Finite Group Databasebeta

← #14690449

Subgroups — #14690449

Order 2816.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622288C211yesmaximal, characteristic, complemented
2C2×#10622566C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622570C211yesmaximal, characteristic
5C2×#10622570C211yesmaximal, characteristic
6C2×#10622260C211yesmaximal, characteristic, complemented
7#13066865C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
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
51#10622570—24no—
52#10622570—24no—
53#10622570—24no—
54#10622566—24no—
55#10622288—24no—
56#10622260—24no—
57C25×C11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11D414yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4—41no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—41no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4D414yes—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—41no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95D414yescomplemented
153#15138—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
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×C11C2×D412yes—
169C24×C11C2411yescharacteristic
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
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×D11C2×D412yes—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
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×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11#4112yes—
226C22×C4×C11#4112yes—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
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×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11#4112yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C22×Dic11#4112yes—
283C11×C22⋊C4—44no—
284C11×C22⋊C4—44no—
285C11×C22⋊C4—44no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288C22⋊Dic11—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295C4⋊Dic11—44no—
296Dic11⋊C4—28no—
297Dic11⋊C4—44no—
298Dic11⋊C4—44no—
299Dic11⋊C4—44no—
300C4×Dic11—44no—
301C4×Dic11—44no—
302C4×Dic11—44no—
303C2×#397—111no—
304C2×#397—111no—
305C2×#390—111no—
306C2×#390—111no—
307C2×#390—111no—
308C2×#389—111no—
309#1440—111no—
310#1440—111no—
311#1440—111no—
312#1440D1111yescharacteristic, complemented
313#1439—111no—
314#1439—111no—
315C4⋊#95—111no—
316C4⋊#95—111no—
317C4×#95—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C2×#4111yescharacteristic
357C23×C11C2×#4111yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C112−1+411yescharacteristic
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C22⋊D11—416no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11#12114yes—
489C2×Dic11#12314yes—
490C2×Dic11#12314yes—
491C2×Dic11#12314yes—
492C2×Dic11#12414yes—
493C2×Dic11#12614yes—
494C2×Dic11#12614yes—
495C23×D4—111no—
496C22×C4⋊C4—111no—
497C22×C4⋊C4—111no—
498C22×C4⋊C4—111no—
499C22×C4⋊C4—111no—
500C22×C4⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4C2×D1111yescharacteristic
511C22×C22⋊C4C2×D1111yescharacteristic
512C22×C22⋊C4C2×D1111yescharacteristic
513C22×C42—111no—
514C22×C42—111no—
515C22×C42—111no—
516#397—224no—
517#397—224no—
518#390—224no—
519#390—224no—
520#390—224no—
521#389—224no—
522C2×#95—111no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95C2×D1111yescharacteristic
533C2×#95C2×D1111yescharacteristic
534C2×#95C2×D1111yescharacteristic
535C2×#95C2×D1111yescharacteristic
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—81no—
544C22×C11—81no—
545C22×C11—81no—
546C22×C11—81no—
547C22×C11—81no—
548C22×C11—81no—
549C22×C11—81no—
550C22×C11—81no—
551C22×C11C2×#12111yescharacteristic
552C22×C11C2×#12311yescharacteristic
553C22×C11C2×#12311yescharacteristic
554C22×C11C2×#12311yescharacteristic
555C22×C11C2×#12411yescharacteristic
556C22×C11C2×#12611yescharacteristic
557C22×C11C2×#12611yescharacteristic
558C22×C11#52911yescharacteristic
559C22×C11#52911yescharacteristic
560C22×C11#52911yescharacteristic
561C22×C11#53211yescharacteristic
562C22×C11#53211yescharacteristic
563C22×C11#53211yescharacteristic
564C22×C11#54011yescharacteristic
565C22×C11#54011yescharacteristic
566C22×C11#54011yescharacteristic
567C22×C11#54211yescharacteristic
568C22×C11#54211yescharacteristic
569C22×C11#54211yescharacteristic
570C22×C11D4211yescharacteristic
571C22×C11D4211yescharacteristic
572C22×C11#54611yescharacteristic
573C22×C11#54611yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#54711yescharacteristic
576C22×C11#54711yescharacteristic
577C22×C11#54811yescharacteristic
578C22×C11#55011yescharacteristic
579C22×C11#55011yescharacteristic
580C22×C11#55311yescharacteristic
581C22×C11#55311yescharacteristic
582C22×C11#55511yescharacteristic
583C22×C11#55611yescharacteristic
584C22×C11#55911yescharacteristic
585C22×C11#55911yescharacteristic
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—81no—
594C2×D11—81no—
595C2×D11—81no—
596C2×D11—81no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11—42no—
605C4×C11—81no—
606C4×C11—81no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—42no—
611Dic11—81no—
612Dic11—81no—
613Dic11#39718yescomplemented
614C25—111no—
615C25C22×D1111yescharacteristic
616C22×D4—114no—
617C22×D4—222no—
618C22×D4—222no—
619C22×D4—222no—
620C22×D4—222no—
621C22×D4—222no—
622C22×D4—222no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C2×C4⋊C4—114no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—222no—
643C2×C4⋊C4—222no—
644C2×C4⋊C4—222no—
645C2×C4⋊C4—222no—
