Finite Group Databasebeta

← #14810698

Subgroups — #14810698

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622681C211yesmaximal, characteristic, complemented
2C2×#10622629C211yesmaximal, characteristic
3#13074104C211yesmaximal, characteristic, complemented
4#13069764C211yesmaximal, characteristic, complemented
5#13069759C211yesmaximal, characteristic, complemented
6#13069754C211yesmaximal, characteristic, complemented
7#13069749C211yesmaximal, characteristic, complemented
8#13069574C211yesmaximal, characteristic, complemented
9#13069553C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic
11#13068964C211yesmaximal, characteristic
12#13068950C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C2×C11×#554C211yesmaximal, characteristic, complemented
16C11×#554—24no—
17C11×#554—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4—21no—
29C22×#4324C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66928C2211yescharacteristic
32#10622844—21no—
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622681—24no—
36#10622629—24no—
37#10622606—21no—
38#10622603—21no—
39#10622603—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C22×D44C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8—22no—
73C11×#125—22no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125D414yes—
77C11×C22⋊Q8—28no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11D414yes—
88C2×C11×C4⋊C4—28no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×#4324—22no—
107C2×#4324—22no—
108C2×#4324—22no—
109C2×#4323—22no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4×Dic11—21no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66928—22no—
126#66928—22no—
127#66896—22no—
128#66896—22no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66874—22no—
135#66874—22no—
136#66874—22no—
137#66873—22no—
138#66873—22no—
139#66873—22no—
140C4⋊(C11⋊C8)—22no—
141C4×C11⋊C8—22no—
142#25938—111nomaximal, Sylow
143C24×C11—21no—
144C23×D11—21no—
145C2×Q8×C11—24no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11—81no—
150C2×Q8×C11—81no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11C2×D412yes—
155C2×D4×C11#4112yes—
156C2×D4×C11#4112yes—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—81no—
166C22×C4×C11—81no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4C2×D412yes—
203C11×C4⋊C4C2×D412yes—
204C11×C4⋊C4C2×D412yes—
205C11×C22⋊C4—24no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—24no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11C2×D412yes—
213C42×C11C2×D412yes—
214#4324—44no—
215#4323—44no—
216(C2×D11)⋊C4—42no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4×Dic11—81no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×#554D1111yescharacteristic, complemented
240C2×#488—111no—
241C2×#463—111no—
242#2592—111no—
243#2026—111no—
244#2025—111no—
245#2024—111no—
246#2023—111no—
247#1989—111no—
248#1984—111no—
249#1879—111no—
250#1879—111no—
251#1877—111no—
252#1877—111no—
253C4×#102—111no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11C22×D411yescharacteristic
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269Q8×C11—44no—
270Q8×C11—84no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11#12414yes—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—48no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—84no—
301C2×C4×C11—84no—
302C2×C4×C11#12012yes—
303C2×C4×C11#12012yes—
304C2×C4×C11#13512yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320D44—41no—
321D44—41no—
322D44—41no—
323D44—41no—
324Dic22—41no—
325Dic22—41no—
326Dic22—41no—
327Dic22—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C11⋊C8—41no—
332C22×SD16—111no—
333C22×D8—111no—
334#554—24no—
335#554—24no—
336C2×C4⋊Q8C2×D1111yescharacteristic
337C2×#125C2×D1111yescharacteristic
338C2×#125C2×D1111yescharacteristic
339C2×#124—111no—
340C2×C22⋊Q8—21no—
341C2×C22⋊Q8—21no—
342C2×C22⋊Q8—21no—
343C2×C4×Q8C2×D1111yescharacteristic
344C2×C4×D4C2×D1111yescharacteristic
345C2×C4×D4C2×D1111yescharacteristic
346C2×C4×D4C2×D1111yescharacteristic
347C22×C4⋊C4—21no—
348#488—224no—
349#463—224no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×C4×C8—111no—
360#397—221no—
361#393—221no—
362#391—111no—
363#391—111no—
364#390—111no—
365#390—111no—
366#388—221no—
367#388—221no—
368C4×C4⋊C4—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#336—111no—
376#336—111no—
377#336—111no—
378#336—111no—
379C22×C11—24no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11C2×#12011yescharacteristic
387C22×C11#54811yescharacteristic
388C22×C11#54811yescharacteristic
389C22×C11C2×#13511yescharacteristic
390C22×C11#57511yescharacteristic
391C22×C11#57611yescharacteristic
392C22×C11#57711yescharacteristic
393C2×D11—81no—
394C2×D11—81no—
395C2×D11—81no—
396C2×D11—81no—
397C2×D11—81no—
398C2×D11—81no—
399C2×D11—81no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—41no—
