Finite Group Databasebeta

← #14679241

Subgroups — #14679241

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622558C211yesmaximal, characteristic, complemented
4C2×#10622823C211yesmaximal, characteristic, complemented
5C2×#10622823C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066857C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C4×D4×C11—24no—
20C2×C4×D4×C11—24no—
21C2×C4×D4×C11—24no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40#10622835C418yescomplemented
41#10622823—24no—
42#10622823—24no—
43C4×C22⋊Dic11—24no—
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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622585—24no—
59#10622558—24no—
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11C2×C414yes—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—22no—
77C23×C4×C11—22no—
78C23×C4×C11—41no—
79C23×C4×C11—41no—
80C23×C4×C11—41no—
81C23×C4×C11—41no—
82C23×C4×C11D414yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C4×D4×C11—232no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4D414yes—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D414yes—
106C2×C42×C11—22no—
107C2×C42×C11—22no—
108C2×C42×C11—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—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—41no—
126C2×C22⋊Dic11—41no—
127C2×C22⋊Dic11—41no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11C2×C414yescomplemented
130C2×C22⋊Dic11C2×C414yescomplemented
131C2×C22⋊Dic11C2×C414yescomplemented
132C2×C22⋊Dic11C2×C414yescomplemented
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—41no—
144C2×Dic11⋊C4C2×C414yescomplemented
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—41no—
150C2×C4×Dic11—41no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—41no—
163C11⋊#95C2×C414yescomplemented
164C11⋊#95D414yescomplemented
165#14185—111nomaximal, Sylow
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×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11C22×C412yes—
191C24×C11C22×C412yes—
192C24×C11C2×D412yes—
193C24×C11C2×D412yes—
194C24×C11#4112yes—
195C24×C11#4112yes—
196C24×C11C2411yescharacteristic
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—28no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
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—28no—
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—28no—
230C22×C4×C11—28no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11C22×C412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11#4112yes—
252C22×C4×C11#4112yes—
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—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×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11C22×C412yes—
302C22×Dic11C22×C412yes—
303C22×Dic11C22×C412yes—
304C22×Dic11C22×C412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11#4112yes—
308C22×Dic11#4112yes—
309C11×C4⋊C4—28no—
310C11×C22⋊C4—28no—
311C11×C22⋊C4—28no—
312C42×C11—28no—
313C22⋊Dic11—28no—
314C22⋊Dic11—28no—
315C22⋊Dic11—28no—
316C22⋊Dic11—28no—
317C22⋊Dic11—28no—
318C22⋊Dic11—44no—
319C22⋊Dic11—44no—
320C22⋊Dic11—44no—
321Dic11⋊C4—28no—
322Dic11⋊C4—44no—
323Dic11⋊C4—44no—
324Dic11⋊C4—44no—
325C4×Dic11—44no—
326C4×Dic11—44no—
327C22×C4×D4D1111yescharacteristic
328C2×#394—111no—
329C2×#389—111no—
330C2×#388—111no—
331C2×#385—111no—
332C2×#385—111no—
333C2×C4×C22⋊C4—111no—
334#1440—111no—
335#1439—111no—
336#1438—111no—
337#1437—111no—
338#1436—111no—
339#1436—111no—
340#1436—111no—
341C22⋊#95—111no—
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—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
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×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11C4×D414yes—
411C23×C11C4×D414yes—
412C23×C11C23×C411yescharacteristic
413C23×C11C22×D411yescharacteristic
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C23×C11C2×#4111yescharacteristic
418C23×C11C2×#4111yescharacteristic
419C23×C11C2×#4111yescharacteristic
420C23×C11C2×#4111yescharacteristic
421C23×C11C2×#4111yescharacteristic
422C23×C11C2×#4111yescharacteristic
423C23×C11H(5,𝔽2)11yescharacteristic
424C23×C11H(5,𝔽2)11yescharacteristic
425C23×C112−1+411yescharacteristic
426C23×C112−1+411yescharacteristic
427D4×C11—232no—
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—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—416no—
453C2×C4×C11—416no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11C4×D414yes—
463C2×C4×C11#12014yes—
464C2×C4×C11#12114yes—
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—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
