Finite Group Databasebeta

← #14681922

Subgroups — #14681922

Order 2816.

2386 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622268C211yesmaximal, characteristic, complemented
5C2×#10622265C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66992—24no—
30C2×#66992—24no—
31C2×#66992C418yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44#10622834—24no—
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622570—24no—
56#10622268—24no—
57#10622265—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11C2×C414yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11C2×C414yes—
86C22×C22⋊D11C2×C414yes—
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—41no—
90C23×Dic11—41no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11C2×C414yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
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—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11—41no—
125C2×C22⋊Dic11—41no—
126C2×C22⋊Dic11C2×C414yes—
127C2×C22⋊Dic11D414yescomplemented
128#66992—232no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4C2×C414yes—
144C2×C4⋊Dic11—22no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11—41no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—41no—
150C2×Dic11⋊C4C2×C414yes—
151C2×Dic11⋊C4D414yes—
152C2×Dic11⋊C4D414yes—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—41no—
158C2×C4×Dic11—41no—
159C11×#95—22no—
160C11×#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171#14418—111nomaximal, Sylow
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×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11C22×C412yes—
199C24×C11C22×C412yes—
200C24×C11C2×D412yes—
201C24×C11#4112yes—
202C24×C11C2411yescharacteristic
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11C22×C412yes—
218C2×D4×C11—28no—
219C2×D4×C11—28no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11—44no—
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×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
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×C11C22×C412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11#4112yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C22×Dic11—28no—
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×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—44no—
315C22×Dic11—44no—
316C22×Dic11—44no—
317C22×Dic11—44no—
318C22×Dic11—44no—
319C22×Dic11—44no—
320C22×Dic11C22×C412yes—
321C22×Dic11C22×C412yes—
322C22×Dic11C22×C412yes—
323C22×Dic11C2×D412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11C2×D412yes—
327C22×Dic11C2×D412yes—
328C22×Dic11C2×D412yes—
329C22×Dic11#4112yes—
330C11×C22⋊C4—44no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C11×C22⋊C4—44no—
334C22⋊Dic11—28no—
335C22⋊Dic11—44no—
336C22⋊Dic11—44no—
337C22⋊Dic11—44no—
338C22⋊Dic11—44no—
339(C2×D11)⋊C4—28no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344C4⋊Dic11—44no—
345Dic11⋊C4—44no—
346Dic11⋊C4C22⋊C4116yescomplemented
347C4×Dic11—44no—
348C4×Dic11—44no—
349C22×#121—111no—
350C2×#390—111no—
351C2×#390—111no—
352C2×#387—111no—
353C2×#387—111no—
354#1439—111no—
355#1439—111no—
356#1438—111no—
357#1438—111no—
358#1438—111no—
359#1438D1111yescharacteristic, complemented
360#1437—111no—
361#1437—111no—
362C22⋊#95—111no—
363C22⋊#95—111no—
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—22no—
379C23×C11—22no—
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—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×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×C11C4×D414yes—
434C23×C11C23×C411yescharacteristic
435C23×C11C22×D411yescharacteristic
436C23×C11C22×D411yescharacteristic
437C23×C11C22×D411yescharacteristic
438C23×C11C2×#4111yescharacteristic
439C23×C11C2×#4111yescharacteristic
440C23×C11C2×#4111yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C23×C11H(5,𝔽2)11yescharacteristic
443C23×C11H(5,𝔽2)11yescharacteristic
444C23×C11H(5,𝔽2)11yescharacteristic
445C23×C11H(5,𝔽2)11yescharacteristic
446C23×C11H(5,𝔽2)11yescharacteristic
447C23×C11H(5,𝔽2)11yescharacteristic
448C23×C112−1+411yescharacteristic
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
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—
484D4×C11—416no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11C2×C22⋊C414yes—
520C22⋊D11—416no—
521C22⋊D11—416no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
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—416no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
571C2×Dic11C2×C22⋊C414yes—
572C23×D4—111no—
