Finite Group Databasebeta

← #14682918

Subgroups — #14682918

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2#13066865C211yesmaximal, characteristic, complemented
3#13066864C211yesmaximal, characteristic, complemented
4#13066864C211yesmaximal, characteristic, complemented
5#13066863C211yesmaximal, characteristic, complemented
6#13066855C211yesmaximal, characteristic
7#13066855C211yesmaximal, characteristic
8#13066854C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066841C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
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#10622570C418yescomplemented
52C25×C11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—41no—
63C22×C22⋊D11—41no—
64C22×C22⋊D11—41no—
65C22×C22⋊D11—41no—
66C22×C22⋊D11C2×C414yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—41no—
78C2×C11×C22⋊C4—41no—
79C2×C11×C22⋊C4—41no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4C2×C414yes—
83C2×C42×C11—41no—
84C2×C42×C11—41no—
85C2×C42×C11—41no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11C2×C414yes—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4C2×C414yes—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4C2×C414yes—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11C2×C414yes—
122C11×#95—22no—
123C11×#95—41no—
124C11×#95—41no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140#14503—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11C22×C412yes—
156C24×C11C2411yescharacteristic
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11C22×C412yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
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×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11#4112yes—
212C22×C4×C11#4112yes—
213C22×C4×C11#4112yes—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
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×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C22×Dic11#4112yes—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C42×C11—44no—
274C22⋊Dic11—44no—
275C22⋊Dic11—44no—
276C22⋊Dic11—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283Dic11⋊C4—44no—
284C4×Dic11—44no—
285C4×Dic11—44no—
286C2×#390—111no—
287#1440—111no—
288#1440—111no—
289#1440—111no—
290#1440—111no—
291#1438—111no—
292#1438—111no—
293#1437—111no—
294#1437—111no—
295#1437—111no—
296#1437D1111yescharacteristic, complemented
297#1436—111no—
298#1436—111no—
299#1434—111no—
300#1434—111no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
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×C11C23×C411yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C11H(5,𝔽2)11yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
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—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
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—
428C22⋊D11—416no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
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#11714yes—
478C23×D4—111no—
479C22×C4⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4C2×D1111yescharacteristic
490C22×C22⋊C4C2×D1111yescharacteristic
491C22×C22⋊C4C2×D1111yescharacteristic
492C22×C42—111no—
493C22×C42—111no—
494C22×C42C2×D1111yescharacteristic
495#390—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95C2×D1111yescharacteristic
512C2×#95C2×D1111yescharacteristic
513C2×#95C2×D1111yescharacteristic
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—81no—
522C22×C11—81no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—81no—
526C22×C11—81no—
527C22×C11—81no—
528C22×C11—81no—
529C22×C11C2×#11711yescharacteristic
530C22×C11C4×#4111yescharacteristic
531C22×C11C4×#4111yescharacteristic
532C22×C11#51811yescharacteristic
533C22×C11#51811yescharacteristic
