Finite Group Databasebeta

← #14677168

Subgroups — #14677168

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×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622602C212yesmaximal, complemented
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13066860C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C2×#66946—24no—
29C2×#66946—24no—
30C2×#66946—24no—
31C11×#389—24no—
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622602—28no—
40#10622601C418yescomplemented
41#10622552—24no—
42C4×Dic11⋊C4—24no—
43C24×D11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
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—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—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4C2×C414yescomplemented
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—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4C2×C418yescomplemented
94C2×(C2×D11)⋊C4C2×C418yescomplemented
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
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×Dic11C2×C414yescomplemented
109C2×C4×Dic11D414yes—
110#66946—232no—
111C11×#95—24no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—42no—
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—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11C22×C414yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D414yes—
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—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
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×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—28no—
221C11×C4⋊C4—48no—
222C42×C11—44no—
223(C2×D11)⋊C4—216no—
224(C2×D11)⋊C4—216no—
225(C2×D11)⋊C4—48no—
226(C2×D11)⋊C4—48no—
227(C2×D11)⋊C4—48no—
228C4⋊Dic11—44no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231C4×Dic11—28no—
232C4×Dic11—28no—
233C22×C4×D4—111no—
234C2×#390—111no—
235C2×#390—111no—
236C2×#389D1111yescharacteristic, complemented
237C2×#385—112no—
238C2×C4×C4⋊C4—111no—
239#1439—112no—
240#1439—112no—
241C4⋊#95—111no—
242C4⋊#95—111no—
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—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—41no—
321C2×C4×C11—42no—
322C2×C4×C11C2×C4⋊C414yes—
323C2×C4×C11C4×D414yes—
324C2×C4×C11C4×D414yes—
325C2×C4×C11#12014yes—
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—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11C4×D414yescomplemented
363C2×Dic11#12114yes—
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⋊C4C2×D1112yes—
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—24no—
388#385—228no—
389C4×C4⋊C4—224no—
390C2×#95—111no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95—111no—
394C2×#95—112no—
395C2×#95—112no—
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—44no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—44no—
451C4×C11#38518yescomplemented
452Dic11—24no—
453Dic11—24no—
454Dic11—42no—
455Dic11—42no—
456Dic11—82no—
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×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1112yes—
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—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—114no—
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—222no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4C4×D1114yescomplemented
500C2×C4⋊C4C22⋊D1114yes—
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—22no—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—222no—
522C2×C42—222no—
523C2×C42—222no—
524C2×C42—222no—
525#95—24no—
526#95—222no—
527#95—222no—
528#95—224no—
529#95—224no—
530#95—442no—
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—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—112no—
603C22×C4—2216no—
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—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—448no—
632C22×C4—448no—
633C22×C4—448no—
634C22×C4—448no—
635C22×C4—448no—
636C22×C4—448no—
637C22×C4C2×C4×D1114yes—
638C22×C4C2×C4×D1112yes—
639C22×C4#433912yes—
640C22×C4D4×D1112yes—
641C22×C4D4×D1112yes—
642C22×C4D4×D1112yes—
643C22×C4Q8×D1112yes—
644C22×C4#434312yes—
645C22×C4#434312yes—
646C22×C4C2×C22⋊D1114yes—
647C22×C4C2×C22⋊D1112yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—48no—
651C4⋊C4—228no—
652C4⋊C4—228no—
653C4⋊C4—444no—
654C22⋊C4—2216no—
655C22⋊C4—2216no—
656C22⋊C4—448no—
657C22⋊C4—448no—
658C22⋊C4—448no—
659C42—44no—
660C42—228no—
661C42—228no—
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
699C23C2×#433911yescharacteristic
700C23C2×D4×D1111yescharacteristic
701C23C2×D4×D1111yescharacteristic
702C23C2×D4×D1111yescharacteristic
703C23#6703711yescharacteristic
704C23C2×Q8×D1111yescharacteristic
705C23C2×#434311yescharacteristic
706C23C2×#434311yescharacteristic
707C23#6704011yescharacteristic
708C23#41×D1111yescharacteristic
709C23#41×D1111yescharacteristic
710C23#6704211yescharacteristic
711C23#6704211yescharacteristic
712C23C22×C22⋊D1111yescharacteristic
713D4—2232no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—114no—
743C2×C4—114no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—4432no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4C4⋊C4×D1114yes—
779C2×C4#6694614yes—
780C2×C4#6694714yes—
781C2×C4#6694914yes—
782C2×C4C4×C22⋊D1114yes—
783C2×C4#6699014yes—
784C2×C4#6699914yes—
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⋊C4×D1111yescharacteristic
801C22C2×#6694611yescharacteristic
802C22C2×#6694711yescharacteristic
803C22C2×#6694911yescharacteristic
804C22C4×D4×D1111yescharacteristic
805C22#1062307611yescharacteristic
806C22#1062308411yescharacteristic
807C22#1062309011yescharacteristic
808C22#1062309911yescharacteristic
809C22C4×#434311yescharacteristic
810C22#1062310511yescharacteristic
811C22#1062311611yescharacteristic
812C22D11×#12111yescharacteristic
813C22#1062313811yescharacteristic
814C22#1062314011yescharacteristic
815C22#1062314311yescharacteristic
816C22#1062315811yescharacteristic
817C22#1062316011yescharacteristic
818C22#1062316111yescharacteristic
819C22#1062316211yescharacteristic
820C22#1062322111yescharacteristic
821C22#1062322111yescharacteristic
822C22#1062322211yescharacteristic
823C22#1062322911yescharacteristic
824C22#1062325611yescharacteristic
825C22#1062325811yescharacteristic
826C22#1062326111yescharacteristic
827C22#1062326411yescharacteristic
828C22C2×C4×C22⋊D1111yescharacteristic
829C22C2×#6699011yescharacteristic
830C22D4×C22⋊D1111yescharacteristic
831C22C2×#6699911yescharacteristic
832C22#1062334811yescharacteristic
833C22#1062336011yescharacteristic
834C22#1062336511yescharacteristic
835C4—44no—
836C4—42no—
837C4—44no—
838C4—42no—
839C4—224no—
840C4—224no—
841C4—442no—
842C4—442no—
843C4—882no—
844C4#1062260218yescomplemented
845C2—448no—
846C2C2×#1062260211yescharacteristic
847C2#1307112411yescharacteristic
848C2#1307130711yescharacteristic
849C2#1307151711yescharacteristic
850C2#1307152511yescharacteristic
851C2#1307167811yescharacteristic
852C2#1307168311yescharacteristic
853C2#1307196311yescharacteristic
854C2#1307196811yescharacteristic
855C2#1307238311yescharacteristic
856C2#1307240511yescharacteristic
857C2#1307246211yescharacteristic
858C2#1307248411yescharacteristic
859C2#1307353711yescharacteristic
860C2#1307397611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11#14018
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#10622602C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#389C2semidirect
40. #10622601C4semidirect
75. C2×C11×C4⋊C4C2×C4semidirect
93. C2×(C2×D11)⋊C4C2×C4semidirect
94. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×Dic11⋊C4D4semidirect
108. C2×C4×Dic11C2×C4semidirect
211. C2×D44C4⋊C4semidirect
236. C2×#389D11semidirect
362. C2×Dic11C4×D4semidirect
451. C4×C11#385semidirect
499. C2×C4⋊C4C4×D11semidirect
662. C11#14018semidirect
844. C4#10622602semidirect

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×#106226022
C2×C4×Dic11⋊C42
#130668602
#130668582
#130668452
(C2×D11)⋊#952
C2×C11×#3892
#1401811