Finite Group Databasebeta

← #14677135

Subgroups — #14677135

Order 2816.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622823C211yesmaximal, characteristic, complemented
5C2×#10622602C212yesmaximal, complemented
6#13066879C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066848C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4—24no—
18C22×C11×C4⋊C4—28no—
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—24no—
25C2×C4×C22⋊D11—24no—
26C2×C4×C22⋊D11—24no—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622826—24no—
34#10622826C418yescomplemented
35#10622823—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622602—28no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—42no—
58C23×C4×C11—42no—
59C23×C4×C11C2×C414yescomplemented
60C23×C4×C11D414yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11C2×C414yes—
70C22×C22⋊D11D414yes—
71C22×C22⋊D11Q814yes—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—24no—
81C22×C4×D11—42no—
82C2×C11×C4⋊C4—232no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4D418yescomplemented
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11C2×C414yescomplemented
97C2×C22⋊Dic11D414yes—
98C4×C22⋊D11—232no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4C2×C418yescomplemented
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—42no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—42no—
123C11⋊#95C2×C418yescomplemented
124#14015—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11C2×D412yes—
133C24×C11C2×Q812yes—
134C24×C11#4112yes—
135C24×C11#4112yes—
136C24×C11C2411yescharacteristic
137C23×D11—22no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—22no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11C22×C412yes—
146C23×D11C2×D412yes—
147C23×D11C2×Q812yes—
148C22×C4×C11—28no—
149C22×C4×C11—216no—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—216no—
160C22×C4×C11—28no—
161C22×C4×C11—28no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—28no—
173C22×C4×C11—44no—
174C22×C4×C11—48no—
175C22×C4×C11—48no—
176C22×C4×C11—48no—
177C22×C4×C11—48no—
178C22×C4×C11—44no—
179C22×C4×C11—44no—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D414yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11#4114yes—
187C2×C22⋊D11—28no—
188C2×C22⋊D11—28no—
189C2×C22⋊D11—28no—
190C2×C22⋊D11—28no—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—28no—
193C2×C22⋊D11C4⋊C4116yescomplemented
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11C22×C414yes—
220C22×Dic11C22×C412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11C2×D412yes—
223C22×Dic11C2×D412yes—
224C22×Dic11C2×Q812yes—
225C2×C4×D11—28no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C11×C4⋊C4—216no—
231C11×C4⋊C4—216no—
232C22⋊Dic11—28no—
233C22⋊Dic11—28no—
234C22⋊Dic11—44no—
235(C2×D11)⋊C4—28no—
236(C2×D11)⋊C4—216no—
237(C2×D11)⋊C4—48no—
238Dic11⋊C4—28no—
239Dic11⋊C4—48no—
240C4×Dic11—28no—
241C22×C4×D4—111no—
242C23×C4⋊C4D1111yescharacteristic, complemented
243C2×#386—111no—
244C2×#386—111no—
245C2×#385—111no—
246C2×#385—112no—
247#1444—112no—
248#1439—112no—
249#1436—112no—
250C22⋊#95—111no—
251C22⋊#95—111no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11C2×C4⋊C414yes—
269C23×C11C4×D414yes—
270C23×C11C4×D414yes—
271C23×C11#12014yes—
272C23×C11C22⋊Q814yes—
273C23×C11C22⋊Q814yes—
274C23×C11#12314yes—
275C23×C11C23×C411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D412yes—
280C23×C11C22×Q811yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4112yes—
283C23×C11C2×#4111yescharacteristic
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—24no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—42no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11C2×C4⋊C414yescomplemented
309C2×C4×C11—232no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—416no—
327C2×C4×C11—416no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C4×D418yescomplemented
335C2×C4×C11#12014yes—
