Finite Group Databasebeta

← #14677586

Subgroups — #14677586

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic
3C2×#10622585C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic
5#13066887C211yesmaximal, characteristic
6#13066886C211yesmaximal, characteristic
7#13066867C211yesmaximal, characteristic
8#13066866C211yesmaximal, characteristic
9#13066849C211yesmaximal, characteristic
10#13066847C211yesmaximal, characteristic
11Dic11⋊#95C211yesmaximal, characteristic
12Dic11⋊#95C211yesmaximal, characteristic
13Dic11⋊#95C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic
15C2×C11×#391C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C2×#66997—24no—
21C2×#66997—24no—
22C2×#66997C418yescomplemented
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C11×#391—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622585—24no—
56C4×Dic11⋊C4—24no—
57#10622259—24no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—41no—
63C22×Q8×C11—41no—
64C22×Q8×C11C2×C414yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—41no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—41no—
93#66997—232no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4C2×C414yes—
109C2×Dic11⋊C4C2×C414yes—
110C2×Dic11⋊C4C2×C414yes—
111C2×Dic11⋊C4C2×C414yes—
112C2×Dic11⋊C4D414yes—
113C2×Dic11⋊C4D414yes—
114C2×Dic11⋊C4Q814yescomplemented
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—41no—
125C2×C4×Dic11C2×C414yes—
126C2×C4×Dic11Q814yescomplemented
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95D414yes—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95Q814yescomplemented
147#14053—111nomaximal, Sylow
148C24×C11C2411yescharacteristic
149C2×Q8×C11—28no—
150C2×Q8×C11—28no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
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×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×Q812yes—
202C22×C4×C11C2×Q812yes—
203C22×C4×C11C2×Q812yes—
204C22×C4×C11#4112yes—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
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×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C2×D412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×Q812yes—
253C22×Dic11C2×Q812yes—
254C22×Dic11C2×Q812yes—
255C22×Dic11C2×Q812yes—
256C22×Dic11C2×Q812yes—
257C22×Dic11C2×Q812yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C2×Dic22—28no—
262C2×Dic22—28no—
263C2×Dic22—44no—
264C2×Dic22—44no—
265C2×Dic22—44no—
266C2×Dic22—44no—
267C2×Dic22—44no—
268C11×C4⋊C4—44no—
269C42×C11—44no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275Dic11⋊C4—44no—
276Dic11⋊C4C22⋊C4116yes—
277C4×Dic11—28no—
278C4×Dic11—28no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C22×C4⋊Q8—111no—
282C2×#391—111no—
283C2×#391D1111yescharacteristic
284C2×#389—111no—
285C2×C4×C4⋊C4—111no—
286#1446—111no—
287#1446—111no—
288#1441—111no—
289#1441—111no—
290#1436—111no—
291#1436—111no—
292C4⋊#95—111no—
293C4⋊#95—111no—
294C4⋊#95—111no—
295C4×#95—111no—
296C23×C11C23×C411yescharacteristic
297C23×C11C22×D411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×Q811yescharacteristic
301C23×C11C22×Q811yescharacteristic
302C23×C11C22×Q811yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C112−1+411yescharacteristic
310C23×C112−1+411yescharacteristic
311Q8×C11—416no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11C2×C22⋊C414yes—
359C2×C4×C11C4×D414yes—
360C2×C4×C11C4⋊Q814yescomplemented
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11C2×C22⋊C414yes—
409C2×Dic11C2×C22⋊C414yes—
410C2×Dic11C4×Q814yes—
411C2×Dic11C4×Q814yes—
412C2×Dic11C4×Q814yes—
413C2×Dic11C22⋊Q814yes—
414C2×Dic11C22⋊Q814yes—
415C2×Dic11#12414yes—
416C2×Dic11C4⋊Q814yes—
417Dic22—416no—
