Finite Group Databasebeta

← #14677171

Subgroups — #14677171

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622281C212yesmaximal, complemented
6C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
7#13066862C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C2×C4×D44—24no—
29C2×C4×D44—24no—
30C2×C4×D44—24no—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38#10622601—24no—
39#10622601C418yescomplemented
40#10622598—24no—
41C4×Dic11⋊C4—24no—
42#10622281—28no—
43C24×D11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
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—24no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4C2×C414yescomplemented
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11D414yes—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
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—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4C2×C418yescomplemented
91C2×(C2×D11)⋊C4C2×C418yescomplemented
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11—42no—
97C2×C4⋊Dic11D414yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4D414yescomplemented
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11C2×C414yescomplemented
110C4×D44—232no—
111C11×#95—24no—
112C11×#95—42no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—42no—
118#14018—111nomaximal, Sylow
119C24×C11C2411yescharacteristic
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×D11—22no—
131C23×D11—22no—
132C23×D11C22×C414yes—
133C23×D11C2×D414yes—
134C23×D11C2×Q814yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
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—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11C22×C414yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×Q812yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
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—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11C22×C412yes—
199C22×Dic11C22×C412yes—
200C22×Dic11C2×D414yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×D412yes—
203C22×Dic11#4112yes—
204C22×Dic11#4112yes—
205C2×D44—28no—
206C2×D44—28no—
207C2×D44—28no—
208C2×D44—28no—
209C2×D44—28no—
210C2×D44—28no—
211C2×D44C4⋊C4116yescomplemented
212C2×C4×D11—216no—
213C2×C4×D11—48no—
214C2×C4×D11—48no—
215C2×C4×D11—48no—
216C2×C4×D11—48no—
217C2×C4×D11—48no—
218C2×C4×D11—48no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—44no—
221C42×C11—28no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—216no—
224(C2×D11)⋊C4—48no—
225(C2×D11)⋊C4—48no—
226(C2×D11)⋊C4—48no—
227C4⋊Dic11—28no—
228C4⋊Dic11—48no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231C4×Dic11—28no—
232C4×Dic11—44no—
233C22×C4×D4—111no—
234C2×#390—111no—
235C2×#390—111no—
236C2×#389—111no—
237C2×#385—112no—
238C2×C4×C4⋊C4—111no—
239#1439—112no—
240#1439—112no—
241C4⋊#95—111no—
242C4⋊#95D1111yescharacteristic, complemented
243C22⋊#95—112no—
244C23×C11C23×C411yescharacteristic
245C23×C11C22×D411yescharacteristic
246C23×C11C22×D411yescharacteristic
247C23×C11C22×D411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C22×Q811yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C112−1+411yescharacteristic
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—24no—
275C22×D11—24no—
276C22×D11—24no—
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×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11C2×C4⋊C418yes—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—42no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11C2×C4⋊C414yes—
322C2×C4×C11C4×D414yes—
323C2×C4×C11C4×D414yes—
324C2×C4×C11#12014yes—
325C2×C4×C11#12114yes—
326C2×C4×C11C22⋊Q814yes—
327C2×C4×C11C22⋊Q814yes—
328C2×C4×C11#12314yes—
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—24no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—24no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11C4×D414yescomplemented
364D44—232no—
365C4×D11—432no—
366C23×D4—111no—
367C24×C4—112no—
368C2×C4×D4—224no—
369C2×C4×D4—224no—
370C2×C4×D4—224no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—112no—
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4—112no—
378C22×C22⋊C4—112no—
379C22×C22⋊C4—112no—
380C22×C22⋊C4—112no—
381C22×C22⋊C4—112no—
382C22×C42—111no—
383C22×C42—111no—
384C22×C42C2×D1111yescharacteristic
385#390—118no—
386#390—224no—
387#389—224no—
388#385—228no—
