Finite Group Databasebeta

← #14801266

Subgroups — #14801266

Order 2816.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622632C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic
3C2×#10622831C211yesmaximal, characteristic
4C2×C4×#4324C211yesmaximal, characteristic, complemented
5#13072215C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic, complemented
8#13069812C211yesmaximal, characteristic, complemented
9#13069698C211yesmaximal, characteristic, complemented
10#13069469C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14#13068877C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66922C2211yescharacteristic, 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#10622831—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622632—24no—
44C4×#4324—24no—
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51#10622564—21no—
52#10622561—21no—
53#10622542C2211yescharacteristic, complemented
54#10622541C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622270—21no—
58#10622260—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×Dic22C2311yescharacteristic
77C22×Dic22C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
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—44no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×#4324—22no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—22no—
102C2×#4324—22no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—22no—
106C2×#4324—22no—
107C2×#4324—41no—
108C2×#4324—41no—
109C2×#4324D414yes—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66977—22no—
115#66977—22no—
116#66977—41no—
117#66977—41no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66922—22no—
128#66922—41no—
129C4×Dic22—22no—
130C4×Dic22—41no—
131C11×#95—21no—
132C11×#95D411yescharacteristic
133C11×#95D411yescharacteristic
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896D414yes—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66874—22no—
144#66874—22no—
145#66874—22no—
146#66874—41no—
147#66872—22no—
148#66872—41no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25156—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
162C2×D4×C11—24no—
163C2×D4×C11—21no—
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—42no—
172C2×D4×C11—42no—
173C2×D4×C11—44no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C2×D4×C11—44no—
177C2×D4×C11C2×D412yes—
178C2×D4×C11C2×D412yes—
179C2×D4×C11#4112yes—
180C2×D4×C11#4112yes—
181C22×C4×C11—21no—
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—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22C2×D412yes—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4SD1614yescomplemented
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C22⋊Dic11—42no—
235C22⋊Dic11—42no—
236#4324—28no—
237#4324—44no—
238#4324—44no—
239#4324—44no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—42no—
244C4⋊Dic11—42no—
245C4⋊Dic11C2×D412yes—
246Dic11⋊C4—42no—
247Dic11⋊C4—42no—
248Dic11⋊C4—42no—
249Dic11⋊C4—42no—
250C4×Dic11—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
262C2×C11⋊C8C2×D412yes—
263C2×#461—111no—
264C2×#450—111no—
265C2×#450—111no—
266C2×C4×SD16—111no—
267#2429—111no—
268D4×C22⋊C4D1111yescharacteristic
269#2065—111no—
270#2035—111no—
271#2035—111no—
272#2013—111no—
273#1968—111no—
274#1923—111no—
275#1880—111no—
276#1877—111no—
277#1864—111no—
278C23×C11—21no—
279C23×C11—22no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—22no—
288C23×C11—48no—
289C23×C11—48no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—84no—
301C23×C11—84no—
302C23×C11—84no—
303C23×C11—84no—
304C23×C11—84no—
305C23×C11C2×SD1612yes—
306C23×C11C22×D411yescharacteristic
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—48no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11#12114yes—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—84no—
340C2×C4×C11—84no—
341C2×C4×C11C2×SD1612yes—
342C2×C4×C11C2×SD1612yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361Dic22—22no—
362Dic22—22no—
363Dic22—41no—
364Dic22—41no—
365Dic22—41no—
366Dic22—41no—
367Dic22—41no—
368Dic22—41no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—41no—
372C11⋊C8—41no—
373C23×D4C2×D1111yescharacteristic
374C22×SD16—111no—
375C22×SD16—111no—
376C22×SD16—111no—
377C22×SD16—111no—
378C2×C4⋊Q8—111no—
379C2×C22⋊Q8—111no—
380C2×C22⋊Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×D4C2×D1111yescharacteristic
383C2×C4×D4C2×D1111yescharacteristic
384C22×C22⋊C4—21no—
385#461—224no—
386#450—224no—
387#450—224no—
388C4×SD16—224no—
389C2×#106—111no—
390C2×#106—111no—
391C2×C4⋊C8—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C4×C8—111no—
403#398—221no—
404#396—221no—
405#391—111no—
406#390C2×D1111yescharacteristic
407#390C2×D1111yescharacteristic
408#389—111no—
409#389—221no—
410#388—221no—
411#386—21no—
412#386—21no—
413#380C2×D1111yescharacteristic
414#379—21no—
415C4×C22⋊C4C2×D1111yescharacteristic
416#340—111no—
417#340—111no—
418#336—111no—
419#336—111no—
420C22×C11—22no—
421C22×C11—24no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—42no—
430C22×C11—41no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—816no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11—81no—
442C22×C11#52511yescharacteristic
