Finite Group Databasebeta

← #14759126

Subgroups — #14759126

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623091C211yesmaximal, characteristic
2#13071211C211yesmaximal, characteristic, complemented
3#13070968C211yesmaximal, characteristic, complemented
4#13069599C212yesmaximal, complemented
5#13069450C212yesmaximal, complemented
6#13069068C212yesmaximal, complemented
7#13069066C212yesmaximal, complemented
8C4×#66870C211yesmaximal, characteristic, complemented
9C4×#66870C211yesmaximal, characteristic, complemented
10C4×#66898C211yesmaximal, characteristic, complemented
11C4×C11×#99C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66992C2211yescharacteristic
14C2×#66990C2211yescharacteristic
15C2×#66983C411yescharacteristic, complemented
16C2×#66982C411yescharacteristic, complemented
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19#10623091—22no—
20#10623091—22no—
21#10623091—22no—
22#10623091—22no—
23C2×#66951C411yescharacteristic, complemented
24C2×#66947C411yescharacteristic, complemented
25C2×#66938C411yescharacteristic, complemented
26C2×#66937C411yescharacteristic, complemented
27C2×#66935C2211yescharacteristic
28C2×C22⋊C4×D11C2212yes—
29C2×#66931C2211yescharacteristic
30C2×#66929C411yescharacteristic, complemented
31C2×#66928C411yescharacteristic, complemented
32C2×C11×#99C2212yes—
33C4×C11×C22⋊C4C2211yescharacteristic
34C4×C11×C22⋊C4C2211yescharacteristic
35C2×#66898C2212yes—
36C4×C22⋊Dic11C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38#10622568C2212yes—
39C2×#66870C2212yes—
40C2×#66870C2212yes—
41#10622555C2212yes—
42C22⋊C4×Dic11C2212yes—
43#10622553—22no—
44C4×(C2×D11)⋊C4—22no—
45#10622282—22no—
46#10622279—22no—
47C11×#342C2212yes—
48#10622165C2212yes—
49#10622165C2212yes—
50#10622164C2212yes—
51C24×D11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11C2×C411yescharacteristic, complemented
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11C2×C411yescharacteristic
56C22×C22⋊D11C2×C411yescharacteristic
57C22×C22⋊D11C2×C411yescharacteristic, complemented
58C22×C22⋊D11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44C2×C411yescharacteristic
61C22×D44C2×C411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11C2×C411yescharacteristic, complemented
64C22×Dic22C2×C411yescharacteristic, complemented
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
70C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
71C2×C11×C22⋊C4C2312yes—
72C2×C11×C22⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4C2312yes—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2×C411yescharacteristic, complemented
77C2×C22⋊Dic11C2×C411yescharacteristic, complemented
78C2×C22⋊Dic11C2312yes—
79C2×C22⋊Dic11C2311yescharacteristic
80C2×C22⋊Dic11C2312yes—
81#66992—22no—
82#66992—22no—
83#66990—22no—
84#66990—22no—
85#66983—22no—
86#66983—22no—
87#66982—22no—
88#66982—22no—
89C4×C22⋊D11—21no—
90C4×C22⋊D11—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
105C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
106C2×(C2×D11)⋊C4D412yes—
107C2×(C2×D11)⋊C4D412yes—
108C2×(C2×D11)⋊C4D412yes—
109C2×(C2×D11)⋊C4D412yes—
110C2×C4⋊Dic11C2×C411yescharacteristic, complemented
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4C2×C411yescharacteristic, complemented
113C2×Dic11⋊C4C2×C411yescharacteristic, complemented
114C2×Dic11⋊C4C2×C411yescharacteristic, complemented
115C2×Dic11⋊C4C2×C411yescharacteristic, complemented
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11C2×C411yescharacteristic, complemented
120#66951—22no—
121#66951—22no—
122#66947—22no—
123#66947—22no—
124#66938—22no—
125#66938—22no—
126#66937—22no—
127#66937—22no—
128#66935—22no—
129#66935—22no—
130C22⋊C4×D11—24no—
131C22⋊C4×D11—24no—
132#66931—22no—
133#66931—22no—
134#66929—22no—
135#66929—22no—
136#66928—22no—
