Finite Group Databasebeta

← #14661752

Subgroups — #14661752

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66871C211yesmaximal, characteristic
2C2×#10622167C211yesmaximal, characteristic
3C2×#10622167C211yesmaximal, characteristic
4C2×#10622167C211yesmaximal, characteristic
5C2×#10622162C211yesmaximal, characteristic
6#13066846C211yesmaximal, characteristic
7C2×C11×#389C211yesmaximal, characteristic
8C22×C11×C4⋊C4—21no—
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#389—22no—
17C11×#389—22no—
18C2×C11×#95—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×#66871—22no—
22C2×#66871—22no—
23C2×#66871C414yescomplemented
24#10622167—22no—
25#10622167—22no—
26#10622167—22no—
27#10622162—22no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—24no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—42no—
45C2×C11×C4⋊C4—42no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C4⋊C4D412yes—
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2×C412yes—
67C2×C4⋊Dic11Q812yes—
68C22×C11⋊C8—21no—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8C2×C412yes—
79C22×C11⋊C8D412yes—
80C22×C11⋊C8Q812yes—
81C22×C11⋊C8Q812yes—
82C11×#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85#66871—28no—
86#11219—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11D812yes—
115C22×C4×C11Q1612yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×Q811yescharacteristic
122C22×C4×C11C2×Q811yescharacteristic
123C22×C4×C11C2×Q811yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—48no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4C22⋊C414yes—
153C42×C11—41no—
154C42×C11—41no—
155C42×C11—41no—
156C42×C11—41no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—41no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8—41no—
177C2×C11⋊C8—41no—
178C2×C11⋊C8C4⋊C414yescomplemented
179C22×#107—111no—
180C2×#389D1111yescharacteristic
181C2×#340—111no—
182C2×#340—111no—
183C2×#340—111no—
184C2×#336—111no—
185C4⋊#95—111no—
186C23×C11C4×D411yescharacteristic
187C23×C11#12011yescharacteristic
188C23×C11#12111yescharacteristic
189C23×C11#12111yescharacteristic
190C23×C11C22⋊Q811yescharacteristic
191C23×C11#12311yescharacteristic
192C23×C11C4⋊Q811yescharacteristic
193C23×C11C2×D811yescharacteristic
194C23×C11C2×Q1611yescharacteristic
195C23×C11#13511yescharacteristic
196C23×C11#13511yescharacteristic
197C23×C11AGL(1,ℤ/8)11yescharacteristic
198C23×C11AGL(1,ℤ/8)11yescharacteristic
199C23×C11#13711yescharacteristic
200C23×C11#13711yescharacteristic
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—81no—
226C2×C4×C11—81no—
227C2×C4×C11—81no—
228C2×C4×C11—81no—
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C4⋊C411yescharacteristic
231C2×C4×C11#11711yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×Q811yescharacteristic
234C2×C4×C11C4×Q811yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11C22⋊Q811yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12411yescharacteristic
249C2×C4×C11#12511yescharacteristic
250C2×C4×C11#12511yescharacteristic
251C2×C4×C11#12511yescharacteristic
252C2×C4×C11#12511yescharacteristic
253C2×C4×C11#12611yescharacteristic
254C2×C4×C11#12611yescharacteristic
255C2×C4×C11C4⋊Q811yescharacteristic
256C2×C4×C11C4⋊Q811yescharacteristic
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—81no—
264C2×Dic11—81no—
265C2×Dic11—81no—
266C2×Dic11—81no—
267C2×Dic11—81no—
268C2×Dic11—81no—
269C2×Dic11—81no—
270C2×Dic11—81no—
271C11⋊C8—24no—
272C11⋊C8—42no—
273C23×C8—111no—
274C23×C8—111no—
275C22×C4⋊C4—21no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C42C2×D1111yescharacteristic
281C2×#107—114no—
282C2×#107—222no—
283C2×#107—222no—
284#389—22no—
285#389—22no—
286C2×#95—21no—
287C2×#95—221no—
288C2×#95—221no—
289#340—222no—
290#340—222no—
291#340—222no—
292#336—222no—
293C22×C11#38611yescharacteristic
294C22×C11#38711yescharacteristic
