Finite Group Databasebeta

← #14681166

Subgroups — #14681166

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622558C211yesmaximal, characteristic, complemented
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622568C211yesmaximal, characteristic
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6#13066864C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066854C211yesmaximal, characteristic, complemented
13#13066854C211yesmaximal, characteristic, complemented
14#13066852C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic, complemented
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×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37C22×Dic11⋊C4C2211yescharacteristic, complemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C2×C11×#95C2211yescharacteristic, complemented
40C2×C11×#95C2211yescharacteristic, complemented
41C2×C11×#95C2211yescharacteristic, complemented
42C2×C11⋊#95C2211yescharacteristic, complemented
43C2×C11⋊#95C2211yescharacteristic, complemented
44C2×C11⋊#95C2211yescharacteristic, complemented
45C2×C11⋊#95C2211yescharacteristic, complemented
46C2×C11⋊#95C2211yescharacteristic, complemented
47C2×C11⋊#95C2211yescharacteristic, complemented
48C2×C11⋊#95C2211yescharacteristic, complemented
49C2×C11⋊#95C2211yescharacteristic, complemented
50C2×C11⋊#95C2211yescharacteristic, complemented
51#10622568—24no—
52#10622568—24no—
53#10622568C418yescomplemented
54#10622558—24no—
55#10622283—24no—
56C25×C11C2311yescharacteristic
57C24×D11—22no—
58C24×D11—22no—
59C24×D11—22no—
60C24×D11—22no—
61C24×D11—22no—
62C24×D11—22no—
63C24×D11—41no—
64C24×D11—41no—
65C24×D11—41no—
66C24×D11—41no—
67C24×D11—41no—
68C24×D11—41no—
69C24×D11—41no—
70C24×D11—41no—
71C24×D11C2×C414yes—
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—41no—
89C2×C11×C22⋊C4—41no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4C2×C414yes—
94C2×C11×C22⋊C4D414yes—
95C2×C42×C11—41no—
96C2×C42×C11—41no—
97C2×C42×C11—41no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11C2×C414yes—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—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—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4C2×C414yes—
139C2×(C2×D11)⋊C4C2×C414yes—
140C2×(C2×D11)⋊C4C2×C414yes—
141C2×(C2×D11)⋊C4C2×C414yes—
142C2×(C2×D11)⋊C4D414yes—
143C2×C4⋊Dic11—22no—
144C2×C4⋊Dic11—41no—
145C2×C4⋊Dic11—41no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—41no—
148C2×Dic11⋊C4—41no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—41no—
152C11×#95—22no—
153C11×#95—41no—
154C11×#95—41no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95—41no—
163C11⋊#95—41no—
164#14365—111nomaximal, Sylow
165C24×C11—21no—
166C24×C11—21no—
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×C11C22×C412yes—
178C24×C11C2×D412yes—
179C24×C11#4112yes—
180C24×C11C2411yescharacteristic
181C23×D11—21no—
182C23×D11—21no—
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×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—28no—
206C23×D11—28no—
207C23×D11—28no—
208C23×D11—44no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—44no—
214C23×D11—44no—
215C23×D11—44no—
216C23×D11—44no—
217C23×D11—44no—
218C23×D11—44no—
219C23×D11—44no—
220C23×D11—44no—
221C23×D11—44no—
222C23×D11—44no—
223C23×D11—44no—
224C23×D11—44no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—44no—
233C23×D11—44no—
234C23×D11—44no—
235C23×D11—44no—
236C23×D11—44no—
237C23×D11—44no—
238C23×D11—44no—
239C23×D11—44no—
240C23×D11C22×C412yes—
241C23×D11C22×C412yes—
242C23×D11C2×D412yes—
243C23×D11#4112yes—
244C23×D11#4112yes—
245C23×D11#4112yes—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11C22×C412yes—
284C22×C4×C11C22×C412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11C2×D412yes—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11C22×C412yes—
