Finite Group Databasebeta

← #14677263

Subgroups — #14677263

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622259C211yesmaximal, characteristic, complemented
5C2×#10622570C211yesmaximal, characteristic
6#13066865C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic, complemented
10Dic11⋊#95C211yesmaximal, characteristic, complemented
11#13066839C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×C4×C22⋊D11—24no—
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66938—24no—
39C2×#66938—24no—
40C2×#66938C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622570—24no—
58#10622259—24no—
59#10622259—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11D414yes—
81C22×C22⋊D11D414yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×Dic22—22no—
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22C2×C414yescomplemented
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4C2×C414yescomplemented
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11C2×C414yescomplemented
118C4×C22⋊D11—232no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×(C2×D11)⋊C4C2×C414yescomplemented
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4D414yes—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11C2×C414yescomplemented
148C2×C4×Dic11D414yes—
149#66938—232no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—41no—
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⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166#14027—111nomaximal, Sylow
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×C11—21no—
179C24×C11C22×C412yes—
180C24×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2411yescharacteristic
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×D11—21no—
195C23×D11C22×C412yes—
196C23×D11C2×D412yes—
197C23×D11C2×D412yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—28no—
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×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11C22×C412yes—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
246C22×C4×C11#4112yes—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11C22⋊C4116yes—
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×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×Dic11C22×C412yes—
292C22×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C22×Dic11#4112yes—
303C2×C4×D11—28no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×Dic22—28no—
311C2×Dic22—28no—
312C2×Dic22—28no—
313C2×Dic22—44no—
314C2×Dic22—44no—
315C2×Dic22—44no—
316C2×Dic22—44no—
317C11×C22⋊C4—28no—
318C11×C22⋊C4—44no—
319C22⋊Dic11—28no—
320C22⋊Dic11—28no—
321C22⋊Dic11—44no—
322(C2×D11)⋊C4—28no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327Dic11⋊C4—28no—
328Dic11⋊C4—44no—
329C4×Dic11—28no—
330C4×Dic11—28no—
331C4×Dic11—44no—
332C22×#124—111no—
333C22×C4×D4—111no—
334C2×#391—111no—
335C2×#391—111no—
336C2×#390—111no—
337#1440—111no—
338#1440—111no—
339#1440—111no—
340#1440—111no—
341C4⋊#95—111no—
342C22⋊#95—111no—
343C22⋊#95—111no—
344C22⋊#95—111no—
345C22⋊#95D1111yescharacteristic, complemented
346C4×#95—111no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11C2×C22⋊C414yes—
382C23×C11C23×C411yescharacteristic
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C112−1+411yescharacteristic
396C23×C112−1+411yescharacteristic
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11C2×C22⋊C414yes—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—416no—
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—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11#12414yescomplemented
475C22⋊D11—232no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
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—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11C2×C22⋊C414yes—
519C2×Dic11C4×D414yes—
520C2×Dic11C4×D414yes—
521C2×Dic11#12014yes—
522C2×Dic11#12114yes—
523C2×Dic11#12114yes—
524C2×Dic11#12314yes—
525C4×D11—416no—
526Dic22—416no—
527C23×Q8—111no—
528C23×D4—111no—
529C24×C4—111no—
530C24×C4C2×D1111yescharacteristic
531C2×#124—118no—