418C23×Q8—111no—
419C23×Q8C2×D1111yescharacteristic
420C2×C4⋊Q8—118no—
421C2×C4⋊Q8—224no—
422C2×C4⋊Q8—224no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C42—111no—
432C22×C42—111no—
433C22×C42—111no—
434C22×C42—111no—
435C22×C42C2×D1111yescharacteristic
436#391—24no—
437#391—224no—
438#389—224no—
439C4×C4⋊C4—224no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C22×C11C22×C22⋊C411yescharacteristic
461C22×C11C2×C4×D411yescharacteristic
462C22×C11C2×C4×Q811yescharacteristic
463C22×C11C2×C4×Q811yescharacteristic
464C22×C11C2×C4×Q811yescharacteristic
465C22×C11#51811yescharacteristic
466C22×C11#51911yescharacteristic
467C22×C11C2×C22⋊Q811yescharacteristic
468C22×C11C2×C22⋊Q811yescharacteristic
469C22×C11C2×#12411yescharacteristic
470C22×C11C2×C4⋊Q811yescharacteristic
471C22×C11C2×C4⋊Q811yescharacteristic
472C22×C11#53211yescharacteristic
473C22×C11#53311yescharacteristic
474C22×C11#53311yescharacteristic
475C22×C11#54211yescharacteristic
476C22×C11#54211yescharacteristic
477C22×C11#54411yescharacteristic
478C22×C11#54411yescharacteristic
479C22×C11D4211yescharacteristic
480C22×C11D4211yescharacteristic
481C22×C11#54611yescharacteristic
482C22×C11#54611yescharacteristic
483C22×C11#54711yescharacteristic
484C22×C11#54811yescharacteristic
485C22×C11#54811yescharacteristic
486C22×C11D4×Q811yescharacteristic
487C22×C11D4×Q811yescharacteristic
488C22×C11D4×Q811yescharacteristic
489C22×C11#55411yescharacteristic
490C22×C11#55411yescharacteristic
491C22×C11#55511yescharacteristic
492C22×C11#55611yescharacteristic
493C22×C11#55711yescharacteristic
494C22×C11Q8211yescharacteristic
495C4×C11—24no—
496C4×C11—24no—
497C4×C11—24no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—81no—
502Dic11—24no—
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11—81no—
509Dic11#39118yescomplemented
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—114no—
517C22×Q8—222no—
518C22×Q8—222no—
519C22×Q8—222no—
520C22×Q8—222no—
521C22×Q8—441no—
522C22×Q8—441no—
523C22×Q8C4×D1114yes—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C4⋊Q8—2232no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—222no—
555C2×C4⋊C4—222no—
556C2×C4⋊C4—222no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—441no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—41no—
567C2×C42—114no—
568C2×C42—114no—
569C2×C42—222no—
570C2×C42—222no—
571C2×C42—222no—
572C2×C42—222no—
573C2×C42—222no—
574C2×C42—222no—
575C2×C42—222no—
576C2×C42—222no—
577C2×C42—222no—
578C2×C42—441no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—114no—
583#95—222no—
584#95—222no—
585#95—222no—
586#95—222no—
587#95—222no—
588#95—222no—
589#95—222no—
590#95—222no—
591#95—222no—
592#95—222no—
593#95—222no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95C22⋊D1114yes—
599C2×C11C2×#39111yescharacteristic
600C2×C11C4×C4⋊Q811yescharacteristic
601C2×C11#233111yescharacteristic
602C2×C11D4×C22⋊C411yescharacteristic
603C2×C11Q8×C22⋊C411yescharacteristic
604C2×C11#236511yescharacteristic
605C2×C11#236911yescharacteristic
606C2×C11#243911yescharacteristic
607C2×C11#244011yescharacteristic
608C2×C11#245111yescharacteristic
609C2×C11#245211yescharacteristic
610C2×C11#249111yescharacteristic
611C2×C11#249211yescharacteristic
612C2×C11#255011yescharacteristic
613C2×C11#255111yescharacteristic
614C24C23×D1111yescharacteristic
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—228no—
623C2×Q8—228no—
624C2×Q8—444no—
625C2×Q8—444no—
626C2×Q8—444no—
627C2×Q8—444no—
628C2×Q8—444no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4C2×C4×D1112yes—
723C22×C4C2×C4×D1112yes—
724C22×C4C2×C4×D1112yes—
725C22×C4#433912yes—
726C22×C4D4×D1112yes—
727C22×C4D4×D1112yes—
728C22×C4Q8×D1112yes—
