Finite Group Databasebeta

← #14676145

Subgroups — #14676145

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622600C212yesmaximal, complemented
6#13066862C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66946—24no—
28C2×#66946—24no—
29C2×#66946C418yescomplemented
30C11×#389—24no—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39#10622601—24no—
40#10622600—28no—
41#10622598—24no—
42#10622552—24no—
43C24×D11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44C2×C414yes—
59C22×D44D414yes—
60C22×D44Q814yes—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11C2×C418yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—42no—
74C2×C11×C4⋊C4C2×C414yes—
75C2×C11×C4⋊C4D414yes—
76C2×C11×C4⋊C4D414yes—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4C2×C418yes—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11—42no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11C2×C414yes—
107#66946—232no—
108C11×#95—24no—
109C11⋊#95—24no—
110C11⋊#95—22no—
111C11⋊#95—24no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—42no—
115C11⋊#95D414yescomplemented
116#13920—111nomaximal, Sylow
117C24×C11C2411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11C22×C414yes—
131C23×D11C2×D414yes—
132C23×D11C2×Q814yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11C22×C414yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×Q812yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11C22×C412yes—
198C22×Dic11C22×C412yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×D412yes—
201C22×Dic11#4112yes—
202C22×Dic11#4112yes—
203C2×D44—28no—
204C2×D44—28no—
205C2×D44—28no—
206C2×D44—28no—
207C2×D44—28no—
208C2×D44—28no—
209C2×D44C4⋊C4116yescomplemented
210C2×C4×D11—216no—
211C2×C4×D11—216no—
212C2×C4×D11—48no—
213C2×C4×D11—48no—
214C2×C4×D11—48no—
215C2×C4×D11—48no—
216C2×C4×D11—48no—
217C11×C4⋊C4—48no—
218C11×C4⋊C4—44no—
219C11×C4⋊C4C22⋊C4116yescomplemented
220C42×C11—44no—
221(C2×D11)⋊C4—216no—
222(C2×D11)⋊C4—48no—
223(C2×D11)⋊C4—48no—
224(C2×D11)⋊C4—48no—
225(C2×D11)⋊C4—48no—
226C4⋊Dic11—48no—
227C4⋊Dic11—44no—
228C4×Dic11—28no—
229C4×Dic11—44no—
230C22×C4×D4—111no—
231C2×#390—111no—
232C2×#390—111no—
233C2×#389—111no—
234C2×#389D1111yescharacteristic, complemented
235C2×#380—112no—
236#1439—112no—
237#1439—112no—
238C4⋊#95—111no—
239C22⋊#95—112no—
240C4×#95—111no—
241C23×C11C23×C411yescharacteristic
242C23×C11C22×D411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C23×C11C22×D411yescharacteristic
245C23×C11C22×D411yescharacteristic
246C23×C11C22×Q811yescharacteristic
247C23×C11C2×#4111yescharacteristic
248C23×C11C2×#4111yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11H(5,𝔽2)11yescharacteristic
253C23×C11H(5,𝔽2)11yescharacteristic
254C23×C11H(5,𝔽2)11yescharacteristic
255C23×C112−1+411yescharacteristic
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11C2×C4⋊C418yes—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C2×C22⋊C418yes—
319C2×C4×C11C2×C22⋊C414yes—
320C2×C4×C11C2×C4⋊C414yes—
321C2×C4×C11#11714yes—
322C2×C4×C11#12114yes—
323C2×C4×C11#12114yes—
324C2×C4×C11C22⋊Q814yes—
325C2×C4×C11C22⋊Q814yes—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11C4×D414yes—
361D44—232no—
362C4×D11—432no—
363C23×D4—111no—
364C24×C4—112no—
365C2×C4×D4—118no—
366C2×C4×D4—224no—
367C2×C4×D4—224no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C4⋊C4C2×D1112yes—
372C22×C4⋊C4C2×D1111yescharacteristic
373C22×C22⋊C4—112no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4—112no—
376C22×C22⋊C4—112no—
377C22×C22⋊C4—112no—
378C22×C42—111no—
379C22×C42—111no—
380C22×C42C2×D1111yescharacteristic
381#390—224no—
382#390—224no—
383#389—24no—
384#389—224no—
385#380—228no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—112no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95C2×D1112yes—
394C22×C11C22×C22⋊C411yescharacteristic
395C22×C11C22×C4⋊C411yescharacteristic
396C22×C11C2×#11711yescharacteristic
397C22×C11C2×C4×D411yescharacteristic
398C22×C11C4×#4111yescharacteristic
399C22×C11#51811yescharacteristic
400C22×C11#52011yescharacteristic
