Finite Group Databasebeta

← #14677229

Subgroups — #14677229

Order 2816.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic, complemented
4C2×#10622833C211yesmaximal, characteristic, complemented
5C2×#10622833C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066865C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066857C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C22×C11×#121C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C2×C11×#121—24no—
24C2×C11×#121—24no—
25C2×C11×#121C418yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C2×D4×Dic11—24no—
39C2×D4×Dic11—24no—
40C2×D4×Dic11—24no—
41C22×C4⋊Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43#10622833—24no—
44#10622833—24no—
45#10622833—24no—
46#10622833—24no—
47C2×C11⋊#95—24no—
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C25×C11C2311yescharacteristic
63C25×C11C2311yescharacteristic
64C25×C11C2311yescharacteristic
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—22no—
71C22×D4×C11—22no—
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11C2×C414yes—
82C22×D4×C11C2×C414yescomplemented
83C22×D4×C11C2×C414yescomplemented
84C22×D4×C11D414yes—
85C22×D4×C11D414yes—
86C23×C4×C11—22no—
87C23×C4×C11—22no—
88C23×C4×C11—22no—
89C23×C4×C11—22no—
90C23×C4×C11—41no—
91C23×C4×C11—41no—
92C23×C4×C11C2×C414yescomplemented
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×Dic11—22no—
98C23×Dic11—22no—
99C23×Dic11—22no—
100C23×Dic11—22no—
101C23×Dic11—22no—
102C23×Dic11—22no—
103C23×Dic11—22no—
104C23×Dic11—22no—
105C23×Dic11—22no—
106C23×Dic11—22no—
107C23×Dic11—22no—
108C23×Dic11—22no—
109C23×Dic11—22no—
110C23×Dic11—22no—
111C23×Dic11—41no—
112C23×Dic11—41no—
113C23×Dic11—41no—
114C23×Dic11—41no—
115C23×Dic11—41no—
116C23×Dic11—41no—
117C23×Dic11D414yescomplemented
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2311yescharacteristic
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C11×#121—232no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4C2×C414yescomplemented
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—22no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4C2×C414yescomplemented
135C2×C11×C22⋊C4C2×C414yescomplemented
136C2×C22⋊Dic11—22no—
137C2×C22⋊Dic11—22no—
138C2×C22⋊Dic11—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—22no—
141C2×C22⋊Dic11—22no—
142C2×C22⋊Dic11—22no—
143C2×C22⋊Dic11—22no—
144C2×C22⋊Dic11—22no—
145C2×C22⋊Dic11—22no—
146C2×C22⋊Dic11—22no—
147C2×C22⋊Dic11—22no—
148C2×C22⋊Dic11—22no—
149C2×C22⋊Dic11—22no—
150C2×C22⋊Dic11—22no—
151C2×C22⋊Dic11—22no—
152C2×C22⋊Dic11—22no—
153C2×C22⋊Dic11—22no—
154C2×C22⋊Dic11—22no—
155C2×C22⋊Dic11—22no—
156C2×C22⋊Dic11—41no—
157C2×C22⋊Dic11—41no—
158C2×C22⋊Dic11—41no—
159C2×C22⋊Dic11—41no—
160C2×C22⋊Dic11—41no—
161C2×C22⋊Dic11—41no—
162C2×C22⋊Dic11D414yescomplemented
163D4×Dic11—232no—
164C2×C4⋊Dic11—22no—
165C2×C4⋊Dic11—22no—
166C2×C4⋊Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169C2×C4×Dic11—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—41no—
182C11⋊#95—41no—
183C11⋊#95D414yescomplemented
184#14023—111nomaximal, Sylow
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11—21no—
207C24×C11—21no—
208C24×C11—21no—
209C24×C11—21no—
210C24×C11—21no—
211C24×C11—21no—
212C24×C11—21no—
213C24×C11—21no—
214C24×C11—21no—
215C24×C11—21no—
216C24×C11—21no—
217C24×C11—21no—
218C24×C11—21no—
219C24×C11C22×C412yes—
220C24×C11C22×C412yes—
221C24×C11C22×C412yes—
222C24×C11C2×D412yes—
223C24×C11C2×D412yes—
224C24×C11C2×D412yes—
225C24×C11C2×D412yes—
226C24×C11C2×D412yes—
227C24×C11C2×D412yes—
228C24×C11#4112yes—
229C24×C11#4112yes—
230C24×C11C2411yescharacteristic
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—28no—
