Finite Group Databasebeta

← #14675905

Subgroups — #14675905

Order 2816.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic, complemented
5C22×C11⋊#95C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066882C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11#13066841C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×(C22⋊D11)⋊C4—24no—
32C2×(C22⋊D11)⋊C4—24no—
33C2×(C22⋊D11)⋊C4C418yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622826—24no—
39C2×C11⋊#95—24no—
40C2×C11⋊#95C2211yescharacteristic
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
56#10622571—24no—
57#10622277—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11C2311yescharacteristic
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⋊D11C2×C414yes—
78C22×C22⋊D11D414yes—
79C22×C22⋊D11D414yes—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11—22no—
86C23×Dic11—22no—
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
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11C2×C414yescomplemented
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4C2×C414yes—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
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—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4C2×C414yescomplemented
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11C2×C414yescomplemented
138(C22⋊D11)⋊C4—232no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—41no—
142C11×#95—41no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95D414yescomplemented
159#13894—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11C22×C412yes—
169C24×C11C2×D412yes—
170C24×C11C2×D412yes—
171C24×C11#4112yes—
172C24×C11#4112yes—
173C24×C11#4112yes—
174C24×C11#4112yes—
175C24×C11C2411yescharacteristic
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11C22×C412yes—
189C23×D11C2×D412yes—
190C23×D11C2×D412yes—
191C22×C4×C11—28no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11C22×C412yes—
237C22×C4×C11C22×C412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11#4112yes—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11C22⋊C4116yes—
247C22×Dic11—28no—
248C22×Dic11—28no—
249C22×Dic11—28no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×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—44no—
291C22×Dic11—44no—
292C22×Dic11—44no—
293C22×Dic11—44no—
294C22×Dic11—44no—
295C22×Dic11—44no—
296C22×Dic11—44no—
297C22×Dic11—44no—
298C22×Dic11—44no—
299C22×Dic11—44no—
300C22×Dic11—44no—
301C22×Dic11C22×C412yes—
302C22×Dic11C22×C412yes—
303C22×Dic11C22×C412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11C2×D412yes—
308C22×Dic11#4112yes—
309C22×Dic11#4112yes—
310C2×C4×D11—28no—
311C2×C4×D11—28no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C11×C22⋊C4—28no—
318C11×C22⋊C4—44no—
319C22⋊Dic11—44no—
320(C2×D11)⋊C4—28no—
321(C2×D11)⋊C4—44no—
322(C2×D11)⋊C4—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
325Dic11⋊C4—28no—
326C4×Dic11—28no—
327C22×C4×D4—111no—
328C2×#386—111no—
329C2×#386—111no—
330C2×#381—111no—
331C22×#95—111no—
332#1445—111no—
333#1445—111no—
334#1440—111no—
335#1440—111no—
336#1434—111no—
337#1434—111no—
338C22⋊#95—111no—
339C22⋊#95—111no—
340C22⋊#95—111no—
341C22⋊#95D1111yescharacteristic, complemented
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
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—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11C2×C22⋊C414yes—
371C23×C11#11714yes—
372C23×C11#11714yes—
373C23×C11#12314yes—
374C23×C11#12314yes—
375C23×C11#12314yes—
376C23×C11#12314yes—
377C23×C11C23×C411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C112−1+411yescharacteristic
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
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—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
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×D11C2×C22⋊C414yes—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—416no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
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—
470C22⋊D11—232no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
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—22no—
492C2×Dic11—416no—
493C2×Dic11—416no—
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×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11C2×C22⋊C414yes—
521C2×Dic11C4×D414yes—
522C4×D11—416no—
523C23×D4—111no—
524C24×C4—111no—
525C24×C4—111no—
526C24×C4—111no—
527C24×C4C2×D1111yescharacteristic
528C2×C4×D4—118no—
529C2×C4×D4—224no—
530C2×C4×D4—224no—