328C22×Dic11C22×C412yes—
329C22×Dic11C2×D412yes—
330C11×C22⋊C4—44no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C42×C11—44no—
334C22⋊Dic11—28no—
335C22⋊Dic11—44no—
336C22⋊Dic11—44no—
337(C2×D11)⋊C4—28no—
338(C2×D11)⋊C4—44no—
339(C2×D11)⋊C4—44no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—44no—
349C4⋊Dic11—44no—
350Dic11⋊C4—44no—
351C4×Dic11—44no—
352C2×#388—111no—
353C2×#388—111no—
354C2×#379—111no—
355C2×#379—111no—
356C2×#379—111no—
357#1440—111no—
358#1440—111no—
359#1439—111no—
360#1439—111no—
361#1439—111no—
362#1439—111no—
363#1437—111no—
364#1437—111no—
365#1437—111no—
366#1437D1111yescharacteristic, complemented
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11C4×D414yes—
402C23×C11C23×C411yescharacteristic
403C23×C11C22×D411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C11H(5,𝔽2)11yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—416no—
454C22×D11—416no—
455C22×D11—416no—
456C22×D11—416no—
457C22×D11—416no—
458C22×D11—416no—
459C22×D11—416no—
460C22×D11—416no—
461C22×D11—416no—
462C22×D11—416no—
463C22×D11—416no—
464C22×D11—416no—
465C22×D11—416no—
466C22×D11—416no—
467C22×D11—416no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11—41no—
496C22×D11—41no—
497C22×D11—41no—
498C22×D11—41no—
499C22×D11—41no—
500C22×D11#11714yes—
501C22×D11C4×D414yes—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—41no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C26—111no—
587C22×C4⋊C4—111no—
588C22×C4⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4C2×D1111yescharacteristic
605C22×C22⋊C4C2×D1111yescharacteristic
606C22×C22⋊C4C2×D1111yescharacteristic
607C22×C42—111no—
608C22×C42C2×D1111yescharacteristic, complemented
609#388—224no—
610#388—224no—
611#379—118no—
612#379—224no—
613#379—224no—
614C2×#95—111no—
615C2×#95—111no—
616C2×#95—111no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95—111no—
621C2×#95—111no—
622C2×#95—111no—
623C2×#95C2×D1111yescharacteristic, complemented
624C2×#95C2×D1111yescharacteristic, complemented
625C2×#95C2×D1111yescharacteristic, complemented
626C22×C11—24no—
627C22×C11—24no—
628C22×C11—24no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11C2×#11711yescharacteristic
642C22×C11C2×C4×D411yescharacteristic
643C22×C11C2×C4×D411yescharacteristic
644C22×C11#51811yescharacteristic
645C22×C11#51811yescharacteristic
646C22×C11#51811yescharacteristic
647C22×C11#51811yescharacteristic
648C22×C11#53411yescharacteristic
649C22×C11#53411yescharacteristic
650C22×C11#53511yescharacteristic
651C22×C11#53511yescharacteristic
652C22×C11#53811yescharacteristic
653C22×C11#53811yescharacteristic
654C22×C11#53811yescharacteristic
655C22×C11#53811yescharacteristic
656C22×C11#53811yescharacteristic
657C22×C11#53811yescharacteristic
658C22×C11#53811yescharacteristic
659C22×C11#53811yescharacteristic
660C22×C11D4211yescharacteristic
661C22×C11#54611yescharacteristic
662C22×C11#54611yescharacteristic
663C22×C11#54611yescharacteristic
664C22×C11#54611yescharacteristic
665C22×C11#54611yescharacteristic
666C22×C11#54611yescharacteristic
667C22×C11#55111yescharacteristic
668C22×C11#55111yescharacteristic
669C22×C11#55111yescharacteristic
670C22×C11#55111yescharacteristic
671C22×C11#55111yescharacteristic
672C22×C11#56011yescharacteristic
673C22×C11#56011yescharacteristic
674C22×C11#56011yescharacteristic
675C22×C11H(3,𝔽4)11yescharacteristic
676C2×D11—24no—
677C2×D11—24no—
678C2×D11—24no—
679C2×D11—24no—
680C2×D11—24no—
681C2×D11—24no—
682C2×D11—464no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C4×C11—42no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11—81no—
713Dic11—42no—
714Dic11—42no—
715Dic11—42no—
716Dic11—81no—
717Dic11—81no—
718Dic11—81no—
719C25—111no—
720C25—111no—
721C25—114no—
722C25—222no—
723C25—222no—
724C25—222no—
725C25—222no—
726C25—222no—
727C25—222no—
