Finite Group Databasebeta

← #14677219

Subgroups — #14677219

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×#66992C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066854C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C2×C4×D4×C11—24no—
24C2×C4×D4×C11—24no—
25C2×C4×D4×C11—24no—
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66992—24no—
35C2×#66992—24no—
36C2×#66992C418yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43#10622833—24no—
44#10622826—24no—
45#10622826—24no—
46C2×C11⋊#95—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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622571—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×C11C2×C414yes—
70C22×D4×C11D414yes—
71C22×D4×C11D414yes—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—22no—
77C23×C4×C11—22no—
78C23×C4×C11—22no—
79C23×C4×C11—22no—
80C23×C4×C11—22no—
81C23×C4×C11—41no—
82C23×C4×C11—41no—
83C23×C4×C11—41no—
84C23×C4×C11—41no—
85C23×C4×C11D414yescomplemented
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—22no—
92C22×C22⋊D11—22no—
93C22×C22⋊D11—22no—
94C22×C22⋊D11—22no—
95C22×C22⋊D11—22no—
96C22×C22⋊D11—22no—
97C22×C22⋊D11—22no—
98C22×C22⋊D11—22no—
99C22×C22⋊D11—22no—
100C22×C22⋊D11—22no—
101C22×C22⋊D11—41no—
102C22×C22⋊D11—41no—
103C22×C22⋊D11C2×C414yescomplemented
104C22×C22⋊D11C2×C414yescomplemented
105C23×Dic11—22no—
106C23×Dic11—22no—
107C23×Dic11—22no—
108C23×Dic11—22no—
109C23×Dic11—22no—
110C23×Dic11—22no—
111C23×Dic11—22no—
112C23×Dic11—22no—
113C23×Dic11—22no—
114C23×Dic11—41no—
115C23×Dic11—41no—
116C23×Dic11—41no—
117C23×Dic11—41no—
118C23×Dic11C2×C414yescomplemented
119C23×Dic11C2311yescharacteristic
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C4×D4×C11—232no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊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—22no—
135C2×C11×C22⋊C4D414yescomplemented
136C2×C42×C11—22no—
137C2×C42×C11—22no—
138C2×C42×C11—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—41no—
149C2×C22⋊Dic11—41no—
150C2×C22⋊Dic11C2×C414yescomplemented
151#66992—232no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
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)⋊C4—22no—
160C2×(C2×D11)⋊C4—22no—
161C2×(C2×D11)⋊C4—22no—
162C2×(C2×D11)⋊C4—41no—
163C2×(C2×D11)⋊C4—41no—
164C2×(C2×D11)⋊C4—41no—
165C2×(C2×D11)⋊C4—41no—
166C2×(C2×D11)⋊C4C2×C414yescomplemented
167C2×Dic11⋊C4—22no—
168C2×Dic11⋊C4—22no—
169C2×Dic11⋊C4C2×C414yescomplemented
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×C11C22×C412yes—
206C24×C11C22×C412yes—
207C24×C11C2×D412yes—
208C24×C11C2×D412yes—
209C24×C11C2×D412yes—
210C24×C11C2×D412yes—
211C24×C11C2×D412yes—
212C24×C11C2×D412yes—
213C24×C11#4112yes—
214C24×C11#4112yes—
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×D11—21no—
225C23×D11—21no—
226C23×D11—21no—
227C23×D11—21no—
228C23×D11—21no—
229C23×D11—21no—
230C23×D11C22×C412yes—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—28no—
236C2×D4×C11—28no—
237C2×D4×C11C22⋊C4116yescomplemented
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—28no—
247C22×C4×C11—28no—
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—28no—
267C22×C4×C11—44no—
268C22×C4×C11—44no—
269C22×C4×C11—44no—
270C22×C4×C11—44no—
271C22×C4×C11—44no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11—44no—
275C22×C4×C11—44no—
276C22×C4×C11—44no—
277C22×C4×C11—44no—
278C22×C4×C11C22×C412yes—
279C22×C4×C11C2×D412yes—
280C22×C4×C11C2×D412yes—
281C22×C4×C11C2×D412yes—
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11#4112yes—
287C2×C22⋊D11—28no—
288C2×C22⋊D11—28no—
289C2×C22⋊D11—28no—
290C2×C22⋊D11—28no—
291C2×C22⋊D11—28no—
292C2×C22⋊D11—44no—
293C2×C22⋊D11—44no—
294C2×C22⋊D11—44no—
295C2×C22⋊D11—44no—
296C2×C22⋊D11—44no—
297C2×C22⋊D11—44no—
298C2×C22⋊D11—44no—
299C2×C22⋊D11—44no—
300C2×C22⋊D11—44no—
301C22×Dic11—28no—
302C22×Dic11—28no—
303C22×Dic11—28no—