295C22×C11#38911yescharacteristic
296C22×C11#39411yescharacteristic
297C22×C11#39511yescharacteristic
298C22×C11#39611yescharacteristic
299C22×C11#39811yescharacteristic
300C22×C11C4×D811yescharacteristic
301C22×C11C4×Q1611yescharacteristic
302C22×C11#44111yescharacteristic
303C22×C11#44211yescharacteristic
304C22×C11#44711yescharacteristic
305C22×C11#44911yescharacteristic
306C22×C11#45111yescharacteristic
307C22×C11#45211yescharacteristic
308C22×C11#45911yescharacteristic
309C22×C11#46211yescharacteristic
310C22×C11#46311yescharacteristic
311C22×C11#46411yescharacteristic
312C22×C11#46611yescharacteristic
313C22×C11#46711yescharacteristic
314C22×C11#46811yescharacteristic
315C22×C11#46811yescharacteristic
316C22×C11#47411yescharacteristic
317C22×C11#47711yescharacteristic
318C22×C11#47811yescharacteristic
319C22×C11#47911yescharacteristic
320C22×C11#48011yescharacteristic
321C22×C11#48211yescharacteristic
322C22×C11#48411yescharacteristic
323C22×C11#48511yescharacteristic
324C22×C11#49911yescharacteristic
325C22×C11#50011yescharacteristic
326C22×C11#50111yescharacteristic
327C22×C11#50111yescharacteristic
328C4×C11—44no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—82no—
332C4×C11#38011yescharacteristic
333C4×C11#38711yescharacteristic
334C4×C11#38911yescharacteristic
335C4×C11#39111yescharacteristic
336C4×C11#39611yescharacteristic
337C4×C11#39811yescharacteristic
338C4×C11#39811yescharacteristic
339C4×C11#40011yescharacteristic
340Dic11—82no—
341Dic11—82no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—221no—
345C23×C4—221no—
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C22×C8—112no—
350C22×C8—112no—
351C22×C8—112no—
352C22×C8—112no—
353C22×C8—221no—
354C22×C8—221no—
355C22×C8—221no—
356C22×C8—221no—
357C22×C8—221no—
358C22×C8—221no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C4×D1112yes—
387C2×C4⋊C4D4412yes—
388C2×C4⋊C4C22⋊D1112yes—
389C2×C4⋊C4C22⋊D1112yes—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396#107—228no—
397#95—24no—
398#95—442no—
399#95—442no—
400C2×C11#144111yescharacteristic
401C2×C11#187811yescharacteristic
402C2×C11#187911yescharacteristic
403C2×C11#191811yescharacteristic
404C2×C11#192111yescharacteristic
405C2×C11#194211yescharacteristic
406C2×C11#194311yescharacteristic
407C2×C11#203311yescharacteristic
408C2×C11#203611yescharacteristic
409C2×C11#205711yescharacteristic
410C2×C11#205911yescharacteristic
411C2×C11#206711yescharacteristic
412C2×C11#206811yescharacteristic
413C2×C11#208311yescharacteristic
414C2×C11#208511yescharacteristic
415C24C2×C22⋊D1111yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4#432312yes—
457C22×C4#432612yes—
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×D4411yescharacteristic
460C22×C4#433911yescharacteristic
461C22×C4#433911yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4#434111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4#434111yescharacteristic
466C22×C4Q8×D1111yescharacteristic
467C22×C4Q8×D1111yescharacteristic
468C22×C4Q8×D1111yescharacteristic
469C22×C4#434311yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C2×C8—114no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—441no—
483C2×C8—441no—
484C2×C8—441no—
485C2×C8—441no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—48no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—441no—
499C4⋊C4—441no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4(C2×D11)⋊C414yes—
503C42—41no—
504C42—41no—
505C42—41no—
506C42—41no—
507C11#1121911yescharacteristic, complemented, Sylow
508C23C4×C22⋊D1111yescharacteristic
509C23#6698311yescharacteristic
510C23C2×#432311yescharacteristic
511C23#6698511yescharacteristic
512C23#6698811yescharacteristic
513C23#6699211yescharacteristic
514C23#6699511yescharacteristic
515C23C2×#432611yescharacteristic
516C23#6699711yescharacteristic