443C22×C11D4211yescharacteristic
444C22×C11D4211yescharacteristic
445C22×C11C22×SD1611yescharacteristic
446C22×C11#57511yescharacteristic
447C22×C11#57711yescharacteristic
448C22×C11#57711yescharacteristic
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11—81no—
455C4×C11—81no—
456C4×C11C2×#12111yescharacteristic
457C4×C11#53811yescharacteristic
458C4×C11#54611yescharacteristic
459C4×C11#54611yescharacteristic
460Dic11—42no—
461Dic11—42no—
462Dic11—81no—
463Dic11—81no—
464C25—21no—
465C22×Q8—111no—
466C22×Q8—111no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4—41no—
473C22×D4—41no—
474C22×D4C22×D1111yescharacteristic
475C22×D4C22×D1111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4C22×D1111yescharacteristic
479C2×SD16—114no—
480C2×SD16—222no—
481C2×SD16—222no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×SD16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×SD16—441no—
490C2×SD16—441no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—111no—
495C4⋊Q8—222no—
496C4⋊Q8—441no—
497C22⋊Q8—222no—
498C22⋊Q8—222no—
499C22⋊Q8—441no—
500C22⋊Q8—441no—
501C4×Q8—222no—
502C4×Q8—441no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—41no—
506C4×D4—41no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4C22⋊D1111yescharacteristic
528C2×C22⋊C4C22⋊D1111yescharacteristic
529C2×C42—221no—
530C2×C42C22×D1111yescharacteristic
531C2×C42C22×D1111yescharacteristic
532#106—222no—
533#106—441no—
534C4⋊C8—222no—
535#103—222no—
536#103—222no—
537#103—222no—
538#103—441no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C4×C8—222no—
546#95—21no—
547#95—221no—
548#95—221no—
549#95—221no—
550#95C22⋊D1111yescharacteristic
551#95C22⋊D1111yescharacteristic
552C2×C11—42no—
553C2×C11—44no—
554C2×C11—82no—
555C2×C11#242411yescharacteristic
556C2×C11#310111yescharacteristic
557C2×C11#312311yescharacteristic
558C2×C11#326711yescharacteristic
559C2×C11#327511yescharacteristic
560C2×C11D4×SD1611yescharacteristic
561C2×C11D4×SD1611yescharacteristic
562C24—21no—
563C24—24no—
564C24—21no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—81no—
570C24—81no—
571C24C2×C22⋊D1111yescharacteristic
572C2×Q8—112no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4#433912yes—
600C2×D4#433912yes—
601C2×D4D4×D1112yes—
602C2×D4D4×D1112yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627SD16—228no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—112no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—442no—
652C4⋊C4—442no—
653C4⋊C4—442no—
654C4⋊C4—442no—
655C4⋊C4—442no—
656C4⋊C4—442no—
657C22⋊C4—41no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4#432414yescomplemented
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—442no—
673C11#2515611yescharacteristic, complemented, Sylow
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×#432412yes—
702C23C22×C22⋊D1111yescharacteristic
703Q8—222no—
704Q8—222no—
705Q8—441no—
706Q8—441no—
707Q8—441no—
708Q8—441no—
709Q8—441no—
710Q8—441no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#6693714yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4C2×#432412yes—
758C2×C4C2×#432412yes—
759C2×C4C2×#433911yescharacteristic
760C2×C4C2×#433911yescharacteristic
761C2×C4C2×D4×D1111yescharacteristic
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4#6703711yescharacteristic
764C2×C4#6703711yescharacteristic
765C8—222no—
766C8—222no—
767C8—441no—
768C8—441no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#1062332211yescharacteristic
792C22C22×#432411yescharacteristic
793C22D4×C22⋊D1111yescharacteristic
794C22D4×C22⋊D1111yescharacteristic
795C22#1062335311yescharacteristic
796C22#1062336711yescharacteristic
797C22#1062336711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—442no—
806C4—442no—
807C4—881no—
808C4—881no—
809C4C2×#6693711yescharacteristic
810C4#1062302111yescharacteristic
811C4#1062302111yescharacteristic
812C4#1062302511yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2#1307215211yescharacteristic
817C2#1307862411yescharacteristic
818C2#1307886811yescharacteristic
819C2#1308013711yescharacteristic
820C2#1308024311yescharacteristic
821C2D4×#432411yescharacteristic
822C2D4×#432411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenterD4×C22⋊C4D11
hypocenterC11#25156
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×#10622632C2semidirect
4. C2×C4×#4324C2semidirect
5. #13072215C2semidirect
6. #13069990C2semidirect
7. #13069812C2semidirect
8. #13069812C2semidirect
9. #13069698C2semidirect
10. #13069469C2semidirect
11. #13069224C2semidirect
12. #13068974C2semidirect
13. #13068950C2semidirect
14. #13068877C2semidirect
26. C2×#66922C22semidirect
27. C2×C4×Dic22C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
49. C2×#66872C22semidirect
50. C2×#66872C22semidirect
53. #10622542C22semidirect
54. #10622541C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
229. C11×C22⋊C4SD16semidirect
667. C22⋊C4#4324semidirect
673. C11#25156semidirect

Maximal subgroups

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

subgroupindex
C2×#106226322
C2×#106228312
C2×C4×#43242
#130722152
#130699902
#130698122
#130696982
#130694692
#130692242
#130689742
#130689502
#130688772
D4×C11×C22⋊C42
#2515611