534C22×C11#51811yescharacteristic
535C22×C11#51811yescharacteristic
536C22×C11#53811yescharacteristic
537C22×C11#53811yescharacteristic
538C22×C11#53811yescharacteristic
539C22×C11#53811yescharacteristic
540C22×C11#53811yescharacteristic
541C22×C11#53811yescharacteristic
542C22×C11#53811yescharacteristic
543C22×C11#53811yescharacteristic
544C22×C11#54011yescharacteristic
545C22×C11#54011yescharacteristic
546C22×C11#54011yescharacteristic
547C22×C11#54011yescharacteristic
548C22×C11#55111yescharacteristic
549C22×C11#55111yescharacteristic
550C22×C11#55311yescharacteristic
551C22×C11#55311yescharacteristic
552C22×C11#55311yescharacteristic
553C22×C11#55311yescharacteristic
554C22×C11#55511yescharacteristic
555C22×C11#55511yescharacteristic
556C22×C11#55911yescharacteristic
557C22×C11#55911yescharacteristic
558C22×C11#55911yescharacteristic
559C22×C11#55911yescharacteristic
560C22×C11#56011yescharacteristic
561C22×C11#56011yescharacteristic
562C22×C11#56011yescharacteristic
563C22×C11#56011yescharacteristic
564C2×D11—42no—
565C2×D11—42no—
566C2×D11—42no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—81no—
572C2×D11—81no—
573C2×D11—81no—
574C2×D11—81no—
575C2×D11—81no—
576C2×D11—81no—
577C2×D11—81no—
578C2×D11—81no—
579C4×C11—42no—
580C4×C11—42no—
581C4×C11—42no—
582C4×C11—42no—
583C4×C11—42no—
584C4×C11—81no—
585Dic11—24no—
586Dic11—42no—
587Dic11—42no—
588Dic11—42no—
589Dic11—81no—
590Dic11—81no—
591Dic11—81no—
592C25—111no—
593C25C22×D1111yescharacteristic
594C22×D4—114no—
595C22×D4—222no—
596C22×D4—222no—
597C22×D4—441no—
598C22×D4—441no—
599C22×D4—441no—
600C22×D4—441no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C23×C4C22×D1111yescharacteristic
613C23×C4C22×D1111yescharacteristic
614C2×C4⋊C4—114no—
615C2×C4⋊C4—441no—
616C2×C4⋊C4—441no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C22⋊C4—441no—
636C2×C22⋊C4—441no—
637C2×C22⋊C4—441no—
638C2×C22⋊C4—441no—
639C2×C22⋊C4—441no—
640C2×C22⋊C4—441no—
641C2×C22⋊C4—441no—
642C2×C22⋊C4—441no—
643C2×C22⋊C4—441no—
644C2×C22⋊C4—441no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4—441no—
647C2×C22⋊C4—441no—
648C2×C22⋊C4—441no—
649C2×C22⋊C4—441no—
650C2×C22⋊C4—441no—
651C2×C22⋊C4—441no—
652C2×C22⋊C4C4×D1114yes—
653C2×C42—41no—
654C2×C42—41no—
655C2×C42—41no—
656C2×C42—114no—
657C2×C42—441no—
658C2×C42—441no—
659C2×C42—441no—
660C2×C42—441no—
661C2×C42—441no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—222no—
671#95—222no—
672#95—441no—
673#95—441no—
674#95—441no—
675#95—441no—
676#95—441no—
677#95—441no—
678#95—441no—
679#95—441no—
680C2×C11—82no—
681C2×C11#231211yescharacteristic
682C2×C11#233311yescharacteristic
683C2×C11#233311yescharacteristic
684C2×C11#235711yescharacteristic
685C2×C11#235711yescharacteristic
686C2×C11#237211yescharacteristic
687C2×C11#238011yescharacteristic
688C2×C11#279711yescharacteristic
689C2×C11#279711yescharacteristic
690C2×C11#279711yescharacteristic
691C2×C11#279711yescharacteristic
692C2×C11#280311yescharacteristic
693C2×C11#280311yescharacteristic
694C2×C11#280311yescharacteristic
695C2×C11#280311yescharacteristic
696D11—82no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—112no—
712C24—221no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24—221no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24—221no—
726C24C2×C4×D1112yes—
727C24C23×D1111yescharacteristic
728C2×D4—228no—
729C2×D4—444no—
730C2×D4—444no—
731C2×D4—444no—
732C2×D4—444no—
733C2×D4—444no—
734C2×D4—444no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4C2×C4×D1112yes—
822C22×C4C2×C4×D1112yes—
823C22×C4#433912yes—
824C22×C4#433912yes—
825C22×C4#434112yes—
826C4⋊C4—444no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—444no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C22⋊C4—444no—
834C22⋊C4—444no—