729C22×C4Q8×D1112yes—
730C22×C4Q8×D1112yes—
731C22×C4C2×C22⋊D1112yes—
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1112yes—
734C4⋊C4—44no—
735C4⋊C4—1116no—
736C4⋊C4—228no—
737C4⋊C4—228no—
738C4⋊C4—228no—
739C4⋊C4—228no—
740C4⋊C4—444no—
741C4⋊C4—444no—
742C42—44no—
743C42—228no—
744C42—228no—
745C42—444no—
746C42—444no—
747C11#1405311yescharacteristic, complemented, Sylow
748C23C22×C4×D1111yescharacteristic
749C23C2×#433911yescharacteristic
750C23C2×D4×D1111yescharacteristic
751C23C2×D4×D1111yescharacteristic
752C23#6703711yescharacteristic
753C23#6703711yescharacteristic
754C23C2×Q8×D1111yescharacteristic
755C23C2×Q8×D1111yescharacteristic
756C23C2×Q8×D1111yescharacteristic
757C23#6704011yescharacteristic
758C23#41×D1111yescharacteristic
759C23#41×D1111yescharacteristic
760C23#41×D1111yescharacteristic
761C23#6704311yescharacteristic
762C23C22×C22⋊D1111yescharacteristic
763Q8—416no—
764Q8—4416no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—441no—
845C2×C4—441no—
846C2×C4—441no—
847C2×C4—441no—
848C2×C4—441no—
849C2×C4—441no—
850C2×C4—441no—
851C2×C4—441no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4C22⋊C4×D1114yes—
868C2×C4C4×C22⋊D1114yes—
869C2×C4#6699714yescomplemented
870C22C2×C22⋊C4×D1111yescharacteristic
871C22#1062301711yescharacteristic
872C22#1062302111yescharacteristic
873C22#1062302111yescharacteristic
874C22#1062309811yescharacteristic
875C22#1062309911yescharacteristic
876C22C4×Q8×D1111yescharacteristic
877C22C4×Q8×D1111yescharacteristic
878C22C4×Q8×D1111yescharacteristic
879C22#1062310311yescharacteristic
880C22#1062310911yescharacteristic
881C22#1062310911yescharacteristic
882C22#1062315411yescharacteristic
883C22D11×C22⋊Q811yescharacteristic
884C22D11×C22⋊Q811yescharacteristic
885C22#1062316311yescharacteristic
886C22#1062316411yescharacteristic
887C22#1062316711yescharacteristic
888C22#1062316711yescharacteristic
889C22#1062317111yescharacteristic
890C22#1062320011yescharacteristic
891C22#1062320111yescharacteristic
892C22D11×#12411yescharacteristic
893C22#1062320811yescharacteristic
894C22#1062325311yescharacteristic
895C22D11×C4⋊Q811yescharacteristic
896C22#1062325811yescharacteristic
897C22#1062326011yescharacteristic
898C22C2×C4×C22⋊D1111yescharacteristic
899C22D4×C22⋊D1111yescharacteristic
900C22D4×C22⋊D1111yescharacteristic
901C22C2×#6699711yescharacteristic
902C22Q8×C22⋊D1111yescharacteristic
903C22#1062335511yescharacteristic
904C22#1062336311yescharacteristic
905C4—24no—
906C4—24no—
907C4—24no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—81no—
912C4—118no—
913C4—224no—
914C4—224no—
915C4—442no—
916C4—442no—
917C4—442no—
918C4—442no—
919C4—881no—
920C2D11×#39111yescharacteristic
921C2C4×#6699711yescharacteristic
922C2#1307135911yescharacteristic
923C2C22⋊C4×C22⋊D1111yescharacteristic
924C2#1307145011yescharacteristic
925C2#1307167011yescharacteristic
926C2#1307170411yescharacteristic
927C2#1307230411yescharacteristic
928C2#1307231511yescharacteristic
929C2#1307245211yescharacteristic
930C2#1307246511yescharacteristic
931C2#1307297611yescharacteristic
932C2#1307298911yescharacteristic
933C2#1307363411yescharacteristic
934C2#1307364311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14053
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
22. C2×#66997C4semidirect
114. C2×Dic11⋊C4Q8semidirect
126. C2×C4×Dic11Q8semidirect
146. C11⋊#95Q8semidirect
360. C2×C4×C11C4⋊Q8semidirect
509. Dic11#391semidirect
747. C11#14053semidirect
869. C2×C4#66997semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106222592
C2×#106225852
C2×C4×Dic11⋊C42
#130668872
#130668862
#130668672
#130668662
#130668492
#130668472
Dic11⋊#952
#95×Dic112
C2×C11×#3912
#1405311