Finite Group Databasebeta

← #14677226

Subgroups — #14677226

Order 2816.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic, complemented
4C2×#10622569C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66991—24no—
33C2×#66991—24no—
34C2×#66991C418yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×(C22⋊D11)⋊C4—24no—
41C2×(C22⋊D11)⋊C4—24no—
42C2×(C22⋊D11)⋊C4—24no—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45#10622833—24no—
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622569—24no—
59#10622569—24no—
60#10622569—24no—
61D11×#95—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×C414yescomplemented
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⋊D11C2×C414yes—
88C22×C22⋊D11C2×C414yescomplemented
89C22×C22⋊D11D414yes—
90C22×C22⋊D11D414yes—
91C23×Dic11—22no—
92C23×Dic11—22no—
93C23×Dic11—22no—
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—41no—
97C23×Dic11—41no—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C4×D11—22no—
111C22×C4×D11—22no—
112C22×C4×D11—22no—
113C22×C4×D11—22no—
114C22×C4×D11—22no—
115C22×C4×D11—22no—
116C22×C4×D11—22no—
117C22×C4×D11—22no—
118C22×C4×D11—41no—
119C22×C4×D11—41no—
120C22×C4×D11—41no—
121C22×C4×D11—41no—
122C22×C4×D11—41no—
123C22×C4×D11—41no—
124C22×C4×D11C2×C414yescomplemented
125C22×C4×D11D414yescomplemented
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—22no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—41no—
135C2×C11×C22⋊C4—41no—
136C2×C11×C22⋊C4—41no—
137C2×C11×C22⋊C4—41no—
138C2×C22⋊Dic11—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—22no—
141C2×C22⋊Dic11—22no—
142C2×C22⋊Dic11—22no—
143C2×C22⋊Dic11—22no—
144C2×C22⋊Dic11—22no—
145C2×C22⋊Dic11—22no—
146C2×C22⋊Dic11—22no—
147C2×C22⋊Dic11—22no—
148C2×C22⋊Dic11—22no—
149C2×C22⋊Dic11—41no—
150C2×C22⋊Dic11—41no—
151C2×C22⋊Dic11C2×C414yescomplemented
152C2×C22⋊Dic11C2×C414yescomplemented
153#66991—232no—
154C2×(C2×D11)⋊C4—22no—
155C2×(C2×D11)⋊C4—22no—
156C2×(C2×D11)⋊C4—22no—
157C2×(C2×D11)⋊C4—22no—
158C2×(C2×D11)⋊C4—22no—
159C2×(C2×D11)⋊C4D414yescomplemented
160C2×C4⋊Dic11—22no—
161C2×C4⋊Dic11—22no—
162C2×C4⋊Dic11C2×C414yescomplemented
163C2×Dic11⋊C4—22no—
164C2×Dic11⋊C4—22no—
165C2×Dic11⋊C4—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169(C22⋊D11)⋊C4—232no—
170C11×#95—22no—
171C11×#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—41no—
182C11⋊#95—41no—
183C11⋊#95D414yescomplemented
184#14023—111nomaximal, Sylow
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×C11—21no—
211C24×C11C22×C412yes—
212C24×C11C22×C412yes—
213C24×C11C2×D412yes—
214C24×C11C2×D412yes—
215C24×C11C2411yescharacteristic
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×D11C22×C412yes—
225C23×D11C2×D412yes—
226C23×D11C2×D412yes—
227C23×D11C2×D412yes—
228C23×D11C2×D412yes—
229C23×D11#4112yes—
230C23×D11#4112yes—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—44no—
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×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11C22×C412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11#4112yes—
272C22×C4×C11#4112yes—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—28no—
279C2×C22⋊D11—28no—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C2×C22⋊D11C22⋊C4116yescomplemented
287C22×Dic11—28no—
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—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—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—44no—
328C22×Dic11—44no—
329C22×Dic11—44no—
330C22×Dic11—44no—
331C22×Dic11—44no—
332C22×Dic11—44no—
333C22×Dic11C22×C412yes—
334C22×Dic11C22×C412yes—
