Finite Group Databasebeta

← #14679198

Subgroups — #14679198

Order 2816.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622559C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#13066876C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#386—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622835C418yescomplemented
39#10622833—24no—
40C4×C22⋊Dic11—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622559—24no—
56#10622557—24no—
57C22⋊C4×Dic11—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11C2×C414yes—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—41no—
85C23×Dic11—41no—
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4D414yes—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11C2×C414yescomplemented
120C2×C22⋊Dic11C2×C414yescomplemented
121C2×C22⋊Dic11C2×C414yescomplemented
122C2×C22⋊Dic11C2×C414yescomplemented
123C2×C22⋊Dic11D414yes—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4—41no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4C2×C414yescomplemented
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—41no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11—41no—
142C11×#95—22no—
143C11×#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95C2×C414yescomplemented
157C11⋊#95D414yescomplemented
158#14182—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11C22×C412yes—
184C24×C11C22×C412yes—
185C24×C11C2×D412yes—
186C24×C11C2×D412yes—
187C24×C11#4112yes—
188C24×C11#4112yes—
189C24×C11C2411yescharacteristic
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—28no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
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—44no—
228C22×C4×C11—44no—
229C22×C4×C11—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×Dic11—28no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
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—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11—44no—
290C22×Dic11—44no—
291C22×Dic11C22×C412yes—
292C22×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C22×C412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11#4112yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C11×C22⋊C4—28no—
303C11×C22⋊C4—44no—
304C11×C22⋊C4—44no—
305C22⋊Dic11—28no—
306C22⋊Dic11—28no—
307C22⋊Dic11—28no—
308C22⋊Dic11—28no—
309C22⋊Dic11—28no—
310C22⋊Dic11—44no—
311C22⋊Dic11—44no—
312Dic11⋊C4—44no—
313Dic11⋊C4—44no—
314Dic11⋊C4—44no—
315C4×Dic11—44no—
316C4×Dic11—44no—
317C4×Dic11—44no—
318C2×#394—111no—
319C2×#388—111no—
320C2×#386—111no—
321C2×#386D1111yescharacteristic
322C2×#385—111no—
323C2×C4×C22⋊C4—111no—
324C2×C4×C22⋊C4—111no—
325#1443—111no—
326#1440—111no—
327#1439—111no—
328#1437—111no—
329#1436—111no—
330#1436—111no—
331C4⋊#95—111no—
332C22⋊#95—111no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11C4×D414yes—
402C23×C11C4×D414yes—
403C23×C11C23×C411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11C2×#4111yescharacteristic
411C23×C11C2×#4111yescharacteristic
412C23×C11C2×#4111yescharacteristic
413C23×C11C2×#4111yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C23×C112−1+411yescharacteristic
418D4×C11—416no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—416no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11#12314yes—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—416no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11C4×D414yes—
511C2×Dic11#12114yes—
512C23×D4C2×D1111yescharacteristic
513C24×C4—111no—
514C24×C4C2×D1111yescharacteristic
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531#394—118no—
532#388—224no—
533#386—24no—
534#386—224no—
535#385—224no—
536C4×C22⋊C4—224no—
537C4×C22⋊C4—224no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—24no—
559C22×C11—24no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11C2×C4×D411yescharacteristic
585C22×C11C2×C4×D411yescharacteristic
586C22×C11C2×C4×D411yescharacteristic
587C22×C11C4×#4111yescharacteristic
588C22×C11C4×#4111yescharacteristic
589C22×C11#51811yescharacteristic
590C22×C11#52011yescharacteristic
591C22×C11C2×#12111yescharacteristic
592C22×C11C2×#12311yescharacteristic
593C22×C11#52511yescharacteristic
594C22×C11#52511yescharacteristic
595C22×C11#52911yescharacteristic
596C22×C11#52911yescharacteristic
597C22×C11#52911yescharacteristic
598C22×C11#53211yescharacteristic
599C22×C11#53811yescharacteristic
600C22×C11#53811yescharacteristic
601C22×C11#54211yescharacteristic
602C22×C11#54211yescharacteristic
603C22×C11D4211yescharacteristic
604C22×C11D4211yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54711yescharacteristic
611C22×C11#54711yescharacteristic
612C22×C11#54811yescharacteristic
613C22×C11#55111yescharacteristic
614C22×C11#55111yescharacteristic
615C22×C11#55211yescharacteristic
616C22×C11#55311yescharacteristic
617C22×C11#55311yescharacteristic
618C22×C11#55311yescharacteristic
619C4×C11—24no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—81no—
624Dic11—24no—
625Dic11—24no—
626Dic11—42no—
627Dic11—42no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—81no—
632C25C22×D1111yescharacteristic
633C25C22×D1111yescharacteristic
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4C4×D1114yes—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—222no—
661C23×C4—441no—
662C23×C4—441no—
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C2×C4⋊C4—114no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—441no—
675C2×C4⋊C4—441no—
676C2×C4⋊C4—441no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—114no—
