Finite Group Databasebeta

← #14690474

Subgroups — #14690474

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622561C211yesmaximal, characteristic, complemented
2C2×#10622607C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622570C211yesmaximal, characteristic
5C2×#10622570C211yesmaximal, characteristic
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622260C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066860C211yesmaximal, characteristic, complemented
13#13066859C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
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
51#10622607—24no—
52#10622585—24no—
53#10622570—24no—
54#10622570—24no—
55#10622570—24no—
56#10622561—24no—
57#10622260—24no—
58#10622260—24no—
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11Q814yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11—41no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11—41no—
125C2×C4⋊Dic11—41no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—41no—
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4D414yes—
142C2×Dic11⋊C4D414yes—
143C2×Dic11⋊C4D414yes—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152C2×C4×Dic11—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⋊#95D414yescomplemented
163#15141—111nomaximal, Sylow
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×C11C2×Q812yes—
179C24×C11C2411yescharacteristic
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11C2×Q812yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
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×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
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×Dic11C2×D412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11C2×D412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×Q812yes—
289C22×Dic11#4112yes—
290C22×Dic11#4112yes—
291C22×Dic11#4112yes—
292C22×Dic11#4112yes—
293C11×C4⋊C4—44no—
294C11×C22⋊C4—44no—
295C11×C22⋊C4—44no—
296C11×C22⋊C4—44no—
297C22⋊Dic11—44no—
298C22⋊Dic11—44no—
299C22⋊Dic11—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306C4⋊Dic11—44no—
307C4⋊Dic11—44no—
308Dic11⋊C4—28no—
309Dic11⋊C4—28no—
310Dic11⋊C4—28no—
311Dic11⋊C4—44no—
312Dic11⋊C4—44no—
313Dic11⋊C4—44no—
314C4×Dic11—44no—
315C4×Dic11—44no—
316C4×Dic11—44no—
317C2×#396—111no—
318C2×#396—111no—
319C2×#390—111no—
320C2×#390—111no—
321C2×#390—111no—
322C2×#389—111no—
323C2×#389—111no—
324C2×#389—111no—
325#1439—111no—
326#1439—111no—
327#1439—111no—
328#1439—111no—
329#1439—111no—
330#1439D1111yescharacteristic, complemented
331C4×#95—111no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
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×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×Q811yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11C2×#4111yescharacteristic
377C23×C11C2×#4111yescharacteristic
378C23×C11H(5,𝔽2)11yescharacteristic
379C23×C11H(5,𝔽2)11yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C112−1+411yescharacteristic
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
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—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
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—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C22⋊D11—416no—
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—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
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#12114yes—
503C2×Dic11#12114yes—
504C2×Dic11#12114yes—
505C2×Dic11C22⋊Q814yes—
506C2×Dic11C22⋊Q814yes—
507C2×Dic11C22⋊Q814yes—
508C2×Dic11#12614yes—
509C23×D4—111no—
510C22×C4⋊C4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4—111no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4C2×D1111yescharacteristic
529C22×C22⋊C4C2×D1111yescharacteristic
530C22×C22⋊C4C2×D1111yescharacteristic
531C22×C42—111no—
532C22×C42—111no—
533C22×C42—111no—
534#396—224no—
535#396—224no—
536#390—224no—
537#390—224no—
538#390—224no—
539#389—224no—
540#389—224no—
541#389—224no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95C2×D1111yescharacteristic
550C2×#95C2×D1111yescharacteristic
551C2×#95C2×D1111yescharacteristic
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—81no—
