386—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#386—111no—
358C2×#385—111no—
359#1442D1111yescharacteristic, complemented
360#1440—111no—
361#1439—111no—
362#1439—111no—
363#1438—111no—
364#1437—111no—
365#1434—111no—
366C22⋊#95—111no—
367C23×C11C23×C411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C2×#4111yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11H(5,𝔽2)11yescharacteristic
375C23×C11H(5,𝔽2)11yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C11H(5,𝔽2)11yescharacteristic
379C23×C11H(5,𝔽2)11yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C112−1+411yescharacteristic
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11C4×D414yes—
486C22×D11C4×D414yes—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11C4×D414yes—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571D44—416no—
572D44—416no—
573D44—416no—
574C4×D11—416no—
575C4×D11—416no—
576C23×D4—111no—
577C23×D4—111no—
578C23×D4—111no—
579C24×C4—111no—
580C24×C4—111no—
581C22×C4⋊C4—111no—
582C22×C4⋊C4C2×D1111yescharacteristic
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C42—111no—
597#392—118no—
598#390—224no—
599#386—224no—
600#386—224no—
601#386—224no—
602#386—224no—
603#385—224no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95C2×D1111yescharacteristic
613C2×#95C2×D1111yescharacteristic
614C2×#95C2×D1111yescharacteristic
615C2×#95C2×D1111yescharacteristic
616C2×#95C2×D1111yescharacteristic
617C2×#95C2×D1111yescharacteristic
618C22×C11C2×C4×D411yescharacteristic
619C22×C11C2×C4×D411yescharacteristic
620C22×C11C2×C4×D411yescharacteristic
621C22×C11#51811yescharacteristic
622C22×C11#51811yescharacteristic
623C22×C11#51811yescharacteristic
624C22×C11#52011yescharacteristic
625C22×C11#53411yescharacteristic
626C22×C11#53411yescharacteristic
627C22×C11#53511yescharacteristic
628C22×C11#53511yescharacteristic
629C22×C11#53511yescharacteristic
630C22×C11#53711yescharacteristic
631C22×C11#53811yescharacteristic
632C22×C11#53811yescharacteristic
633C22×C11#53811yescharacteristic
634C22×C11#53911yescharacteristic
635C22×C11#54011yescharacteristic
636C22×C11#54011yescharacteristic
637C22×C11D4211yescharacteristic
638C22×C11D4211yescharacteristic
639C22×C11D4211yescharacteristic
640C22×C11#54611yescharacteristic
641C22×C11#54611yescharacteristic
642C22×C11#54611yescharacteristic
643C22×C11#54611yescharacteristic
644C22×C11#54711yescharacteristic
645C22×C11#54811yescharacteristic
646C22×C11#55111yescharacteristic
647C22×C11#55111yescharacteristic
648C22×C11#55311yescharacteristic
649C22×C11#56011yescharacteristic
650C22×C11#56011yescharacteristic
651C22×C11#56211yescharacteristic
652C22×C11#56211yescharacteristic
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—24no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C2×D11—81no—
694C2×D11—81no—
695C2×D11—81no—
696C2×D11—81no—
697C2×D11—81no—
698C4×C11—24no—
699C4×C11—42no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—81no—
704C4×C11—81no—
705Dic11—42no—
706Dic11—42no—
707Dic11—42no—
708Dic11—42no—
709Dic11—42no—
710C25—111no—
711C25—111no—
712C25—111no—
713C22×D4—114no—
714C22×D4—114no—
715C22×D4—114no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—222no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4—441no—
730C22×D4—441no—
731C22×D4—441no—
732C22×D4—441no—
733C22×D4—441no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—222no—
740C23×C4—222no—
741C23×C4—222no—
742C23×C4—222no—
743C23×C4—222no—
744C23×C4—222no—
745C23×C4—441no—
746C23×C4—441no—
747C23×C4—441no—
748C23×C4—441no—
749C23×C4—441no—
750C23×C4—441no—
751C23×C4—441no—
752C23×C4—441no—
753C23×C4C22×D1111yescharacteristic
754C23×C4C22×D1111yescharacteristic
755C23×C4C22×D1111yescharacteristic
756C23×C4C22×D1111yescharacteristic
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—222no—
764C2×C4⋊C4—441no—
765C2×C4⋊C4—441no—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—114no—
769C2×C22⋊C4—114no—
770C2×C22⋊C4—114no—
771C2×C22⋊C4—222no—
772C2×C22⋊C4—222no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—441no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C42—222no—
806C2×C42—222no—
807C2×C42—441no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—114no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—441no—
819#95—441no—
820#95—441no—
821#95C4×D1114yescomplemented
822C2×C11#232111yescharacteristic
823C2×C11#232511yescharacteristic
824C2×C11#232811yescharacteristic
825C2×C11#235811yescharacteristic
826C2×C11#235811yescharacteristic
827C2×C11#236111yescharacteristic
828C2×C11#237711yescharacteristic
829C2×C11#266911yescharacteristic
830C2×C11#267111yescharacteristic
831C2×C11#267611yescharacteristic
832C2×C11#267811yescharacteristic
833C2×C11#268811yescharacteristic
834C2×C11#269611yescharacteristic
835C2×C11#270611yescharacteristic
836C2×C11#274911yescharacteristic
837D11—44no—
838D11—44no—
839D11—82no—
840C24—112no—
841C24—112no—
842C24—112no—
843C24—112no—
844C24—112no—
845C24—112no—
846C24—112no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24—221no—
885C24C23×D1111yescharacteristic
886C2×D4—228no—
887C2×D4—228no—
888C2×D4—228no—
889C2×D4—228no—
890C2×D4—228no—