335C22×Dic11C22×C412yes—
336C22×Dic11C2×D412yes—
337C22×Dic11C2×D412yes—
338C22×Dic11C2×D412yes—
339C22×Dic11C2×D412yes—
340C22×Dic11C2×D412yes—
341C22×Dic11C2×D412yes—
342C22×Dic11#4112yes—
343C2×C4×D11—28no—
344C2×C4×D11—28no—
345C2×C4×D11—28no—
346C2×C4×D11—28no—
347C2×C4×D11—28no—
348C2×C4×D11—44no—
349C2×C4×D11—44no—
350C2×C4×D11—44no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C2×C4×D11—44no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11—44no—
363C2×C4×D11—44no—
364C11×C22⋊C4—28no—
365C11×C22⋊C4—44no—
366C11×C22⋊C4—44no—
367C11×C22⋊C4—44no—
368C22⋊Dic11—28no—
369C22⋊Dic11—28no—
370C22⋊Dic11—44no—
371C22⋊Dic11—44no—
372C22⋊Dic11—44no—
373(C2×D11)⋊C4—28no—
374(C2×D11)⋊C4—44no—
375C4⋊Dic11—28no—
376Dic11⋊C4—28no—
377C4×Dic11—28no—
378C22×#121—111no—
379C22×C4×D4—111no—
380C2×#386—111no—
381C2×#386—111no—
382C2×#386—111no—
383C2×#386—111no—
384C22×#95—111no—
385#1441—111no—
386#1440—111no—
387#1439—111no—
388#1438D1111yescharacteristic, complemented
389#1437—111no—
390#1436—111no—
391C22⋊#95—111no—
392C22⋊#95—111no—
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—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
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×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11—41no—
458C23×C11—41no—
459C23×C11—41no—
460C23×C11—41no—
461C23×C11—41no—
462C23×C11C2×C22⋊C414yes—
463C23×C11C23×C411yescharacteristic
464C23×C11C22×D411yescharacteristic
465C23×C11C22×D411yescharacteristic
466C23×C11C22×D411yescharacteristic
467C23×C11C22×D411yescharacteristic
468C23×C11C22×D411yescharacteristic
469C23×C11C2×#4111yescharacteristic
470C23×C11C2×#4111yescharacteristic
471C23×C11C2×#4111yescharacteristic
472C23×C11C2×#4111yescharacteristic
473C23×C11C2×#4111yescharacteristic
474C23×C11H(5,𝔽2)11yescharacteristic
475C23×C11H(5,𝔽2)11yescharacteristic
476C23×C11H(5,𝔽2)11yescharacteristic
477C23×C112−1+411yescharacteristic
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—22no—
490C22×D11—22no—
491C22×D11—22no—
492C22×D11—22no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—22no—
498C22×D11—22no—
499C22×D11—22no—
500C22×D11—22no—
501C22×D11—22no—
502C22×D11—22no—
503C22×D11—22no—
504C22×D11—22no—
505C22×D11—22no—
506C22×D11C2×C22⋊C414yes—
507C22×D11C4×D414yes—
508C22×D11C4×D414yes—
509C22×D11#12014yes—
510C22×D11#12114yes—
511C22×D11#12114yes—
512C22×D11#12314yes—
513D4×C11—416no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11C4×D414yescomplemented
549C22⋊D11—232no—
550C22⋊D11—416no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—22no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—416no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—41no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11—41no—
599C2×Dic11C2×C22⋊C414yes—
600C2×Dic11#12114yescomplemented
601C4×D11—416no—
602C4×D11—416no—
603C4×D11—416no—
604C23×D4—111no—
605C23×D4—111no—
606C23×D4C2×D1111yescharacteristic
607C24×C4—111no—
608C24×C4—111no—
609C24×C4—111no—
610C24×C4—111no—
611C2×#121—118no—
612C2×#121—224no—
613C2×#121—224no—
614C2×C4×D4—224no—
615C2×C4×D4—224no—
616C2×C4×D4—224no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4C2×D1111yescharacteristic
627C22×C22⋊C4C2×D1111yescharacteristic
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42—111no—
631#386—224no—
632#386—224no—
633#386—224no—
634#386—224no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—111no—
646C2×#95—111no—
647C2×#95—224no—
648C2×#95C2×D1111yescharacteristic
649C2×#95C2×D1111yescharacteristic
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—81no—
673C22×C11—81no—
674C22×C11—81no—
