Finite Group Databasebeta

← #14680183

Subgroups — #14680183

Order 2816.

3390 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622281C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic, complemented
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066858C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic, complemented
39C2×C22⋊C4×D11—24no—
40C2×C22⋊C4×D11—24no—
41C2×C22⋊C4×D11—24no—
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
51C2×C11⋊#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54#10622602—24no—
55#10622568—24no—
56#10622568C418yescomplemented
57#10622281—24no—
58C25×C11C2311yescharacteristic
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×D11D414yes—
73C24×D11Q814yes—
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11D414yes—
101C22×C4×D11D414yes—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4—41no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4C2×C414yescomplemented
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11C2×C414yescomplemented
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4C2×C414yes—
150C2×(C2×D11)⋊C4C2×C414yes—
151C2×(C2×D11)⋊C4C2×C414yescomplemented
152C2×(C2×D11)⋊C4C2×C414yescomplemented
153C2×C4⋊Dic11—22no—
154C2×C4⋊Dic11—41no—
155C2×C4⋊Dic11—41no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—41no—
159C2×Dic11⋊C4—41no—
160C2×Dic11⋊C4—41no—
161C2×Dic11⋊C4—41no—
162C22⋊C4×D11—232no—
163C11×#95—22no—
164C11×#95—41no—
165C11×#95—41no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171C11⋊#95—41no—
172C11⋊#95—41no—
173C11⋊#95—41no—
174C11⋊#95—41no—
175#14262—111nomaximal, Sylow
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C22×C412yes—
189C24×C11C2×D412yes—
190C24×C11C2×Q812yes—
191C24×C11C2411yescharacteristic
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—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—28no—
213C23×D11—28no—
214C23×D11—28no—
215C23×D11—28no—
216C23×D11—28no—
217C23×D11—28no—
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×D11—44no—
241C23×D11—44no—
242C23×D11—44no—
243C23×D11—44no—
244C23×D11—44no—
245C23×D11—44no—
246C23×D11C4⋊C4116yescomplemented
247C23×D11C22×C412yes—
248C23×D11C22×C412yes—
249C23×D11C2×D412yes—
250C23×D11C2×D412yes—
251C23×D11C2×D412yes—
252C23×D11C2×D412yes—
253C23×D11C2×Q812yes—
254C23×D11C2×Q812yes—
255C23×D11#4112yes—
256C23×D11#4112yes—
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×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11C22×C412yes—
296C22×C4×C11C22×C412yes—
297C22×C4×C11C2×D412yes—
298C22×C4×C11C2×D412yes—
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×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—21no—
335C22×Dic11—21no—
336C22×Dic11—21no—
337C22×Dic11C22×C412yes—
338C22×Dic11C22×C412yes—
339C22×Dic11C2×D412yes—
340C22×Dic11C2×D412yes—
341C2×C4×D11—28no—
342C2×C4×D11—28no—
343C2×C4×D11—44no—
344C2×C4×D11—44no—
345C2×C4×D11—44no—
346C2×C4×D11—44no—
347C2×C4×D11—44no—
348C2×C4×D11—44no—
349C2×C4×D11—44no—
350C2×C4×D11—44no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C11×C4⋊C4—44no—
356C11×C22⋊C4—28no—
357C11×C22⋊C4—44no—
358C11×C22⋊C4—44no—
359C22⋊Dic11—28no—
360C22⋊Dic11—44no—