401C22×C11C2×#12111yescharacteristic
402C22×C11C2×#12111yescharacteristic
403C22×C11C2×C22⋊Q811yescharacteristic
404C22×C11C2×C22⋊Q811yescharacteristic
405C22×C11#52911yescharacteristic
406C22×C11#52911yescharacteristic
407C22×C11#53211yescharacteristic
408C22×C11#53211yescharacteristic
409C22×C11#54011yescharacteristic
410C22×C11#54011yescharacteristic
411C22×C11#54211yescharacteristic
412C22×C11#54211yescharacteristic
413C22×C11D4211yescharacteristic
414C22×C11D4211yescharacteristic
415C22×C11D4211yescharacteristic
416C22×C11#54611yescharacteristic
417C22×C11#54611yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11#54611yescharacteristic
420C22×C11#54711yescharacteristic
421C22×C11#54811yescharacteristic
422C22×C11#54811yescharacteristic
423C22×C11D4×Q811yescharacteristic
424C22×C11#55011yescharacteristic
425C22×C11#55011yescharacteristic
426C22×C11#55411yescharacteristic
427C22×C11#55411yescharacteristic
428C22×C11#55411yescharacteristic
429C2×D11—28no—
430C2×D11—28no—
431C2×D11—28no—
432C2×D11—44no—
433C2×D11—44no—
434C2×D11—44no—
435C2×D11—44no—
436C2×D11—44no—
437C2×D11—44no—
438C2×D11—44no—
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—44no—
442C2×D11—44no—
443C2×D11—44no—
444C4×C11—28no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—82no—
448C4×C11#38018yescomplemented
449Dic11—24no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11—82no—
454C25—112no—
455C22×D4—114no—
456C22×D4—114no—
457C22×D4—114no—
458C22×D4—222no—
459C22×D4—222no—
460C22×D4—222no—
461C22×D4—222no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—118no—
467C23×C4—112no—
468C23×C4—224no—
469C23×C4—224no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—442no—
473C23×C4—442no—
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1112yes—
478C23×C4C22×D1111yescharacteristic
479C4×D4—2232no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—442no—
492C2×C4⋊C4C4×D1114yes—
493C2×C4⋊C4D4414yes—
494C2×C4⋊C4C22⋊D1114yes—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—224no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—224no—
506C2×C22⋊C4—442no—
507C2×C22⋊C4—442no—
508C2×C22⋊C4—442no—
509C2×C22⋊C4—442no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—114no—
514C2×C42—222no—
515C2×C42—222no—
516C2×C42—222no—
517C2×C42—222no—
518C2×C42—222no—
519#95—24no—
520#95—114no—
521#95—222no—
522#95—222no—
523#95—224no—
524#95—224no—
525#95—222no—
526#95—442no—
527C2×C11C2×#38011yescharacteristic
528C2×C11#229311yescharacteristic
529C2×C11#231911yescharacteristic
530C2×C11D4×C22⋊C411yescharacteristic
531C2×C11#234111yescharacteristic
532C2×C11D4×C4⋊C411yescharacteristic
533C2×C11#234911yescharacteristic
534C2×C11#242711yescharacteristic
535C2×C11#242711yescharacteristic
536C2×C11#242811yescharacteristic
537C2×C11#242811yescharacteristic
538C2×C11#245211yescharacteristic
539C2×C11#245211yescharacteristic
540C2×C11#245411yescharacteristic
541C2×C11#245411yescharacteristic
542D11—48no—
543C24—114no—
544C24—114no—
545C24—114no—
546C24—222no—
547C24—222no—
548C24—222no—
549C24—222no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24C23×D1111yescharacteristic
559C2×D4—1116no—
560C2×D4—228no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—228no—
564C2×D4—228no—
565C2×D4—228no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—2216no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—2216no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—448no—
627C22×C4—448no—
628C22×C4—448no—
629C22×C4—448no—
630C22×C4—448no—
631C22×C4C2×C4×D1114yes—
632C22×C4C2×C4×D1112yes—
633C22×C4C2×D4414yes—
634C22×C4C2×D4412yes—
635C22×C4D4×D1112yes—
636C22×C4D4×D1112yes—
637C22×C4#434112yes—
638C22×C4Q8×D1112yes—
639C22×C4#434312yes—
640C22×C4#434312yes—
641C22×C4C2×C22⋊D1114yes—
642C22×C4C2×C22⋊D1112yes—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4—448no—
646C4⋊C4—444no—
647C4⋊C4(C2×D11)⋊C4116yescomplemented
648C22⋊C4—2216no—
649C22⋊C4—448no—
650C22⋊C4—448no—
651C22⋊C4—448no—
652C22⋊C4—448no—
653C42—44no—
654C42—228no—
655C42—444no—