236C2×D4×C11—28no—
237C2×D4×C11—28no—
238C2×D4×C11—28no—
239C2×D4×C11—28no—
240C2×D4×C11—28no—
241C2×D4×C11—28no—
242C2×D4×C11—44no—
243C2×D4×C11—44no—
244C2×D4×C11—44no—
245C2×D4×C11—44no—
246C2×D4×C11—44no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11C22⋊C4116yescomplemented
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×C11—21no—
260C22×C4×C11—28no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—28no—
274C22×C4×C11—44no—
275C22×C4×C11—44no—
276C22×C4×C11—44no—
277C22×C4×C11—44no—
278C22×C4×C11—44no—
279C22×C4×C11C22×C412yes—
280C22×C4×C11C22×C412yes—
281C22×C4×C11C22×C412yes—
282C22×C4×C11C22×C412yes—
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11#4112yes—
287C22×Dic11—28no—
288C22×Dic11—28no—
289C22×Dic11—28no—
290C22×Dic11—28no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—21no—
335C22×Dic11—21no—
336C22×Dic11—21no—
337C22×Dic11—21no—
338C22×Dic11—21no—
339C22×Dic11—44no—
340C22×Dic11—44no—
341C22×Dic11—44no—
342C22×Dic11—44no—
343C22×Dic11—44no—
344C22×Dic11—44no—
345C22×Dic11—44no—
346C22×Dic11—44no—
347C22×Dic11—44no—
348C22×Dic11—44no—
349C22×Dic11—44no—
350C22×Dic11—44no—
351C22×Dic11—44no—
352C22×Dic11—44no—
353C22×Dic11—44no—
354C22×Dic11—44no—
355C22×Dic11—44no—
356C22×Dic11C2×D412yes—
357C22×Dic11C2×D412yes—
358C22×Dic11C2×D412yes—
359C22×Dic11C2×D412yes—
360C22×Dic11C2×D412yes—
361C22×Dic11C2×D412yes—
362C22×Dic11#4112yes—
363C22×Dic11#4112yes—
364C11×C4⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—28no—
367C22⋊Dic11—28no—
368C22⋊Dic11—28no—
369C22⋊Dic11—44no—
370C22⋊Dic11—44no—
371C22⋊Dic11—44no—
372C22⋊Dic11—44no—
373C22⋊Dic11—44no—
374C22⋊Dic11—44no—
375C22⋊Dic11—44no—
376C4⋊Dic11—28no—
377C4×Dic11—28no—
378C22×#121D1111yescharacteristic
379C22×C4×D4—111no—
380C2×#386—111no—
381C2×#386—111no—
382C2×#386—111no—
383C2×#386—111no—
384C22×#95—111no—
385#1441—111no—
386#1440—111no—
387#1439—111no—
388#1438—111no—
389#1437—111no—
390#1436—111no—
391C22⋊#95—111no—
392C22⋊#95—111no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11—41no—
458C23×C11—41no—
459C23×C11—41no—
460C23×C11—41no—
461C23×C11—41no—
462C23×C11—41no—
463C23×C11—41no—
464C23×C11—41no—
465C23×C11—41no—
466C23×C11—41no—
467C23×C11—41no—
468C23×C11—41no—
469C23×C11—41no—
470C23×C11—41no—
471C23×C11—41no—
472C23×C11—41no—
473C23×C11—41no—
474C23×C11—41no—
475C23×C11—41no—
476C23×C11—41no—
477C23×C11—41no—
478C23×C11—41no—
479C23×C11—41no—
480C23×C11—41no—
481C23×C11—41no—
482C23×C11—41no—
483C23×C11—41no—
484C23×C11—41no—
485C23×C11—41no—
486C23×C11—41no—
487C23×C11—41no—
488C23×C11—41no—
489C23×C11—41no—
490C23×C11C2×C22⋊C414yes—
491C23×C11C2×C22⋊C414yes—
492C23×C11C4×D414yes—
493C23×C11C4×D414yes—
494C23×C11#12014yes—
495C23×C11#12114yes—
496C23×C11#12114yes—
497C23×C11#12314yes—
498C23×C11C23×C411yescharacteristic
499C23×C11C22×D411yescharacteristic
500C23×C11C22×D411yescharacteristic
501C23×C11C22×D411yescharacteristic
502C23×C11C22×D411yescharacteristic
503C23×C11C22×D411yescharacteristic
504C23×C11C2×#4111yescharacteristic
505C23×C11C2×#4111yescharacteristic
506C23×C11C2×#4111yescharacteristic
507C23×C11C2×#4111yescharacteristic
508C23×C11C2×#4111yescharacteristic
509C23×C11H(5,𝔽2)11yescharacteristic
510C23×C11H(5,𝔽2)11yescharacteristic
511C23×C11H(5,𝔽2)11yescharacteristic
512C23×C112−1+411yescharacteristic
513D4×C11—232no—
514D4×C11—416no—
515D4×C11—416no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—416no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11C2×C22⋊C414yes—
544C2×C4×C11C4×D414yescomplemented
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—416no—
567C2×Dic11—416no—