532C2×#124—224no—
533C2×#124—224no—
534C2×C4×D4—224no—
535C2×C4×D4—224no—
536C2×C4×D4—224no—
537C22×C4⋊C4—111no—
538C22×C4⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4C2×D1111yescharacteristic
548C22×C22⋊C4C2×D1111yescharacteristic
549C22×C42—111no—
550C22×C42—111no—
551C22×C42—111no—
552#391—224no—
553#391—224no—
554#390—224no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95C2×D1111yescharacteristic
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C2×#95C2×D1111yescharacteristic
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11C22×C22⋊C411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11C4×#4111yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11#52011yescharacteristic
593C22×C11C2×#12011yescharacteristic
594C22×C11C2×#12111yescharacteristic
595C22×C11C2×#12111yescharacteristic
596C22×C11C2×#12311yescharacteristic
597C22×C11C2×#12411yescharacteristic
598C22×C11#52911yescharacteristic
599C22×C11#52911yescharacteristic
600C22×C11#53211yescharacteristic
601C22×C11#53511yescharacteristic
602C22×C11#53611yescharacteristic
603C22×C11#54211yescharacteristic
604C22×C11#54211yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54611yescharacteristic
611C22×C11#54711yescharacteristic
612C22×C11#54711yescharacteristic
613C22×C11#54711yescharacteristic
614C22×C11#54711yescharacteristic
615C22×C11#54811yescharacteristic
616C22×C11#54811yescharacteristic
617C22×C11#55611yescharacteristic
618C22×C11#55611yescharacteristic
619C22×C11#55911yescharacteristic
620C22×C11#55911yescharacteristic
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C4×C11—24no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—81no—
642Dic11—42no—
643Dic11—42no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648Dic11#38618yes—
649C25—111no—
650C25C22×D1111yescharacteristic
651C22×Q8—114no—
652C22×Q8—222no—
653C22×Q8—222no—
654C22×Q8—222no—
655C22×Q8—222no—
656C22×Q8—222no—
657C22×Q8—222no—
658C22×D4—114no—
659C22×D4—114no—
660C22×D4—114no—
661C22×D4—222no—
662C22×D4—222no—
663C22×D4—222no—
664C22×D4—222no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—441no—
685C23×C4—441no—
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692#124—2232no—
693C4×D4—2232no—
694C2×C4⋊C4—114no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—114no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—441no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4C4×D1114yescomplemented
730C2×C42—114no—
731C2×C42—114no—
732C2×C42—222no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737C2×C42—222no—
738C2×C42—222no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—41no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—441no—
753#95—441no—
754#95—441no—
755C2×C11—44no—
756C2×C11C2×#38611yescharacteristic
757C2×C11C4×#12411yescharacteristic
758C2×C11#232611yescharacteristic
759C2×C11#233911yescharacteristic
760C2×C11#233911yescharacteristic
761C2×C11#236711yescharacteristic
762C2×C11#236711yescharacteristic
763C2×C11#242711yescharacteristic
764C2×C11#242711yescharacteristic
765C2×C11#243211yescharacteristic
766C2×C11#243511yescharacteristic
767C2×C11#244711yescharacteristic
768C2×C11#244711yescharacteristic
769C2×C11#254411yescharacteristic
770C2×C11#254711yescharacteristic
771D11—44no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24C2×C4×D1112yes—
800C24D4×D1112yes—
801C24D4×D1112yes—
802C24C23×D1111yescharacteristic
803C2×Q8—228no—
804C2×Q8—228no—
805C2×Q8—228no—
806C2×Q8—444no—
807C2×Q8—444no—
808C2×Q8—444no—
809C2×Q8—444no—
810C2×D4—1116no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C2×D4—228no—
816C2×D4—228no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—228no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4C2×C4×D1112yes—
916C22×C4C2×C4×D1112yes—
917C22×C4#433912yes—
918C22×C4#433912yes—
919C22×C4D4×D1112yes—
920C22×C4D4×D1112yes—
921C22×C4#434112yes—
922C4⋊C4—228no—
923C4⋊C4—444no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—228no—
927C22⋊C4—228no—
928C22⋊C4—228no—
929C22⋊C4—228no—
