Finite Group Databasebeta

← #14801206

Subgroups — #14801206

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622629C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic, complemented
3C2×#10622830C211yesmaximal, characteristic
4C2×C4×#4324C211yesmaximal, characteristic, complemented
5#13072182C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069819C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069692C211yesmaximal, characteristic, complemented
10#13069481C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic, complemented
13#13068964C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66928C2211yescharacteristic, complemented
27C2×C4×Dic22C2211yescharacteristic, complemented
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#386—21no—
31C11×#386—21no—
32C11×#380C2211yescharacteristic
33C11×#379—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622831—24no—
36#10622830—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C4×#4324—24no—
44#10622629—24no—
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66873C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622572—21no—
52#10622570—21no—
53#10622552C2211yescharacteristic, complemented
54#10622541C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622289—21no—
58#10622282—21no—
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—21no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×D44C2311yescharacteristic
78C22×Dic22C2311yescharacteristic
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—44no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×#4324—22no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—22no—
102C2×#4324—41no—
103C2×#4324D414yescomplemented
104C2×#4323—22no—
105C2×#4323—22no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323—41no—
110#66983—22no—
111#66983—41no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—22no—
120#66977—41no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129#66928—22no—
130#66928—41no—
131C4×Dic22—22no—
132C4×Dic22—41no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#66896—22no—
137#66896—22no—
138#66896—22no—
139#66896D414yes—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66874—22no—
144#66874—22no—
145#66873—22no—
146#66873—41no—
147#66872—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25152—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—24no—
154C24×C11—21no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—81no—
160C24×C11—81no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11C2×D412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11#4112yes—
181C2×D4×C11#4112yes—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—81no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22C2×D412yes—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C22⋊Dic11—42no—
238#4324—28no—
239#4324—44no—
240#4323—44no—
241#4323—44no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—81no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11C2×D412yes—
251Dic11⋊C4—42no—
252Dic11⋊C4—42no—
253Dic11⋊C4—81no—
254C4×Dic11—42no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C2×#463—111no—
268C2×#450—111no—
269C2×#447—111no—
270C2×C4×SD16—111no—
271#2426—111no—
272D4×C22⋊C4D1111yescharacteristic, complemented
273#2065—111no—
274#2036—111no—
275#2034—111no—
276#2012—111no—
277#1970—111no—
278#1923—111no—
279#1880—111no—
280#1879—111no—
281#1862—111no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—22no—
292C23×C11—48no—
293C23×C11—48no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—84no—
305C23×C11—84no—
306C23×C11—84no—
307C23×C11—84no—
308C23×C11—84no—
309C23×C11#13512yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11#12114yes—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—84no—
352C2×C4×C11—84no—
353C2×C4×C11AGL(1,ℤ/8)12yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—84no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370D44—41no—
371D44—41no—
372D44—41no—
373D44—41no—
374Dic22—22no—
375Dic22—22no—
376Dic22—41no—
377Dic22—41no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C23×D4C2×D1111yescharacteristic
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×D8—111no—
387C2×#124—111no—
388C2×C22⋊Q8—111no—
389C2×#121—111no—
390C2×C4×Q8—111no—
391C2×C4×D4C2×D1111yescharacteristic
392C2×C4×D4C2×D1111yescharacteristic
393C22×C22⋊C4—21no—
394#463—224no—
395#450—224no—
396#447—224no—
397C4×SD16—224no—
398C2×#107—111no—
399C2×#106—111no—
400C2×C4⋊C8—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×C4×C8—111no—
412#396—221no—
413#394—221no—
414#390—111no—
415#390—221no—
416#390C2×D1111yescharacteristic
417#390C2×D1111yescharacteristic
418#389—111no—
419#388—221no—
420#386—21no—
421#386—21no—
422#380C2×D1111yescharacteristic
423#379—21no—
424C4×C22⋊C4C2×D1111yescharacteristic
425#340—111no—
426#340—111no—
427#336—111no—
428#336—111no—
429C22×C11—22no—
430C22×C11—24no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—42no—
434C22×C11—41no—
435C22×C11—42no—
436C22×C11—41no—
437C22×C11—42no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—816no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11#52511yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11C2×#13511yescharacteristic
455C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C11#57611yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—81no—
459C2×D11—81no—
460C2×D11—81no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C4×C11—22no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—81no—