404C4×C11—42no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11C2×#12411yescharacteristic
410C4×C11#53611yescharacteristic
411C4×C11#54811yescharacteristic
412C4×C11#54811yescharacteristic
413Dic11—81no—
414Dic11—81no—
415Dic11—81no—
416C22×Q8—21no—
417C22×Q8—111no—
418C22×Q8C22⋊D1111yescharacteristic
419C22×D4—111no—
420C22×D4C22×D1111yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C2×SD16—222no—
425C2×SD16—222no—
426C2×SD16—222no—
427C2×D8—222no—
428C2×D8—222no—
429C2×D8—222no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436#125—22no—
437#125—22no—
438#125—22no—
439#125C22⋊D1114yes—
440#124—222no—
441#124—222no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4C22⋊D1114yes—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4C22⋊D1111yescharacteristic
462C2×C4⋊C4C22⋊D1111yescharacteristic
463C2×C4⋊C4C22⋊D1111yescharacteristic
464C2×C4⋊C4C22×D1111yescharacteristic
465C2×C4⋊C4C22×D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C42—221no—
477C2×C42C22×D1111yescharacteristic
478C2×C42C22×D1111yescharacteristic
479C2×C42C22×D1111yescharacteristic
480C4⋊C8—222no—
481#103—222no—
482#103—222no—
483#103—222no—
484#102—222no—
485#102—222no—
486#102—222no—
487#102—222no—
488#102—222no—
489C4×C8—222no—
490#95—221no—
491#95—221no—
492#95—221no—
493#95—221no—
494#95—221no—
495C2×C11—44no—
496C2×C11#243611yescharacteristic
497C2×C11#300211yescharacteristic
498C2×C11#301211yescharacteristic
499C2×C11#336011yescharacteristic
500C2×C11#336111yescharacteristic
501C2×C11#337011yescharacteristic
502C2×C11#337611yescharacteristic
503D11—161no—
504C24—21no—
505C24—221no—
506C2×Q8—24no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—41no—
510C2×Q8—81no—
511C2×Q8—81no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×Q8—221no—
515C2×Q8—221no—
516C2×Q8—221no—
517C2×Q8—221no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—221no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4#434312yes—
528C2×D4#434312yes—
529C2×D4C2×C22⋊D1112yes—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552SD16—444no—
553D8—444no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4C2×C22⋊D1112yes—
582C4⋊C4C2×C22⋊D1112yes—
583C4⋊C4C2×C22⋊D1112yes—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—442no—
588C22⋊C4—442no—
589C22⋊C4—442no—
590C22⋊C4—442no—
591C22⋊C4—881no—
592C22⋊C4—881no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—881no—
598C42C2×C22⋊D1112yes—
599C42C2×C22⋊D1112yes—
600C11#2593811yescharacteristic, complemented, Sylow
601C23—22no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—441no—
609C23—441no—
610C23—441no—
611C23—441no—
612C23—441no—
613C23—441no—
614C23—441no—
615C23C22×C22⋊D1111yescharacteristic
616Q8—44no—
617Q8—84no—
618Q8—441no—
619Q8—441no—
620Q8—441no—
621Q8—441no—
622D4—22no—
623D4—22no—
624D4—22no—
625D4—441no—
626D4—441no—
627D4—441no—
628D4—441no—
629D4#6700014yes—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—441no—
666C2×C4#6700312yes—
667C2×C4#6700612yes—
668C2×C4#6700612yes—
669C2×C4C2×#434311yescharacteristic
670C2×C4C2×#434311yescharacteristic
671C2×C4#6704011yescharacteristic
672C2×C4#6704011yescharacteristic
673C2×C4C22×C22⋊D1111yescharacteristic
674C2×C4C22×C22⋊D1111yescharacteristic
675C8—441no—
676C8—441no—
677C8—441no—
678C8—441no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—881no—
687C22—881no—
688C22—881no—
689C22—881no—
690C22—881no—
691C22—881no—
692C22—881no—
693C22#1062334811yescharacteristic
694C22#1062334811yescharacteristic
695C22C2×#6700311yescharacteristic
696C22#1062335311yescharacteristic
697C22#1062336611yescharacteristic
698C22#1062336711yescharacteristic
699C22C2×#6700611yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—881no—
710C4—881no—
711C4—881no—
712C4C2×#6700011yescharacteristic
713C4#1062334711yescharacteristic
714C4#1062334811yescharacteristic
715C4#1062334811yescharacteristic
716C2—44no—
717C2—1761no—
718C2#1307227011yescharacteristic
719C2#1307783411yescharacteristic
720C2#1307792011yescharacteristic
721C2#1308126511yescharacteristic
722C2#1308127611yescharacteristic
723C2#1308136911yescharacteristic
724C2#1308144311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#554D11
hypocenterC11#25938
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622681C2semidirect
3. #13074104C2semidirect
4. #13069764C2semidirect
5. #13069759C2semidirect
6. #13069754C2semidirect
7. #13069749C2semidirect
8. #13069574C2semidirect
9. #13069553C2semidirect
12. #13068950C2semidirect
13. #13068950C2semidirect
14. C4×#66896C2semidirect
15. C2×C11×#554C2semidirect
239. C2×#554D11semidirect
600. C11#25938semidirect

Maximal subgroups

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

subgroupindex
C2×#106226812
C2×#106226292
#130741042
#130697642
#130697592
#130697542
#130697492
#130695742
#130695532
#130689642
#130689502
C4×#668962
C2×C11×#5542
#2593811