675C22×C11—81no—
676C22×C11—81no—
677C22×C11—81no—
678C22×C11—81no—
679C22×C11—81no—
680C22×C11C22×C22⋊C411yescharacteristic
681C22×C11C2×C4×D411yescharacteristic
682C22×C11C2×C4×D411yescharacteristic
683C22×C11C2×C4×D411yescharacteristic
684C22×C11C4×#4111yescharacteristic
685C22×C11#51811yescharacteristic
686C22×C11#52011yescharacteristic
687C22×C11C2×#12011yescharacteristic
688C22×C11C2×#12111yescharacteristic
689C22×C11C2×#12111yescharacteristic
690C22×C11C2×#12111yescharacteristic
691C22×C11C2×#12311yescharacteristic
692C22×C11#52511yescharacteristic
693C22×C11#52911yescharacteristic
694C22×C11#53211yescharacteristic
695C22×C11#53411yescharacteristic
696C22×C11#53711yescharacteristic
697C22×C11#53811yescharacteristic
698C22×C11#53911yescharacteristic
699C22×C11D4211yescharacteristic
700C22×C11D4211yescharacteristic
701C22×C11D4211yescharacteristic
702C22×C11#54611yescharacteristic
703C22×C11#54611yescharacteristic
704C22×C11#54611yescharacteristic
705C22×C11#54611yescharacteristic
706C22×C11#54611yescharacteristic
707C22×C11#54611yescharacteristic
708C22×C11#54711yescharacteristic
709C22×C11#54711yescharacteristic
710C22×C11#54711yescharacteristic
711C22×C11#54811yescharacteristic
712C22×C11#55311yescharacteristic
713C22×C11#55311yescharacteristic
714C22×C11#55311yescharacteristic
715C2×D11—24no—
716C2×D11—24no—
717C2×D11—24no—
718C2×D11—24no—
719C2×D11—24no—
720C2×D11—24no—
721C2×D11—24no—
722C2×D11—24no—
723C2×D11—24no—
724C2×D11—24no—
725C2×D11—24no—
726C2×D11—24no—
727C2×D11—24no—
728C2×D11—24no—
729C2×D11#38618yescomplemented
730C4×C11—24no—
731C4×C11—42no—
732C4×C11—42no—
733C4×C11—42no—
734C4×C11—81no—
735Dic11—24no—
736Dic11—24no—
737Dic11—42no—
738Dic11—42no—
739Dic11—42no—
740Dic11—42no—
741Dic11—81no—
742C25—111no—
743C25C22×D1111yescharacteristic
744C25C22×D1111yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—41no—
750C22×D4—41no—
751C22×D4—114no—
752C22×D4—114no—
753C22×D4—114no—
754C22×D4—114no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—222no—
761C22×D4—222no—
762C22×D4—222no—
763C22×D4—222no—
764C22×D4—222no—
765C22×D4C4×D1114yescomplemented
766C23×C4—111no—
767C23×C4—111no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—114no—
773C23×C4—114no—
774C23×C4—111no—
775C23×C4—222no—
776C23×C4—222no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—222no—
793C23×C4—441no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4—441no—
800C23×C4—441no—
801C23×C4C22×D1111yescharacteristic
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—2232no—
807C4×D4—2232no—
808C2×C4⋊C4—114no—
809C2×C4⋊C4—222no—
810C2×C4⋊C4—222no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4—222no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—114no—
827C2×C22⋊C4—114no—
828C2×C22⋊C4—114no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—222no—
840C2×C22⋊C4—222no—
841C2×C22⋊C4—222no—
842C2×C22⋊C4—222no—
843C2×C22⋊C4—222no—
844C2×C22⋊C4—222no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4—441no—
847C2×C42—222no—
848C2×C42—222no—
849C2×C42—222no—
850#95—22no—
851#95—22no—
852#95—114no—
853#95—222no—
854#95—222no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—441no—
863#95—441no—
864C2×C11—44no—
865C2×C11—82no—
866C2×C11C2×#38611yescharacteristic
867C2×C11C4×#12111yescharacteristic
868C2×C11#232511yescharacteristic
869C2×C11D4×C22⋊C411yescharacteristic
870C2×C11#233911yescharacteristic
871C2×C11#236111yescharacteristic
872C2×C11#236411yescharacteristic
873C2×C11#241011yescharacteristic
874C2×C11#241611yescharacteristic
875C2×C11#242411yescharacteristic