471C4×C11—81no—
472C4×C11C2×#12111yescharacteristic
473C4×C11#53811yescharacteristic
474C4×C11#54611yescharacteristic
475C4×C11#54611yescharacteristic
476Dic11—42no—
477Dic11—42no—
478Dic11—81no—
479C25—21no—
480C22×Q8—111no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4—111no—
489C22×D4—221no—
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C22×D1111yescharacteristic
495C2×SD16—114no—
496C2×SD16—222no—
497C2×SD16—222no—
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—441no—
501C2×D8—222no—
502C2×D8—222no—
503C2×D8—222no—
504C2×D8—222no—
505C2×D8—222no—
506C2×D8—441no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511#124—222no—
512#124—441no—
513C22⋊Q8—222no—
514C22⋊Q8—441no—
515#121—222no—
516#121—441no—
517C4×Q8—222no—
518C4×Q8—441no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—41no—
522C4×D4—41no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—44no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C22⋊C4C22⋊D1111yescharacteristic
546C2×C42—221no—
547C2×C42C22×D1111yescharacteristic
548C2×C42C22×D1111yescharacteristic
549#107—441no—
550#106—222no—
551C4⋊C8—222no—
552#103—222no—
553#103—222no—
554#102—114no—
555#102—222no—
556#102—222no—
557#102—222no—
558#102—222no—
559#102—441no—
560C22⋊C8—222no—
561C22⋊C8—222no—
562C4×C8—222no—
563#95—21no—
564#95—221no—
565#95C22⋊D1111yescharacteristic
566#95C22⋊D1111yescharacteristic
567C2×C11—42no—
568C2×C11—44no—
569C2×C11—82no—
570C2×C11#242411yescharacteristic
571C2×C11#310511yescharacteristic
572C2×C11#311811yescharacteristic
573C2×C11#326511yescharacteristic
574C2×C11#327411yescharacteristic
575C2×C11#328011yescharacteristic
576C2×C11#328211yescharacteristic
577D11—161no—
578C24—21no—
579C24—24no—
580C24—21no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24—221no—
588C24C2×C22⋊D1111yescharacteristic
589C2×Q8—112no—
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×D4—24no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—442no—
617C2×D4—442no—
618C2×D4—881no—
619C2×D4#433912yes—
620C2×D4#433912yes—
621C2×D4D4×D1112yes—
622C2×D4D4×D1112yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C2×C22⋊D1111yescharacteristic
642C22×C4C2×C22⋊D1111yescharacteristic
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C23×D1111yescharacteristic
646SD16—228no—
647SD16—444no—
648D8—444no—
649D8—444no—
650C2×C8—112no—
651C2×C8—112no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—112no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—442no—
671C4⋊C4—442no—
672C4⋊C4—881no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—442no—
683C22⋊C4—442no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—881no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—442no—
693C11#2515211yescharacteristic, complemented, Sylow
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23—441no—
725C23—441no—
726C23—441no—
727C23—441no—
728C23#6700312yes—
729C23C22×C22⋊D1111yescharacteristic
730Q8—222no—
731Q8—222no—
732Q8—441no—
733Q8—441no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—441no—
743D4—441no—
744D4—441no—
745D4—441no—
746D4—884no—
747D4#6693714yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4#6698512yes—
784C2×C4C2×#433911yescharacteristic
785C2×C4C2×#433911yescharacteristic
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6703711yescharacteristic
789C2×C4#6703711yescharacteristic
790C8—222no—
791C8—222no—
792C8—441no—
793C8—441no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—881no—
817C22—881no—
818C22—881no—
819C22—881no—
820C22—881no—
821C22—881no—
822C22—881no—
823C22#1062332211yescharacteristic
824C22C2×#6698511yescharacteristic
825C22D4×C22⋊D1111yescharacteristic
826C22D4×C22⋊D1111yescharacteristic
827C22C2×#6700311yescharacteristic
828C22#1062336611yescharacteristic
829C22#1062336711yescharacteristic
830C4—22no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—81no—
836C4—81no—
837C4—442no—
838C4—442no—
839C4—881no—
840C4C2×#6693711yescharacteristic
841C4#1062302111yescharacteristic
842C4#1062302111yescharacteristic
843C4#1062302511yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—1761no—
848C2#1307215211yescharacteristic
849C2#1307866311yescharacteristic
850C2#1307880011yescharacteristic
851C2#1308010711yescharacteristic
852C2#1308023211yescharacteristic
853C2#1308029711yescharacteristic
854C2#1308031911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterD4×C22⋊C4D11
hypocenterC11#25152
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622629C2semidirect
2. C2×#10622831C2semidirect
4. C2×C4×#4324C2semidirect
5. #13072182C2semidirect
6. #13069990C2semidirect
7. #13069819C2semidirect
8. #13069805C2semidirect
9. #13069692C2semidirect
10. #13069481C2semidirect
11. #13069224C2semidirect
12. #13068974C2semidirect
13. #13068964C2semidirect
14. #13068863C2semidirect
15. D4×C11×C22⋊C4C2semidirect
26. C2×#66928C22semidirect
27. C2×C4×Dic22C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66873C22semidirect
48. C2×#66873C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
53. #10622552C22semidirect
54. #10622541C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
103. C2×#4324D4semidirect
272. D4×C22⋊C4D11semidirect
693. C11#25152semidirect

Maximal subgroups

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

subgroupindex
C2×#106226292
C2×#106228312
C2×#106228302
C2×C4×#43242
#130721822
#130699902
#130698192
#130698052
#130696922
#130694812
#130692242
#130689742
#130689642
#130688632
D4×C11×C22⋊C42
#2515211