Finite Group Databasebeta

← #14676915

Subgroups — #14676915

Order 2816.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic, complemented
5C2×#10622585C211yesmaximal, characteristic, complemented
6C2×#10622555C211yesmaximal, characteristic, complemented
7C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066857C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066854C211yesmaximal, characteristic, complemented
14#13066853C211yesmaximal, characteristic, complemented
15C2×C11×#390C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊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
31C2×#66992—24no—
32C2×#66992—24no—
33C2×#66992C418yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C11×#390—24no—
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#10622585—24no—
56#10622570—24no—
57#10622570—24no—
58#10622570—24no—
59#10622555—24no—
60C22⋊C4×Dic11—24no—
61C4×Dic11⋊C4—24no—
62C25×C11C2311yescharacteristic
63C25×C11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yes—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—41no—
88C22×C22⋊D11—41no—
89C22×C22⋊D11C2×C414yes—
90C22×C22⋊D11C2×C414yes—
91C23×Dic11—22no—
92C23×Dic11—22no—
93C23×Dic11—22no—
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—22no—
97C23×Dic11C2×C414yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—41no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4D414yescomplemented
120C2×C42×C11—22no—
121C2×C42×C11—22no—
122C2×C42×C11—41no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—22no—
131C2×C22⋊Dic11—22no—
132C2×C22⋊Dic11—22no—
133C2×C22⋊Dic11—41no—
134C2×C22⋊Dic11—41no—
135C2×C22⋊Dic11—41no—
136C2×C22⋊Dic11—41no—
137C2×C22⋊Dic11C2×C414yes—
138#66992—232no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—41no—
150C2×(C2×D11)⋊C4—41no—
151C2×(C2×D11)⋊C4—41no—
152C2×(C2×D11)⋊C4—41no—
153C2×(C2×D11)⋊C4C2×C414yes—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—22no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—22no—
160C2×Dic11⋊C4—22no—
161C2×Dic11⋊C4—41no—
162C2×Dic11⋊C4C2×C414yes—
163C2×Dic11⋊C4D414yes—
164C2×Dic11⋊C4D414yes—
165C2×Dic11⋊C4D414yescomplemented
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169C2×C4×Dic11—22no—
170C2×C4×Dic11—22no—
171C2×C4×Dic11—22no—
172C2×C4×Dic11—22no—
173C2×C4×Dic11—41no—
174C2×C4×Dic11D414yescomplemented
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—22no—
182C11⋊#95—22no—
183#13998—111nomaximal, Sylow
184C24×C11—21no—
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×C11C22×C412yes—
211C24×C11C22×C412yes—
212C24×C11C2×D412yes—
213C24×C11#4112yes—
214C24×C11C2411yescharacteristic
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—21no—
225C23×D11—21no—
226C23×D11—21no—
227C23×D11—21no—
228C23×D11—21no—
229C23×D11C22×C412yes—
230C2×D4×C11—28no—
231C2×D4×C11—28no—
232C2×D4×C11—44no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11C22×C412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11#4112yes—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
280C2×C22⋊D11—44no—
281C2×C22⋊D11—44no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C22×Dic11—28no—
287C22×Dic11—28no—
288C22×Dic11—28no—
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×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—44no—
325C22×Dic11—44no—
326C22×Dic11—44no—
327C22×Dic11—44no—
328C22×Dic11C22×C412yes—
329C22×Dic11C22×C412yes—