361C22⋊Dic11—44no—
362(C2×D11)⋊C4—28no—
363(C2×D11)⋊C4—28no—
364(C2×D11)⋊C4—28no—
365(C2×D11)⋊C4—28no—
366(C2×D11)⋊C4—44no—
367(C2×D11)⋊C4—44no—
368(C2×D11)⋊C4—44no—
369(C2×D11)⋊C4—44no—
370(C2×D11)⋊C4—44no—
371(C2×D11)⋊C4—44no—
372C4⋊Dic11—44no—
373Dic11⋊C4—44no—
374Dic11⋊C4—44no—
375C23×C22⋊C4—111no—
376C2×#385—111no—
377C2×#385—111no—
378C2×#379—111no—
379C2×#379—111no—
380#1439—111no—
381#1439—111no—
382#1439—111no—
383#1439—111no—
384#1439—111no—
385#1439—111no—
386#1439—111no—
387#1439D1111yescharacteristic, complemented
388C22⋊#95—111no—
389C22⋊#95—111no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11C2×C4⋊C414yes—
425C23×C11C23×C411yescharacteristic
426C23×C11C22×D411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C22×D411yescharacteristic
429C23×C11C22×Q811yescharacteristic
430C23×C11C2×#4111yescharacteristic
431C23×C11C2×#4111yescharacteristic
432C23×C11H(5,𝔽2)11yescharacteristic
433C23×C11H(5,𝔽2)11yescharacteristic
434C23×C11H(5,𝔽2)11yescharacteristic
435C23×C11H(5,𝔽2)11yescharacteristic
436C23×C11H(5,𝔽2)11yescharacteristic
437C23×C11H(5,𝔽2)11yescharacteristic
438C23×C11H(5,𝔽2)11yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—232no—
487C22×D11—416no—
488C22×D11—416no—
489C22×D11—416no—
490C22×D11—416no—
491C22×D11—416no—
492C22×D11—416no—
493C22×D11—416no—
494C22×D11—416no—
495C22×D11—416no—
496C22×D11—416no—
497C22×D11—416no—
498C22×D11—416no—
499C22×D11—416no—
500C22×D11—416no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11—41no—
508C22×D11—41no—
509C22×D11—41no—
510C22×D11—41no—
511C22×D11—41no—
512C22×D11—41no—
513C22×D11—41no—
514C22×D11—41no—
515C22×D11—41no—
516C22×D11—41no—
517C22×D11C2×C4⋊C414yes—
518C22×D11C2×C4⋊C414yes—
519C22×D11C4×D414yes—
520C22×D11C4×D414yes—
521C22×D11#12014yes—
522C22×D11C22⋊Q814yes—
523C22×D11C22⋊Q814yes—
524C22×D11#12314yes—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
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×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11—41no—
556C2×C4×C11—41no—
557C2×C4×C11—41no—
558C2×C4×C11—41no—
559C2×C4×C11—41no—
560C2×C4×C11—41no—
561C2×C4×C11—41no—
562C2×C4×C11—41no—
563C2×C4×C11—41no—
564C2×C4×C11—41no—
565C2×C4×C11—41no—
566C2×C4×C11—41no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—22no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—41no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11—41no—
599C2×Dic11—41no—
600C2×Dic11—41no—
601C2×Dic11—41no—
602C2×Dic11—41no—
603C2×Dic11—41no—
604C2×Dic11—41no—
605C2×Dic11—41no—
606C2×Dic11—41no—
607C2×Dic11—41no—
608C2×Dic11—41no—
609C4×D11—416no—
610C4×D11—416no—
611C26—111no—
612C24×C4—111no—
613C24×C4—111no—
614C22×C4⋊C4—111no—
615C22×C4⋊C4—111no—
616C22×C4⋊C4—111no—
617C22×C4⋊C4C2×D1111yescharacteristic, complemented
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4—111no—
629C22×C22⋊C4—111no—
630C22×C22⋊C4—111no—
631C22×C22⋊C4—224no—
632C22×C22⋊C4—224no—
633C22×C22⋊C4—224no—
634C22×C22⋊C4C2×D1111yescharacteristic
635C22×C22⋊C4C2×D1111yescharacteristic
636C22×C22⋊C4C2×D1111yescharacteristic
637#385—224no—
638#385—224no—
639#379—118no—
640#379—224no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—111no—