336C22⋊D11—232no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11C2×C4⋊C414yescomplemented
368C4×D11—416no—
369C23×D4—111no—
370C24×C4—111no—
371C24×C4C2×D1111yescharacteristic
372C24×C4C2×D1111yescharacteristic
373C24×C4C2×D1111yescharacteristic
374C2×C4×D4—224no—
375C2×C4×D4—224no—
376C2×C4×D4—224no—
377C22×C4⋊C4—24no—
378C22×C4⋊C4—28no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—112no—
381C22×C4⋊C4C2×D1112yes—
382C22×C4⋊C4C2×D1112yes—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4—112no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—112no—
389C22×C42—111no—
390#386—118no—
391#386—224no—
392#385—224no—
393#385—228no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95—112no—
400C2×#95—112no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—28no—
404C22×C11—28no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—28no—
409C22×C11—28no—
410C22×C11—24no—
411C22×C11#38518yescomplemented
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C2×C4×D412yes—
416C22×C11#52012yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×#12011yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×C22⋊Q811yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52512yes—
424C22×C11#53411yescharacteristic
425C22×C11#53611yescharacteristic
426C22×C11#53912yes—
427C22×C11D4212yes—
428C22×C11D4212yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#54812yes—
432C22×C11D4×Q812yes—
433C22×C11#55312yes—
434C22×C11#55412yes—
435C2×D11—28no—
436C2×D11—24no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—42no—
446C4×C11—24no—
447C4×C11—28no—
448C4×C11—42no—
449C4×C11—44no—
450Dic11—24no—
451Dic11—44no—
452Dic11—42no—
453Dic11—42no—
454Dic11—82no—
455C25—111no—
456C25C22×D1111yescharacteristic
457C22×D4—114no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—222no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—42no—
476C23×C4—42no—
477C23×C4—111no—
478C23×C4—112no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—112no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—224no—
486C23×C4—442no—
487C23×C4C4×D1114yescomplemented
488C23×C4C22⋊D1114yes—
489C23×C4C22×D1112yes—
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1112yes—
492C23×C4C22×D1111yescharacteristic
493C4×D4—2232no—
494C2×C4⋊C4—232no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—224no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4—442no—
506C2×C4⋊C4C22⋊D1118yescomplemented
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—118no—
510C2×C22⋊C4—222no—
511C2×C22⋊C4—222no—
512C2×C22⋊C4—222no—
513C2×C22⋊C4—222no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—222no—
522C2×C22⋊C4—222no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—442no—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528#95—118no—
529#95—224no—
530#95—224no—
531#95—224no—
532#95—224no—
533#95—224no—
534#95—442no—
535C2×C11—28no—
536C2×C11C2×#38511yescharacteristic
537C2×C11C4×#12011yescharacteristic
538C2×C11#232211yescharacteristic
539C2×C11D4×C4⋊C412yes—
540C2×C11#236112yes—
541C2×C11#240311yescharacteristic
542C2×C11#240611yescharacteristic
543C2×C11#240911yescharacteristic
544C2×C11#244312yes—
545C2×C11#244912yes—
546C2×C11#257911yescharacteristic
547D11—44no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—112no—
553C24—112no—
554C24—112no—
555C24—222no—
556C24—221no—
557C24—221no—
558C24—222no—
559C24—221no—
560C24—222no—
561C24—222no—
562C24—221no—
563C24C2×C4×D1112yes—
564C24#433912yes—
565C24D4×D1112yes—
566C24D4×D1112yes—
567C24Q8×D1112yes—
568C24#434312yes—
569C24C2×C22⋊D1112yes—
570C24C23×D1111yescharacteristic
571C2×D4—1116no—
572C2×D4—228no—
573C2×D4—228no—
574C2×D4—228no—
575C2×D4—228no—
576C2×D4—228no—
577C2×D4—228no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—216no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—112no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—228no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—448no—