560C22×C11—81no—
561C22×C11—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11C2×#12111yescharacteristic
568C22×C11C2×#12111yescharacteristic
569C22×C11C2×#12111yescharacteristic
570C22×C11C2×C22⋊Q811yescharacteristic
571C22×C11C2×C22⋊Q811yescharacteristic
572C22×C11C2×C22⋊Q811yescharacteristic
573C22×C11C2×#12611yescharacteristic
574C22×C11#52911yescharacteristic
575C22×C11#52911yescharacteristic
576C22×C11#52911yescharacteristic
577C22×C11#53211yescharacteristic
578C22×C11#53211yescharacteristic
579C22×C11#53211yescharacteristic
580C22×C11#54011yescharacteristic
581C22×C11#54011yescharacteristic
582C22×C11#54011yescharacteristic
583C22×C11#54211yescharacteristic
584C22×C11#54211yescharacteristic
585C22×C11#54211yescharacteristic
586C22×C11D4211yescharacteristic
587C22×C11D4211yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11#54611yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54811yescharacteristic
593C22×C11#54811yescharacteristic
594C22×C11#54811yescharacteristic
595C22×C11D4×Q811yescharacteristic
596C22×C11#55011yescharacteristic
597C22×C11#55011yescharacteristic
598C22×C11#55011yescharacteristic
599C22×C11#55411yescharacteristic
600C22×C11#55411yescharacteristic
601C22×C11#55411yescharacteristic
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—81no—
610C2×D11—81no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C2×D11—81no—
615C2×D11—81no—
616C2×D11—81no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627Dic11—42no—
628Dic11—42no—
629Dic11#39618yescomplemented
630C25—111no—
631C25C22×D1111yescharacteristic
632C22×D4—114no—
633C22×D4—222no—
634C22×D4—222no—
635C22×D4—222no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4C22×D1111yescharacteristic
647C23×C4C22×D1111yescharacteristic
648C23×C4C22×D1111yescharacteristic
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—114no—
656C2×C4⋊C4—114no—
657C2×C4⋊C4—114no—
658C2×C4⋊C4—222no—
659C2×C4⋊C4—222no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
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—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×C4⋊C4—441no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
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—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C22⋊C4—441no—
710C2×C22⋊C4—441no—
711C2×C22⋊C4—441no—
712C2×C22⋊C4—441no—
713C2×C22⋊C4—441no—
714C2×C22⋊C4—441no—
715C2×C42—222no—
716C2×C42—222no—
717C2×C42—222no—
718C2×C42—222no—
719C2×C42—222no—
720C2×C42—222no—
721C2×C42—222no—
722C2×C42—222no—
723C2×C42—222no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—114no—
728#95—222no—
729#95—222no—
730#95—222no—
731#95—222no—
732#95—222no—
733#95—222no—
734C2×C11—82no—
735C2×C11C2×#39611yescharacteristic
736C2×C11#242611yescharacteristic
737C2×C11#242611yescharacteristic
738C2×C11#242611yescharacteristic
739C2×C11#242811yescharacteristic
740C2×C11#242811yescharacteristic
741C2×C11#242811yescharacteristic
742C2×C11#245211yescharacteristic
743C2×C11#245211yescharacteristic
744C2×C11#245211yescharacteristic
745C2×C11#245411yescharacteristic
746C2×C11#245411yescharacteristic
747C2×C11#245411yescharacteristic
748C2×C11#264411yescharacteristic
749C2×C11#286011yescharacteristic
750D11—82no—
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—112no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24Q8×D1112yes—
781C24C23×D1111yescharacteristic
782C2×D4—228no—
783C2×D4—228no—
784C2×D4—228no—
785C2×D4—444no—
786C2×D4—444no—
787C2×D4—444no—
788C2×D4—444no—
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—21no—
814C22×C4—21no—
815C22×C4—21no—
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—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—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—221no—
839C22×C4—221no—
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—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4#433912yes—
875C22×C4D4×D1112yes—
876C22×C4D4×D1112yes—
877C22×C4D4×D1112yes—
878C22×C4D4×D1112yes—
879C22×C4#434112yes—
880C4⋊C4—44no—
881C4⋊C4—228no—
882C4⋊C4—228no—
883C4⋊C4—228no—
884C4⋊C4—444no—
885C4⋊C4—444no—
886C4⋊C4—444no—
887C4⋊C4—444no—