646C2×#95—111no—
647C2×#95—111no—
648C2×#95—111no—
649C2×#95—111no—
650C2×#95C2×D1111yescharacteristic, complemented
651C2×#95C2×D1111yescharacteristic, complemented
652C2×#95C2×D1111yescharacteristic, complemented
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11C22×C4⋊C411yescharacteristic
669C22×C11C2×C4×D411yescharacteristic
670C22×C11C2×C4×D411yescharacteristic
671C22×C11#51811yescharacteristic
672C22×C11#51811yescharacteristic
673C22×C11#51811yescharacteristic
674C22×C11#51811yescharacteristic
675C22×C11C2×#12011yescharacteristic
676C22×C11C2×C22⋊Q811yescharacteristic
677C22×C11C2×C22⋊Q811yescharacteristic
678C22×C11C2×#12311yescharacteristic
679C22×C11#53411yescharacteristic
680C22×C11#53411yescharacteristic
681C22×C11#53411yescharacteristic
682C22×C11#53411yescharacteristic
683C22×C11#53411yescharacteristic
684C22×C11#53411yescharacteristic
685C22×C11#53411yescharacteristic
686C22×C11#53411yescharacteristic
687C22×C11#53511yescharacteristic
688C22×C11#53511yescharacteristic
689C22×C11#53511yescharacteristic
690C22×C11#53511yescharacteristic
691C22×C11#53811yescharacteristic
692C22×C11#53811yescharacteristic
693C22×C11#53811yescharacteristic
694C22×C11#53811yescharacteristic
695C22×C11#53811yescharacteristic
696C22×C11#53811yescharacteristic
697C22×C11#53811yescharacteristic
698C22×C11#53811yescharacteristic
699C22×C11#54311yescharacteristic
700C22×C11#54311yescharacteristic
701C22×C11#54311yescharacteristic
702C22×C11#54311yescharacteristic
703C2×D11—24no—
704C2×D11—24no—
705C2×D11—24no—
706C2×D11—24no—
707C2×D11—24no—
708C2×D11—24no—
709C2×D11—24no—
710C2×D11—24no—
711C2×D11—24no—
712C2×D11—24no—
713C2×D11—24no—
714C2×D11—24no—
715C2×D11—24no—
716C2×D11—24no—
717C2×D11—24no—
718C2×D11—24no—
719C2×D11—24no—
720C2×D11—464no—
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—42no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—42no—
731C2×D11—42no—
732C2×D11—42no—
733C2×D11#38518yes—
734C4×C11—42no—
735C4×C11—42no—
736C4×C11—42no—
737C4×C11—42no—
738C4×C11—81no—
739C4×C11—81no—
740Dic11—42no—
741Dic11—42no—
742Dic11—42no—
743Dic11—42no—
744Dic11—81no—
745Dic11—81no—
746C25—111no—
747C25—111no—
748C25—114no—
749C25—114no—
750C25—114no—
751C25—222no—
752C25—222no—
753C25—222no—
754C25—222no—
755C25—441no—
756C25—441no—
757C25—441no—
758C25—441no—
759C25—441no—
760C25—441no—
761C25—441no—
762C25—441no—
763C25C22×D1111yescharacteristic
764C23×C4—111no—
765C23×C4—111no—
766C23×C4—111no—
767C23×C4—111no—
768C23×C4—114no—
769C23×C4—114no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—222no—
773C23×C4—222no—
774C23×C4—222no—
775C23×C4—222no—
776C23×C4—441no—
777C23×C4—441no—
778C23×C4—441no—
779C23×C4—441no—
780C23×C4—441no—
781C23×C4—441no—
782C23×C4—441no—
783C23×C4—441no—
784C23×C4C22×D1111yescharacteristic
785C23×C4C22×D1111yescharacteristic
786C23×C4C22×D1111yescharacteristic
787C23×C4C22×D1111yescharacteristic
788C23×C4C22×D1111yescharacteristic
789C23×C4C22×D1111yescharacteristic
790C2×C4⋊C4—22no—
791C2×C4⋊C4—41no—
792C2×C4⋊C4—41no—
793C2×C4⋊C4—222no—
794C2×C4⋊C4—222no—
795C2×C4⋊C4—222no—
796C2×C4⋊C4—441no—
797C2×C4⋊C4—441no—
798C2×C4⋊C4—441no—