573C23×D4—111no—
574C23×D4C2×D1111yescharacteristic
575C24×C4—111no—
576C2×#121—118no—
577C2×#121—224no—
578C2×#121—224no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4—111no—
581C22×C4⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4C2×D1111yescharacteristic
593C22×C22⋊C4C2×D1111yescharacteristic
594C22×C22⋊C4C2×D1111yescharacteristic
595C22×C22⋊C4C2×D1111yescharacteristic
596C22×C42—111no—
597C22×C42—111no—
598#390—224no—
599#390—224no—
600#387—224no—
601#387—224no—
602C2×#95—111no—
603C2×#95—111no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95C2×D1111yescharacteristic
613C2×#95C2×D1111yescharacteristic
614C22×C11—24no—
615C22×C11—24no—
616C22×C11—24no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—81no—
637C22×C11—81no—
638C22×C11—81no—
639C22×C11—81no—
640C22×C11—81no—
641C22×C11—81no—
642C22×C11—81no—
643C22×C11—81no—
644C22×C11C22×C22⋊C411yescharacteristic
645C22×C11C2×C4×D411yescharacteristic
646C22×C11C4×#4111yescharacteristic
647C22×C11#51811yescharacteristic
648C22×C11#51811yescharacteristic
649C22×C11#51811yescharacteristic
650C22×C11#52011yescharacteristic
651C22×C11#53411yescharacteristic
652C22×C11#53511yescharacteristic
653C22×C11#53511yescharacteristic
654C22×C11#53511yescharacteristic
655C22×C11#53511yescharacteristic
656C22×C11#53711yescharacteristic
657C22×C11#53811yescharacteristic
658C22×C11#53811yescharacteristic
659C22×C11#53811yescharacteristic
660C22×C11#53911yescharacteristic
661C22×C11#54011yescharacteristic
662C22×C11#54011yescharacteristic
663C22×C11D4211yescharacteristic
664C22×C11D4211yescharacteristic
665C22×C11#54611yescharacteristic
666C22×C11#54611yescharacteristic
667C22×C11#54611yescharacteristic
668C22×C11#54611yescharacteristic
669C22×C11#54811yescharacteristic
670C22×C11#54811yescharacteristic
671C22×C11#55011yescharacteristic
672C22×C11#55011yescharacteristic
673C22×C11#55311yescharacteristic
674C22×C11#55311yescharacteristic
675C22×C11#56011yescharacteristic
676C22×C11#56011yescharacteristic
677C22×C11#56211yescharacteristic
678C22×C11#56211yescharacteristic
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—81no—
687C2×D11—81no—
688C2×D11—81no—
689C2×D11—81no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C2×D11—81no—
694C4×C11—24no—
695C4×C11—42no—
696C4×C11—81no—
697C4×C11—81no—
698C4×C11—81no—
699Dic11—24no—
700Dic11—24no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705Dic11—81no—
706C25—111no—
707C25C22×D1111yescharacteristic
708C25C22×D1111yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—114no—
716C22×D4—114no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4C4×D1114yes—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—114no—
737C23×C4—111no—
738C23×C4—222no—
739C23×C4—222no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4—441no—
743C23×C4—441no—
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749#121—2232no—
750C2×C4⋊C4—114no—
751C2×C4⋊C4—114no—
752C2×C4⋊C4—114no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—222no—
755C2×C4⋊C4—222no—
756C2×C4⋊C4—222no—
757C2×C4⋊C4—441no—
758C2×C4⋊C4—441no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—114no—
772C2×C22⋊C4—114no—
773C2×C22⋊C4—114no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—441no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C42—222no—
802C2×C42—222no—
803C2×C42—222no—
804C2×C42—222no—
805C2×C42—441no—
806C2×C42—441no—
807#95—22no—
808#95—22no—
809#95—222no—
810#95—222no—
811#95—222no—
812#95—222no—
813#95—222no—
814#95—222no—
815#95—441no—
816#95—441no—
817#95—441no—
818#95—441no—
819C2×C11—44no—
820C2×C11—82no—
821C2×C11#230911yescharacteristic
822C2×C11#232511yescharacteristic
823C2×C11#233311yescharacteristic
824C2×C11D4×C22⋊C411yescharacteristic
825C2×C11#234111yescharacteristic
826C2×C11#236411yescharacteristic
827C2×C11#237711yescharacteristic
828C2×C11#267311yescharacteristic
829C2×C11#267311yescharacteristic
830C2×C11#267611yescharacteristic
831C2×C11#267611yescharacteristic
832C2×C11#271111yescharacteristic
833C2×C11#271111yescharacteristic
834C2×C11#271411yescharacteristic
835C2×C11#271411yescharacteristic
836D11—82no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—112no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24C2×C4×D1112yes—
879C24C2×C4×D1112yes—
880C24D4×D1112yes—
881C24#434112yes—
882C24C23×D1111yescharacteristic
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—228no—
891C2×D4—228no—
892C2×D4—228no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—228no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