137#66928—22no—
138C11×#99—24no—
139C11×#95—21no—
140C11×#95—21no—
141#66898—24no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146#66870—24no—
147#66870—24no—
148#21422—111nomaximal, Sylow
149C24×C11C22×C411yescharacteristic
150C24×C11C2411yescharacteristic
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—81no—
154C23×D11—81no—
155C23×D11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C23×D11C22×C411yescharacteristic
158C23×D11C2×D412yes—
159C23×D11C2×D412yes—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C2×C22⋊D11—22no—
180C2×C22⋊D11—21no—
181C2×C22⋊D11—21no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11—22no—
186C2×C22⋊D11—81no—
187C2×C22⋊D11—81no—
188C2×C22⋊D11—81no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—81no—
192C22×Dic11C22×C411yescharacteristic
193C22×Dic11C22×C411yescharacteristic
194C22×Dic11C22×C411yescharacteristic
195C22×Dic11C22×C411yescharacteristic
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C2×D412yes—
198C22×Dic11C2×D412yes—
199C2×D44—22no—
200C2×D44—22no—
201C2×D44—81no—
202C2×D44—81no—
203C2×C4×D11—28no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—82no—
207C2×C4×D11—82no—
208C2×C4×D11—81no—
209C2×Dic22—22no—
210C2×Dic22—81no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4#4114yes—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—81no—
224C42×C11—81no—
225C22⋊Dic11—22no—
226C22⋊Dic11—21no—
227C22⋊Dic11—21no—
228C22⋊Dic11—22no—
229C22⋊Dic11—22no—
230C22⋊Dic11—22no—
231C22⋊Dic11#4114yes—
232(C2×D11)⋊C4—28no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—21no—
239(C2×D11)⋊C4—21no—
240(C2×D11)⋊C4—82no—
241(C2×D11)⋊C4—82no—
242(C2×D11)⋊C4C22⋊C412yes—
243(C2×D11)⋊C4C22⋊C412yes—
244(C2×D11)⋊C4C22⋊C412yes—
245(C2×D11)⋊C4C22⋊C412yes—
246(C2×D11)⋊C4C22⋊C412yes—
247(C2×D11)⋊C4C22⋊C412yes—
248(C2×D11)⋊C4C22⋊C412yes—
249(C2×D11)⋊C4C22⋊C412yes—
250C4⋊Dic11—22no—
251Dic11⋊C4—22no—
252Dic11⋊C4—22no—
253Dic11⋊C4—22no—
254Dic11⋊C4—21no—
255Dic11⋊C4—21no—
256Dic11⋊C4—82no—
257C4×Dic11—21no—
258C4×Dic11—21no—
259C4×Dic11—81no—
260C4×Dic11—81no—
261C4×Dic11—82no—
262C2×#538—111no—
263#2312—111no—
264#2273—111no—
265#1996—112no—
266#1964—112no—
267#1898—112no—
268#1898—112no—
269C4×#99—111no—
270C4×#99—111no—
271C4×#99—111no—
272C4×#99D1111yescharacteristic, complemented
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11C23×C411yescharacteristic
281C23×C11C22×D411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C2×#4112yes—
284C23×C11C2×#4112yes—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—24no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—84no—
306C22×D11—84no—
307C22×D11C2×C22⋊C412yes—
308C22×D11C2×C22⋊C412yes—
309D4×C11—42no—
310D4×C11—42no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—24no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—81no—
331C2×C4×C11—81no—
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C2×C22⋊C411yescharacteristic
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C22⋊D11—42no—
337C22⋊D11—42no—
338C22⋊D11—82no—
339C22⋊D11—82no—
340C22⋊D11—82no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—24no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C2×C22⋊C412yes—
359C2×Dic11C2×C22⋊C412yes—
360D44—82no—
361D44—82no—
362C4×D11—81no—
363C4×D11—81no—
364C4×D11—88no—
365Dic22—82no—
366#538—222no—
367#538—222no—
368#538—222no—
369#538—222no—
370C2×#126—111no—
371C2×#126—111no—
372C2×#124—111no—
373C2×#124—111no—
374C2×#123—111no—
375C2×#123—111no—
376C2×C22⋊Q8—111no—
377C2×#121—111no—
378C2×#121—111no—
379C2×#121—111no—
380C2×#120—111no—
381C2×#120—111no—
382C2×C4×D4—111no—
383C2×C4×D4C2×D1111yescharacteristic
384C22×C22⋊C4—111no—
385C22×C22⋊C4—112no—
386C2×#99—112no—
387C2×#99—112no—
388C2×#99—112no—
389C2×#99C2×D1112yes—
390#388—222no—
391#388—222no—