876C2×C11#242511yescharacteristic
877C2×C11#243011yescharacteristic
878C2×C11#244311yescharacteristic
879C2×C11#244411yescharacteristic
880C2×C11#254311yescharacteristic
881D11—28no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—112no—
909C24—112no—
910C24—112no—
911C24—112no—
912C24—112no—
913C24—112no—
914C24—112no—
915C24—221no—
916C24—221no—
917C24—221no—
918C24—221no—
919C24—221no—
920C24—221no—
921C24—221no—
922C24—221no—
923C24C2×C4×D1112yes—
924C24C2×C4×D1112yes—
925C24D4×D1112yes—
926C24D4×D1112yes—
927C24C23×D1111yescharacteristic
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—1116no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—228no—
940C2×D4—228no—
941C2×D4—228no—
942C2×D4—228no—
943C2×D4—228no—
944C2×D4—228no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
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—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—112no—
979C22×C4—112no—
980C22×C4—112no—
981C22×C4—112no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—228no—
989C22×C4—228no—
990C22×C4—228no—
991C22×C4—228no—
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—228no—
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—221no—
1012C22×C4—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—228no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—444no—
1034C22×C4—444no—
1035C22×C4—444no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4—444no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4—444no—
1054C22×C4—444no—
1055C22×C4C2×C4×D1112yes—
1056C22×C4D4×D1112yes—
1057C22×C4D4×D1112yes—
1058C22×C4D4×D1112yes—
1059C22×C4#434112yes—
1060C22×C4#434112yes—
1061C4⋊C4—228no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—228no—
1068C22⋊C4—228no—
1069C22⋊C4—228no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—228no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
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—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—114no—
1146C23—114no—
1147C23—114no—
1148C23—114no—
1149C23—114no—
1150C23—114no—
1151C23—114no—
1152C23—222no—
1153C23—222no—
1154C23—222no—
1155C23—222no—
1156C23—222no—
1157C23—222no—
1158C23—222no—
1159C23—222no—
1160C23—222no—
1161C23—222no—
1162C23—222no—
1163C23—222no—
1164C23—222no—
1165C23—222no—
1166C23—222no—
1167C23—222no—
1168C23—222no—
1169C23—222no—
1170C23—222no—
1171C23—222no—
1172C23—222no—
1173C23—222no—
1174C23—222no—
1175C23—222no—
1176C23—222no—
1177C23—222no—
1178C23—222no—
1179C23—222no—
1180C23C22⋊C4×D1114yes—
1181C23C22×C4×D1111yescharacteristic
1182C23C2×D4×D1111yescharacteristic
1183C23C2×D4×D1111yescharacteristic
1184C23C2×D4×D1111yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×D4×D1111yescharacteristic
1187C23C2×#434111yescharacteristic
1188C23C2×#434111yescharacteristic
1189C23#6703711yescharacteristic
1190C23#6703711yescharacteristic
1191C23#6703711yescharacteristic
1192C23#41×D1111yescharacteristic
1193C23#41×D1111yescharacteristic
1194C23#41×D1111yescharacteristic
1195C23#6704311yescharacteristic
1196D4—416no—
1197D4—2232no—
1198D4—4416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—114no—
1234C2×C4—114no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—222no—
1238C2×C4—222no—
1239C2×C4—222no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—222no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—222no—
1249C2×C4—222no—
1250C2×C4—222no—
1251C2×C4—222no—
1252C2×C4—222no—
1253C2×C4—222no—
1254C2×C4—222no—
1255C2×C4—222no—
1256C2×C4—222no—
1257C2×C4—222no—
1258C2×C4—222no—
1259C2×C4—4416no—
1260C2×C4—4416no—
1261C2×C4—4416no—
