Finite Group Databasebeta

← #14677220

Subgroups — #14677220

Order 2816.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic, complemented
4C2×#10622569C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×#66946—24no—
38C2×#66946—24no—
39C2×#66946—24no—
40C2×#66937—24no—
41C2×#66937—24no—
42C2×#66937C418yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622569—24no—
58#10622569—24no—
59#10622569—24no—
60#10622278—24no—
61D11×#95—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11C2×C414yescomplemented
84C22×C22⋊D11C2×C414yescomplemented
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×D44—22no—
92C22×D44—22no—
93C22×D44—22no—
94C22×D44—22no—
95C22×D44C2×C414yes—
96C22×D44D414yes—
97C22×D44D414yes—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C4×D11—22no—
111C22×C4×D11—22no—
112C22×C4×D11—22no—
113C22×C4×D11—22no—
114C22×C4×D11—22no—
115C22×C4×D11—22no—
116C22×C4×D11—41no—
117C22×C4×D11—41no—
118C22×C4×D11—41no—
119C22×C4×D11—41no—
120C22×C4×D11—41no—
121C22×C4×D11—41no—
122C22×C4×D11—41no—
123C22×C4×D11—41no—
124C22×C4×D11C2×C414yescomplemented
125C22×C4×D11D414yescomplemented
126C2×C11×C4⋊C4—22no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—22no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—41no—
135C2×C11×C22⋊C4—41no—
136C2×C11×C22⋊C4—41no—
137C2×C11×C22⋊C4C2×C414yescomplemented
138C2×C22⋊Dic11—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—22no—
141C2×C22⋊Dic11—22no—
142C2×C22⋊Dic11—22no—
143C2×C22⋊Dic11—41no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—22no—
155C2×(C2×D11)⋊C4—22no—
156C2×(C2×D11)⋊C4—22no—
157C2×(C2×D11)⋊C4—22no—
158C2×(C2×D11)⋊C4—41no—
159C2×(C2×D11)⋊C4—41no—
160C2×(C2×D11)⋊C4C2×C414yescomplemented
161C2×(C2×D11)⋊C4D414yescomplemented
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4—22no—
164C2×Dic11⋊C4C2×C414yescomplemented
165C2×C4×Dic11—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168#66946—232no—
169#66937—232no—
170C11×#95—22no—
171C11×#95—22no—
172C11×#95—41no—
173C11⋊#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—22no—
182C11⋊#95—41no—
183C11⋊#95D414yescomplemented
184#14023—111nomaximal, Sylow
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11C22×C412yes—
200C24×C11C2411yescharacteristic
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—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11C22×C412yes—
222C23×D11C22×C412yes—
223C23×D11C2×D412yes—
224C23×D11C2×D412yes—
225C23×D11C2×D412yes—
226C23×D11C2×D412yes—
227C23×D11C2×D412yes—
228C23×D11C2×D412yes—
229C23×D11#4112yes—
230C23×D11#4112yes—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
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×C11C22×C412yes—
267C22×C4×C11C22×C412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11C2×D412yes—
272C22×C4×C11C2×D412yes—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
280C2×C22⋊D11—44no—
281C2×C22⋊D11—44no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C2×C22⋊D11—44no—
287C22×Dic11—21no—
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×Dic11C22×C412yes—
321C22×Dic11C22×C412yes—
322C22×Dic11C2×D412yes—
323C22×Dic11C2×D412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11#4112yes—
327C22×Dic11#4112yes—
328C22×Dic11#4112yes—
329C2×D44—28no—
330C2×D44—28no—
331C2×D44—28no—
332C2×D44—28no—
333C2×D44—28no—
334C2×D44—28no—
335C2×D44C22⋊C4116yescomplemented
336C2×C4×D11—28no—
337C2×C4×D11—28no—
338C2×C4×D11—28no—
339C2×C4×D11—28no—
340C2×C4×D11—28no—
341C2×C4×D11—28no—
342C2×C4×D11—44no—
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—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C2×C4×D11—44no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11—44no—
363C2×C4×D11—44no—
364C11×C4⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—44no—
367C11×C22⋊C4—44no—
368C22⋊Dic11—44no—
369C22⋊Dic11—44no—
370(C2×D11)⋊C4—28no—
371(C2×D11)⋊C4—28no—
372(C2×D11)⋊C4—28no—
373(C2×D11)⋊C4—44no—
374(C2×D11)⋊C4—44no—
375(C2×D11)⋊C4—44no—
376Dic11⋊C4—28no—
377C4×Dic11—28no—
378C22×#121—111no—
379C22×C4×D4—111no—
380C2×#386—111no—
381C2×#386—111no—
382C2×#386—111no—
383C2×#386—111no—
384C22×#95—111no—
385#1441—111no—
386#1440—111no—
387#1439D1111yescharacteristic, complemented