389C4×C4⋊C4—224no—
390C2×#95—111no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95—111no—
394C2×#95—112no—
395C2×#95C2×D1112yes—
396C2×#95C2×D1112yes—
397C22×C11C22×C4⋊C411yescharacteristic
398C22×C11C2×C4×D411yescharacteristic
399C22×C11C2×C4×D411yescharacteristic
400C22×C11C2×C4×D411yescharacteristic
401C22×C11C4×#4111yescharacteristic
402C22×C11#51811yescharacteristic
403C22×C11#52011yescharacteristic
404C22×C11C2×#12011yescharacteristic
405C22×C11C2×#12111yescharacteristic
406C22×C11C2×C22⋊Q811yescharacteristic
407C22×C11C2×C22⋊Q811yescharacteristic
408C22×C11C2×#12311yescharacteristic
409C22×C11#52511yescharacteristic
410C22×C11#52911yescharacteristic
411C22×C11#53211yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#53711yescharacteristic
414C22×C11#54011yescharacteristic
415C22×C11#54211yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11#54611yescharacteristic
420C22×C11#54611yescharacteristic
421C22×C11#54711yescharacteristic
422C22×C11#54811yescharacteristic
423C22×C11D4×Q811yescharacteristic
424C22×C11#55011yescharacteristic
425C22×C11#55011yescharacteristic
426C22×C11#55411yescharacteristic
427C22×C11#55411yescharacteristic
428C22×C11#55411yescharacteristic
429C22×C11#55611yescharacteristic
430C22×C11#55911yescharacteristic
431C22×C11#55911yescharacteristic
432C2×D11—28no—
433C2×D11—28no—
434C2×D11—28no—
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—
444C2×D11—44no—
445C2×D11—44no—
446C2×D11—44no—
447C4×C11—24no—
448C4×C11—44no—
449C4×C11—42no—
450C4×C11—82no—
451C4×C11#38518yescomplemented
452Dic11—24no—
453Dic11—42no—
454Dic11—42no—
455Dic11—44no—
456Dic11—42no—
457C25—112no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—114no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—112no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—224no—
473C23×C4—224no—
474C23×C4—224no—
475C23×C4—442no—
476C23×C4—442no—
477C23×C4C22×D1112yes—
478C23×C4C22×D1112yes—
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—222no—
494C2×C4⋊C4—222no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—222no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—442no—
500C2×C4⋊C4C4×D1114yescomplemented
501C2×C22⋊C4—118no—
502C2×C22⋊C4—118no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—224no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—442no—
513C2×C22⋊C4—442no—
514C2×C22⋊C4—442no—
515C2×C22⋊C4—442no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—114no—
519C2×C42—222no—
520C2×C42—222no—
521C2×C42—222no—
522C2×C42—222no—
523C2×C42—222no—
524C2×C42D4414yes—
525#95—24no—
526#95—42no—
527#95—224no—
528#95—224no—
529#95—222no—
530#95—222no—
531#95—442no—
532C2×C11C2×#38511yescharacteristic
533C2×C11C4×#12111yescharacteristic
534C2×C11#232411yescharacteristic
535C2×C11D4×C4⋊C411yescharacteristic
536C2×C11#234911yescharacteristic
537C2×C11#236611yescharacteristic
538C2×C11#236711yescharacteristic
539C2×C11#240711yescharacteristic
540C2×C11#240811yescharacteristic
541C2×C11#244511yescharacteristic
542C2×C11#244711yescharacteristic
543C2×C11#245211yescharacteristic
544C2×C11#245411yescharacteristic
545C2×C11#253811yescharacteristic
546C2×C11#258011yescharacteristic
547D11—48no—
548C24—114no—
549C24—114no—
550C24—114no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24C23×D1111yescharacteristic
564C2×D4—1116no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—228no—
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—228no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—114no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—2216no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—222no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—222no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—222no—
630C22×C4—448no—
631C22×C4—448no—
632C22×C4—448no—
633C22×C4—448no—
634C22×C4—448no—
635C22×C4—448no—
636C22×C4C2×C4×D1114yes—
637C22×C4C2×C4×D1112yes—
638C22×C4C2×D4412yes—
639C22×C4C2×D4412yes—
640C22×C4C2×D4412yes—
641C22×C4#433912yes—
642C22×C4D4×D1112yes—
643C22×C4D4×D1112yes—
644C22×C4D4×D1112yes—
645C22×C4#434112yes—
646C22×C4Q8×D1112yes—
647C22×C4#434312yes—
648C4⋊C4—28no—
649C4⋊C4—44no—
650C4⋊C4—228no—
651C4⋊C4—228no—
652C4⋊C4—228no—
653C4⋊C4—448no—
654C22⋊C4—2216no—
655C22⋊C4—2216no—
656C22⋊C4—448no—
657C22⋊C4—448no—
658C22⋊C4—448no—
659C42—28no—
660C42—228no—
661C42—444no—