517C23#6699911yescharacteristic
518C23#6700211yescharacteristic
519C23#6700311yescharacteristic
520C23#6700311yescharacteristic
521C23#6700411yescharacteristic
522C23#6700611yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—881no—
558C2×C4—881no—
559C2×C4—881no—
560C2×C4—881no—
561C2×C4—881no—
562C2×C4—881no—
563C2×C4—881no—
564C2×C4—881no—
565C2×C4#6694011yescharacteristic
566C2×C4#6694011yescharacteristic
567C2×C4#6694211yescharacteristic
568C2×C4#6694211yescharacteristic
569C2×C4#6694211yescharacteristic
570C2×C4#6694211yescharacteristic
571C2×C4C4⋊C4×D1111yescharacteristic
572C2×C4#6694511yescharacteristic
573C2×C4#6694811yescharacteristic
574C2×C4#6694911yescharacteristic
575C2×C4#6694911yescharacteristic
576C2×C4#6695011yescharacteristic
577C2×C4#6695011yescharacteristic
578C2×C4#6695011yescharacteristic
579C2×C4#6695111yescharacteristic
580C2×C4#6695111yescharacteristic
581C2×C4C2×(C2×D11)⋊C411yescharacteristic
582C2×C4C4×C22⋊D1111yescharacteristic
583C2×C4#6698211yescharacteristic
584C2×C4#6698311yescharacteristic
585C2×C4#6698811yescharacteristic
586C2×C4#6698911yescharacteristic
587C2×C4#6699111yescharacteristic
588C2×C4#6699211yescharacteristic
589C2×C4#6699711yescharacteristic
590C2×C4#6699711yescharacteristic
591C2×C4#6699911yescharacteristic
592C2×C4#6699911yescharacteristic
593C8—224no—
594C8—442no—
595C22#1062258511yescharacteristic
596C22#1062259111yescharacteristic
597C22#1062259611yescharacteristic
598C22#1062260711yescharacteristic
599C22C4×#432311yescharacteristic
600C22#1062262711yescharacteristic
601C22#1062262811yescharacteristic
602C22#1062262911yescharacteristic
603C22#1062264111yescharacteristic
604C22C4×#432611yescharacteristic
605C22#1062264311yescharacteristic
606C22#1062264411yescharacteristic
607C22#1062264611yescharacteristic
608C22#1062264811yescharacteristic
609C22#1062265111yescharacteristic
610C22#1062265511yescharacteristic
611C22#1062265711yescharacteristic
612C22#1062265811yescharacteristic
613C22#1062266211yescharacteristic
614C22#1062266411yescharacteristic
615C22#1062267611yescharacteristic
616C22#1062267711yescharacteristic
617C22#1062267811yescharacteristic
618C22#1062267911yescharacteristic
619C22#1062269111yescharacteristic
620C22#1062269311yescharacteristic
621C22#1062270011yescharacteristic
622C22#1062270411yescharacteristic
623C22#1062282611yescharacteristic
624C22#1062283011yescharacteristic
625C22#1062283511yescharacteristic
626C22#1062284111yescharacteristic
627C22#1062284211yescharacteristic
628C22#1062285111yescharacteristic
629C22#1062285211yescharacteristic
630C4—44no—
631C4—42no—
632C4—42no—
633C4—82no—
634C4—882no—
635C4—882no—
636C4#1062258511yescharacteristic
637C4#1062258711yescharacteristic
638C4#1062259111yescharacteristic
639C4#1062259311yescharacteristic
640C4#1062259511yescharacteristic
641C4#1062259611yescharacteristic
642C4#1062260011yescharacteristic
643C4#1062260711yescharacteristic
644C2#1306686611yescharacteristic
645C2#1306895711yescharacteristic
646C2#1306896411yescharacteristic
647C2#1306918411yescharacteristic
648C2#1306920511yescharacteristic
649C2#1306934611yescharacteristic
650C2#1306935111yescharacteristic
651C2#1306979511yescharacteristic
652C2#1306981611yescharacteristic
653C2#1306994111yescharacteristic
654C2#1306995111yescharacteristic
655C2#1307000111yescharacteristic
656C2#1307000811yescharacteristic
657C2#1307008711yescharacteristic
658C2#1307009711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#389C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#389D11
hypocenterC11#11219
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
23. C2×#66871C4semidirect
178. C2×C11⋊C8C4⋊C4semidirect
507. C11#11219semidirect

Maximal subgroups

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

subgroupindex
C22×#668712
C2×#106221672
C2×#106221622
#130668462
C2×C11×#3892
#1121911