388#1438—111no—
389#1437—111no—
390#1436—111no—
391C22⋊#95—111no—
392C22⋊#95—111no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
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×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11C23×C411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C23×C11C22×D411yescharacteristic
432C23×C11C22×D411yescharacteristic
433C23×C11C22×D411yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11C2×#4111yescharacteristic
436C23×C11C2×#4111yescharacteristic
437C23×C11C2×#4111yescharacteristic
438C23×C11C2×#4111yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C23×C11H(5,𝔽2)11yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C23×C112−1+411yescharacteristic
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—22no—
487C22×D11—22no—
488C22×D11—22no—
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—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11C2×C22⋊C414yes—
506C22×D11C2×C22⋊C414yes—
507C22×D11C4×D414yes—
508C22×D11C4×D414yes—
509C22×D11#12014yes—
510C22×D11#12114yes—
511C22×D11#12114yes—
512C22×D11#12314yes—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
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—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×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×C11C2×C22⋊C414yes—
555C22⋊D11—416no—
556C22⋊D11—416no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—22no—
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—41no—
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×Dic11C4×D414yescomplemented
598C2×Dic11#12114yescomplemented
599D44—232no—
600C4×D11—416no—
601C4×D11—416no—
602C4×D11—416no—
603C4×D11—416no—
604C23×D4—111no—
605C23×D4—111no—
606C23×D4—111no—
607C24×C4—111no—
608C24×C4—111no—
609C24×C4—111no—
610C24×C4—111no—
611C2×#121—118no—
612C2×#121—224no—
613C2×#121—224no—
614C2×C4×D4—224no—
615C2×C4×D4—224no—
616C2×C4×D4—224no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42—111no—
631#386—224no—
632#386—224no—
633#386—224no—
634#386—224no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—111no—
646C2×#95—224no—
647C2×#95C2×D1111yescharacteristic
648C2×#95C2×D1111yescharacteristic
649C2×#95C2×D1111yescharacteristic
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11—81no—
660C22×C11—81no—
661C22×C11—81no—
662C22×C11—81no—
663C22×C11—81no—
664C22×C11—81no—
665C22×C11C22×C22⋊C411yescharacteristic
666C22×C11C2×C4×D411yescharacteristic
667C22×C11C2×C4×D411yescharacteristic
668C22×C11C2×C4×D411yescharacteristic
669C22×C11C4×#4111yescharacteristic
670C22×C11#51811yescharacteristic
671C22×C11#52011yescharacteristic
672C22×C11C2×#12011yescharacteristic
673C22×C11C2×#12111yescharacteristic
674C22×C11C2×#12111yescharacteristic
675C22×C11C2×#12111yescharacteristic
676C22×C11C2×#12311yescharacteristic
677C22×C11#52511yescharacteristic
678C22×C11#52911yescharacteristic
679C22×C11#53211yescharacteristic
680C22×C11#53411yescharacteristic
681C22×C11#53711yescharacteristic
682C22×C11#53811yescharacteristic
683C22×C11#53911yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11D4211yescharacteristic
686C22×C11D4211yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54611yescharacteristic
689C22×C11#54611yescharacteristic
690C22×C11#54611yescharacteristic
691C22×C11#54611yescharacteristic
692C22×C11#54611yescharacteristic
693C22×C11#54711yescharacteristic
694C22×C11#54711yescharacteristic
695C22×C11#54711yescharacteristic
696C22×C11#54811yescharacteristic
697C22×C11#55311yescharacteristic
698C22×C11#55311yescharacteristic
699C22×C11#55311yescharacteristic
700C2×D11—24no—
701C2×D11—24no—
702C2×D11—24no—
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—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
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#38618yescomplemented
730C4×C11—24no—
731C4×C11—42no—
732C4×C11—42no—
733C4×C11—42no—
734C4×C11—42no—
735C4×C11—81no—
736Dic11—24no—
737Dic11—24no—
738Dic11—42no—
739Dic11—42no—
740Dic11—42no—
741Dic11—81no—
742C25—111no—
743C25—111no—
744C25C22×D1111yescharacteristic
745C22×D4—114no—
746C22×D4—114no—
747C22×D4—114no—
748C22×D4—114no—
749C22×D4—114no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—222no—