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×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11C4×D414yescomplemented
521C23×D4C2×D1111yescharacteristic
522C24×C4C2×D1111yescharacteristic
523C24×C4C2×D1111yescharacteristic
524C2×C4×D4—24no—
525C2×C4×D4—24no—
526C2×C4×D4—24no—
527C22×C4⋊C4—111no—
528C22×C4⋊C4—111no—
529C22×C4⋊C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊C4C2×D1111yescharacteristic
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4C2×D1111yescharacteristic
541C22×C22⋊C4C2×D1111yescharacteristic
542C22×C42—111no—
543C22×C42—111no—
544C22×C42C2×D1111yescharacteristic
545#394—118no—
546#389—224no—
547#388—224no—
548#385—224no—
549#385—224no—
550C4×C22⋊C4—224no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—24no—
569C22×C11—24no—
570C22×C11—24no—
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×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—42no—
595C22×C11C2×C4×D411yescharacteristic
596C22×C11C2×C4×D411yescharacteristic
597C22×C11C2×C4×D411yescharacteristic
598C22×C11C2×C4×D411yescharacteristic
599C22×C11C4×#4111yescharacteristic
600C22×C11#52011yescharacteristic
601C22×C11#52011yescharacteristic
602C22×C11C2×#12011yescharacteristic
603C22×C11C2×#12111yescharacteristic
604C22×C11#52511yescharacteristic
605C22×C11#52511yescharacteristic
606C22×C11#52511yescharacteristic
607C22×C11#52511yescharacteristic
608C22×C11#52911yescharacteristic
609C22×C11#53211yescharacteristic
610C22×C11#53411yescharacteristic
611C22×C11#53611yescharacteristic
612C22×C11#53911yescharacteristic
613C22×C11#53911yescharacteristic
614C22×C11D4211yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11#54611yescharacteristic
617C22×C11#54611yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54711yescharacteristic
620C22×C11#54711yescharacteristic
621C22×C11#54811yescharacteristic
622C22×C11#54811yescharacteristic
623C22×C11#54811yescharacteristic
624C22×C11#55111yescharacteristic
625C22×C11#55211yescharacteristic
626C22×C11#55311yescharacteristic
627C22×C11#55311yescharacteristic
628C22×C11#55611yescharacteristic
629C22×C11#55911yescharacteristic
630C4×C11—24no—
631C4×C11—24no—
632C4×C11—24no—
633C4×C11—42no—
634C4×C11—42no—
635Dic11—24no—
636Dic11—42no—
637Dic11—42no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641Dic11—81no—
642Dic11—81no—
643C25C22×D1111yescharacteristic
644C25C22×D1111yescharacteristic
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4C4×D1114yes—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—111no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—111no—
673C23×C4C22⋊D1114yes—
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678C23×C4C22×D1111yescharacteristic
679C4×D4—232no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—222no—
687C2×C4⋊C4—222no—
688C2×C4⋊C4—222no—
689C2×C4⋊C4—222no—
690C2×C4⋊C4—222no—
691C2×C4⋊C4—222no—
692C2×C4⋊C4—222no—
693C2×C4⋊C4—441no—
694C2×C4⋊C4C22⋊D1114yes—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—441no—
721C2×C22⋊C4—441no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4C22⋊D1114yes—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—222no—
729C2×C42—222no—
730C2×C42—222no—
731C2×C42—222no—
732C2×C42—441no—
733C2×C42—441no—
734#95—114no—
735#95—114no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—441no—
748C2×C11—44no—
749C2×C11—44no—
750C2×C11C4×#12011yescharacteristic
751C2×C11C4×#12111yescharacteristic
752C2×C11#232211yescharacteristic
753C2×C11#235911yescharacteristic
754C2×C11#236111yescharacteristic
755C2×C11#236111yescharacteristic
756C2×C11#236711yescharacteristic
757C2×C11#241011yescharacteristic
758C2×C11#241511yescharacteristic
759C2×C11#243211yescharacteristic
760C2×C11#245511yescharacteristic
761C2×C11#246011yescharacteristic
762C2×C11#246311yescharacteristic
763C2×C11#246611yescharacteristic
764C2×C11#260211yescharacteristic
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24C2×C4×D1112yes—
790C24C2×C4×D1112yes—
791C24#433912yes—
792C24#433912yes—
793C24C2×C22⋊D1112yes—
794C24C2×C22⋊D1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
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—28no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
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—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4C2×C4×D1112yes—
898C22×C4#433912yes—
899C22×C4D4×D1112yes—
900C22×C4#434112yes—
901C22×C4C2×C22⋊D1112yes—
902C22×C4C2×C22⋊D1112yes—
903C22×C4C2×C22⋊D1112yes—
904C22×C4C2×C22⋊D1112yes—
905C22×C4C2×C22⋊D1112yes—