531C22×C4⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4C2×D1111yescharacteristic
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C42—111no—
541#386—224no—
542#386—224no—
543#381—224no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—224no—
561C2×#95C2×D1111yescharacteristic
562C2×#95C2×D1111yescharacteristic
563C2×#95C2×D1111yescharacteristic
564C2×#95C2×D1111yescharacteristic
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—24no—
569C22×C11—24no—
570C22×C11—24no—
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—24no—
575C22×C11—24no—
576C22×C11—24no—
577C22×C11—24no—
578C22×C11—24no—
579C22×C11#38118yescomplemented
580C22×C11C22×C22⋊C411yescharacteristic
581C22×C11C2×#11711yescharacteristic
582C22×C11C2×#11711yescharacteristic
583C22×C11C2×C4×D411yescharacteristic
584C22×C11C4×#4111yescharacteristic
585C22×C11#51811yescharacteristic
586C22×C11#52011yescharacteristic
587C22×C11C2×#12311yescharacteristic
588C22×C11C2×#12311yescharacteristic
589C22×C11C2×#12311yescharacteristic
590C22×C11C2×#12311yescharacteristic
591C22×C11#52511yescharacteristic
592C22×C11#52511yescharacteristic
593C22×C11#52911yescharacteristic
594C22×C11#52911yescharacteristic
595C22×C11#53811yescharacteristic
596C22×C11#53811yescharacteristic
597C22×C11#53911yescharacteristic
598C22×C11#53911yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54611yescharacteristic
604C22×C11#54611yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54711yescharacteristic
607C22×C11#54711yescharacteristic
608C22×C11#54811yescharacteristic
609C22×C11#55111yescharacteristic
610C22×C11#55111yescharacteristic
611C22×C11#55211yescharacteristic
612C22×C11#55311yescharacteristic
613C22×C11#55311yescharacteristic
614C22×C11#55311yescharacteristic
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C4×C11—42no—
631C4×C11—42no—
632C4×C11—42no—
633C4×C11—42no—
634C4×C11—81no—
635C4×C11—81no—
636Dic11—24no—
637Dic11—24no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641Dic11—81no—
642Dic11—81no—
643C25—111no—
644C25C22×D1111yescharacteristic
645C22×D4—114no—
646C22×D4—114no—
647C22×D4—114no—
648C22×D4—222no—
649C22×D4—222no—
650C22×D4—222no—
651C22×D4—222no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—41no—
658C23×C4—41no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—114no—
665C23×C4—114no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—441no—
682C23×C4—441no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4—441no—
686C23×C4—441no—
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692C23×C4C22×D1111yescharacteristic
693C4×D4—2232no—
694C2×C4⋊C4—114no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
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—441no—
717C2×C22⋊C4—441no—
718C2×C22⋊C4—441no—
719C2×C22⋊C4—441no—
720C2×C22⋊C4C4×D1114yes—
721C2×C42—114no—
722C2×C42—222no—
723C2×C42—222no—
724#95—22no—
725#95—22no—
726#95—41no—
727#95—41no—
728#95—114no—
729#95—222no—
730#95—222no—
731#95—222no—
732#95—222no—
733#95—222no—
734#95—222no—
735#95—222no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—441no—
741#95—441no—
742#95—441no—
743#95—441no—
744C2×C11—28no—
745C2×C11C2×#38111yescharacteristic
746C2×C11#229011yescharacteristic
747C2×C11#231811yescharacteristic
748C2×C11D4×C22⋊C411yescharacteristic
749C2×C11#233911yescharacteristic
750C2×C11#235211yescharacteristic
751C2×C11#235311yescharacteristic
752C2×C11#241811yescharacteristic
753C2×C11#241811yescharacteristic
754C2×C11#241911yescharacteristic
755C2×C11#241911yescharacteristic
756C2×C11#244311yescharacteristic
757C2×C11#244311yescharacteristic
758C2×C11#244411yescharacteristic
759C2×C11#244411yescharacteristic
760D11—44no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—112no—
770C24—112no—
771C24—112no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24C2×C4×D1112yes—
785C24#433912yes—
786C24#433912yes—
787C24D4×D1112yes—
788C24D4×D1112yes—
789C24#434112yes—
790C24#434312yes—
791C24C23×D1111yescharacteristic
792C2×D4—1116no—
793C2×D4—228no—
794C2×D4—228no—
795C2×D4—228no—
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C22×C4—28no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—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—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—228no—
854C22×C4—228no—
855C22×C4—228no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—228no—
865C22×C4—228no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—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—444no—
899C22×C4—444no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4C2×C4×D1112yes—