799C2×C4⋊C4—441no—
800C2×C4⋊C4—441no—
801C2×C4⋊C4—441no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—114no—
811C2×C22⋊C4—114no—
812C2×C22⋊C4—114no—
813C2×C22⋊C4—114no—
814C2×C22⋊C4—114no—
815C2×C22⋊C4—2232no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—222no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—222no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—441no—
839C2×C22⋊C4—441no—
840C2×C22⋊C4—441no—
841C2×C22⋊C4—441no—
842C2×C22⋊C4—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4—441no—
847C2×C22⋊C4—441no—
848C2×C22⋊C4—441no—
849C2×C22⋊C4—441no—
850C2×C22⋊C4C4×D1114yescomplemented
851#95—22no—
852#95—41no—
853#95—41no—
854#95—222no—
855#95—222no—
856#95—222no—
857#95—441no—
858#95—441no—
859#95—441no—
860#95—441no—
861#95—441no—
862#95—441no—
863C2×C11—44no—
864C2×C11C2×#38511yescharacteristic
865C2×C11#231511yescharacteristic
866C2×C11#231511yescharacteristic
867C2×C11#232111yescharacteristic
868C2×C11#232111yescharacteristic
869C2×C11#232111yescharacteristic
870C2×C11#232111yescharacteristic
871C2×C11#261311yescharacteristic
872C2×C11#261311yescharacteristic
873C2×C11#262211yescharacteristic
874C2×C11#262211yescharacteristic
875C2×C11#262611yescharacteristic
876C2×C11#262611yescharacteristic
877C2×C11#262611yescharacteristic
878C2×C11#262611yescharacteristic
879D11—28no—
880D11—44no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—112no—
894C24—112no—
895C24—112no—
896C24—112no—
897C24—112no—
898C24—112no—
899C24—112no—
900C24—112no—
901C24—112no—
902C24—112no—
903C24—1116no—
904C24—228no—
905C24—228no—
906C24—228no—
907C24—228no—
908C24—228no—
909C24—228no—
910C24—221no—
911C24—221no—
912C24—221no—
913C24—221no—
914C24—221no—
915C24—221no—
916C24—221no—
917C24—221no—
918C24—221no—
919C24—221no—
920C24—221no—
921C24—221no—
922C24—221no—
923C24—221no—
924C24—221no—
925C24—221no—
926C24—221no—
927C24—221no—
928C24—221no—
929C24—221no—
930C24—444no—
931C24—444no—
932C24—444no—
933C24—444no—
934C24—444no—
935C24—444no—
936C24—444no—
937C24—444no—
938C24—444no—
939C24—444no—
940C24—444no—
941C24—444no—
942C24—444no—
943C24—444no—
944C24—444no—
945C24—444no—
946C24—444no—
947C24—444no—
948C24—444no—
949C24—444no—
950C24—444no—
951C24—444no—
952C24—444no—
953C24—444no—
954C24—444no—
955C24—444no—
956C24—444no—
957C24—444no—
958C24C2×C4×D1112yes—
959C24D4×D1112yes—
960C24Q8×D1112yes—
961C24C23×D1111yescharacteristic
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—112no—
1001C22×C4—112no—
1002C22×C4—112no—
1003C22×C4—112no—
1004C22×C4—228no—
1005C22×C4—228no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—221no—
1038C22×C4—221no—
1039C22×C4—221no—
1040C22×C4—221no—
1041C22×C4—221no—
1042C22×C4—221no—
1043C22×C4—221no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4—444no—
1054C22×C4—444no—
1055C22×C4—444no—
1056C22×C4C2×C4×D1112yes—
1057C22×C4C2×C4×D1112yes—
1058C22×C4D4×D1112yes—
1059C22×C4D4×D1112yes—
1060C4⋊C4—44no—
1061C4⋊C4—444no—
1062C4⋊C4—444no—
1063C4⋊C4—444no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—228no—
1068C22⋊C4—228no—
1069C22⋊C4—228no—
1070C22⋊C4—228no—
1071C22⋊C4—228no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C22⋊C4—444no—