568C2×Dic11—416no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—41no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11—41no—
599C2×Dic11—41no—
600C2×Dic11—41no—
601C2×Dic11—41no—
602C2×Dic11—41no—
603C2×Dic11#12114yescomplemented
604C23×D4C2×D1111yescharacteristic
605C23×D4C2×D1111yescharacteristic
606C23×D4C2×D1111yescharacteristic
607C24×C4—111no—
608C24×C4—111no—
609C24×C4—111no—
610C24×C4C2×D1111yescharacteristic
611C2×#121—24no—
612C2×#121—24no—
613C2×#121Dic1118yescomplemented
614C2×C4×D4—224no—
615C2×C4×D4—224no—
616C2×C4×D4—224no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4C2×D1111yescharacteristic
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42—111no—
631#386—224no—
632#386—224no—
633#386—224no—
634#386—224no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—111no—
646C2×#95—111no—
647C2×#95—111no—
648C2×#95—111no—
649C2×#95—224no—
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—81no—
687C22×C11—81no—
688C22×C11—81no—
689C22×C11—81no—
690C22×C11—81no—
691C22×C11—81no—
692C22×C11—81no—
693C22×C11—81no—
694C22×C11#38618yescomplemented
695C22×C11C22×C22⋊C411yescharacteristic
696C22×C11C2×C4×D411yescharacteristic
697C22×C11C2×C4×D411yescharacteristic
698C22×C11C2×C4×D411yescharacteristic
699C22×C11C4×#4111yescharacteristic
700C22×C11#51811yescharacteristic
701C22×C11#52011yescharacteristic
702C22×C11C2×#12011yescharacteristic
703C22×C11C2×#12111yescharacteristic
704C22×C11C2×#12111yescharacteristic
705C22×C11C2×#12111yescharacteristic
706C22×C11C2×#12311yescharacteristic
707C22×C11#52511yescharacteristic
708C22×C11#52911yescharacteristic
709C22×C11#53211yescharacteristic
710C22×C11#53411yescharacteristic
711C22×C11#53711yescharacteristic
712C22×C11#53811yescharacteristic
713C22×C11#53911yescharacteristic
714C22×C11D4211yescharacteristic
715C22×C11D4211yescharacteristic
716C22×C11D4211yescharacteristic
717C22×C11#54611yescharacteristic
718C22×C11#54611yescharacteristic
719C22×C11#54611yescharacteristic
720C22×C11#54611yescharacteristic
721C22×C11#54611yescharacteristic
722C22×C11#54611yescharacteristic
723C22×C11#54711yescharacteristic
724C22×C11#54711yescharacteristic
725C22×C11#54711yescharacteristic
726C22×C11#54811yescharacteristic
727C22×C11#55311yescharacteristic
728C22×C11#55311yescharacteristic
729C22×C11#55311yescharacteristic
730C4×C11—24no—
731C4×C11—24no—
732C4×C11—42no—
733C4×C11—42no—
734Dic11—24no—
735Dic11—42no—
736Dic11—42no—
737Dic11—42no—
738Dic11—42no—
739Dic11—42no—
740Dic11—81no—
741Dic11—81no—
742C25C22×D1111yescharacteristic
743C25C22×D1111yescharacteristic
744C25C22×D1111yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×Dic1114yes—
762C22×D4C2×Dic1114yescomplemented
763C22×D4C2×Dic1114yescomplemented
764C22×D4C22⋊D1114yes—
765C22×D4C22⋊D1114yes—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—41no—
771C23×C4—41no—
772C23×C4—111no—
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—114no—
779C23×C4—111no—
780C23×C4—111no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—222no—
793C23×C4—222no—
794C23×C4—222no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4—441no—
800C23×C4—441no—
801C23×C4C2×Dic1114yescomplemented
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—232no—
807C4×D4—2232no—
808C2×C4⋊C4—22no—
809C2×C4⋊C4—22no—
810C2×C4⋊C4—222no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4C2×Dic1114yescomplemented
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—114no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—222no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—441no—
840C2×C22⋊C4—441no—
841C2×C22⋊C4—441no—
842C2×C22⋊C4—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4C2×Dic1114yescomplemented
846C2×C22⋊C4C2×Dic1114yescomplemented