330C22×Dic11C22×C412yes—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11C2×D412yes—
335C22×Dic11C2×D412yes—
336C22×Dic11C2×D412yes—
337C22×Dic11C2×D412yes—
338C22×Dic11C2×D412yes—
339C22×Dic11#4112yes—
340C22×Dic11#4112yes—
341C22×Dic11#4112yes—
342C11×C4⋊C4—44no—
343C11×C22⋊C4—28no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C11×C22⋊C4—44no—
347C42×C11—44no—
348C22⋊Dic11—28no—
349C22⋊Dic11—28no—
350C22⋊Dic11—44no—
351C22⋊Dic11—44no—
352C22⋊Dic11—44no—
353(C2×D11)⋊C4—28no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356(C2×D11)⋊C4—44no—
357(C2×D11)⋊C4—44no—
358Dic11⋊C4—28no—
359Dic11⋊C4—44no—
360Dic11⋊C4—44no—
361Dic11⋊C4C22⋊C4116yescomplemented
362C4×Dic11—28no—
363C4×Dic11—44no—
364C4×Dic11—44no—
365C22×#121—111no—
366C2×#390—111no—
367C2×#390—111no—
368C2×#390—111no—
369C2×#390D1111yescharacteristic, complemented
370C2×#389—111no—
371C2×#380—111no—
372C2×C4×C4⋊C4—111no—
373C2×C4×C22⋊C4—111no—
374#1439—111no—
375#1439—111no—
376#1438—111no—
377#1438—111no—
378#1437—111no—
379#1437—111no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
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—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11C4×D414yes—
450C23×C11C23×C411yescharacteristic
451C23×C11C22×D411yescharacteristic
452C23×C11C22×D411yescharacteristic
453C23×C11C22×D411yescharacteristic
454C23×C11C22×D411yescharacteristic
455C23×C11C22×D411yescharacteristic
456C23×C11C2×#4111yescharacteristic
457C23×C11C2×#4111yescharacteristic
458C23×C11C2×#4111yescharacteristic
459C23×C11C2×#4111yescharacteristic
460C23×C11C2×#4111yescharacteristic
461C23×C11H(5,𝔽2)11yescharacteristic
462C23×C11H(5,𝔽2)11yescharacteristic
463C23×C11H(5,𝔽2)11yescharacteristic
464C23×C112−1+411yescharacteristic
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11—41no—
496C22×D11—41no—
497C22×D11—41no—
498C22×D11—41no—
499C22×D11—41no—
500D4×C11—416no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11C2×C22⋊C414yes—
535C2×C4×C11#12114yescomplemented
536C22⋊D11—416no—
537C22⋊D11—416no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—416no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11C2×C22⋊C414yes—
581C2×Dic11C2×C22⋊C414yes—
582C2×Dic11C4×D414yes—
583C2×Dic11C4×D414yes—
584C2×Dic11#12114yes—
585C2×Dic11#12114yes—
586C2×Dic11#12414yes—
587C2×Dic11#12714yes—
588C23×D4—111no—
589C23×D4—111no—
590C23×D4C2×D1111yescharacteristic
591C24×C4—111no—
592C2×#121—118no—
593C2×#121—224no—
594C2×#121—224no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4—111no—
597C22×C4⋊C4—111no—
598C22×C4⋊C4—111no—
599C22×C4⋊C4C2×D1111yescharacteristic
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4—111no—
605C22×C22⋊C4—111no—
606C22×C22⋊C4—111no—
607C22×C22⋊C4—111no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4C2×D1111yescharacteristic
611C22×C22⋊C4C2×D1111yescharacteristic
612C22×C22⋊C4C2×D1111yescharacteristic
613C22×C22⋊C4C2×D1111yescharacteristic
614C22×C42—111no—
615C22×C42—111no—
616C22×C42—111no—
617C22×C42C2×D1111yescharacteristic
618#390—24no—
619#390—224no—
620#390—224no—
621#390—224no—
622#389—224no—
623#380—224no—
624C4×C4⋊C4—224no—
625C4×C22⋊C4—224no—
626C2×#95—111no—
627C2×#95—111no—
628C2×#95—111no—
629C2×#95—111no—
630C2×#95—111no—
631C2×#95—111no—
632C2×#95—111no—
633C2×#95—111no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—81no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11—81no—