1075C22⋊C4—444no—
1076C22⋊C4—444no—
1077C22⋊C4—444no—
1078C22⋊C4—444no—
1079C22⋊C4—444no—
1080C11#1426211yescharacteristic, complemented, Sylow
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—114no—
1116C23—114no—
1117C23—114no—
1118C23—114no—
1119C23—114no—
1120C23—114no—
1121C23—114no—
1122C23—114no—
1123C23—2232no—
1124C23—222no—
1125C23—222no—
1126C23—222no—
1127C23—222no—
1128C23—222no—
1129C23—222no—
1130C23—222no—
1131C23—222no—
1132C23—222no—
1133C23—222no—
1134C23—222no—
1135C23—222no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—222no—
1140C23—222no—
1141C23—222no—
1142C23—222no—
1143C23—222no—
1144C23—222no—
1145C23—222no—
1146C23—222no—
1147C23—222no—
1148C23—222no—
1149C23—222no—
1150C23—222no—
1151C23—222no—
1152C23—222no—
1153C23—222no—
1154C23—222no—
1155C23—222no—
1156C23—222no—
1157C23—222no—
1158C23—222no—
1159C23—222no—
1160C23—222no—
1161C23—222no—
1162C23—222no—
1163C23—222no—
1164C23—222no—
1165C23—222no—
1166C23—222no—
1167C23—222no—
1168C23—222no—
1169C23—222no—
1170C23—4416no—
1171C23—4416no—
1172C23—4416no—
1173C23—4416no—
1174C23—4416no—
1175C23—4416no—
1176C23—4416no—
1177C23—4416no—
1178C23—4416no—
1179C23—4416no—
1180C23—4416no—
1181C23—4416no—
1182C23—4416no—
1183C23—4416no—
1184C23—441no—
1185C23—441no—
1186C23—441no—
1187C23—441no—
1188C23—441no—
1189C23—441no—
1190C23—441no—
1191C23—441no—
1192C23—441no—
1193C23—441no—
1194C23—441no—
1195C23—441no—
1196C23—441no—
1197C23—441no—
1198C23—441no—
1199C23—441no—
1200C23C4⋊C4×D1114yes—
1201C23C22×C4×D1111yescharacteristic
1202C23C2×D4×D1111yescharacteristic
1203C23C2×D4×D1111yescharacteristic
1204C23C2×D4×D1111yescharacteristic
1205C23#6703711yescharacteristic
1206C23#6703711yescharacteristic
1207C23#6703711yescharacteristic
1208C23#6703711yescharacteristic
1209C23C2×Q8×D1111yescharacteristic
1210C23#41×D1111yescharacteristic
1211C23#41×D1111yescharacteristic
1212C23#6704211yescharacteristic
1213C23#6704211yescharacteristic
1214C23#6704211yescharacteristic
1215C23#6704211yescharacteristic
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—222no—
1259C2×C4—222no—
1260C2×C4—222no—
1261C2×C4—222no—
1262C2×C4—222no—
1263C2×C4—222no—
1264C2×C4—222no—
1265C2×C4—222no—
1266C2×C4—222no—
1267C2×C4—222no—
1268C2×C4—222no—
1269C2×C4—222no—
1270C2×C4—4416no—
1271C2×C4—4416no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4—441no—
1286C2×C4—441no—
1287C2×C4—441no—
1288C2×C4—441no—
1289C2×C4—441no—
1290C2×C4—441no—
1291C2×C4—441no—
1292C2×C4—441no—
1293C2×C4—441no—
1294C2×C4—441no—
1295C2×C4—441no—
1296C2×C4—441no—
1297C2×C4—441no—
1298C2×C4—441no—
1299C2×C4—441no—
1300C2×C4—441no—
1301C2×C4—441no—
1302C22—24no—
1303C22—24no—
1304C22—24no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—118no—
1318C22—224no—
1319C22—224no—
1320C22—224no—
1321C22—224no—
1322C22—224no—
1323C22—224no—
1324C22—224no—
1325C22—224no—
1326C22—224no—
1327C22—224no—
1328C22—224no—
1329C22—224no—
1330C22—224no—
1331C22—224no—
1332C22—224no—
1333C22—224no—
1334C22—224no—
1335C22—4464no—
1336C22—442no—
1337C22—442no—
1338C22—442no—
1339C22—442no—
1340C22—442no—
1341C22—442no—
1342C22—442no—
1343C22—442no—