888C4⋊C4—444no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—444no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C22⋊C4—444no—
898C22⋊C4—444no—
899C22⋊C4—444no—
900C22⋊C4—444no—
901C42—444no—
902C42—444no—
903C42—444no—
904C11#1514111yescharacteristic, complemented, Sylow
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
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—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23C2×#433911yescharacteristic
976C23C2×D4×D1111yescharacteristic
977C23C2×D4×D1111yescharacteristic
978C23C2×D4×D1111yescharacteristic
979C23C2×D4×D1111yescharacteristic
980C23C2×#434111yescharacteristic
981C23#6703711yescharacteristic
982C23#6703711yescharacteristic
983C23C2×Q8×D1111yescharacteristic
984C23#41×D1111yescharacteristic
985C23#41×D1111yescharacteristic
986C23#41×D1111yescharacteristic
987C23#41×D1111yescharacteristic
988C23#6704211yescharacteristic
989C23#6704311yescharacteristic
990D4—4416no—
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—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—114no—
1034C2×C4—114no—
1035C2×C4—114no—
1036C2×C4—114no—
1037C2×C4—114no—
1038C2×C4—114no—
1039C2×C4—114no—
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—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×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—881no—
1105C22—881no—
1106C22—881no—
1107C22—881no—
1108C22—881no—
1109C22—881no—
1110C22—881no—
1111C22—881no—
1112C22#1062302111yescharacteristic
1113C22#1062304211yescharacteristic
1114C22#1062305911yescharacteristic
1115C22#1062306911yescharacteristic
1116C22#1062307911yescharacteristic
1117C22#1062308311yescharacteristic
1118C22#1062308411yescharacteristic
1119C22#1062312111yescharacteristic
1120C22#1062312111yescharacteristic
1121C22#1062312211yescharacteristic
1122C22#1062312711yescharacteristic
1123C22#1062312911yescharacteristic
1124C22#1062313011yescharacteristic
1125C22D11×#12111yescharacteristic
1126C22D11×#12111yescharacteristic
1127C22D11×#12111yescharacteristic
1128C22#1062314011yescharacteristic
1129C22#1062314611yescharacteristic
1130C22D11×C22⋊Q811yescharacteristic
1131C22D11×C22⋊Q811yescharacteristic
1132C22D11×C22⋊Q811yescharacteristic
1133C22#1062316311yescharacteristic
1134C22#1062316611yescharacteristic
1135C22#1062316711yescharacteristic
1136C22#1062318011yescharacteristic
1137C22#1062318511yescharacteristic
1138C22#1062319311yescharacteristic
1139C22#1062319411yescharacteristic
1140C22#1062319411yescharacteristic
1141C22#1062319911yescharacteristic
1142C22#1062320011yescharacteristic
1143C22#1062320811yescharacteristic
1144C22D11×#12611yescharacteristic
1145C22#1062324111yescharacteristic
1146C22#1062324911yescharacteristic
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—118no—
1154C4—442no—
1155C4—442no—
1156C4—442no—
1157C4—442no—
1158C4—442no—
1159C4—442no—
1160C2—82no—
1161C2—882no—
1162C2D11×#39611yescharacteristic
1163C2#1307217511yescharacteristic
1164C2#1307217911yescharacteristic
1165C2#1307218111yescharacteristic
1166C2#1307219711yescharacteristic
1167C2#1307219911yescharacteristic
1168C2#1307220311yescharacteristic
1169C2#1307245911yescharacteristic
1170C2#1307246111yescharacteristic
1171C2#1307246311yescharacteristic
1172C2#1307248311yescharacteristic
1173C2#1307248511yescharacteristic
1174C2#1307248711yescharacteristic
1175C2#1307457511yescharacteristic
1176C2#1307698211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1439C2
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#15141
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#10622561C2semidirect
2. C2×#10622607C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622260C2semidirect
8. C2×#10622585C2semidirect
9. #13066862C2semidirect
10. #13066861C2semidirect
11. #13066860C2semidirect
12. #13066860C2semidirect
13. #13066859C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1439C2semidirect
162. C11⋊#95D4semidirect
330. #1439D11semidirect
629. Dic11#396semidirect
904. C11#15141semidirect

Maximal subgroups

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

subgroupindex
C2×#106225612
C2×#106226072
C2×#106225702
C2×#106222602
C2×#106225852
#130668622
#130668612
#130668602
#130668592
#95×Dic112
C11×#14392
#1514111