930C22⋊C4—228no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C22⋊C4—444no—
934C42—228no—
935C42—228no—
936C42—444no—
937C11#1402711yescharacteristic, complemented, Sylow
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—114no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—441no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23C22⋊C4×D1114yes—
1008C23C22×C4×D1111yescharacteristic
1009C23C2×#433911yescharacteristic
1010C23C2×#433911yescharacteristic
1011C23C2×D4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×D4×D1111yescharacteristic
1014C23C2×D4×D1111yescharacteristic
1015C23C2×#434111yescharacteristic
1016C23#6703711yescharacteristic
1017C23#6703711yescharacteristic
1018C23#6704011yescharacteristic
1019C23#41×D1111yescharacteristic
1020C23#41×D1111yescharacteristic
1021C23#41×D1111yescharacteristic
1022C23#6704311yescharacteristic
1023Q8—4416no—
1024D4—2232no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—114no—
1068C2×C4—114no—
1069C2×C4—114no—
1070C2×C4—114no—
1071C2×C4—114no—
1072C2×C4—114no—
1073C2×C4—114no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—4416no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4#6693814yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22C4×#433911yescharacteristic
1149C22C2×C22⋊C4×D1111yescharacteristic
1150C22#1062302111yescharacteristic
1151C22#1062302111yescharacteristic
1152C22#1062302111yescharacteristic
1153C22C2×#6693811yescharacteristic
1154C22#1062303511yescharacteristic
1155C22#1062303811yescharacteristic
1156C22#1062303811yescharacteristic
1157C22#1062305911yescharacteristic
1158C22#1062306411yescharacteristic
1159C22C4×#434111yescharacteristic
1160C22#1062306911yescharacteristic
1161C22C4×D4×D1111yescharacteristic
1162C22C4×D4×D1111yescharacteristic
1163C22#1062307711yescharacteristic
1164C22#1062307911yescharacteristic
1165C22#1062308311yescharacteristic
1166C22#1062309011yescharacteristic
1167C22D11×#12011yescharacteristic
1168C22#1062312211yescharacteristic
1169C22#1062312211yescharacteristic
1170C22#1062312311yescharacteristic
1171C22D11×#12111yescharacteristic
1172C22D11×#12111yescharacteristic
1173C22#1062314111yescharacteristic
1174C22#1062314211yescharacteristic
1175C22#1062315911yescharacteristic
1176C22#1062316411yescharacteristic
1177C22#1062317111yescharacteristic
1178C22#1062317211yescharacteristic
1179C22D11×#12311yescharacteristic
1180C22#1062318611yescharacteristic
1181C22#1062319311yescharacteristic
1182C22#1062319511yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—118no—
1190C4—442no—
1191C4—442no—
1192C4—442no—
1193C4—442no—
1194C4—442no—
1195C4—881no—
1196C2—44no—
1197C2—444no—
1198C2D11×#38611yescharacteristic
1199C2C4×#6693811yescharacteristic
1200C2#1307132211yescharacteristic
1201C2#1307144211yescharacteristic
1202C2#1307144311yescharacteristic
1203C2#1307168411yescharacteristic
1204C2#1307168811yescharacteristic
1205C2#1307219011yescharacteristic
1206C2#1307219211yescharacteristic
1207C2#1307224211yescharacteristic
1208C2#1307226511yescharacteristic
1209C2#1307240011yescharacteristic
1210C2#1307240211yescharacteristic
1211C2#1307358511yescharacteristic
1212C2#1307361011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622259C2semidirect
4. C2×#10622259C2semidirect
6. #13066865C2semidirect
7. #13066864C2semidirect
8. #13066864C2semidirect
9. #13066863C2semidirect
10. Dic11⋊#95C2semidirect
11. #13066839C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×C22⋊#95C2semidirect
40. C2×#66938C4semidirect
102. C22×Dic22C2×C4semidirect
108. C2×C11×C22⋊C4C2×C4semidirect
117. C2×C22⋊Dic11C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
147. C2×C4×Dic11C2×C4semidirect
345. C22⋊#95D11semidirect
474. C2×C4×C11#124semidirect
729. C2×C22⋊C4C4×D11semidirect
937. C11#14027semidirect
1117. C2×C4#66938semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C22×C4×C22⋊D112
C2×#106222592
C2×#106225702
#130668652
#130668642
#130668632
Dic11⋊#952
#130668392
(C2×D11)⋊#952
#95×Dic112
C11×C22⋊#952
#1402711