1344C22—442no—
1345C22—442no—
1346C22—442no—
1347C22—442no—
1348C22#1062301711yescharacteristic
1349C22C2×C4⋊C4×D1111yescharacteristic
1350C22#1062305211yescharacteristic
1351C22C4×D4×D1111yescharacteristic
1352C22C4×D4×D1111yescharacteristic
1353C22#1062307611yescharacteristic
1354C22#1062307611yescharacteristic
1355C22D11×#12011yescharacteristic
1356C22#1062312011yescharacteristic
1357C22#1062312011yescharacteristic
1358C22#1062313611yescharacteristic
1359C22#1062313611yescharacteristic
1360C22#1062313611yescharacteristic
1361C22#1062313611yescharacteristic
1362C22#1062313811yescharacteristic
1363C22#1062313811yescharacteristic
1364C22#1062314411yescharacteristic
1365C22#1062314411yescharacteristic
1366C22D11×C22⋊Q811yescharacteristic
1367C22D11×C22⋊Q811yescharacteristic
1368C22#1062316511yescharacteristic
1369C22#1062316511yescharacteristic
1370C22#1062316511yescharacteristic
1371C22#1062316511yescharacteristic
1372C22D11×#12311yescharacteristic
1373C22#1062318411yescharacteristic
1374C22#1062318411yescharacteristic
1375C22#1062318811yescharacteristic
1376C22#1062318811yescharacteristic
1377C22#1062320511yescharacteristic
1378C22#1062320911yescharacteristic
1379C22#1062320911yescharacteristic
1380C22#1062323511yescharacteristic
1381C22#1062323511yescharacteristic
1382C22#1062324611yescharacteristic
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—81no—
1388C4—81no—
1389C4—442no—
1390C4—442no—
1391C4—442no—
1392C4—442no—
1393C4—881no—
1394C4—881no—
1395C2—44no—
1396C2—228no—
1397C2—444no—
1398C2D11×#38511yescharacteristic
1399C2#1307122711yescharacteristic
1400C2#1307122911yescharacteristic
1401C2#1307126911yescharacteristic
1402C2#1307127211yescharacteristic
1403C2#1307127511yescharacteristic
1404C2#1307127811yescharacteristic
1405C2#1307432711yescharacteristic
1406C2#1307432911yescharacteristic
1407C2#1307438811yescharacteristic
1408C2#1307439011yescharacteristic
1409C2#1307442011yescharacteristic
1410C2#1307442211yescharacteristic
1411C2#1307442611yescharacteristic
1412C2#1307442611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1439D11
hypocenterC11#14262
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622281C2semidirect
3. C2×#10622602C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066860C2semidirect
10. #13066859C2semidirect
11. #13066859C2semidirect
12. #13066858C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
19. C22×C11×C4⋊C4C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×Dic11⋊C4C22semidirect
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
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
56. #10622568C4semidirect
113. C2×C11×C22⋊C4C2×C4semidirect
122. C2×C22⋊Dic11C2×C4semidirect
151. C2×(C2×D11)⋊C4C2×C4semidirect
152. C2×(C2×D11)⋊C4C2×C4semidirect
246. C23×D11C4⋊C4semidirect
387. #1439D11semidirect
617. C22×C4⋊C4C2×D11semidirect
650. C2×#95C2×D11semidirect
651. C2×#95C2×D11semidirect
652. C2×#95C2×D11semidirect
850. C2×C22⋊C4C4×D11semidirect
1080. C11#14262semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×#106222812
C2×#106226022
C2×#106225682
#130668622
#130668612
#130668602
#130668592
#130668582
(C2×D11)⋊#952
C11×#14392
#1426211