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—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—21no—
335C22×Dic11—21no—
336C22×Dic11—21no—
337C22×Dic11—21no—
338C22×Dic11—21no—
339C22×Dic11—21no—
340C22×Dic11—21no—
341C22×Dic11—21no—
342C22×Dic11—21no—
343C22×Dic11—21no—
344C22×Dic11—21no—
345C22×Dic11—21no—
346C22×Dic11—44no—
347C22×Dic11—44no—
348C22×Dic11—44no—
349C22×Dic11—44no—
350C22×Dic11—44no—
351C22×Dic11—44no—
352C22×Dic11—44no—
353C22×Dic11—44no—
354C22×Dic11—44no—
355C22×Dic11—44no—
356C22×Dic11—44no—
357C22×Dic11C22×C412yes—
358C22×Dic11C22×C412yes—
359C22×Dic11C22×C412yes—
360C22×Dic11C2×D412yes—
361C22×Dic11C2×D412yes—
362C22×Dic11#4112yes—
363C22×Dic11#4112yes—
364C11×C4⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—28no—
367C42×C11—28no—
368C22⋊Dic11—28no—
369C22⋊Dic11—44no—
370C22⋊Dic11—44no—
371C22⋊Dic11—44no—
372(C2×D11)⋊C4—28no—
373(C2×D11)⋊C4—44no—
374(C2×D11)⋊C4—44no—
375(C2×D11)⋊C4—44no—
376(C2×D11)⋊C4—44no—
377Dic11⋊C4—28no—
378C22×#121—111no—
379C22×C4×D4D1111yescharacteristic, complemented
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#1438—111no—
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—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
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×C11C2×C22⋊C414yes—
456C23×C11C2×C22⋊C414yes—
457C23×C11C4×D414yes—
458C23×C11C4×D414yes—
459C23×C11#12014yes—
460C23×C11#12114yes—
461C23×C11#12114yes—
462C23×C11#12314yes—
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—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—
500C22×D11—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11—41no—
508C22×D11—41no—
509C22×D11—41no—
510C22×D11—41no—
511C22×D11—41no—
512C22×D11—41no—
513D4×C11—232no—
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—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—416no—
536C2×C4×C11—416no—
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×C11—41no—
549C2×C4×C11C2×C22⋊C414yes—
550C2×C4×C11#12114yescomplemented
551C22⋊D11—416no—
552C22⋊D11—416no—
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—416no—
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×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×Dic11—41no—
600C2×Dic11—41no—
601C2×Dic11—41no—
602C2×Dic11—41no—
603C2×Dic11C4×D414yescomplemented
604C23×D4—111no—
605C23×D4—111no—
606C23×D4C2×D1111yescharacteristic
607C24×C4—111no—
608C24×C4—111no—
609C24×C4C2×D1111yescharacteristic
610C24×C4C2×D1111yescharacteristic
611C2×#121—118no—
612C2×#121—224no—
613C2×#121—224no—
614C2×C4×D4—24no—
615C2×C4×D4—24no—
616C2×C4×D4—24no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42C2×D1111yescharacteristic
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—111no—
648C2×#95—111no—
649C2×#95—224no—
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11#38618yescomplemented
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—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—81no—
723C2×D11—81no—
724C2×D11—81no—
725C2×D11—81no—
726C2×D11—81no—
727C2×D11—81no—
728C2×D11—81no—
729C2×D11—81no—
730C4×C11—24no—
731C4×C11—24no—
732C4×C11—42no—
733C4×C11—42no—
734C4×C11—42no—
735Dic11—24no—
736Dic11—42no—
737Dic11—42no—
738Dic11—42no—
739Dic11—42no—
740Dic11—81no—
741Dic11—81no—
742C25—111no—
743C25C22×D1111yescharacteristic
744C25C22×D1111yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—114no—
750C22×D4—114no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—222no—
761C22×D4—441no—
762C22×D4—441no—
763C22×D4C4×D1114yes—
764C22×D4D4414yes—
765C22×D4C22⋊D1114yes—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4—111no—
780C23×C4—111no—
781C23×C4—111no—
782C23×C4—111no—
783C23×C4—111no—
784C23×C4—114no—
785C23×C4—111no—
786C23×C4—111no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—222no—
793C23×C4—222no—
794C23×C4—222no—
795C23×C4—222no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4—441no—
