Finite Group Databasebeta

← #14678210

Subgroups — #14678210

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622268C211yesmaximal, characteristic, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066851C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
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
29C2×#66988—24no—
30C2×#66988—24no—
31C2×#66988C418yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42#10622834—24no—
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
55C22⋊C4×Dic11—24no—
56#10622268—24no—
57#10622262—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×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11C2×C414yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
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—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11C2×C414yes—
117C2×C22⋊Dic11C2×C414yes—
118C2×C22⋊Dic11C2×C414yes—
119C2×C22⋊Dic11D414yes—
120#66988—232no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—41no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4C2×C414yes—
130C2×Dic11⋊C4C2×C414yes—
131C2×Dic11⋊C4D414yes—
132C2×Dic11⋊C4D414yes—
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—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—41no—
143C2×C4×Dic11—41no—
144C2×C4×Dic11—41no—
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—22no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159#14095—111nomaximal, Sylow
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×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11C22×C412yes—
187C24×C11C22×C412yes—
188C24×C11C2×D412yes—
189C24×C11#4112yes—
190C24×C11C2411yescharacteristic
191C2×D4×C11—28no—
192C2×D4×C11—28no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
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×C11C22×C412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C22×Dic11—28no—
234C22×Dic11—28no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
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—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11C22×C412yes—
284C22×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C11×C22⋊C4—28no—
297C11×C22⋊C4—44no—
298C11×C22⋊C4—44no—
299C11×C22⋊C4—44no—
300C22⋊Dic11—28no—
301C22⋊Dic11—28no—
302C22⋊Dic11—28no—
303C22⋊Dic11—28no—
304C22⋊Dic11—44no—
305C22⋊Dic11—44no—
306C22⋊Dic11—44no—
307C4⋊Dic11—44no—
308Dic11⋊C4—28no—
309Dic11⋊C4—28no—
310Dic11⋊C4C22⋊C4116yescomplemented
311C4×Dic11—28no—
312C4×Dic11—44no—
313C4×Dic11—44no—
314C4×Dic11—44no—
315C22×#123—111no—
316C2×#390—111no—
317C2×#387—111no—
318C2×C4×C4⋊C4—111no—
319C2×C4×C22⋊C4—111no—
320#1441—111no—
321#1439—111no—
322#1439—111no—
323#1438D1111yescharacteristic
324#1437—111no—
325#1437—111no—
326#1437—111no—
327#1437—111no—
328#1436—111no—
329C22⋊#95—111no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
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—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
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×C11C4×D414yes—
400C23×C11C23×C411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C23×C11C22×D411yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11C2×#4111yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C11H(5,𝔽2)11yescharacteristic
414C23×C112−1+411yescharacteristic
415D4×C11—416no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
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—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
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—416no—
482C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
506C2×Dic11C2×C22⋊C414yes—
507C2×Dic11#12314yescomplemented
508C23×D4C2×D1111yescharacteristic
509C24×C4—111no—
510C2×#123—118no—
511C2×#123—224no—
512C2×#123—224no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C22⋊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⋊C4C2×D1111yescharacteristic
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531C22×C42—111no—
532#390—224no—
533#387—224no—
534C4×C4⋊C4—224no—
535C4×C22⋊C4—224no—
536C2×#95—111no—
537C2×#95—111no—
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×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—24no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
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—81no—
573C22×C11—81no—
574C22×C11—81no—
575C22×C11—81no—
576C22×C11—81no—
577C22×C11—81no—
578C22×C11—81no—
579C22×C11—81no—
580C22×C11C22×C22⋊C411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11C4×#4111yescharacteristic
583C22×C11C4×#4111yescharacteristic
584C22×C11C4×#4111yescharacteristic
585C22×C11#51811yescharacteristic
586C22×C11#52011yescharacteristic
587C22×C11C2×#12311yescharacteristic
588C22×C11#52511yescharacteristic
589C22×C11#52511yescharacteristic
590C22×C11#52511yescharacteristic
591C22×C11#52911yescharacteristic
592C22×C11#52911yescharacteristic
593C22×C11#53211yescharacteristic
594C22×C11#53211yescharacteristic
595C22×C11#53811yescharacteristic
596C22×C11#53911yescharacteristic
597C22×C11#54011yescharacteristic
598C22×C11#54211yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54611yescharacteristic
604C22×C11#54711yescharacteristic
605C22×C11#54811yescharacteristic
606C22×C11#54811yescharacteristic
607C22×C11#55011yescharacteristic
608C22×C11#55011yescharacteristic
609C22×C11#55111yescharacteristic
610C22×C11#55111yescharacteristic
611C22×C11#55211yescharacteristic
612C22×C11#55311yescharacteristic
613C22×C11#55311yescharacteristic
614C22×C11#55911yescharacteristic
615C4×C11—24no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—81no—
620Dic11—24no—
621Dic11—24no—
622Dic11—24no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627Dic11—81no—
628C25C22×D1111yescharacteristic
629C25C22×D1111yescharacteristic
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4C4×D1114yes—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—114no—
645C23×C4—111no—
646C23×C4—222no—
647C23×C4—222no—
648C23×C4—222no—
649C23×C4—222no—
650C23×C4—441no—
651C23×C4—441no—
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657#123—2232no—
658C2×C4⋊C4—114no—
659C2×C4⋊C4—114no—
660C2×C4⋊C4—114no—
661C2×C4⋊C4—114no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—222no—