906C22×C4C2×C22⋊D1112yes—
907C22×C4C2×C22⋊D1112yes—
908C4⋊C4—28no—
909C4⋊C4—228no—
910C4⋊C4—444no—
911C4⋊C4—444no—
912C4⋊C4—444no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—228no—
916C22⋊C4—228no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—444no—
921C22⋊C4—444no—
922C22⋊C4—444no—
923C42—28no—
924C42—444no—
925C42—444no—
926C11#1418511yescharacteristic, complemented, Sylow
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—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
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—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23C4×C22⋊D1114yes—
996C23C4×C22⋊D1114yes—
997C23C22×C4×D1111yescharacteristic
998C23C2×#433911yescharacteristic
999C23C2×#433911yescharacteristic
1000C23C2×#433911yescharacteristic
1001C23C2×D4×D1111yescharacteristic
1002C23C2×#434111yescharacteristic
1003C23#6703711yescharacteristic
1004C23#6703711yescharacteristic
1005C23#41×D1111yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#6704311yescharacteristic
1008C23#6704311yescharacteristic
1009C23C22×C22⋊D1111yescharacteristic
1010C23C22×C22⋊D1111yescharacteristic
1011C23C22×C22⋊D1111yescharacteristic
1012D4—232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—416no—
1038C2×C4—416no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—114no—
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—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
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—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4C4×C22⋊D1114yes—
1104C2×C4#6699214yes—
1105C2×C4#6700614yes—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C4×#434111yescharacteristic
1137C22#1062306911yescharacteristic
1138C22#1062307111yescharacteristic
1139C22#1062307211yescharacteristic
1140C22#1062307311yescharacteristic
1141C22C4×D4×D1111yescharacteristic
1142C22#1062307711yescharacteristic
1143C22#1062307711yescharacteristic
1144C22#1062307811yescharacteristic
1145C22#1062308211yescharacteristic
1146C22#1062308311yescharacteristic
1147C22#1062308711yescharacteristic
1148C22#1062308911yescharacteristic
1149C22#1062309011yescharacteristic
1150C22#1062309511yescharacteristic
1151C22#1062309511yescharacteristic
1152C22C2×C4×C22⋊D1111yescharacteristic
1153C22C2×C4×C22⋊D1111yescharacteristic
1154C22C2×C4×C22⋊D1111yescharacteristic
1155C22#1062332211yescharacteristic
1156C22#1062332211yescharacteristic
1157C22#1062332211yescharacteristic
1158C22D4×C22⋊D1111yescharacteristic
1159C22D4×C22⋊D1111yescharacteristic
1160C22C2×#6699211yescharacteristic
1161C22#1062333511yescharacteristic
1162C22#1062333711yescharacteristic
1163C22#1062333711yescharacteristic
1164C22#1062335511yescharacteristic
1165C22#1062335511yescharacteristic
1166C22#1062335611yescharacteristic
1167C22#1062336211yescharacteristic
1168C22#1062336211yescharacteristic
1169C22#1062336311yescharacteristic
1170C22C2×#6700611yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—42no—
1175C4—42no—
1176C4—224no—
1177C4—442no—
1178C4—442no—
1179C4—442no—
1180C4—442no—
1181C4—442no—
1182C4—881no—
1183C4—881no—
1184C2—44no—
1185C2—44no—
1186C2C4×#6700611yescharacteristic
1187C2C4×#6699211yescharacteristic
1188C2#1307128111yescharacteristic
1189C2#1307160211yescharacteristic
1190C2#1307162811yescharacteristic
1191C2#1307163311yescharacteristic
1192C2#1307168911yescharacteristic
1193C2#1307199011yescharacteristic
1194C2#1307204511yescharacteristic
1195C2#1307224011yescharacteristic
1196C2#1307249311yescharacteristic
1197C2#1307256211yescharacteristic
1198C2#1307260711yescharacteristic
1199C2#1307264611yescharacteristic
1200C2#1307422811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#14185
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
3. C2×#10622558C2semidirect
4. C2×#10622823C2semidirect
5. C2×#10622823C2semidirect
6. C2×C4×C22⋊Dic11C2semidirect
7. #13066863C2semidirect
8. #13066859C2semidirect
10. #13066853C2semidirect
11. #13066849C2semidirect
12. #13066849C2semidirect
13. #13066848C2semidirect
14. #13066839C2semidirect
40. #10622835C4semidirect
129. C2×C22⋊Dic11C2×C4semidirect
130. C2×C22⋊Dic11C2×C4semidirect
131. C2×C22⋊Dic11C2×C4semidirect
132. C2×C22⋊Dic11C2×C4semidirect
144. C2×Dic11⋊C4C2×C4semidirect
163. C11⋊#95C2×C4semidirect
164. C11⋊#95D4semidirect
520. C2×Dic11C4×D4semidirect
926. C11#14185semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106225852
C2×#106225582
C2×#106228232
C2×C4×C22⋊Dic112
#130668632
#130668592
#130668572
#130668532
#130668492
#130668482
#130668392
C22×C4×D4×C112
#1418511