835C22⋊C4—444no—
836C22⋊C4—444no—
837C22⋊C4—444no—
838C22⋊C4—444no—
839C42—44no—
840C42—444no—
841C42—444no—
842C11#1450311yescharacteristic, complemented, Sylow
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—441no—
886C23—441no—
887C23—441no—
888C23—441no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23C22×C4×D1111yescharacteristic
914C23C2×#433911yescharacteristic
915C23C2×#433911yescharacteristic
916C23C2×#434111yescharacteristic
917C23#6703711yescharacteristic
918C23#6703711yescharacteristic
919C23#6703711yescharacteristic
920C23#6703711yescharacteristic
921C23#6703711yescharacteristic
922C23#41×D1111yescharacteristic
923C23#41×D1111yescharacteristic
924C23#41×D1111yescharacteristic
925C23#6704211yescharacteristic
926C23#6704211yescharacteristic
927C23#6704211yescharacteristic
928D4—4416no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—114no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C2×C4—441no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—442no—
1036C22—442no—
1037C22—442no—
1038C22—442no—
1039C22—442no—
1040C22—442no—
1041C22—442no—
1042C22—881no—
1043C22—881no—
1044C22—881no—
1045C22—881no—
1046C22—881no—
1047C22—881no—
1048C22—881no—
1049C22—881no—
1050C22C4×#433911yescharacteristic
1051C22#1062301711yescharacteristic
1052C22#1062302511yescharacteristic
1053C22#1062302611yescharacteristic
1054C22D11×#11711yescharacteristic
1055C22#1062306311yescharacteristic
1056C22#1062306611yescharacteristic
1057C22C4×#434111yescharacteristic
1058C22#1062307111yescharacteristic
1059C22#1062307111yescharacteristic
1060C22#1062307611yescharacteristic
1061C22#1062307611yescharacteristic
1062C22#1062307611yescharacteristic
1063C22#1062308711yescharacteristic
1064C22#1062309011yescharacteristic
1065C22#1062309011yescharacteristic
1066C22#1062309111yescharacteristic
1067C22#1062309311yescharacteristic
1068C22#1062309411yescharacteristic
1069C22#1062312611yescharacteristic
1070C22#1062313211yescharacteristic
1071C22#1062314411yescharacteristic
1072C22#1062314611yescharacteristic
1073C22#1062314811yescharacteristic
1074C22#1062315111yescharacteristic
1075C22#1062315111yescharacteristic
1076C22#1062318811yescharacteristic
1077C22#1062319511yescharacteristic
1078C22#1062319711yescharacteristic
1079C22#1062320911yescharacteristic
1080C22#1062320911yescharacteristic
1081C22#1062321211yescharacteristic
1082C22#1062323511yescharacteristic
1083C22#1062324011yescharacteristic
1084C22#1062325011yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—81no—
1091C4—224no—
1092C4—442no—
1093C4—442no—
1094C4—442no—
1095C4—881no—
1096C4—881no—
1097C4—881no—
1098C2—82no—
1099C2—882no—
1100C2#1307121011yescharacteristic
1101C2#1307137511yescharacteristic
1102C2#1307137611yescharacteristic
1103C2#1307158611yescharacteristic
1104C2#1307159011yescharacteristic
1105C2#1307172411yescharacteristic
1106C2#1307179111yescharacteristic
1107C2#1307646711yescharacteristic
1108C2#1307646911yescharacteristic
1109C2#1307647311yescharacteristic
1110C2#1307647611yescharacteristic
1111C2#1307654411yescharacteristic
1112C2#1307654611yescharacteristic
1113C2#1307655011yescharacteristic
1114C2#1307655211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#14503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13066865C2semidirect
3. #13066864C2semidirect
4. #13066864C2semidirect
5. #13066863C2semidirect
8. #13066854C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
13. #13066841C2semidirect
14. #13066840C2semidirect
15. C11×#1437C2semidirect
51. #10622570C4semidirect
296. #1437D11semidirect
842. C11#14503semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
#130668652
#130668642
#130668632
#130668552
#130668542
#130668532
#130668522
#130668492
#130668472
#130668412
#130668402
C11×#14372
#1450311