847C2×C42—222no—
848C2×C42—222no—
849C2×C42—222no—
850#95—114no—
851#95—222no—
852#95—222no—
853#95—222no—
854#95—222no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—441no—
863#95—441no—
864C2×C11—28no—
865C2×C11—44no—
866C2×C11—82no—
867C2×C11C2×#38611yescharacteristic
868C2×C11C4×#12111yescharacteristic
869C2×C11#232511yescharacteristic
870C2×C11D4×C22⋊C411yescharacteristic
871C2×C11#233911yescharacteristic
872C2×C11#236111yescharacteristic
873C2×C11#236411yescharacteristic
874C2×C11#241011yescharacteristic
875C2×C11#241611yescharacteristic
876C2×C11#242411yescharacteristic
877C2×C11#242511yescharacteristic
878C2×C11#243011yescharacteristic
879C2×C11#244311yescharacteristic
880C2×C11#244411yescharacteristic
881C2×C11#254311yescharacteristic
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—21no—
910C24—21no—
911C24—21no—
912C24—21no—
913C24—21no—
914C24—21no—
915C24—21no—
916C24D4×D1112yes—
917C24D4×D1112yes—
918C24#434112yes—
919C24#434112yes—
920C24C22×Dic1112yes—
921C24C22×Dic1112yes—
922C24C22×Dic1112yes—
923C24C2×C22⋊D1112yes—
924C24C2×C22⋊D1112yes—
925C24C2×C22⋊D1112yes—
926C24C2×C22⋊D1112yes—
927C24C23×D1111yescharacteristic
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4C22⋊Dic11116yescomplemented
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—28no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—28no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—112no—
977C22×C4—112no—
978C22×C4—112no—
979C22×C4—112no—
980C22×C4—112no—
981C22×C4—112no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—228no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—228no—
990C22×C4—228no—
991C22×C4—228no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4—444no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4D4×D1112yes—
1054C22×C4#434112yes—
1055C22×C4C22×Dic1112yes—
1056C22×C4C22×Dic1112yes—
1057C22×C4C22×Dic1112yes—
1058C22×C4C22×Dic1112yes—
1059C22×C4C2×C22⋊D1112yes—
1060C22×C4C2×C22⋊D1112yes—
1061C4⋊C4—28no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—228no—
1066C22⋊C4—228no—
1067C22⋊C4—444no—
1068C22⋊C4—444no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—228no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23D4×Dic1114yes—
1174C23D4×Dic1114yes—
1175C23#6698814yes—
1176C23#6699014yes—
1177C23#6699214yes—
1178C23#6699214yes—
1179C23C2×C22⋊Dic1114yes—
1180C23C2×C22⋊Dic1114yes—
1181C23C2×D4×D1111yescharacteristic
1182C23C2×D4×D1111yescharacteristic
1183C23C2×D4×D1111yescharacteristic
1184C23C2×#434111yescharacteristic
1185C23C2×#434111yescharacteristic
1186C23C2×#434111yescharacteristic
1187C23#6703711yescharacteristic
1188C23#6703711yescharacteristic
1189C23#41×D1111yescharacteristic
1190C23#41×D1111yescharacteristic
1191C23#6704211yescharacteristic
1192C23#6704311yescharacteristic
1193C23C23×Dic1111yescharacteristic
1194C23C22×C22⋊D1111yescharacteristic
1195C23C22×C22⋊D1111yescharacteristic
1196D4—232no—
1197D4—416no—
1198D4—416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—114no—
1227C2×C4—222no—
1228C2×C4—222no—
1229C2×C4—222no—
1230C2×C4—222no—
1231C2×C4—222no—
1232C2×C4—222no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—222no—
1238C2×C4—222no—
1239C2×C4—222no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—222no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—4416no—
1249C2×C4—4416no—
1250C2×C4—4416no—
1251C2×C4—441no—
1252C2×C4—441no—
1253C2×C4—441no—
1254C2×C4—441no—
1255C2×C4—441no—
1256C2×C4—441no—
1257C2×C4—441no—
1258C2×C4—441no—
1259C2×C4—441no—
1260C2×C4—441no—
1261C2×C4—441no—
1262C2×C4—441no—
1263C2×C4—441no—
1264C2×C4—441no—
1265C2×C4—441no—
1266C2×C4—441no—
1267C2×C4—441no—