800C23×C4C22⋊D1114yescomplemented
801C23×C4C22×D1111yescharacteristic
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—2232no—
807C4×D4—232no—
808C2×C4⋊C4—22no—
809C2×C4⋊C4—22no—
810C2×C4⋊C4—22no—
811C2×C4⋊C4—114no—
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—114no—
820C2×C22⋊C4—114no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
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—441no—
841C2×C22⋊C4—441no—
842C2×C22⋊C4—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4C22⋊D1114yescomplemented
847C2×C42—22no—
848C2×C42—22no—
849C2×C42—22no—
850#95—114no—
851#95—222no—
852#95—222no—
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—28no—
865C2×C11—44no—
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—82no—
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—112no—
903C24—221no—
904C24—221no—
905C24—221no—
906C24—221no—
907C24—221no—
908C24—221no—
909C24—221no—
910C24—221no—
911C24—221no—
912C24—221no—
913C24—221no—
914C24—221no—
915C24—221no—
916C24—221no—
917C24C2×C4×D1112yes—
918C24C2×C4×D1112yes—
919C24C2×D4412yes—
920C24C2×D4412yes—
921C24#433912yes—
922C24#433912yes—
923C24C2×C22⋊D1112yes—
924C24C2×C22⋊D1112yes—
925C24C2×C22⋊D1112yes—
926C24C2×C22⋊D1112yes—
927C24C23×D1111yescharacteristic
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—444no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4(C2×D11)⋊C4116yescomplemented
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—28no—
958C22×C4—28no—
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—28no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—112no—
995C22×C4—112no—
996C22×C4—228no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—228no—
1002C22×C4—228no—
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—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—221no—
1038C22×C4—221no—
1039C22×C4—221no—
1040C22×C4—221no—
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×C4C2×C4×D1112yes—
1053C22×C4C2×D4412yes—
1054C22×C4D4×D1112yes—
1055C22×C4#434112yes—
1056C22×C4C2×C22⋊D1112yes—
1057C22×C4C2×C22⋊D1112yes—
1058C22×C4C2×C22⋊D1112yes—
1059C22×C4C2×C22⋊D1112yes—
1060C22×C4C2×C22⋊D1112yes—
1061C4⋊C4—28no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—228no—
1066C22⋊C4—228no—
1067C22⋊C4—444no—
1068C22⋊C4—444no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—28no—
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—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
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—222no—
1139C23—222no—
1140C23—222no—
1141C23—222no—
1142C23—222no—
1143C23—222no—
1144C23—222no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23—441no—
1152C23—441no—
1153C23—441no—
1154C23—441no—
1155C23—441no—
1156C23—441no—
1157C23—441no—
1158C23—441no—
1159C23—441no—
1160C23—441no—
1161C23—441no—
1162C23—441no—
1163C23—441no—
1164C23—441no—
1165C23—441no—
1166C23—441no—
1167C23—441no—
1168C23—441no—
1169C23—441no—
1170C23—441no—
1171C23—441no—
1172C23—441no—
1173C23C2×(C2×D11)⋊C414yes—
1174C23C2×(C2×D11)⋊C414yes—
1175C23C4×C22⋊D1114yes—
1176C23C4×C22⋊D1114yes—
1177C23#6698214yes—
1178C23#6698314yes—
1179C23#6698314yes—
1180C23#6700614yes—
1181C23C22×C4×D1111yescharacteristic
1182C23C22×D4411yescharacteristic
1183C23C2×#433911yescharacteristic
1184C23C2×#433911yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×#434111yescharacteristic
1187C23#6703711yescharacteristic
1188C23#6703711yescharacteristic
1189C23#41×D1111yescharacteristic
1190C23#41×D1111yescharacteristic
1191C23#6704211yescharacteristic
1192C23#6704311yescharacteristic
1193C23C22×C22⋊D1111yescharacteristic
1194C23C22×C22⋊D1111yescharacteristic
1195C23C22×C22⋊D1111yescharacteristic
1196D4—232no—
1197D4—4416no—
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—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—416no—
1221C2×C4—416no—
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—41no—