728C25—441no—
729C25—441no—
730C25—441no—
731C25—441no—
732C25—441no—
733C25—441no—
734C25—441no—
735C25—441no—
736C25C22×D1111yescharacteristic
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749C2×C4⋊C4—222no—
750C2×C4⋊C4—222no—
751C2×C4⋊C4—441no—
752C2×C4⋊C4—441no—
753C2×C4⋊C4—441no—
754C2×C4⋊C4—441no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—41no—
758C2×C22⋊C4—41no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4—41no—
762C2×C22⋊C4—114no—
763C2×C22⋊C4—114no—
764C2×C22⋊C4—114no—
765C2×C22⋊C4—114no—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—222no—
769C2×C22⋊C4—222no—
770C2×C22⋊C4—222no—
771C2×C22⋊C4—222no—
772C2×C22⋊C4—222no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—222no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4—441no—
807C2×C22⋊C4C4×D1114yes—
808C2×C22⋊C4D4414yes—
809C2×C42—41no—
810C2×C42—41no—
811C2×C42—41no—
812C2×C42—222no—
813C2×C42—222no—
814C2×C42—441no—
815#95—22no—
816#95—41no—
817#95—41no—
818#95—222no—
819#95—222no—
820#95—222no—
821#95—441no—
822#95—441no—
823#95—441no—
824#95—441no—
825#95—441no—
826#95—441no—
827C2×C11—44no—
828C2×C11#231211yescharacteristic
829C2×C11#232111yescharacteristic
830C2×C11#232111yescharacteristic
831C2×C11#234211yescharacteristic
832C2×C11#234211yescharacteristic
833C2×C11#235811yescharacteristic
834C2×C11#237511yescharacteristic
835C2×C11#267811yescharacteristic
836C2×C11#267811yescharacteristic
837C2×C11#268411yescharacteristic
838C2×C11#268411yescharacteristic
839C2×C11#268511yescharacteristic
840C2×C11#268511yescharacteristic
841C2×C11#273511yescharacteristic
842C2×C11#273511yescharacteristic
843D11—44no—
844D11—44no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—112no—
858C24—112no—
859C24—112no—
860C24—112no—
861C24—112no—
862C24—112no—
863C24—228no—
864C24—228no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24—221no—
885C24—221no—
886C24—221no—
887C24—221no—
888C24—221no—
889C24—228no—
890C24—444no—
891C24—444no—
892C24—444no—
893C24—444no—
894C24—444no—
895C24—444no—
896C24—444no—
897C24—444no—
898C24—444no—
899C24—444no—
900C24—444no—
901C24—444no—
902C24—444no—
903C24—444no—
904C24—444no—
905C24—444no—
906C24—444no—
907C24—444no—
908C24—444no—
909C24—444no—
910C24—444no—
911C24—444no—
912C24—444no—
913C24—444no—
914C24—444no—
915C24—444no—
916C24—444no—
917C24—444no—
918C24—444no—
919C24—444no—
920C24—444no—
921C24—444no—
922C24C2×C4×D1112yes—
923C24C2×D4412yes—
924C24#433912yes—
925C24C23×D1111yescharacteristic
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4C2×C4×D1112yes—
1006C22×C4C2×C4×D1112yes—
1007C22×C4C2×D4412yes—
1008C22×C4C2×D4412yes—
1009C22×C4D4×D1112yes—
1010C4⋊C4—444no—
1011C4⋊C4—444no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—228no—
1016C22⋊C4—228no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C22⋊C4—444no—
1021C22⋊C4—444no—
1022C22⋊C4—444no—
1023C22⋊C4—444no—
1024C22⋊C4—444no—
1025C22⋊C4—444no—
1026C22⋊C4—444no—
1027C22⋊C4—444no—
1028C22⋊C4—444no—
1029C22⋊C4—444no—
1030C42—44no—
1031C42—444no—
1032C11#1436511yescharacteristic, complemented, Sylow
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—114no—
1068C23—114no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—4416no—
1106C23—4416no—
1107C23—4416no—
1108C23—4416no—
1109C23—4416no—
1110C23—4416no—
1111C23—4416no—
1112C23—4416no—
1113C23—4416no—
1114C23—4416no—
1115C23—4416no—
1116C23—4416no—
1117C23—4416no—
1118C23—4416no—
1119C23—4416no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23—441no—
1152C23C4×D4414yes—
1153C23C22×C4×D1111yescharacteristic
1154C23C22×D4411yescharacteristic
1155C23C2×#433911yescharacteristic
1156C23C2×D4×D1111yescharacteristic
1157C23#6703711yescharacteristic
1158C23#6703711yescharacteristic
1159C23#6703711yescharacteristic
1160C23#6703711yescharacteristic
1161C23#6703711yescharacteristic