915C22×C4C2×C4×D1112yes—
916C22×C4D4×D1112yes—
917C22×C4#434112yes—
918C4⋊C4—228no—
919C22⋊C4—28no—
920C22⋊C4—44no—
921C22⋊C4—228no—
922C22⋊C4—444no—
923C22⋊C4—444no—
924C22⋊C4—444no—
925C22⋊C4—444no—
926C22⋊C4—444no—
927C42—228no—
928C11#1389411yescharacteristic, complemented, Sylow
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
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—22no—
957C23—114no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23—441no—
991C23—441no—
992C23#6692514yes—
993C23C22⋊C4×D1114yes—
994C23#6693614yes—
995C23#6693614yes—
996C23#6694514yes—
997C23#6694714yes—
998C23#6694714yes—
999C23C22×C4×D1111yescharacteristic
1000C23C2×#433911yescharacteristic
1001C23C2×#433911yescharacteristic
1002C23C2×D4×D1111yescharacteristic
1003C23C2×D4×D1111yescharacteristic
1004C23C2×D4×D1111yescharacteristic
1005C23C2×#434111yescharacteristic
1006C23C2×#434111yescharacteristic
1007C23#6703711yescharacteristic
1008C23#6703711yescharacteristic
1009C23C2×#434311yescharacteristic
1010C23#41×D1111yescharacteristic
1011C23#41×D1111yescharacteristic
1012C23#6704211yescharacteristic
1013C23#6704311yescharacteristic
1014D4—2232no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
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—114no—
1059C2×C4—114no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—4416no—
1082C2×C4—4416no—
1083C2×C4—4416no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
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—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—224no—
1125C22—224no—
1126C22—224no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22#1062227718yescomplemented
1140C22C2×#6692511yescharacteristic
1141C22C2×C22⋊C4×D1111yescharacteristic
1142C22C2×#6693611yescharacteristic
1143C22C2×#6693611yescharacteristic
1144C22#1062302111yescharacteristic
1145C22#1062302611yescharacteristic
1146C22C2×#6694511yescharacteristic
1147C22C2×#6694711yescharacteristic
1148C22C2×#6694711yescharacteristic
1149C22#1062305811yescharacteristic
1150C22#1062306211yescharacteristic
1151C22C4×#434111yescharacteristic
1152C22#1062307111yescharacteristic
1153C22#1062307111yescharacteristic
1154C22C4×D4×D1111yescharacteristic
1155C22#1062307611yescharacteristic
1156C22#1062307711yescharacteristic
1157C22#1062308311yescharacteristic
1158C22#1062309611yescharacteristic
1159C22#1062311711yescharacteristic
1160C22#1062312111yescharacteristic
1161C22#1062312211yescharacteristic
1162C22#1062312411yescharacteristic
1163C22#1062314011yescharacteristic
1164C22#1062314111yescharacteristic
1165C22#1062314111yescharacteristic
1166C22#1062314211yescharacteristic
1167C22#1062315511yescharacteristic
1168C22#1062315811yescharacteristic
1169C22#1062317511yescharacteristic
1170C22#1062317611yescharacteristic
1171C22#1062318011yescharacteristic
1172C22#1062318511yescharacteristic
1173C22#1062318611yescharacteristic
1174C22#1062319611yescharacteristic
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—81no—
1180C4—81no—
1181C4—224no—
1182C4—224no—
1183C4—442no—
1184C4—442no—
1185C4—442no—
1186C4—881no—
1187C4—881no—
1188C2—28no—
1189C2—444no—
1190C2C2×#1062227711yescharacteristic
1191C2#1307105211yescharacteristic
1192C2#1307124411yescharacteristic
1193C2#1307143411yescharacteristic
1194C2#1307144211yescharacteristic
1195C2#1307153911yescharacteristic
1196C2#1307155011yescharacteristic
1197C2#1307208211yescharacteristic
1198C2#1307208411yescharacteristic
1199C2#1307209711yescharacteristic
1200C2#1307209911yescharacteristic
1201C2#1307235511yescharacteristic
1202C2#1307235711yescharacteristic
1203C2#1307237011yescharacteristic
1204C2#1307237211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13894
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622277C2semidirect
5. C22×C11⋊#95C2semidirect
6. #13066882C2semidirect
7. #13066882C2semidirect
8. #13066864C2semidirect
9. #13066864C2semidirect
10. #13066842C2semidirect
11. #13066841C2semidirect
12. #13066838C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
33. C2×(C22⋊D11)⋊C4C4semidirect
107. C22×C4×D11C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
134. C2×Dic11⋊C4C2×C4semidirect
137. C2×C4×Dic11C2×C4semidirect
158. C11⋊#95D4semidirect
341. C22⋊#95D11semidirect
579. C22×C11#381semidirect
928. C11#13894semidirect
1139. C22#10622277semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106228262
C2×#106225712
C2×#106222772
C22×C11⋊#952
#130668822
#130668642
#130668422
#130668412
#130668382
(C2×D11)⋊#952
C11×C22⋊#952
#1389411