Finite Group Databasebeta

← #14677146

Subgroups — #14677146

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 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
5#13066874C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C22×C11×#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C2×C4×C22⋊D11—24no—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95—24no—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32#10622826—24no—
33#10622826C418yescomplemented
34#10622823—24no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11—42no—
56C23×C4×C11—42no—
57C23×C4×C11C2×C414yescomplemented
58C23×C4×C11D414yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11C2×C414yes—
68C22×C22⋊D11D414yes—
69C22×C22⋊D11Q814yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—24no—
79C22×C4×D11—42no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11C2×C414yescomplemented
88C2×C22⋊Dic11D414yes—
89C4×C22⋊D11—232no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4C2×C418yescomplemented
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—42no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C11×#95—24no—
109C11×#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—42no—
114C11⋊#95—42no—
115C11⋊#95—42no—
116C11⋊#95C2×C418yescomplemented
117#14016—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C22×C412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11C2×D412yes—
126C24×C11C2×Q812yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11C22×C412yes—
139C23×D11C2×D412yes—
140C23×D11C2×Q812yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—28no—
164C22×C4×C11—48no—
165C22×C4×C11—44no—
166C22×C4×C11—48no—
167C22×C4×C11—48no—
168C22×C4×C11—48no—
169C22×C4×C11—48no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11—44no—
173C22×C4×C11—48no—
174C22×C4×C11—44no—
175C22×C4×C11C22×C414yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11#4114yes—
179C22×C4×C11#4114yes—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11—28no—
184C2×C22⋊D11—28no—
185C2×C22⋊D11—28no—
186C2×C22⋊D11C4⋊C4116yescomplemented
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11C22×C414yes—
213C22×Dic11C22×C412yes—
214C22×Dic11C2×D412yes—
215C22×Dic11C2×D412yes—
216C22×Dic11C2×D412yes—
217C22×Dic11C2×Q812yes—
218C2×C4×D11—28no—
219C2×C4×D11—48no—
220C2×C4×D11—48no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C22⋊Dic11—28no—
224C22⋊Dic11—28no—
225C22⋊Dic11—44no—
226(C2×D11)⋊C4—28no—
227(C2×D11)⋊C4—48no—
228(C2×D11)⋊C4—48no—
229Dic11⋊C4—28no—
230Dic11⋊C4—48no—
231C4×Dic11—28no—
232C22×C4×D4—111no—
233C2×#386—111no—
234C2×#386—111no—
235C2×#385—111no—
236C22×#95D1111yescharacteristic, complemented
237#1442—112no—
238#1439—112no—
239#1436—112no—
240C22⋊#95—112no—
241C22⋊#95—111no—
242C22⋊#95—111no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11C2×C4⋊C414yes—
260C23×C11C4×D414yes—
261C23×C11C4×D414yes—
262C23×C11#12014yes—
263C23×C11C22⋊Q814yes—
264C23×C11C22⋊Q814yes—
265C23×C11#12314yes—
266C23×C11C23×C411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×Q811yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4112yes—
273C23×C11C2×#4112yes—
274C23×C11C2×#4111yescharacteristic
275C23×C11H(5,𝔽2)12yes—
276C23×C11H(5,𝔽2)12yes—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—24no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—42no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11C2×C4⋊C414yes—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—416no—
314C2×C4×C11—416no—
315C2×C4×C11—416no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11#12314yes—
327C22⋊D11—232no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C2×C4⋊C414yes—
359C4×D11—416no—
360C23×D4—111no—
361C24×C4—111no—
362C24×C4C2×D1111yescharacteristic
363C24×C4C2×D1111yescharacteristic
364C24×C4C2×D1111yescharacteristic
365C2×C4×D4—224no—
366C2×C4×D4—224no—
367C2×C4×D4—224no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—112no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—112no—
376C22×C42—111no—
377#386—118no—
378#386—224no—
379#385—224no—
380C2×#95—24no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95C2×D1112yes—
389C2×#95C2×D1112yes—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—28no—
393C22×C11—28no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—28no—
397C22×C11—28no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11#38518yes—
401C22×C11C22×C4⋊C411yescharacteristic
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11C4×#4112yes—
405C22×C11#51812yes—
406C22×C11C2×#12011yescharacteristic
407C22×C11C2×C22⋊Q811yescharacteristic
408C22×C11C2×C22⋊Q811yescharacteristic
409C22×C11C2×#12311yescharacteristic
410C22×C11C2×#12311yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#52912yes—
413C22×C11#53411yescharacteristic
414C22×C11#53511yescharacteristic
415C22×C11#53812yes—
416C22×C11#54612yes—
417C22×C11#54612yes—
418C22×C11#54612yes—
419C22×C11#54612yes—
420C22×C11#55312yes—
421C22×C11#55312yes—
422C22×C11#55412yes—
423C22×C11#55412yes—
424C2×D11—28no—
425C2×D11—24no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—44no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—44no—
432C2×D11—44no—
433C2×D11—42no—
434C2×D11—42no—
435C4×C11—24no—
436C4×C11—44no—
437C4×C11—44no—
438C4×C11—42no—
439Dic11—24no—
440Dic11—44no—
441Dic11—42no—
442Dic11—42no—
443Dic11—82no—
444C25—111no—
