Finite Group Databasebeta

← #14677210

Subgroups — #14677210

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622283C212yesmaximal, complemented
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
7#13066864C212yesmaximal, complemented
8#13066862C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622601—24no—
36#10622601—24no—
37C4⋊C4×Dic11—24no—
38#10622552C418yescomplemented
39C4×C4⋊Dic11—24no—
40#10622283—28no—
41C24×D11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44C2×C414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11C2×C414yes—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C418yes—
85C2×(C2×D11)⋊C4C2×C418yes—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2×C414yes—
94C2×C4⋊Dic11D414yescomplemented
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—42no—
103C2×C4×Dic11D414yes—
104C11×#95—24no—
105C11×#95—42no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—42no—
111#14022—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
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×D11C22×C414yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11C22×C414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4112yes—
197C22×Dic11#4112yes—
198C2×D44—28no—
199C2×D44—28no—
200C2×D44—28no—
201C2×D44—44no—
202C2×D44—44no—
203C2×D44—44no—
204C2×D44—44no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—44no—
207C42×C11—28no—
208(C2×D11)⋊C4—216no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4—48no—
214C4⋊Dic11—28no—
215C4⋊Dic11—28no—
216C4⋊Dic11—28no—
217C4×Dic11—28no—
218C4×Dic11—48no—
219C4×Dic11—44no—
220C2×#390—111no—
221C2×#390—111no—
222C2×#390—111no—
223C2×#388—112no—
224C2×C4×C4⋊C4—111no—
225C2×C4×C4⋊C4—111no—
226#1440—112no—
227#1439—112no—
228#1437—112no—
229C4⋊#95—111no—
230C4⋊#95D1111yescharacteristic, complemented
231C23×C11C23×C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11H(5,𝔽2)11yescharacteristic
243C23×C11H(5,𝔽2)11yescharacteristic
244C23×C11H(5,𝔽2)11yescharacteristic
245C23×C112−1+411yescharacteristic
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—41no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11#11714yes—
309C2×C4×C11C4×D414yes—
310C2×C4×C11C4×D414yes—
311C2×C4×C11C4×D414yes—
312C2×C4×C11#12114yes—
313C2×C4×C11#12314yes—
314C2×C4×C11#12414yes—
315C2×C4×C11#12614yes—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
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—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—42no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—42no—
350C2×Dic11#12114yes—
351D44—416no—
352C23×D4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—112no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C42—111no—
365C22×C42—111no—
366C22×C42—112no—
367C22×C42C2×D1111yescharacteristic
368#390—118no—
369#390—224no—
370#390—224no—
371#388—228no—
372C4×C4⋊C4—224no—
373C4×C4⋊C4—224no—
374C2×#95—112no—
375C2×#95—111no—
376C2×#95—112no—
377C2×#95—111no—
378C2×#95—112no—
379C2×#95C2×D1112yes—
380C2×#95C2×D1112yes—
381C22×C11C2×#11711yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C2×C4×D411yescharacteristic
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C4×#4111yescharacteristic
386C22×C11#51811yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11C2×#12111yescharacteristic
389C22×C11C2×#12111yescharacteristic
390C22×C11C2×#12311yescharacteristic
391C22×C11#52511yescharacteristic
392C22×C11C2×#12411yescharacteristic
393C22×C11C2×#12611yescharacteristic
394C22×C11#52911yescharacteristic
395C22×C11#53211yescharacteristic
396C22×C11#53511yescharacteristic
397C22×C11#53711yescharacteristic
398C22×C11#54011yescharacteristic
399C22×C11#54211yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11#54711yescharacteristic
403C22×C11#54811yescharacteristic
404C22×C11#55011yescharacteristic
405C22×C11#55011yescharacteristic
406C22×C11#55011yescharacteristic
407C22×C11#55311yescharacteristic
408C22×C11#55311yescharacteristic
409C22×C11#55511yescharacteristic
410C22×C11#55611yescharacteristic
411C22×C11#55611yescharacteristic
412C22×C11#55911yescharacteristic
413C22×C11#55911yescharacteristic
414C22×C11#55911yescharacteristic
415C22×C11#55911yescharacteristic
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—44no—
423C2×D11—82no—
424C2×D11—82no—
425C2×D11—82no—
426C2×D11—82no—
427C2×D11—82no—
428C2×D11—82no—
429C2×D11—82no—
430C2×D11—82no—
431C4×C11—24no—
432C4×C11—42no—
433C4×C11—44no—
434C4×C11—82no—
435C4×C11#38818yescomplemented
436Dic11—24no—
437Dic11—44no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C25—112no—
442C22×D4—114no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—222no—
448C22×D4—222no—
449C23×C4—111no—
450C23×C4—112no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4D4414yes—
474C2×C22⋊C4—118no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—442no—
487C2×C22⋊C4—442no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—114no—
495C2×C42—222no—
496C2×C42—222no—
497C2×C42—224no—
498C2×C42—224no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—442no—
503C2×C42C4×D1114yes—
504#95—24no—
505#95—42no—
506#95—222no—
507#95—222no—
508#95—224no—
509#95—224no—