761C22×D4—222no—
762C22×D4—222no—
763C22×D4—222no—
764C22×D4—441no—
765C22×D4—441no—
766C23×C4—111no—
767C23×C4—111no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—114no—
772C23×C4—114no—
773C23×C4—111no—
774C23×C4—222no—
775C23×C4—222no—
776C23×C4—222no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—441no—
793C23×C4—441no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4—441no—
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—2232no—
807C4×D4—2232no—
808C2×C4⋊C4—22no—
809C2×C4⋊C4—22no—
810C2×C4⋊C4—22no—
811C2×C4⋊C4—114no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4—222no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—114no—
823C2×C22⋊C4—114no—
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—222no—
839C2×C22⋊C4—222no—
840C2×C22⋊C4—222no—
841C2×C22⋊C4—222no—
842C2×C22⋊C4—222no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4C4×D1114yescomplemented
847C2×C42—222no—
848C2×C42—222no—
849C2×C42—222no—
850#95—22no—
851#95—22no—
852#95—41no—
853#95—114no—
854#95—222no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—222no—
863#95—441no—
864C2×C11—82no—
865C2×C11C2×#38611yescharacteristic
866C2×C11C4×#12111yescharacteristic
867C2×C11#232511yescharacteristic
868C2×C11D4×C22⋊C411yescharacteristic
869C2×C11#233911yescharacteristic
870C2×C11#236111yescharacteristic
871C2×C11#236411yescharacteristic
872C2×C11#241011yescharacteristic
873C2×C11#241611yescharacteristic
874C2×C11#242411yescharacteristic
875C2×C11#242511yescharacteristic
876C2×C11#243011yescharacteristic
877C2×C11#244311yescharacteristic
878C2×C11#244411yescharacteristic
879C2×C11#254311yescharacteristic
880D11—28no—
881D11—44no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—112no—
897C24—112no—
898C24—112no—
899C24—112no—
900C24—112no—
901C24—112no—
902C24—112no—
903C24—112no—
904C24—112no—
905C24—112no—
906C24—221no—
907C24—221no—
908C24—221no—
909C24—221no—
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—
926C24C2×C4×D1112yes—
927C24C23×D1111yescharacteristic
928C2×D4—1116no—
929C2×D4—228no—
930C2×D4—228no—
931C2×D4—228no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—228no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
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—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—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—228no—
994C22×C4—228no—
995C22×C4—228no—
996C22×C4—228no—
997C22×C4—228no—
998C22×C4—228no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
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—444no—
1033C22×C4—444no—
1034C22×C4—444no—
1035C22×C4—444no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4—444no—
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×C4C2×C4×D1112yes—
1055C22×C4C2×C4×D1112yes—
1056C22×C4D4×D1112yes—
1057C22×C4D4×D1112yes—
1058C22×C4D4×D1112yes—
1059C22×C4D4×D1112yes—
1060C22×C4D4×D1112yes—
1061C4⋊C4—28no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—228no—
1067C22⋊C4—228no—
1068C22⋊C4—228no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—228no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
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—114no—
1112C23—114no—
1113C23—114no—
1114C23—114no—
1115C23—114no—
1116C23—114no—
1117C23—114no—
1118C23—114no—
1119C23—222no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
1123C23—222no—
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—441no—
1166C23—441no—
1167C23—441no—
1168C23—441no—
1169C23—441no—
1170C23—441no—
1171C23—441no—
1172C23—441no—
1173C23—441no—
1174C23—441no—
1175C23—441no—
1176C23—441no—
1177C23—441no—
1178C23—441no—
1179C23—441no—
1180C23—441no—
1181C23C22×C4×D1111yescharacteristic
1182C23C2×D4×D1111yescharacteristic
1183C23C2×D4×D1111yescharacteristic
1184C23C2×D4×D1111yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×D4×D1111yescharacteristic
1187C23#6703711yescharacteristic
1188C23#6703711yescharacteristic
1189C23#6704011yescharacteristic
1190C23#41×D1111yescharacteristic
1191C23#41×D1111yescharacteristic
1192C23#41×D1111yescharacteristic
1193C23#41×D1111yescharacteristic
1194C23#41×D1111yescharacteristic
1195C23#6704211yescharacteristic
1196D4—2232no—
1197D4—4416no—