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—4416no—
1254C2×C4—4416no—
1255C2×C4—441no—
1256C2×C4—441no—
1257C2×C4—441no—
1258C2×C4—441no—
1259C2×C4—441no—
1260C2×C4—441no—
1261C2×C4—441no—
1262C2×C4—441no—
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×C4C2×(C2×D11)⋊C414yes—
1286C2×C4#6699214yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—442no—
1317C22—442no—
1318C22—442no—
1319C22—442no—
1320C22—442no—
1321C22—442no—
1322C22—442no—
1323C22—881no—
1324C22—881no—
1325C22—881no—
1326C22—881no—
1327C22—881no—
1328C22—881no—
1329C22—881no—
1330C22—881no—
1331C22#1062282618yescomplemented
1332C22C4×#434111yescharacteristic
1333C22#1062306911yescharacteristic
1334C22#1062307111yescharacteristic
1335C22#1062307111yescharacteristic
1336C22C4×D4×D1111yescharacteristic
1337C22#1062307611yescharacteristic
1338C22#1062307711yescharacteristic
1339C22#1062307811yescharacteristic
1340C22D4×D4411yescharacteristic
1341C22#1062308311yescharacteristic
1342C22#1062308511yescharacteristic
1343C22#1062308511yescharacteristic
1344C22#1062308611yescharacteristic
1345C22#1062309111yescharacteristic
1346C22#1062309511yescharacteristic
1347C22#1062309611yescharacteristic
1348C22C22×(C2×D11)⋊C411yescharacteristic
1349C22C2×C4×C22⋊D1111yescharacteristic
1350C22C2×C4×C22⋊D1111yescharacteristic
1351C22C2×#6698211yescharacteristic
1352C22C2×#6698311yescharacteristic
1353C22C2×#6698311yescharacteristic
1354C22D4×C22⋊D1111yescharacteristic
1355C22D4×C22⋊D1111yescharacteristic
1356C22C2×#6699211yescharacteristic
1357C22#1062333511yescharacteristic
1358C22#1062333711yescharacteristic
1359C22#1062333711yescharacteristic
1360C22#1062335511yescharacteristic
1361C22#1062335511yescharacteristic
1362C22#1062336011yescharacteristic
1363C22#1062336011yescharacteristic
1364C22#1062336311yescharacteristic
1365C22#1062336411yescharacteristic
1366C22C2×#6700611yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—224no—
1373C4—442no—
1374C4—442no—
1375C4—442no—
1376C4—442no—
1377C4—881no—
1378C4—881no—
1379C2—28no—
1380C2—44no—
1381C2—882no—
1382C2C2×#1062282611yescharacteristic
1383C2C4×#6699211yescharacteristic
1384C2#1307131411yescharacteristic
1385C2D4×(C2×D11)⋊C411yescharacteristic
1386C2#1307144111yescharacteristic
1387C2#1307163311yescharacteristic
1388C2#1307166111yescharacteristic
1389C2#1307199011yescharacteristic
1390C2#1307205611yescharacteristic
1391C2#1307214611yescharacteristic
1392C2#1307216111yescharacteristic
1393C2#1307222011yescharacteristic
1394C2#1307234511yescharacteristic
1395C2#1307236011yescharacteristic
1396C2#1307357211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenterC22×C4×D4D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622833C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622571C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066866C2semidirect
8. #13066863C2semidirect
9. #13066858C2semidirect
10. #13066855C2semidirect
11. #13066854C2semidirect
12. #13066849C2semidirect
13. #13066839C2semidirect
14. #13066838C2semidirect
15. C22×C4×D4×C11C2semidirect
36. C2×#66992C4semidirect
85. C23×C4×C11D4semidirect
103. C22×C22⋊D11C2×C4semidirect
104. C22×C22⋊D11C2×C4semidirect
118. C23×Dic11C2×C4semidirect
135. C2×C11×C22⋊C4D4semidirect
150. C2×C22⋊Dic11C2×C4semidirect
166. C2×(C2×D11)⋊C4C2×C4semidirect
169. C2×Dic11⋊C4C2×C4semidirect
183. C11⋊#95D4semidirect
237. C2×D4×C11C22⋊C4semidirect
379. C22×C4×D4D11semidirect
550. C2×C4×C11#121semidirect
603. C2×Dic11C4×D4semidirect
679. C22×C11#386semidirect
800. C23×C4C22⋊D11semidirect
846. C2×C22⋊C4C22⋊D11semidirect
948. C2×D4(C2×D11)⋊C4semidirect
1075. C11#14023semidirect
1286. C2×C4#66992semidirect
1331. C22#10622826semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106228332
C2×#106228262
C2×#106225712
C22×C11⋊#952
#130668662
#130668632
#130668582
#130668552
#130668542
#130668492
#130668392
#130668382
C22×C4×D4×C112
#1402311