1262C2×C4—4416no—
1263C2×C4—441no—
1264C2×C4—441no—
1265C2×C4—441no—
1266C2×C4—441no—
1267C2×C4—441no—
1268C2×C4—441no—
1269C2×C4—441no—
1270C2×C4—441no—
1271C2×C4—441no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4—441no—
1286C2×C4(C22⋊D11)⋊C414yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—118no—
1318C22—224no—
1319C22—224no—
1320C22—224no—
1321C22—224no—
1322C22—224no—
1323C22—224no—
1324C22—224no—
1325C22—224no—
1326C22—224no—
1327C22—224no—
1328C22—224no—
1329C22—224no—
1330C22—224no—
1331C22—224no—
1332C22C2×C22⋊C4×D1111yescharacteristic
1333C22C2×(C22⋊D11)⋊C411yescharacteristic
1334C22#1062301711yescharacteristic
1335C22C4×#434111yescharacteristic
1336C22C4×D4×D1111yescharacteristic
1337C22C4×D4×D1111yescharacteristic
1338C22#1062307711yescharacteristic
1339C22D11×#12011yescharacteristic
1340C22#1062312011yescharacteristic
1341C22#1062312111yescharacteristic
1342C22#1062312111yescharacteristic
1343C22#1062312211yescharacteristic
1344C22#1062312211yescharacteristic
1345C22#1062312211yescharacteristic
1346C22#1062312211yescharacteristic
1347C22D11×#12111yescharacteristic
1348C22D11×#12111yescharacteristic
1349C22D11×#12111yescharacteristic
1350C22#1062313711yescharacteristic
1351C22#1062313911yescharacteristic
1352C22#1062314111yescharacteristic
1353C22#1062314211yescharacteristic
1354C22#1062314211yescharacteristic
1355C22#1062314311yescharacteristic
1356C22#1062314411yescharacteristic
1357C22#1062314511yescharacteristic
1358C22#1062314511yescharacteristic
1359C22D11×#12311yescharacteristic
1360C22#1062318611yescharacteristic
1361C22#1062319111yescharacteristic
1362C22#1062319211yescharacteristic
1363C22#1062320811yescharacteristic
1364C22#1062321111yescharacteristic
1365C22#1062324711yescharacteristic
1366C22#1062324811yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—224no—
1373C4—224no—
1374C4—442no—
1375C4—442no—
1376C4—442no—
1377C4—442no—
1378C4—881no—
1379C2—44no—
1380C2—82no—
1381C2—228no—
1382C2D11×#38611yescharacteristic
1383C2#1307113211yescharacteristic
1384C2#1307131811yescharacteristic
1385C2#1307143211yescharacteristic
1386C2#1307144211yescharacteristic
1387C2#1307163711yescharacteristic
1388C2#1307166511yescharacteristic
1389C2#1307198311yescharacteristic
1390C2#1307204911yescharacteristic
1391C2#1307215511yescharacteristic
1392C2#1307216811yescharacteristic
1393C2#1307221911yescharacteristic
1394C2#1307234411yescharacteristic
1395C2#1307235911yescharacteristic
1396C2#1307357111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenter#1438D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622569C2semidirect
5. C2×#10622569C2semidirect
6. C2×#10622569C2semidirect
7. C2×D11×#95C2semidirect
8. #13066868C2semidirect
9. #13066863C2semidirect
10. #13066859C2semidirect
11. #13066853C2semidirect
12. #13066850C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1438C2semidirect
34. C2×#66991C4semidirect
71. C22×D4×C11C2×C4semidirect
88. C22×C22⋊D11C2×C4semidirect
124. C22×C4×D11C2×C4semidirect
125. C22×C4×D11D4semidirect
151. C2×C22⋊Dic11C2×C4semidirect
152. C2×C22⋊Dic11C2×C4semidirect
159. C2×(C2×D11)⋊C4D4semidirect
162. C2×C4⋊Dic11C2×C4semidirect
183. C11⋊#95D4semidirect
286. C2×C22⋊D11C22⋊C4semidirect
388. #1438D11semidirect
548. C2×C4×C11C4×D4semidirect
600. C2×Dic11#121semidirect
729. C2×D11#386semidirect
765. C22×D4C4×D11semidirect
1075. C11#14023semidirect
1286. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C22×(C22⋊D11)⋊C42
C2×#106228332
C2×#106225692
C2×D11×#952
#130668682
#130668632
#130668592
#130668532
#130668502
#130668382
(C2×D11)⋊#952
C11×#14382
#1402311