392#380—112no—
393#379—112no—
394C4×C22⋊C4—111no—
395C4×C22⋊C4—111no—
396C4×C22⋊C4—112no—
397C4×C22⋊C4—222no—
398C4×C22⋊C4—222no—
399C4×C22⋊C4C2×D1111yescharacteristic
400C4×C22⋊C4C2×D1111yescharacteristic
401#342—112no—
402#342—112no—
403#342—112no—
404#342C2×D1112yes—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11C22×C22⋊C411yescharacteristic
419C22×C11C4×#4111yescharacteristic
420C22×C11C4×#4111yescharacteristic
421C22×C11#52512yes—
422C22×C11#53212yes—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—44no—
430C2×D11—44no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—84no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C4×C11—21no—
442C4×C11—21no—
443C4×C11—21no—
444C4×C11—21no—
445C4×C11—44no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—82no—
450Dic11—22no—
451Dic11—22no—
452Dic11—44no—
453Dic11—41no—
454Dic11—41no—
455Dic11—41no—
456Dic11—82no—
457C25—111no—
458C22×Q8—111no—
459C22×D4—111no—
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—111no—
463C22×D4—111no—
464C22×D4—111no—
465C22×D4C22×D1111yescharacteristic
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—222no—
469C23×C4C4×D1111yescharacteristic, complemented
470C23×C4C22×D1111yescharacteristic
471#126—222no—
472#126—222no—
473#126—222no—
474#126—222no—
475#124—222no—
476#124—222no—
477#124—222no—
478#124—222no—
479#123—222no—
480#123—222no—
481#123—222no—
482#123—222no—
483C22⋊Q8—222no—
484C22⋊Q8—222no—
485#121—222no—
486#121—222no—
487#121—222no—
488#121—222no—
489#121—222no—
490#121—222no—
491#120—222no—
492#120—222no—
493#120—222no—
494#120—222no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—221no—
500C4×D4—221no—
501C4×D4—221no—
502C4×D4—221no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4C4×D1111yescharacteristic, complemented
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—112no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—224no—
529C2×C22⋊C4—222no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—222no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4C4×D1111yescharacteristic, complemented
534C2×C22⋊C4C22×D1112yes—
535C2×C22⋊C4C22×D1111yescharacteristic
536C2×C22⋊C4C22×D1112yes—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—111no—
540C2×C42—222no—
541C2×C42—221no—
542C2×C42—221no—
543C2×C42C4×D1111yescharacteristic, complemented
544#99—24no—
545#99—224no—
546#99—224no—
547#99—224no—
548#95—21no—
549#95—21no—
550#95—222no—
551#95—222no—
552#95—221no—
553#95—221no—
554C2×C11—22no—
555C2×C11—22no—
556C2×C11—21no—
557C2×C11—21no—
558C2×C11—81no—
559C2×C11#229711yescharacteristic
560C2×C11#288311yescharacteristic
561C2×C11#288311yescharacteristic
562D11—42no—
563D11—42no—
564D11—81no—
565C24—111no—
566C24—111no—
567C24—112no—
568C24—112no—
569C24—111no—
570C24—222no—
571C24—222no—
572C24—881no—
573C24—881no—
574C24C2×C4×D1111yescharacteristic
575C24C23×D1111yescharacteristic
576C2×Q8—222no—
577C2×Q8—881no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—881no—
592C2×D4—881no—
593C2×D4—881no—
594C2×D4—881no—
595C2×D4—881no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—228no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4—881no—
617C22×C4—881no—
618C22×C4C2×C4×D1111yescharacteristic
619C22×C4C2×C4×D1111yescharacteristic
620C22×C4C2×C4×D1111yescharacteristic
621C22×C4C2×C4×D1111yescharacteristic
622C22×C4C2×C4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—222no—
630C4⋊C4—222no—
631C4⋊C4—222no—
632C4⋊C4—222no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—882no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—22no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—112no—
644C22⋊C4—112no—
645C22⋊C4—112no—
646C22⋊C4—112no—
647C22⋊C4—112no—
648C22⋊C4—112no—
649C22⋊C4—112no—
650C22⋊C4—112no—