660C22×C11—81no—
661C22×C11—81no—
662C22×C11—81no—
663C22×C11—81no—
664C22×C11C22×C22⋊C411yescharacteristic
665C22×C11C2×C4×D411yescharacteristic
666C22×C11C2×C4×D411yescharacteristic
667C22×C11C2×C4×D411yescharacteristic
668C22×C11C4×#4111yescharacteristic
669C22×C11#51811yescharacteristic
670C22×C11#52011yescharacteristic
671C22×C11C2×#12111yescharacteristic
672C22×C11C2×#12111yescharacteristic
673C22×C11C2×#12111yescharacteristic
674C22×C11#52511yescharacteristic
675C22×C11C2×#12411yescharacteristic
676C22×C11#52911yescharacteristic
677C22×C11C2×#12711yescharacteristic
678C22×C11#53211yescharacteristic
679C22×C11#53511yescharacteristic
680C22×C11#53711yescharacteristic
681C22×C11#54011yescharacteristic
682C22×C11#54211yescharacteristic
683C22×C11D4211yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11D4211yescharacteristic
686C22×C11#54611yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54611yescharacteristic
689C22×C11#54711yescharacteristic
690C22×C11#54811yescharacteristic
691C22×C11#54811yescharacteristic
692C22×C11#54811yescharacteristic
693C22×C11#55011yescharacteristic
694C22×C11#55011yescharacteristic
695C22×C11#55011yescharacteristic
696C22×C11#55311yescharacteristic
697C22×C11#55311yescharacteristic
698C22×C11#55511yescharacteristic
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—81no—
707C2×D11—81no—
708C2×D11—81no—
709C2×D11—81no—
710C2×D11—81no—
711C2×D11—81no—
712C2×D11—81no—
713C2×D11—81no—
714C4×C11—24no—
715C4×C11—24no—
716C4×C11—42no—
717C4×C11—42no—
718C4×C11—81no—
719Dic11—24no—
720Dic11—42no—
721Dic11—42no—
722Dic11—42no—
723Dic11—42no—
724Dic11—81no—
725Dic11#39018yescomplemented
726C25—111no—
727C25C22×D1111yescharacteristic
728C25C22×D1111yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—114no—
736C22×D4—114no—
737C22×D4—222no—
738C22×D4—222no—
739C22×D4—222no—
740C22×D4—222no—
741C22×D4—222no—
742C22×D4—222no—
743C22×D4—222no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4—222no—
747C22×D4—441no—
748C22×D4—441no—
749C22×D4C4×D1114yes—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—114no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—222no—
759C23×C4—222no—
760C23×C4—222no—
761C23×C4—222no—
762C23×C4—222no—
763C23×C4—222no—
764C23×C4C22×D1111yescharacteristic
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1111yescharacteristic
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769#121—2232no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—114no—
774C2×C4⋊C4—114no—
775C2×C4⋊C4—114no—
776C2×C4⋊C4—114no—
777C2×C4⋊C4—222no—
778C2×C4⋊C4—222no—
779C2×C4⋊C4—222no—
780C2×C4⋊C4—222no—
781C2×C4⋊C4—222no—
782C2×C4⋊C4—222no—
783C2×C4⋊C4—222no—
784C2×C4⋊C4—441no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—114no—
797C2×C22⋊C4—114no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—222no—
805C2×C22⋊C4—222no—
806C2×C22⋊C4—222no—
807C2×C22⋊C4—222no—
808C2×C22⋊C4—222no—
809C2×C22⋊C4—222no—
810C2×C22⋊C4—222no—
811C2×C22⋊C4—222no—
812C2×C22⋊C4—222no—
813C2×C22⋊C4—222no—
814C2×C22⋊C4—222no—
815C2×C22⋊C4—222no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—441no—
819C2×C22⋊C4—441no—
820C2×C22⋊C4—441no—
821C2×C22⋊C4—441no—
822C2×C22⋊C4—441no—
823C2×C22⋊C4—441no—
824C2×C22⋊C4—441no—
825C2×C22⋊C4—441no—
826C2×C22⋊C4C22⋊D1114yescomplemented
827C2×C42—22no—
828C2×C42—22no—
829C2×C42—41no—
830C2×C42—114no—