1268C2×C4—441no—
1269C2×C4—441no—
1270C2×C4—441no—
1271C2×C4—441no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4D4×Dic1114yescomplemented
1286C2×C4C2×C22⋊Dic1114yes—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22#1062283318yescomplemented
1332C22#1062312711yescharacteristic
1333C22#1062312811yescharacteristic
1334C22#1062312911yescharacteristic
1335C22#1062313111yescharacteristic
1336C22#1062313211yescharacteristic
1337C22#1062313211yescharacteristic
1338C22#1062313311yescharacteristic
1339C22D11×#12111yescharacteristic
1340C22#1062313611yescharacteristic
1341C22#1062313711yescharacteristic
1342C22#1062314011yescharacteristic
1343C22#1062314111yescharacteristic
1344C22#1062314111yescharacteristic
1345C22#1062314211yescharacteristic
1346C22#1062314811yescharacteristic
1347C22#1062314911yescharacteristic
1348C22C2×D4×Dic1111yescharacteristic
1349C22C2×D4×Dic1111yescharacteristic
1350C22C2×D4×Dic1111yescharacteristic
1351C22C2×#6698811yescharacteristic
1352C22#1062332911yescharacteristic
1353C22C2×#6699011yescharacteristic
1354C22D4×C22⋊D1111yescharacteristic
1355C22D4×C22⋊D1111yescharacteristic
1356C22C2×#6699211yescharacteristic
1357C22C2×#6699211yescharacteristic
1358C22#1062333711yescharacteristic
1359C22#1062333711yescharacteristic
1360C22#1062335511yescharacteristic
1361C22#1062335511yescharacteristic
1362C22#41×Dic1111yescharacteristic
1363C22#1062335811yescharacteristic
1364C22#1062336011yescharacteristic
1365C22#1062336011yescharacteristic
1366C22C22×C22⋊Dic1111yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—224no—
1372C4—442no—
1373C4—442no—
1374C4—442no—
1375C4—442no—
1376C4—442no—
1377C4—881no—
1378C4—881no—
1379C2—28no—
1380C2—44no—
1381C2—82no—
1382C2C2×#1062283311yescharacteristic
1383C2#121×Dic1111yescharacteristic
1384C2#1307132111yescharacteristic
1385C2D4×C22⋊Dic1111yescharacteristic
1386C2#1307144611yescharacteristic
1387C2#1307163611yescharacteristic
1388C2#1307166811yescharacteristic
1389C2#1307198711yescharacteristic
1390C2#1307205311yescharacteristic
1391C2#1307215811yescharacteristic
1392C2#1307217311yescharacteristic
1393C2#1307222211yescharacteristic
1394C2#1307234711yescharacteristic
1395C2#1307236211yescharacteristic
1396C2#1307357411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#121C2
socle, cosocleC24×C11C24
hypercenterC22×#121D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. C2×#10622833C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622833C2semidirect
5. C2×#10622833C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066869C2semidirect
8. #13066865C2semidirect
9. #13066861C2semidirect
10. #13066857C2semidirect
11. #13066853C2semidirect
12. #13066848C2semidirect
13. #13066839C2semidirect
14. #13066838C2semidirect
25. C2×C11×#121C4semidirect
82. C22×D4×C11C2×C4semidirect
83. C22×D4×C11C2×C4semidirect
92. C23×C4×C11C2×C4semidirect
117. C23×Dic11D4semidirect
129. C2×C11×C4⋊C4C2×C4semidirect
134. C2×C11×C22⋊C4C2×C4semidirect
135. C2×C11×C22⋊C4C2×C4semidirect
162. C2×C22⋊Dic11D4semidirect
183. C11⋊#95D4semidirect
251. C2×D4×C11C22⋊C4semidirect
544. C2×C4×C11C4×D4semidirect
603. C2×Dic11#121semidirect
613. C2×#121Dic11semidirect
694. C22×C11#386semidirect
762. C22×D4C2×Dic11semidirect
763. C22×D4C2×Dic11semidirect
801. C23×C4C2×Dic11semidirect
813. C2×C4⋊C4C2×Dic11semidirect
845. C2×C22⋊C4C2×Dic11semidirect
846. C2×C22⋊C4C2×Dic11semidirect
948. C2×D4C22⋊Dic11semidirect
1075. C11#14023semidirect
1285. C2×C4D4×Dic11semidirect
1331. C22#10622833semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228332
C22×C11⋊#952
#130668692
#130668652
#130668612
#130668572
#130668532
#130668482
#130668392
#130668382
C22×C11×#1212
#1402311