1198D4—4416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
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—114no—
1241C2×C4—114no—
1242C2×C4—222no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—222no—
1249C2×C4—222no—
1250C2×C4—222no—
1251C2×C4—222no—
1252C2×C4—222no—
1253C2×C4—222no—
1254C2×C4—222no—
1255C2×C4—222no—
1256C2×C4—222no—
1257C2×C4—222no—
1258C2×C4—222no—
1259C2×C4—222no—
1260C2×C4—222no—
1261C2×C4—222no—
1262C2×C4—222no—
1263C2×C4—4416no—
1264C2×C4—4416no—
1265C2×C4—4416no—
1266C2×C4—4416no—
1267C2×C4—441no—
1268C2×C4—441no—
1269C2×C4—441no—
1270C2×C4—441no—
1271C2×C4—441no—
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×C4C22⋊C4×D1114yes—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—118no—
1303C22—224no—
1304C22—224no—
1305C22—224no—
1306C22—224no—
1307C22—224no—
1308C22—224no—
1309C22—224no—
1310C22—224no—
1311C22—224no—
1312C22—224no—
1313C22—224no—
1314C22—224no—
1315C22—224no—
1316C22—224no—
1317C22—224no—
1318C22—224no—
1319C22—224no—
1320C22—442no—
1321C22—442no—
1322C22—442no—
1323C22—442no—
1324C22—442no—
1325C22—442no—
1326C22—442no—
1327C22—442no—
1328C22—442no—
1329C22—442no—
1330C22—442no—
1331C22—442no—
1332C22C2×C22⋊C4×D1111yescharacteristic
1333C22#1062303511yescharacteristic
1334C22#1062305311yescharacteristic
1335C22C4×D4×D1111yescharacteristic
1336C22C4×D4×D1111yescharacteristic
1337C22C4×D4×D1111yescharacteristic
1338C22#1062307611yescharacteristic
1339C22D11×#12011yescharacteristic
1340C22#1062312011yescharacteristic
1341C22#1062312111yescharacteristic
1342C22D11×#12111yescharacteristic
1343C22D11×#12111yescharacteristic
1344C22D11×#12111yescharacteristic
1345C22#1062314011yescharacteristic
1346C22#1062314111yescharacteristic
1347C22#1062314311yescharacteristic
1348C22#1062314311yescharacteristic
1349C22#1062314311yescharacteristic
1350C22#1062316011yescharacteristic
1351C22#1062316211yescharacteristic
1352C22#1062316211yescharacteristic
1353C22#1062316211yescharacteristic
1354C22#1062316411yescharacteristic
1355C22#1062316911yescharacteristic
1356C22D11×#12311yescharacteristic
1357C22#1062318711yescharacteristic
1358C22#1062318811yescharacteristic
1359C22#1062319211yescharacteristic
1360C22#1062319211yescharacteristic
1361C22#1062319911yescharacteristic
1362C22#1062320711yescharacteristic
1363C22#1062320711yescharacteristic
1364C22#1062323711yescharacteristic
1365C22#1062324011yescharacteristic
1366C22#1062324811yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—224no—
1374C4—224no—
1375C4—442no—
1376C4—442no—
1377C4—442no—
1378C4—881no—
1379C2—82no—
1380C2—228no—
1381C2—444no—
1382C2D11×#38611yescharacteristic
1383C2#1307112811yescharacteristic
1384C2#1307131311yescharacteristic
1385C2#1307143711yescharacteristic
1386C2#1307144411yescharacteristic
1387C2#1307163511yescharacteristic
1388C2#1307166011yescharacteristic
1389C2#1307198311yescharacteristic
1390C2#1307205111yescharacteristic
1391C2#1307214511yescharacteristic
1392C2#1307216211yescharacteristic
1393C2#1307222911yescharacteristic
1394C2#1307235411yescharacteristic
1395C2#1307236911yescharacteristic
1396C2#1307357911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1439D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. C2×#10622278C2semidirect
4. C2×#10622569C2semidirect
5. C2×#10622569C2semidirect
6. C2×#10622569C2semidirect
7. C2×D11×#95C2semidirect
8. #13066866C2semidirect
9. #13066864C2semidirect
10. #13066855C2semidirect
11. #13066853C2semidirect
12. #13066851C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
42. C2×#66937C4semidirect
83. C22×C22⋊D11C2×C4semidirect
84. C22×C22⋊D11C2×C4semidirect
124. C22×C4×D11C2×C4semidirect
125. C22×C4×D11D4semidirect
137. C2×C11×C22⋊C4C2×C4semidirect
160. C2×(C2×D11)⋊C4C2×C4semidirect
161. C2×(C2×D11)⋊C4D4semidirect
164. C2×Dic11⋊C4C2×C4semidirect
183. C11⋊#95D4semidirect
335. C2×D44C22⋊C4semidirect
387. #1439D11semidirect
597. C2×Dic11C4×D4semidirect
598. C2×Dic11#121semidirect
729. C2×D11#386semidirect
846. C2×C22⋊C4C4×D11semidirect
1075. C11#14023semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669462
C2×#106222782
C2×#106225692
C2×D11×#952
#130668662
#130668642
#130668552
#130668532
#130668512
(C2×D11)⋊#952
C11×#14392
#1402311