643C22×C4—448no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4C2×C4×D1114yes—
647C22×C4#433914yes—
648C22×C4C2×C22⋊D1112yes—
649C22×C4C2×C22⋊D1114yes—
650C22×C4C2×C22⋊D1114yes—
651C22×C4C2×C22⋊D1114yes—
652C22×C4C2×C22⋊D1112yes—
653C4⋊C4—216no—
654C4⋊C4—216no—
655C4⋊C4—228no—
656C4⋊C4—448no—
657C22⋊C4—228no—
658C22⋊C4—228no—
659C22⋊C4—228no—
660C22⋊C4—2216no—
661C22⋊C4—448no—
662C22⋊C4—444no—
663C42—228no—
664C11#1401511yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—114no—
682C23—222no—
683C23—224no—
684C23—222no—
685C23—224no—
686C23—222no—
687C23—224no—
688C23—224no—
689C23—222no—
690C23—222no—
691C23—224no—
692C23—222no—
693C23—224no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23—441no—
699C23—442no—
700C23—441no—
701C23—441no—
702C23—442no—
703C23—441no—
704C23C4⋊C4×D1114yes—
705C23#6694614yes—
706C23#6694714yes—
707C23#6694914yes—
708C23C4×C22⋊D1114yes—
709C23#6699014yes—
710C23#6699914yes—
711C23C22×C4×D1111yescharacteristic
712C23C2×#433911yescharacteristic
713C23C2×#433912yes—
714C23C2×D4×D1111yescharacteristic
715C23C2×D4×D1111yescharacteristic
716C23#6703712yes—
717C23C2×Q8×D1111yescharacteristic
718C23C2×#434311yescharacteristic
719C23#6704012yes—
720C23C22×C22⋊D1111yescharacteristic
721C23C22×C22⋊D1112yes—
722D4—2232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—114no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—4416no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—441no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—442no—
772C2×C4—441no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4C4×C22⋊D1118yescomplemented
781C2×C4#6700614yes—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—228no—
793C22—224no—
794C22—442no—
795C22—444no—
796C22—444no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22#1062260218yescomplemented
804C22C2×C4⋊C4×D1111yescharacteristic
805C22C2×#6694611yescharacteristic
806C22#1062303512yes—
807C22C2×#6694711yescharacteristic
808C22#1062303812yes—
809C22#1062303812yes—
810C22C2×#6694911yescharacteristic
811C22#1062304212yes—
812C22#1062304512yes—
813C22#1062304612yes—
814C22C2×C4×C22⋊D1112yes—
815C22C2×C4×C22⋊D1111yescharacteristic
816C22#1062332212yes—
817C22#1062332211yescharacteristic
818C22C2×#6699011yescharacteristic
819C22D4×C22⋊D1112yes—
820C22D4×C22⋊D1112yes—
821C22#1062333511yescharacteristic
822C22C2×#6699911yescharacteristic
823C22Q8×C22⋊D1112yes—
824C22#1062334711yescharacteristic
825C22#1062334812yes—
826C22C2×#6700611yescharacteristic
827C4—28no—
828C4—24no—
829C4—42no—
830C4—44no—
831C4—224no—
832C4—444no—
833C4—442no—
834C4—442no—
835C4—882no—
836C2—28no—
837C2—444no—
838C2C2×#1062260211yescharacteristic
839C2C4×#6700611yescharacteristic
840C2#1307128511yescharacteristic
841C2C4⋊C4×C22⋊D1112yes—
842C2#1307163212yes—
843C2#1307192611yescharacteristic
844C2#1307195111yescharacteristic
845C2#1307197511yescharacteristic
846C2#1307235112yes—
847C2#1307242512yes—
848C2#1307396311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC23×C4⋊C4D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#10622823C2semidirect
5. C2×#10622602C2semidirect
6. #13066879C2semidirect
7. #13066858C2semidirect
8. #13066848C2semidirect
9. #13066839C2semidirect
10. #13066839C2semidirect
11. C23×C11×C4⋊C4C2semidirect
34. #10622826C4semidirect
59. C23×C4×C11C2×C4semidirect
88. C2×C11×C4⋊C4D4semidirect
96. C2×C22⋊Dic11C2×C4semidirect
107. C2×(C2×D11)⋊C4C2×C4semidirect
123. C11⋊#95C2×C4semidirect
193. C2×C22⋊D11C4⋊C4semidirect
242. C23×C4⋊C4D11semidirect
308. C22×D11C2×C4⋊C4semidirect
334. C2×C4×C11C4×D4semidirect
367. C2×Dic11C2×C4⋊C4semidirect
411. C22×C11#385semidirect
487. C23×C4C4×D11semidirect
506. C2×C4⋊C4C22⋊D11semidirect
664. C11#14015semidirect
780. C2×C4C4×C22⋊D11semidirect
803. C22#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228262
C2×#106228232
C2×#106226022
#130668792
#130668582
#130668482
#130668392
C23×C11×C4⋊C42
#1401511