662C11#1401811yescharacteristic, complemented, Sylow
663C23—118no—
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—224no—
677C23—224no—
678C23—224no—
679C23—224no—
680C23—224no—
681C23—224no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—442no—
688C23—442no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23C22×C4×D1111yescharacteristic
699C23C22×D4411yescharacteristic
700C23C2×#433911yescharacteristic
701C23C2×D4×D1111yescharacteristic
702C23C2×D4×D1111yescharacteristic
703C23C2×D4×D1111yescharacteristic
704C23C2×#434111yescharacteristic
705C23#6703711yescharacteristic
706C23C2×Q8×D1111yescharacteristic
707C23C2×#434311yescharacteristic
708C23#6704011yescharacteristic
709C23#41×D1111yescharacteristic
710C23#41×D1111yescharacteristic
711C23#6704211yescharacteristic
712C23#6704211yescharacteristic
713D4—2232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—114no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—224no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—4432no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—442no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—442no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4C4×D4414yes—
778C2×C4(C22⋊D11)⋊C414yes—
779C2×C4#6693514yes—
780C2×C4#6693614yes—
781C2×C4C4⋊C4×D1114yes—
782C2×C4#6694814yes—
783C2×C4#6694914yes—
784C2×C4#6695014yes—
785C22—228no—
786C22—228no—
787C22—228no—
788C22—444no—
789C22—444no—
790C22—444no—
791C22—444no—
792C22—444no—
793C22—444no—
794C22—444no—
795C22—444no—
796C22—444no—
797C22—444no—
798C22—444no—
799C22—444no—
800C22C2×C4×D4411yescharacteristic
801C22C2×(C22⋊D11)⋊C411yescharacteristic
802C22C2×#6693511yescharacteristic
803C22C2×#6693611yescharacteristic
804C22C2×C4⋊C4×D1111yescharacteristic
805C22C2×#6694811yescharacteristic
806C22C2×#6694911yescharacteristic
807C22C2×#6695011yescharacteristic
808C22#1062304111yescharacteristic
809C22#1062305511yescharacteristic
810C22#1062305611yescharacteristic
811C22C4×D4×D1111yescharacteristic
812C22#1062307611yescharacteristic
813C22#1062307911yescharacteristic
814C22#1062309311yescharacteristic
815C22C4×#434311yescharacteristic
816C22#1062310511yescharacteristic
817C22#1062311111yescharacteristic
818C22#1062311311yescharacteristic
819C22#1062313011yescharacteristic
820C22#1062314011yescharacteristic
821C22#1062314011yescharacteristic
822C22#1062314311yescharacteristic
823C22#1062316111yescharacteristic
824C22#1062316111yescharacteristic
825C22#1062316211yescharacteristic
826C22#1062316411yescharacteristic
827C22#1062321211yescharacteristic
828C22#1062321211yescharacteristic
829C22#1062322111yescharacteristic
830C22#1062322111yescharacteristic
831C22#1062324911yescharacteristic
832C22#1062325811yescharacteristic
833C22#1062326111yescharacteristic
834C22#1062326311yescharacteristic
835C4—24no—
836C4—44no—
837C4—42no—
838C4—82no—
839C4—224no—
840C4—442no—
841C4—444no—
842C4—442no—
843C4—442no—
844C4#1062228118yescomplemented
845C2—448no—
846C2C2×#1062228111yescharacteristic
847C2C4×#6694811yescharacteristic
848C2#1307131011yescharacteristic
849C2#1307151711yescharacteristic
850C2#1307152511yescharacteristic
851C2#1307167711yescharacteristic
852C2#1307169211yescharacteristic
853C2#1307196211yescharacteristic
854C2#1307197311yescharacteristic
855C2#1307238211yescharacteristic
856C2#1307240411yescharacteristic
857C2#1307246711yescharacteristic
858C2#1307248911yescharacteristic
859C2#1307353911yescharacteristic
860C2#1307397511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14018
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622598C2semidirect
5. C2×#10622281C2semidirect
6. C2×C4×Dic11⋊C4C2semidirect
7. #13066862C2semidirect
8. #13066860C2semidirect
9. #13066845C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C4⋊#95C2semidirect
39. #10622601C4semidirect
73. C2×C11×C4⋊C4C2×C4semidirect
90. C2×(C2×D11)⋊C4C2×C4semidirect
91. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×Dic11⋊C4D4semidirect
109. C2×C4×Dic11C2×C4semidirect
211. C2×D44C4⋊C4semidirect
242. C4⋊#95D11semidirect
363. C2×Dic11C4×D4semidirect
451. C4×C11#385semidirect
500. C2×C4⋊C4C4×D11semidirect
662. C11#14018semidirect
844. C4#10622281semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106226012
C2×#106225982
C2×#106222812
C2×C4×Dic11⋊C42
#130668622
#130668602
#130668452
(C2×D11)⋊#952
C11×C4⋊#952
#1401811