510#95—442no—
511C2×C11C2×#38811yescharacteristic
512C2×C11C4×#12111yescharacteristic
513C2×C11#232411yescharacteristic
514C2×C11#235411yescharacteristic
515C2×C11#235711yescharacteristic
516C2×C11#236611yescharacteristic
517C2×C11#236711yescharacteristic
518C2×C11#241411yescharacteristic
519C2×C11#241611yescharacteristic
520C2×C11#244511yescharacteristic
521C2×C11#244811yescharacteristic
522C2×C11#251211yescharacteristic
523C2×C11#251311yescharacteristic
524C2×C11#254811yescharacteristic
525C2×C11#259211yescharacteristic
526D11—84no—
527C24—114no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24C23×D1111yescharacteristic
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—228no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
549C2×D4—444no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—114no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4C2×C4×D1112yes—
609C22×C4C2×C4×D1112yes—
610C22×C4C2×C4×D1112yes—
611C22×C4C2×D4414yes—
612C22×C4C2×D4412yes—
613C22×C4#433912yes—
614C22×C4D4×D1112yes—
615C22×C4D4×D1112yes—
616C22×C4#434112yes—
617C22×C4#434112yes—
618C22×C4#434312yes—
619C22×C4#434312yes—
620C4⋊C4—28no—
621C4⋊C4—44no—
622C4⋊C4—228no—
623C4⋊C4—228no—
624C4⋊C4—228no—
625C22⋊C4—2216no—
626C22⋊C4—448no—
627C22⋊C4—448no—
628C22⋊C4—448no—
629C22⋊C4—448no—
630C22⋊C4—448no—
631C42—28no—
632C42—228no—
633C42—448no—
634C42—444no—
635C11#1402211yescharacteristic, complemented, Sylow
636C23—224no—
637C23—224no—
638C23—224no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23C22×C4×D1111yescharacteristic
672C23C22×D4411yescharacteristic
673C23C2×#433911yescharacteristic
674C23C2×D4×D1111yescharacteristic
675C23C2×D4×D1111yescharacteristic
676C23C2×#434111yescharacteristic
677C23C2×#434111yescharacteristic
678C23#6703711yescharacteristic
679C23C2×#434311yescharacteristic
680C23C2×#434311yescharacteristic
681C23#6704011yescharacteristic
682C23#41×D1111yescharacteristic
683C23#41×D1111yescharacteristic
684C23#6704211yescharacteristic
685C23#6704211yescharacteristic
686D4—4416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—114no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—442no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4C4×D4414yes—
750C2×C4(C22⋊D11)⋊C414yes—
751C2×C4#6693814yes—
752C2×C4#6693914yes—
753C2×C4#6694514yes—
754C2×C4#6694614yes—
755C2×C4#6694814yes—
756C2×C4#6695114yes—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—444no—
761C22—444no—
762C22—444no—
763C22—444no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22—882no—
769C22—882no—
770C22—882no—
771C22—882no—
772C22C2×C4×D4411yescharacteristic
773C22C2×(C22⋊D11)⋊C411yescharacteristic
774C22C2×#6693811yescharacteristic
775C22C2×#6693911yescharacteristic
776C22C2×#6694511yescharacteristic
777C22C2×#6694611yescharacteristic
778C22#1062303511yescharacteristic
779C22C2×#6694811yescharacteristic
780C22C2×#6695111yescharacteristic
781C22#1062305211yescharacteristic
782C22#1062305311yescharacteristic
783C22D4×D4411yescharacteristic
784C22#1062308411yescharacteristic
785C22#1062308511yescharacteristic
786C22#1062309011yescharacteristic
787C22#1062309911yescharacteristic
788C22#1062310711yescharacteristic
789C22#1062310811yescharacteristic
790C22#1062311611yescharacteristic
791C22#1062312711yescharacteristic
792C22D11×#12111yescharacteristic
793C22#1062313811yescharacteristic
794C22#1062315011yescharacteristic
795C22#1062315511yescharacteristic
796C22#1062315811yescharacteristic
797C22#1062316011yescharacteristic
798C22#1062317411yescharacteristic
799C22#1062321211yescharacteristic
800C22#1062321211yescharacteristic
801C22#1062322611yescharacteristic
802C22#1062322611yescharacteristic
803C22#1062324911yescharacteristic
804C22#1062325711yescharacteristic
805C22#1062326311yescharacteristic
806C22#1062326511yescharacteristic
807C4—24no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—224no—
812C4—444no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4#1062228318yescomplemented
817C2—884no—
818C2C2×#1062228311yescharacteristic
819C2#1307112211yescharacteristic
820C2#1307130511yescharacteristic
821C2#1307156711yescharacteristic
822C2#1307159111yescharacteristic
823C2#1307168011yescharacteristic
824C2#1307168711yescharacteristic
825C2#1307203211yescharacteristic
826C2#1307205411yescharacteristic
827C2#1307237911yescharacteristic
828C2#1307241211yescharacteristic
829C2#1307320511yescharacteristic
830C2#1307321611yescharacteristic
831C2#1307361711yescharacteristic
832C2#1307410311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14022
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622283C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
6. C2×C4×C4⋊Dic11C2semidirect
7. #13066864C2semidirect
8. #13066862C2semidirect
9. #13066852C2semidirect
10. #13066845C2semidirect
11. C11×C4⋊#95C2semidirect
38. #10622552C4semidirect
94. C2×C4⋊Dic11D4semidirect
230. C4⋊#95D11semidirect
435. C4×C11#388semidirect
635. C11#14022semidirect
816. C4#10622283semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106226012
C2×#106222832
C2×C4⋊C4×Dic112
C2×C4×C4⋊Dic112
#130668642
#130668622
#130668522
#130668452
C11×C4⋊#952
#1402211