651C22⋊C4—114no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—222no—
657C22⋊C4—228no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—221no—
661C22⋊C4—221no—
662C22⋊C4—221no—
663C22⋊C4—221no—
664C22⋊C4—222no—
665C22⋊C4—222no—
666C22⋊C4—882no—
667C22⋊C4—882no—
668C22⋊C4#433914yes—
669C42—21no—
670C42—21no—
671C42—81no—
672C42—81no—
673C42—221no—
674C42—221no—
675C42—881no—
676C42—881no—
677C42—882no—
678C11#2142211yescharacteristic, complemented, Sylow
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—112no—
687C23—112no—
688C23—222no—
689C23—222no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23—221no—
694C23—224no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—442no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—441no—
703C23—441no—
704C23—441no—
705C23—441no—
706C23—441no—
707C23—441no—
708C23—884no—
709C23—884no—
710C23C22×C4×D1111yescharacteristic
711C23C2×#433912yes—
712C23C2×D4×D1111yescharacteristic
713C23C2×D4×D1111yescharacteristic
714C23#41×D1112yes—
715Q8—882no—
716D4—42no—
717D4—42no—
718D4—442no—
719D4—442no—
720D4—882no—
721D4—882no—
722D4—882no—
723D4—882no—
724D4—882no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—112no—
747C2×C4—112no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—224no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—881no—
766C2×C4—881no—
767C2×C4—888no—
768C2×C4C22⋊C4×D1111yescharacteristic
769C2×C4C22⋊C4×D1111yescharacteristic
770C2×C4C22⋊C4×D1111yescharacteristic
771C2×C4C22⋊C4×D1111yescharacteristic
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—81no—
784C22—81no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—222no—
791C22—444no—
792C22—444no—
793C22—441no—
794C22—441no—
795C22—441no—
796C22—884no—
797C22—881no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22—881no—
803C22C4×#433911yescharacteristic
804C22C2×C22⋊C4×D1111yescharacteristic
805C22#1062305311yescharacteristic
806C22#1062307812yes—
807C22#1062307912yes—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—222no—
818C4—222no—
819C4—444no—
820C4—441no—
821C4—441no—
822C4—441no—
823C4—882no—
824C2—22no—
825C2—22no—
826C2—21no—
827C2—21no—
828C2—81no—
829C2—442no—
830C2—442no—
831C2—881no—
832C2#1307110211yescharacteristic
833C2#1307707411yescharacteristic
834C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#99C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623091C2
cosocleC24×C11C24
hypercenterC4×#99D11
hypocenterC11#21422
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13071211C2semidirect
3. #13070968C2semidirect
4. #13069599C2semidirect
5. #13069450C2semidirect
6. #13069068C2semidirect
7. #13069066C2semidirect
8. C4×#66870C2semidirect
9. C4×#66870C2semidirect
10. C4×#66898C2semidirect
11. C4×C11×#99C2semidirect
15. C2×#66983C4semidirect
16. C2×#66982C4semidirect
23. C2×#66951C4semidirect
24. C2×#66947C4semidirect
25. C2×#66938C4semidirect
26. C2×#66937C4semidirect
30. C2×#66929C4semidirect
31. C2×#66928C4semidirect
53. C23×C4×C11C2×C4semidirect
57. C22×C22⋊D11C2×C4semidirect
63. C22×C4×D11C2×C4semidirect
64. C22×Dic22C2×C4semidirect
69. C2×C11×C4⋊C4C2×C4semidirect
70. C2×C11×C22⋊C4C2×C4semidirect
76. C2×C42×C11C2×C4semidirect
77. C2×C22⋊Dic11C2×C4semidirect
104. C2×(C2×D11)⋊C4C2×C4semidirect
105. C2×(C2×D11)⋊C4C2×C4semidirect
110. C2×C4⋊Dic11C2×C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
113. C2×Dic11⋊C4C2×C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
115. C2×Dic11⋊C4C2×C4semidirect
119. C2×C4×Dic11C2×C4semidirect
272. C4×#99D11semidirect
469. C23×C4C4×D11semidirect
509. C2×C4⋊C4C4×D11semidirect
533. C2×C22⋊C4C4×D11semidirect
543. C2×C42C4×D11semidirect
678. C11#21422semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
#130712112
#130709682
#130695992
#130694502
#130690682
#130690662
C4×#668702
C4×#668982
C4×C11×#992
#2142211