686C2×C22⋊C4—114no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4C22⋊D1114yes—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—441no—
714C2×C42—441no—
715C2×C42—441no—
716#95—22no—
717#95—22no—
718#95—114no—
719#95—114no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—441no—
731#95—441no—
732C2×C11—44no—
733C2×C11—44no—
734C2×C11C4×#12111yescharacteristic
735C2×C11C4×#12311yescharacteristic
736C2×C11#233711yescharacteristic
737C2×C11#235811yescharacteristic
738C2×C11#235911yescharacteristic
739C2×C11#236111yescharacteristic
740C2×C11#236411yescharacteristic
741C2×C11#241811yescharacteristic
742C2×C11#242211yescharacteristic
743C2×C11#242411yescharacteristic
744C2×C11#242711yescharacteristic
745C2×C11#247011yescharacteristic
746C2×C11#247711yescharacteristic
747C2×C11#255911yescharacteristic
748C2×C11#257611yescharacteristic
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C2×C4×D1112yes—
774C24C2×C4×D1112yes—
775C24#433912yes—
776C24D4×D1112yes—
777C24#434112yes—
778C24C2×C22⋊D1112yes—
779C24C23×D1111yescharacteristic
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—28no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—228no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4—444no—
886C22×C4C2×C4×D1112yes—
887C22×C4D4×D1112yes—
888C22×C4#434112yes—
889C22×C4#434112yes—
890C22×C4C2×C22⋊D1112yes—
891C22×C4C2×C22⋊D1112yes—
892C4⋊C4—444no—
893C4⋊C4—444no—
894C4⋊C4—444no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—228no—
902C22⋊C4—228no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C42—444no—
906C42—444no—
907C42—444no—
908C11#1418211yescharacteristic, complemented, Sylow
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23(C22⋊D11)⋊C414yes—
978C23C4×C22⋊D1114yes—
979C23C22×C4×D1111yescharacteristic
980C23C2×#433911yescharacteristic
981C23C2×D4×D1111yescharacteristic
982C23C2×D4×D1111yescharacteristic
983C23C2×#434111yescharacteristic
984C23C2×#434111yescharacteristic
985C23C2×#434111yescharacteristic
986C23#6703711yescharacteristic
987C23#6703711yescharacteristic
988C23#6703711yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23#41×D1111yescharacteristic
992C23#6704311yescharacteristic
993C23C22×C22⋊D1111yescharacteristic
994D4—416no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—416no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—114no—
1031C2×C4—114no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—4416no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4#6698814yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C2×(C22⋊D11)⋊C411yescharacteristic
1119C22#1062301711yescharacteristic
1120C22#1062302111yescharacteristic
1121C22#1062302611yescharacteristic
1122C22C4×#434111yescharacteristic
1123C22C4×#434111yescharacteristic
1124C22#1062306911yescharacteristic
1125C22#1062306911yescharacteristic
1126C22#1062307111yescharacteristic
1127C22C4×D4×D1111yescharacteristic
1128C22#1062307711yescharacteristic
1129C22#1062308311yescharacteristic
1130C22#1062311711yescharacteristic
1131C22#1062311811yescharacteristic
1132C22#1062312211yescharacteristic
1133C22#1062312411yescharacteristic
1134C22#1062312711yescharacteristic
1135C22#1062313411yescharacteristic
1136C22D11×#12111yescharacteristic
1137C22#1062314111yescharacteristic
1138C22#1062314211yescharacteristic
1139C22#1062314311yescharacteristic
1140C22#1062314411yescharacteristic
1141C22#1062314511yescharacteristic
1142C22#1062318011yescharacteristic
1143C22#1062318111yescharacteristic
1144C22#1062319211yescharacteristic
1145C22#1062319311yescharacteristic
1146C22C2×C4×C22⋊D1111yescharacteristic
1147C22C2×#6698811yescharacteristic
1148C22D4×C22⋊D1111yescharacteristic
1149C22D4×C22⋊D1111yescharacteristic
1150C22#1062333711yescharacteristic
1151C22#1062335511yescharacteristic
1152C22#1062335911yescharacteristic
1153C4—24no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—81no—
1158C4—224no—
1159C4—224no—
1160C4—442no—
1161C4—442no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C4—881no—
1166C2—44no—
1167C2—44no—
1168C2#1307112611yescharacteristic
1169C2C4×#6698811yescharacteristic
1170C2#1307142511yescharacteristic
1171C2#1307159511yescharacteristic
1172C2#1307161411yescharacteristic
1173C2#1307163311yescharacteristic
1174C2#1307166511yescharacteristic
1175C2#1307207411yescharacteristic
1176C2#1307212611yescharacteristic
1177C2#1307214911yescharacteristic
1178C2#1307219011yescharacteristic
1179C2#1307270811yescharacteristic
1180C2#1307281411yescharacteristic
1181C2#1307374211yescharacteristic
1182C2#1307392411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14182
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622557C2semidirect
4. C2×#10622559C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C2×C4×C22⋊Dic11C2semidirect
7. #13066876C2semidirect
8. #13066863C2semidirect
9. #13066859C2semidirect
10. #13066853C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
14. #13066839C2semidirect
38. #10622835C4semidirect
119. C2×C22⋊Dic11C2×C4semidirect
120. C2×C22⋊Dic11C2×C4semidirect
121. C2×C22⋊Dic11C2×C4semidirect
122. C2×C22⋊Dic11C2×C4semidirect
132. C2×Dic11⋊C4C2×C4semidirect
156. C11⋊#95C2×C4semidirect
157. C11⋊#95D4semidirect
908. C11#14182semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106225572
C2×#106228332
C2×#106225592
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668762
#130668632
#130668592
#130668532
#130668472
Dic11⋊#952
#130668392
C2×C11×#3862
#1418211