656C11#1392011yescharacteristic, complemented, Sylow
657C23—118no—
658C23—224no—
659C23—224no—
660C23—224no—
661C23—224no—
662C23—224no—
663C23—224no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—224no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—442no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—442no—
688C23—442no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23C22×C4×D1111yescharacteristic
693C23C22×D4411yescharacteristic
694C23C2×D4×D1111yescharacteristic
695C23C2×D4×D1111yescharacteristic
696C23C2×#434111yescharacteristic
697C23#6703711yescharacteristic
698C23C2×Q8×D1111yescharacteristic
699C23C2×#434311yescharacteristic
700C23C2×#434311yescharacteristic
701C23#6704011yescharacteristic
702C23#41×D1111yescharacteristic
703C23#41×D1111yescharacteristic
704C23#6704211yescharacteristic
705C23#6704211yescharacteristic
706C23C22×C22⋊D1111yescharacteristic
707D4—2232no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—114no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—4432no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4C4⋊C4×D1114yes—
772C2×C4#6694514yes—
773C2×C4#6694814yes—
774C2×C4#6695014yes—
775C2×C4C2×(C2×D11)⋊C418yes—
776C2×C4C2×(C2×D11)⋊C414yes—
777C2×C4#6699114yes—
778C2×C4#6699914yes—
779C22—228no—
780C22—228no—
781C22—228no—
782C22—444no—
783C22—444no—
784C22—444no—
785C22—444no—
786C22—444no—
787C22—444no—
788C22—444no—
789C22—444no—
790C22—444no—
791C22—444no—
792C22—444no—
793C22—444no—
794C22C2×C4⋊C4×D1111yescharacteristic
795C22C2×#6694511yescharacteristic
796C22C2×#6694811yescharacteristic
797C22C2×#6695011yescharacteristic
798C22C4×D4×D1111yescharacteristic
799C22#1062307611yescharacteristic
800C22D4×D4411yescharacteristic
801C22#1062308511yescharacteristic
802C22C4×#434311yescharacteristic
803C22#1062310511yescharacteristic
804C22#1062310711yescharacteristic
805C22#1062310811yescharacteristic
806C22#1062312711yescharacteristic
807C22#1062314011yescharacteristic
808C22#1062314311yescharacteristic
809C22#1062315011yescharacteristic
810C22#1062315511yescharacteristic
811C22#1062316111yescharacteristic
812C22#1062316211yescharacteristic
813C22#1062317411yescharacteristic
814C22#1062322111yescharacteristic
815C22#1062322111yescharacteristic
816C22#1062322211yescharacteristic
817C22#1062322911yescharacteristic
818C22#1062325611yescharacteristic
819C22#1062325811yescharacteristic
820C22#1062326111yescharacteristic
821C22#1062326411yescharacteristic
822C22C22×(C2×D11)⋊C411yescharacteristic
823C22C2×#6699111yescharacteristic
824C22D4×C22⋊D1111yescharacteristic
825C22C2×#6699911yescharacteristic
826C22#1062334811yescharacteristic
827C22#1062336011yescharacteristic
828C22#1062336511yescharacteristic
829C4—28no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—224no—
834C4—442no—
835C4—442no—
836C4—442no—
837C4—882no—
838C4#1062260018yescomplemented
839C2—448no—
840C2C2×#1062260011yescharacteristic
841C2#1307107411yescharacteristic
842C2#1307125511yescharacteristic
843C2D4×(C2×D11)⋊C411yescharacteristic
844C2#1307145411yescharacteristic
845C2#1307151711yescharacteristic
846C2#1307152511yescharacteristic
847C2#1307218911yescharacteristic
848C2#1307219111yescharacteristic
849C2#1307220011yescharacteristic
850C2#1307220211yescharacteristic
851C2#1307246211yescharacteristic
852C2#1307246411yescharacteristic
853C2#1307248411yescharacteristic
854C2#1307248611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11#13920
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#10622598C2semidirect
5. C2×#10622600C2semidirect
6. #13066862C2semidirect
7. #13066858C2semidirect
8. #13066845C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#389C2semidirect
29. C2×#66946C4semidirect
115. C11⋊#95D4semidirect
209. C2×D44C4⋊C4semidirect
219. C11×C4⋊C4C22⋊C4semidirect
234. C2×#389D11semidirect
448. C4×C11#380semidirect
647. C4⋊C4(C2×D11)⋊C4semidirect
656. C11#13920semidirect
838. C4#10622600semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106226002
#130668622
#130668582
#130668452
(C2×D11)⋊#952
C4×C11⋊#952
C2×C11×#3892
#1392011