646C2×C4⋊C4—222no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—441no—
650C2×C4⋊C4—441no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C42—222no—
688C2×C42—222no—
689C2×C42—222no—
690C2×C42—222no—
691C2×C42—222no—
692C2×C42—222no—
693C2×C42—222no—
694C2×C42—222no—
695C2×C42—222no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—41no—
700#95—114no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—441no—
708#95—441no—
709#95—441no—
710C2×C11—82no—
711C2×C11C2×#39711yescharacteristic
712C2×C11#242011yescharacteristic
713C2×C11#242211yescharacteristic
714C2×C11#242711yescharacteristic
715C2×C11#242811yescharacteristic
716C2×C11#244511yescharacteristic
717C2×C11#244511yescharacteristic
718C2×C11#244711yescharacteristic
719C2×C11#244811yescharacteristic
720C2×C11#249011yescharacteristic
721C2×C11#249111yescharacteristic
722C2×C11#251211yescharacteristic
723C2×C11#251311yescharacteristic
724C2×C11#264411yescharacteristic
725C2×C11#286011yescharacteristic
726D11—82no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—112no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24D4×D1112yes—
757C24C23×D1111yescharacteristic
758C2×D4—228no—
759C2×D4—228no—
760C2×D4—228no—
761C2×D4—444no—
762C2×D4—444no—
763C2×D4—444no—
764C2×D4—444no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4#433912yes—
853C22×C4D4×D1112yes—
854C22×C4D4×D1112yes—
855C22×C4#434112yes—
856C4⋊C4—228no—
857C4⋊C4—444no—
858C4⋊C4—444no—
859C4⋊C4—444no—
860C4⋊C4—444no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—444no—
865C22⋊C4—444no—
866C22⋊C4—444no—
867C22⋊C4—444no—
868C22⋊C4—444no—
869C22⋊C4—444no—
870C22⋊C4—444no—
871C22⋊C4—444no—
872C22⋊C4—444no—
873C42—444no—
874C42—444no—
875C42—444no—
876C11#1513811yescharacteristic, complemented, Sylow
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23C2×#433911yescharacteristic
948C23C2×D4×D1111yescharacteristic
949C23C2×D4×D1111yescharacteristic
950C23C2×D4×D1111yescharacteristic
951C23C2×#434111yescharacteristic
952C23#6703711yescharacteristic
953C23#6703711yescharacteristic
954C23#41×D1111yescharacteristic
955C23#41×D1111yescharacteristic
956C23#41×D1111yescharacteristic
957C23#41×D1111yescharacteristic
958C23#41×D1111yescharacteristic
959C23#41×D1111yescharacteristic
960C23#6704211yescharacteristic
961C23#6704311yescharacteristic
962D4—4416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—114no—
1008C2×C4—114no—
1009C2×C4—114no—
1010C2×C4—114no—
1011C2×C4—114no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—442no—
1075C22—442no—
1076C22—881no—
1077C22—881no—
1078C22—881no—
1079C22—881no—
1080C22—881no—
1081C22—881no—
1082C22—881no—
1083C22—881no—
1084C22#1062302111yescharacteristic
1085C22#1062305911yescharacteristic
1086C22#1062306411yescharacteristic
1087C22#1062306911yescharacteristic
1088C22#1062307111yescharacteristic
1089C22#1062307911yescharacteristic
1090C22#1062308411yescharacteristic
1091C22#1062312111yescharacteristic
1092C22#1062312211yescharacteristic
1093C22#1062312711yescharacteristic
1094C22#1062312911yescharacteristic
1095C22#1062313011yescharacteristic
1096C22D11×#12111yescharacteristic
1097C22#1062314011yescharacteristic
1098C22#1062314111yescharacteristic
1099C22#1062314611yescharacteristic
1100C22#1062314711yescharacteristic
1101C22#1062318011yescharacteristic
1102C22D11×#12311yescharacteristic
1103C22D11×#12311yescharacteristic
1104C22D11×#12311yescharacteristic
1105C22#1062318611yescharacteristic
1106C22#1062318611yescharacteristic
1107C22#1062319311yescharacteristic
1108C22#1062319411yescharacteristic
1109C22#1062319411yescharacteristic
1110C22#1062319511yescharacteristic
1111C22#1062319911yescharacteristic
1112C22#1062320011yescharacteristic
1113C22D11×#12411yescharacteristic
1114C22#1062321211yescharacteristic
1115C22D11×#12611yescharacteristic
1116C22D11×#12611yescharacteristic
1117C22#1062324011yescharacteristic
1118C22#1062324111yescharacteristic
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—81no—
1124C4—81no—
1125C4—118no—
1126C4—442no—
1127C4—442no—
1128C4—442no—
1129C4—442no—
1130C4—881no—
1131C4—881no—
1132C2—82no—
1133C2—882no—
1134C2D11×#39711yescharacteristic
1135C2#1307210511yescharacteristic
1136C2#1307212511yescharacteristic
1137C2#1307218611yescharacteristic
1138C2#1307220311yescharacteristic
1139C2#1307237411yescharacteristic
1140C2#1307237611yescharacteristic
1141C2#1307240211yescharacteristic
1142C2#1307241111yescharacteristic
1143C2#1307296711yescharacteristic
1144C2#1307297211yescharacteristic
1145C2#1307319911yescharacteristic
1146C2#1307320811yescharacteristic
1147C2#1307457511yescharacteristic
1148C2#1307698211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1440C2
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#15138
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. C2×#10622288C2semidirect
2. C2×#10622566C2semidirect
6. C2×#10622260C2semidirect
7. #13066865C2semidirect
8. #13066864C2semidirect
9. #13066864C2semidirect
10. #13066862C2semidirect
11. #13066859C2semidirect
12. Dic11⋊#95C2semidirect
13. Dic11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1440C2semidirect
152. C11⋊#95D4semidirect
312. #1440D11semidirect
613. Dic11#397semidirect
876. C11#15138semidirect

Maximal subgroups

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

subgroupindex
C2×#106222882
C2×#106225662
C2×#106225702
C2×#106222602
#130668652
#130668642
#130668622
#130668592
Dic11⋊#952
#95×Dic112
C11×#14402
#1513811