1162C23#41×D1111yescharacteristic
1163C23#41×D1111yescharacteristic
1164C23#41×D1111yescharacteristic
1165C23#6704211yescharacteristic
1166C23#6704211yescharacteristic
1167C23#6704211yescharacteristic
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4—441no—
1248C2×C4—441no—
1249C2×C4—441no—
1250C2×C4—441no—
1251C2×C4—441no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—224no—
1268C22—224no—
1269C22—224no—
1270C22—224no—
1271C22—224no—
1272C22—224no—
1273C22—4464no—
1274C22—442no—
1275C22—442no—
1276C22—442no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—442no—
1293C22—442no—
1294C22—442no—
1295C22—442no—
1296C22—442no—
1297C22—442no—
1298C22C2×C4×D4411yescharacteristic
1299C22#1062301711yescharacteristic
1300C22#1062302111yescharacteristic
1301C22#1062302411yescharacteristic
1302C22D11×#11711yescharacteristic
1303C22#1062305611yescharacteristic
1304C22#1062305811yescharacteristic
1305C22C4×D4×D1111yescharacteristic
1306C22#1062307611yescharacteristic
1307C22#1062307611yescharacteristic
1308C22#1062307611yescharacteristic
1309C22D4×D4411yescharacteristic
1310C22#1062308511yescharacteristic
1311C22#1062308511yescharacteristic
1312C22#1062308511yescharacteristic
1313C22#1062308711yescharacteristic
1314C22#1062308711yescharacteristic
1315C22#1062309111yescharacteristic
1316C22#1062309111yescharacteristic
1317C22#1062312511yescharacteristic
1318C22#1062313611yescharacteristic
1319C22#1062314111yescharacteristic
1320C22#1062314411yescharacteristic
1321C22#1062314411yescharacteristic
1322C22#1062315111yescharacteristic
1323C22#1062315111yescharacteristic
1324C22#1062318811yescharacteristic
1325C22#1062319011yescharacteristic
1326C22#1062319711yescharacteristic
1327C22#1062320711yescharacteristic
1328C22#1062320911yescharacteristic
1329C22#1062320911yescharacteristic
1330C22#1062323511yescharacteristic
1331C22#1062323611yescharacteristic
1332C22#1062324611yescharacteristic
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—81no—
1339C4—442no—
1340C4—442no—
1341C4—442no—
1342C4—881no—
1343C4—881no—
1344C4—881no—
1345C2—44no—
1346C2—444no—
1347C2—444no—
1348C2#1307121011yescharacteristic
1349C2#1307127511yescharacteristic
1350C2#1307127611yescharacteristic
1351C2#1307146411yescharacteristic
1352C2#1307146811yescharacteristic
1353C2#1307159811yescharacteristic
1354C2#1307175411yescharacteristic
1355C2#1307493611yescharacteristic
1356C2#1307493911yescharacteristic
1357C2#1307499311yescharacteristic
1358C2#1307499511yescharacteristic
1359C2#1307500211yescharacteristic
1360C2#1307500511yescharacteristic
1361C2#1307565411yescharacteristic
1362C2#1307565511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1437D11
hypocenterC11#14365
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#10622558C2semidirect
2. C2×#10622283C2semidirect
6. #13066864C2semidirect
7. #13066863C2semidirect
8. #13066862C2semidirect
9. #13066861C2semidirect
10. #13066860C2semidirect
11. #13066860C2semidirect
12. #13066854C2semidirect
13. #13066854C2semidirect
14. #13066852C2semidirect
15. C11×#1437C2semidirect
20. C22×C42×C11C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
39. C2×C11×#95C22semidirect
40. C2×C11×#95C22semidirect
41. C2×C11×#95C22semidirect
42. C2×C11⋊#95C22semidirect
43. C2×C11⋊#95C22semidirect
44. C2×C11⋊#95C22semidirect
45. C2×C11⋊#95C22semidirect
46. C2×C11⋊#95C22semidirect
47. C2×C11⋊#95C22semidirect
48. C2×C11⋊#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. C2×C11⋊#95C22semidirect
53. #10622568C4semidirect
366. #1437D11semidirect
608. C22×C42C2×D11semidirect
623. C2×#95C2×D11semidirect
624. C2×#95C2×D11semidirect
625. C2×#95C2×D11semidirect
1032. C11#14365semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106222832
C2×#106225682
#130668642
#130668632
#130668622
#130668612
#130668602
#130668542
#130668522
C11×#14372
#1436511