891C2×D4—444no—
892C2×D4—444no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—112no—
950C22×C4—112no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—444no—
985C22×C4—444no—
986C22×C4—444no—
987C22×C4—444no—
988C22×C4—444no—
989C22×C4—444no—
990C22×C4—444no—
991C22×C4—444no—
992C22×C4—444no—
993C22×C4—444no—
994C22×C4—444no—
995C22×C4—444no—
996C22×C4—444no—
997C22×C4—444no—
998C22×C4C2×C4×D1112yes—
999C22×C4C2×C4×D1112yes—
1000C22×C4C2×C4×D1112yes—
1001C22×C4D4×D1112yes—
1002C22×C4D4×D1112yes—
1003C22×C4D4×D1112yes—
1004C22×C4#434312yes—
1005C4⋊C4—44no—
1006C4⋊C4—444no—
1007C22⋊C4—228no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C22⋊C4—444no—
1011C22⋊C4—444no—
1012C22⋊C4—444no—
1013C22⋊C4—444no—
1014C22⋊C4—444no—
1015C22⋊C4—444no—
1016C22⋊C4—444no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C42—444no—
1021C11#1451911yescharacteristic, complemented, Sylow
1022C23—114no—
1023C23—114no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23C22×C4×D1111yescharacteristic
1128C23C2×D4×D1111yescharacteristic
1129C23C2×D4×D1111yescharacteristic
1130C23C2×D4×D1111yescharacteristic
1131C23#6703711yescharacteristic
1132C23C2×#434311yescharacteristic
1133C23#6704011yescharacteristic
1134C23#41×D1111yescharacteristic
1135C23#41×D1111yescharacteristic
1136C23#6704211yescharacteristic
1137C23#6704211yescharacteristic
1138C23#6704211yescharacteristic
1139C23#6704211yescharacteristic
1140C23#6704211yescharacteristic
1141C23#6704211yescharacteristic
1142D4—4416no—
1143D4—4416no—
1144D4—4416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—4416no—
1209C2×C4—4416no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4#6694614yes—
1231C22—224no—
1232C22—224no—
1233C22—224no—
1234C22—224no—
1235C22—224no—
1236C22—224no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—442no—
1248C22—442no—
1249C22—442no—
1250C22—442no—
1251C22—442no—
1252C22—442no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—442no—
1260C22—442no—
1261C22—442no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—881no—
1269C22—881no—
1270C22—881no—
1271C22—881no—
1272C22—881no—
1273C22—881no—
1274C22—881no—
1275C22—881no—
1276C22C2×#6694611yescharacteristic
1277C22#1062305211yescharacteristic
1278C22#1062305211yescharacteristic
1279C22C4×D4×D1111yescharacteristic
1280C22C4×D4×D1111yescharacteristic
1281C22#1062307611yescharacteristic
1282C22#1062310511yescharacteristic
1283C22#1062312111yescharacteristic
1284C22#1062313811yescharacteristic
1285C22#1062314011yescharacteristic
1286C22#1062314011yescharacteristic
1287C22#1062316011yescharacteristic
1288C22#1062316111yescharacteristic
1289C22#1062316411yescharacteristic
1290C22#1062316811yescharacteristic
1291C22#1062317811yescharacteristic
1292C22#1062318411yescharacteristic
1293C22#1062318411yescharacteristic
1294C22#1062318511yescharacteristic
1295C22#1062318511yescharacteristic
1296C22#1062319711yescharacteristic
1297C22#1062320511yescharacteristic
1298C22#1062320511yescharacteristic
1299C22#1062320711yescharacteristic
1300C22#1062320911yescharacteristic
1301C22#1062322311yescharacteristic
1302C22#1062322611yescharacteristic
1303C22#1062322911yescharacteristic
1304C22#1062322911yescharacteristic
1305C22#1062323111yescharacteristic
1306C22#1062323511yescharacteristic
1307C22#1062323511yescharacteristic
1308C22#1062323611yescharacteristic
1309C22#1062324211yescharacteristic
1310C22#1062325711yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—81no—
1317C4—81no—
1318C4—442no—
1319C4—442no—
1320C4—442no—
1321C4—442no—
1322C4—442no—
1323C2—444no—
1324C2—444no—
1325C2—882no—
1326C2#1307127811yescharacteristic
1327C2#1307131511yescharacteristic
1328C2#1307133911yescharacteristic
1329C2#1307159211yescharacteristic
1330C2#1307159411yescharacteristic
1331C2#1307163111yescharacteristic
1332C2#1307177111yescharacteristic
1333C2#1307483211yescharacteristic
1334C2#1307485911yescharacteristic
1335C2#1307491611yescharacteristic
1336C2#1307494011yescharacteristic
1337C2#1307505911yescharacteristic
1338C2#1307515911yescharacteristic
1339C2#1307530611yescharacteristic
1340C2#1307584611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1442D11
hypocenterC11#14519
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622278C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622278C2semidirect
7. C2×#10622602C2semidirect
8. #13066864C2semidirect
9. #13066860C2semidirect
10. #13066860C2semidirect
11. #13066856C2semidirect
12. #13066852C2semidirect
13. #13066841C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1442C2semidirect
53. #10622284C4semidirect
92. C22×D44C2×C4semidirect
93. C22×D44C2×C4semidirect
145. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×(C2×D11)⋊C4C2×C4semidirect
147. C2×(C2×D11)⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4D4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
161. C11×#95C2×C4semidirect
169. C11⋊#95D4semidirect
359. #1442D11semidirect
821. #95C4×D11semidirect
1021. C11#14519semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106226012
C2×#106222782
C2×#106226022
#130668642
#130668602
#130668562
#130668522
#130668412
(C2×D11)⋊#952
C11×#14422
#1451911