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—444no—
986C22×C4—444no—
987C22×C4—444no—
988C22×C4—444no—
989C22×C4—444no—
990C22×C4—444no—
991C22×C4C2×C4×D1112yes—
992C22×C4D4×D1112yes—
993C22×C4D4×D1112yes—
994C22×C4#434112yes—
995C4⋊C4—1116no—
996C4⋊C4—444no—
997C4⋊C4—444no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—228no—
1003C22⋊C4—228no—
1004C22⋊C4—444no—
1005C22⋊C4—444no—
1006C22⋊C4—444no—
1007C22⋊C4—444no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C22⋊C4—444no—
1011C22⋊C4—444no—
1012C42—444no—
1013C42—444no—
1014C11#1441811yescharacteristic, complemented, Sylow
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
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—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23(C22⋊D11)⋊C414yes—
1120C23C22×C4×D1111yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23C2×D4×D1111yescharacteristic
1123C23C2×D4×D1111yescharacteristic
1124C23C2×#434111yescharacteristic
1125C23C2×#434111yescharacteristic
1126C23#6703711yescharacteristic
1127C23#6703711yescharacteristic
1128C23#6703711yescharacteristic
1129C23#6703711yescharacteristic
1130C23#6703711yescharacteristic
1131C23#41×D1111yescharacteristic
1132C23#6704211yescharacteristic
1133C23#6704211yescharacteristic
1134C23#6704311yescharacteristic
1135D4—416no—
1136D4—4416no—
1137D4—4416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—114no—
1173C2×C4—114no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—4416no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4—441no—
1205C2×C4—441no—
1206C2×C4—441no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4C22⋊C4×D1114yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—442no—
1260C22—881no—
1261C22—881no—
1262C22—881no—
1263C22—881no—
1264C22—881no—
1265C22—881no—
1266C22—881no—
1267C22—881no—
1268C22C2×C22⋊C4×D1111yescharacteristic
1269C22C2×(C22⋊D11)⋊C411yescharacteristic
1270C22#1062301711yescharacteristic
1271C22C4×#434111yescharacteristic
1272C22#1062307611yescharacteristic
1273C22#1062307611yescharacteristic
1274C22#1062307711yescharacteristic
1275C22#1062312111yescharacteristic
1276C22#1062312111yescharacteristic
1277C22#1062312211yescharacteristic
1278C22#1062312211yescharacteristic
1279C22#1062312211yescharacteristic
1280C22#1062312411yescharacteristic
1281C22#1062312411yescharacteristic
1282C22#1062312611yescharacteristic
1283C22#1062312811yescharacteristic
1284C22#1062312911yescharacteristic
1285C22#1062313011yescharacteristic
1286C22#1062313211yescharacteristic
1287C22#1062313611yescharacteristic
1288C22#1062313811yescharacteristic
1289C22#1062313811yescharacteristic
1290C22#1062314411yescharacteristic
1291C22#1062314911yescharacteristic
1292C22#1062315011yescharacteristic
1293C22#1062315111yescharacteristic
1294C22#1062315211yescharacteristic
1295C22#1062318511yescharacteristic
1296C22#1062319411yescharacteristic
1297C22#1062319611yescharacteristic
1298C22#1062319811yescharacteristic
1299C22#1062320511yescharacteristic
1300C22#1062320811yescharacteristic
1301C22#1062324611yescharacteristic
1302C22#1062324911yescharacteristic
1303C4—24no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—224no—
1309C4—224no—
1310C4—442no—
1311C4—442no—
1312C4—442no—
1313C4—442no—
1314C4—881no—
1315C2—44no—
1316C2—82no—
1317C2—882no—
1318C2#1307119511yescharacteristic
1319C2#1307131711yescharacteristic
1320C2#1307138211yescharacteristic
1321C2#1307143211yescharacteristic
1322C2#1307145511yescharacteristic
1323C2#1307166411yescharacteristic
1324C2#1307177411yescharacteristic
1325C2#1307487511yescharacteristic
1326C2#1307488111yescharacteristic
1327C2#1307491011yescharacteristic
1328C2#1307491911yescharacteristic
1329C2#1307536611yescharacteristic
1330C2#1307537511yescharacteristic
1331C2#1307540511yescharacteristic
1332C2#1307541411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenter#1438D11
hypocenterC11#14418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622268C2semidirect
5. C2×#10622265C2semidirect
6. #13066862C2semidirect
7. #13066859C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066855C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. #13066838C2semidirect
14. #13066838C2semidirect
15. C11×#1438C2semidirect
31. C2×#66992C4semidirect
127. C2×C22⋊Dic11D4semidirect
346. Dic11⋊C4C22⋊C4semidirect
359. #1438D11semidirect
1014. C11#14418semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106228342
C2×#106225702
C2×#106222682
C2×#106222652
#130668622
#130668592
#130668552
#130668532
#130668522
#130668382
C11×#14382
#1441811