445C25C22×D1111yescharacteristic
446C22×D4—114no—
447C22×D4—114no—
448C22×D4—114no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—222no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—42no—
463C23×C4—42no—
464C23×C4—42no—
465C23×C4—42no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—112no—
469C23×C4—111no—
470C23×C4—112no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—222no—
474C23×C4—224no—
475C23×C4—442no—
476C23×C4C4×D1114yescomplemented
477C23×C4C22⋊D1114yes—
478C23×C4C22×D1112yes—
479C23×C4C22×D1112yes—
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—442no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—118no—
492C2×C22⋊C4—222no—
493C2×C22⋊C4—222no—
494C2×C22⋊C4—222no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4—442no—
506C2×C22⋊C4—442no—
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—222no—
510#95—24no—
511#95—24no—
512#95—118no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—442no—
517#95—442no—
518#95—442no—
519C2×C11—28no—
520C2×C11C2×#38511yescharacteristic
521C2×C11C4×#12311yescharacteristic
522C2×C11#232111yescharacteristic
523C2×C11#234912yes—
524C2×C11#236412yes—
525C2×C11#240411yescharacteristic
526C2×C11#240511yescharacteristic
527C2×C11#244412yes—
528C2×C11#245012yes—
529C2×C11#248711yescharacteristic
530C2×C11#257911yescharacteristic
531D11—44no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—112no—
537C24—112no—
538C24—112no—
539C24—222no—
540C24—222no—
541C24—221no—
542C24—221no—
543C24—222no—
544C24—222no—
545C24—221no—
546C24—221no—
547C24C2×C4×D1112yes—
548C24#433912yes—
549C24D4×D1112yes—
550C24D4×D1112yes—
551C24Q8×D1112yes—
552C24#434312yes—
553C24C2×C22⋊D1112yes—
554C24C23×D1111yescharacteristic
555C2×D4—1116no—
556C2×D4—228no—
557C2×D4—228no—
558C2×D4—228no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—228no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—48no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—114no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—228no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—448no—
629C22×C4—448no—
630C22×C4—444no—
631C22×C4—444no—
632C22×C4C2×C4×D1114yes—
633C22×C4#433914yes—
634C22×C4#433914yes—
635C22×C4C2×C22⋊D1112yes—
636C22×C4C2×C22⋊D1112yes—
637C4⋊C4—228no—
638C4⋊C4—448no—
639C22⋊C4—228no—
640C22⋊C4—228no—
641C22⋊C4—228no—
642C22⋊C4—448no—
643C22⋊C4—448no—
644C22⋊C4—444no—
645C42—228no—
646C11#1401611yescharacteristic, complemented, Sylow
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—114no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—224no—
672C23—224no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—442no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23C4⋊C4×D1114yes—
687C23#6694614yes—
688C23#6694714yes—
689C23#6694914yes—
690C23C4×C22⋊D1114yes—
691C23#6699014yes—
692C23#6699914yes—
693C23C22×C4×D1111yescharacteristic
694C23C2×#433912yes—
695C23C2×#433912yes—
696C23C2×#433911yescharacteristic
697C23C2×D4×D1111yescharacteristic
698C23C2×D4×D1111yescharacteristic
699C23#6703712yes—
700C23#6703712yes—
701C23C2×Q8×D1111yescharacteristic
702C23C2×#434311yescharacteristic
703C23C22×C22⋊D1111yescharacteristic
704D4—2232no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—114no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—4416no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4#6698214yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—28no—
774C22—228no—
775C22—224no—
776C22—442no—
777C22—442no—
778C22—442no—
779C22—444no—
780C22—444no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—444no—
785C22#1062260218yes—
786C22C4×#433912yes—
787C22#1062301012yes—
788C22#1062301712yes—
789C22#1062302112yes—
790C22#1062302112yes—
791C22#1062302112yes—
792C22#1062302112yes—
793C22#1062302512yes—
794C22C2×C4⋊C4×D1111yescharacteristic
795C22C2×#6694611yescharacteristic
796C22C2×#6694711yescharacteristic
797C22C2×#6694911yescharacteristic
798C22#1062304212yes—
799C22#1062304212yes—
800C22#1062304512yes—
801C22#1062304512yes—
802C22C2×C4×C22⋊D1111yescharacteristic
803C22C2×#6698211yescharacteristic
804C22#1062332211yescharacteristic
805C22C2×#6699011yescharacteristic
806C22#1062333511yescharacteristic
807C22#1062333611yescharacteristic
808C22C2×#6699911yescharacteristic
809C4—24no—
810C4—44no—
811C4—42no—
812C4—44no—
813C4—224no—
814C4—444no—
815C4—442no—
816C4—442no—
817C4—882no—
818C2—28no—
819C2—444no—
820C2C2×#1062260211yescharacteristic
821C2C4×#6698211yescharacteristic
822C2#1307127411yescharacteristic
823C2#1307152312yes—
824C2#1307166312yes—
825C2#1307193511yescharacteristic
826C2#1307194311yescharacteristic
827C2#1307236612yes—
828C2#1307244012yes—
829C2#1307292711yescharacteristic
830C2#1307396311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#95D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622823C2semidirect
5. #13066874C2semidirect
6. #13066860C2semidirect
7. #13066847C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C22×C11×#95C2semidirect
33. #10622826C4semidirect
57. C23×C4×C11C2×C4semidirect
87. C2×C22⋊Dic11C2×C4semidirect
98. C2×(C2×D11)⋊C4C2×C4semidirect
116. C11⋊#95C2×C4semidirect
186. C2×C22⋊D11C4⋊C4semidirect
236. C22×#95D11semidirect
476. C23×C4C4×D11semidirect
646. C11#14016semidirect

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
#130668742
#130668602
#130668472
#130668392
(C2×D11)⋊#952
C22×C11×#952
#1401611