667C2×C4⋊C4—222no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—441no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
685C2×C22⋊C4—114no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
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—441no—
702C2×C22⋊C4—441no—
703C2×C42—222no—
704C2×C42—222no—
705C2×C42—222no—
706C2×C42—222no—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—441no—
713C2×C42—441no—
714C2×C42—441no—
715#95—22no—
716#95—22no—
717#95—222no—
718#95—222no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—441no—
726#95—441no—
727#95—441no—
728#95—441no—
729C2×C11—44no—
730C2×C11—82no—
731C2×C11#229711yescharacteristic
732C2×C11C4×#12311yescharacteristic
733C2×C11#233511yescharacteristic
734C2×C11D4×C22⋊C411yescharacteristic
735C2×C11#234111yescharacteristic
736C2×C11#235911yescharacteristic
737C2×C11#237411yescharacteristic
738C2×C11#244311yescharacteristic
739C2×C11#244511yescharacteristic
740C2×C11#245611yescharacteristic
741C2×C11#245811yescharacteristic
742C2×C11#246111yescharacteristic
743C2×C11#247111yescharacteristic
744C2×C11#255411yescharacteristic
745C2×C11#255811yescharacteristic
746C24—21no—
747C24—21no—
748C24—21no—
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—
772C24C2×C4×D1112yes—
773C24C2×C4×D1112yes—
774C24D4×D1112yes—
775C24#434112yes—
776C24C23×D1111yescharacteristic
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
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—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—112no—
818C22×C4—112no—
819C22×C4—112no—
820C22×C4—112no—
821C22×C4—112no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—228no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—228no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
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—444no—
872C22×C4—444no—
873C22×C4—444no—
874C22×C4—444no—
875C22×C4—444no—
876C22×C4C2×C4×D1112yes—
877C22×C4D4×D1112yes—
878C22×C4D4×D1112yes—
879C22×C4#434112yes—
880C22×C4#434112yes—
881C22×C4#434112yes—
882C4⋊C4—1116no—
883C4⋊C4—228no—
884C4⋊C4—228no—
885C4⋊C4—444no—
886C22⋊C4—28no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—228no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C42—228no—
898C42—444no—
899C42—444no—
900C42—444no—
901C11#1409511yescharacteristic, complemented, Sylow
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
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—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
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(C22⋊D11)⋊C414yes—
972C23C22×C4×D1111yescharacteristic
973C23C2×D4×D1111yescharacteristic
974C23C2×D4×D1111yescharacteristic
975C23C2×D4×D1111yescharacteristic
976C23C2×#434111yescharacteristic
977C23C2×#434111yescharacteristic
978C23C2×#434111yescharacteristic
979C23C2×#434111yescharacteristic
980C23#6703711yescharacteristic
981C23#6703711yescharacteristic
982C23#6703711yescharacteristic
983C23#41×D1111yescharacteristic
984C23#41×D1111yescharacteristic
985C23#41×D1111yescharacteristic
986C23#6704311yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
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—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
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—114no—
1023C2×C4—114no—
1024C2×C4—114no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
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—4416no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
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×C4C22⋊C4×D1114yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C22⋊C4×D1111yescharacteristic
1111C22C2×(C22⋊D11)⋊C411yescharacteristic
1112C22#1062301711yescharacteristic
1113C22C4×#434111yescharacteristic
1114C22C4×#434111yescharacteristic
1115C22C4×#434111yescharacteristic
1116C22#1062307711yescharacteristic
1117C22#1062311711yescharacteristic
1118C22#1062311811yescharacteristic
1119C22#1062311811yescharacteristic
1120C22#1062312111yescharacteristic
1121C22#1062312111yescharacteristic
1122C22#1062312211yescharacteristic
1123C22#1062312211yescharacteristic
1124C22#1062312411yescharacteristic
1125C22#1062312911yescharacteristic
1126C22#1062313011yescharacteristic
1127C22#1062313111yescharacteristic
1128C22#1062313111yescharacteristic
1129C22#1062313411yescharacteristic
1130C22#1062313711yescharacteristic
1131C22#1062313711yescharacteristic
1132C22#1062314111yescharacteristic
1133C22#1062314211yescharacteristic
1134C22#1062314511yescharacteristic
1135C22#1062314511yescharacteristic
1136C22#1062314611yescharacteristic
1137C22#1062318111yescharacteristic
1138C22D11×#12311yescharacteristic
1139C22#1062319111yescharacteristic
1140C22#1062319511yescharacteristic
1141C22#1062319911yescharacteristic
1142C22#1062320811yescharacteristic
1143C22#1062324711yescharacteristic
1144C22#1062324911yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—224no—
1151C4—224no—
1152C4—224no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C4—442no—
1157C4—881no—
1158C2—44no—
1159C2—82no—
1160C2#1307110311yescharacteristic
1161C2#1307114111yescharacteristic
1162C2#1307140711yescharacteristic
1163C2#1307143211yescharacteristic
1164C2#1307145511yescharacteristic
1165C2#1307161411yescharacteristic
1166C2#1307174911yescharacteristic
1167C2#1307234411yescharacteristic
1168C2#1307237611yescharacteristic
1169C2#1307250911yescharacteristic
1170C2#1307253911yescharacteristic
1171C2#1307257811yescharacteristic
1172C2#1307272811yescharacteristic
1173C2#1307367711yescharacteristic
1174C2#1307373111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14095
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#10622268C2semidirect
4. C2×#10622262C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066870C2semidirect
7. #13066859C2semidirect
8. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066853C2semidirect
12. #13066853C2semidirect
13. #13066851C2semidirect
14. #13066838C2semidirect
31. C2×#66988C4semidirect
310. Dic11⋊C4C22⋊C4semidirect
507. C2×Dic11#123semidirect
901. C11#14095semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106228342
C2×#106222682
C2×#106222622
C2×C22⋊C4×Dic112
#130668702
#130668592
#130668532
#130668512
#130668382
C11×#14382
#1409511