831C2×C42—222no—
832C2×C42—222no—
833C2×C42—222no—
834C2×C42—222no—
835C2×C42—222no—
836C2×C42—222no—
837C2×C42—222no—
838C2×C42—441no—
839#95—222no—
840#95—222no—
841#95—222no—
842#95—222no—
843#95—222no—
844#95—222no—
845#95—222no—
846#95—222no—
847C2×C11—44no—
848C2×C11—82no—
849C2×C11C2×#39011yescharacteristic
850C2×C11C4×#12111yescharacteristic
851C2×C11#232411yescharacteristic
852C2×C11D4×C22⋊C411yescharacteristic
853C2×C11#234111yescharacteristic
854C2×C11#236111yescharacteristic
855C2×C11#236311yescharacteristic
856C2×C11#241411yescharacteristic
857C2×C11#241611yescharacteristic
858C2×C11#242611yescharacteristic
859C2×C11#242811yescharacteristic
860C2×C11#249011yescharacteristic
861C2×C11#249111yescharacteristic
862C2×C11#254011yescharacteristic
863C2×C11#254111yescharacteristic
864D11—82no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—112no—
892C24—221no—
893C24—221no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24—221no—
899C24—221no—
900C24—221no—
901C24—221no—
902C24—221no—
903C24—221no—
904C24—221no—
905C24—221no—
906C24C2×C4×D1112yes—
907C24C2×C4×D1112yes—
908C24#433912yes—
909C24C2×C22⋊D1112yes—
910C24C23×D1111yescharacteristic
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—228no—
919C2×D4—228no—
920C2×D4—228no—
921C2×D4—228no—
922C2×D4—228no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—444no—
929C2×D4—444no—
930C2×D4—444no—
931C2×D4—444no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—112no—
960C22×C4—112no—
961C22×C4—112no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—112no—
967C22×C4—112no—
968C22×C4—112no—
969C22×C4—112no—
970C22×C4—112no—
971C22×C4—112no—
972C22×C4—112no—
973C22×C4—228no—
974C22×C4—228no—
975C22×C4—228no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
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—444no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4C2×C4×D1112yes—
1016C22×C4D4×D1112yes—
1017C22×C4D4×D1112yes—
1018C22×C4D4×D1112yes—
1019C22×C4D4×D1112yes—
1020C22×C4#434112yes—
1021C22×C4C2×C22⋊D1112yes—
1022C22×C4C2×C22⋊D1112yes—
1023C4⋊C4—44no—
1024C4⋊C4—1116no—
1025C4⋊C4—228no—
1026C4⋊C4—444no—
1027C4⋊C4—444no—
1028C22⋊C4—28no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—228no—
1033C22⋊C4—228no—
1034C22⋊C4—228no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4—444no—
1038C22⋊C4—444no—
1039C22⋊C4—444no—
1040C22⋊C4—444no—
1041C22⋊C4—444no—
1042C42—44no—
1043C42—228no—
1044C42—444no—
1045C42—444no—
1046C11#1399811yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23C4×C22⋊D1114yes—
1152C23C22×C4×D1111yescharacteristic
1153C23C2×#433911yescharacteristic
1154C23C2×D4×D1111yescharacteristic
1155C23C2×D4×D1111yescharacteristic
1156C23C2×D4×D1111yescharacteristic
1157C23C2×D4×D1111yescharacteristic
1158C23C2×#434111yescharacteristic
1159C23#6703711yescharacteristic
1160C23#6703711yescharacteristic
1161C23#6703711yescharacteristic
1162C23#41×D1111yescharacteristic
1163C23#41×D1111yescharacteristic
1164C23#41×D1111yescharacteristic
1165C23#6704311yescharacteristic
1166C23C22×C22⋊D1111yescharacteristic
1167D4—416no—
1168D4—4416no—
1169D4—4416no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—114no—
1204C2×C4—114no—
1205C2×C4—114no—
1206C2×C4—114no—
1207C2×C4—114no—
1208C2×C4—114no—
1209C2×C4—114no—
1210C2×C4—114no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—222no—
1223C2×C4—222no—
1224C2×C4—222no—
1225C2×C4—222no—
1226C2×C4—222no—
1227C2×C4—222no—
1228C2×C4—222no—
1229C2×C4—4416no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4—441no—
1248C2×C4—441no—
1249C2×C4—441no—
1250C2×C4—441no—
1251C2×C4—441no—
1252C2×C4—441no—
1253C2×C4C22⋊C4×D1114yes—
1254C2×C4#6699214yescomplemented
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—881no—
1293C22—881no—
1294C22—881no—
1295C22—881no—
1296C22—881no—
1297C22—881no—
1298C22—881no—
1299C22—881no—
1300C22C2×C22⋊C4×D1111yescharacteristic
1301C22#1062301711yescharacteristic
1302C22#1062302111yescharacteristic
1303C22#1062302111yescharacteristic
1304C22C4×#434111yescharacteristic
1305C22#1062306911yescharacteristic
1306C22#1062307111yescharacteristic
1307C22C4×D4×D1111yescharacteristic
1308C22C4×D4×D1111yescharacteristic
1309C22#1062307711yescharacteristic
1310C22#1062307811yescharacteristic
1311C22#1062308311yescharacteristic
1312C22#1062312811yescharacteristic
1313C22#1062312911yescharacteristic
1314C22#1062313011yescharacteristic
1315C22#1062313211yescharacteristic
1316C22D11×#12111yescharacteristic
1317C22D11×#12111yescharacteristic
1318C22#1062314111yescharacteristic
1319C22#1062314611yescharacteristic
1320C22#1062320011yescharacteristic
1321C22#1062320111yescharacteristic
1322C22D11×#12411yescharacteristic
1323C22#1062320811yescharacteristic
1324C22D11×#12711yescharacteristic
1325C22#1062324611yescharacteristic
1326C22#1062324911yescharacteristic
1327C22#1062324911yescharacteristic
1328C22C2×C4×C22⋊D1111yescharacteristic
1329C22D4×C22⋊D1111yescharacteristic
1330C22D4×C22⋊D1111yescharacteristic
1331C22D4×C22⋊D1111yescharacteristic
1332C22C2×#6699211yescharacteristic
1333C22#1062335511yescharacteristic
1334C22#1062336311yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—118no—
1341C4—224no—
1342C4—442no—
1343C4—442no—
1344C4—442no—
1345C4—442no—
1346C4—881no—
1347C2—44no—
1348C2—82no—
1349C2—882no—
1350C2D11×#39011yescharacteristic
1351C2C4×#6699211yescharacteristic
1352C2#1307130211yescharacteristic
1353C2C22⋊C4×C22⋊D1111yescharacteristic
1354C2#1307145511yescharacteristic
1355C2#1307163311yescharacteristic
1356C2#1307165111yescharacteristic
1357C2#1307203111yescharacteristic
1358C2#1307205311yescharacteristic
1359C2#1307217911yescharacteristic
1360C2#1307220111yescharacteristic
1361C2#1307296511yescharacteristic
1362C2#1307297611yescharacteristic
1363C2#1307355311yescharacteristic
1364C2#1307356011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#390D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622585C2semidirect
6. C2×#10622555C2semidirect
7. C2×C4×Dic11⋊C4C2semidirect
8. C2×C22⋊C4×Dic11C2semidirect
9. #13066859C2semidirect
10. #13066858C2semidirect
11. #13066857C2semidirect
12. #13066855C2semidirect
13. #13066854C2semidirect
14. #13066853C2semidirect
15. C2×C11×#390C2semidirect
33. C2×#66992C4semidirect
119. C2×C11×C22⋊C4D4semidirect
165. C2×Dic11⋊C4D4semidirect
174. C2×C4×Dic11D4semidirect
361. Dic11⋊C4C22⋊C4semidirect
369. C2×#390D11semidirect
535. C2×C4×C11#121semidirect
725. Dic11#390semidirect
826. C2×C22⋊C4C22⋊D11semidirect
1046. C11#13998semidirect
1254. C2×C4#66992semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106225702
C2×#106225852
C2×#106225552
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
#130668592
#130668582
#130668572
#130668552
#130668542
#130668532
C2×C11×#3902
#1399811