Finite Group Databasebeta

← #14813774

Subgroups — #14813774

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622766C211yesmaximal, characteristic
2#13072397C211yesmaximal, characteristic, complemented
3#13071521C211yesmaximal, characteristic, complemented
4#13070161C211yesmaximal, characteristic, complemented
5#13070105C211yesmaximal, characteristic, complemented
6#13070032C211yesmaximal, characteristic, complemented
7#13069855C211yesmaximal, characteristic, complemented
8#13069292C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic
11#13068950C211yesmaximal, characteristic, complemented
12#13068948C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068875C211yesmaximal, characteristic, complemented
15C2×C4×C11×D8C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66989C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C4×C11×D8—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622824—21no—
33#10622823—21no—
34#10622823—21no—
35C2×C11⋊#95—21no—
36#10622766—24no—
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622590C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622565—21no—
47#10622565—21no—
48#10622559—21no—
49#10622555—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22C2311yescharacteristic
68C2×C11×D8—22no—
69C2×C11×D8—22no—
70C2×C11×D8D414yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—41no—
76C4×D4×C11—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66989—22no—
89#66989—41no—
90D4×Dic11—22no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93D4×Dic11—41no—
94C2×#4324—22no—
95C2×#4324—22no—
96C2×#4324—22no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×Dic11⋊C4D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C11×#107—22no—
110C11×#102—22no—
111C11×#102—22no—
112C4×C8×C11—22no—
113#66896—22no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66880—22no—
128#66880—22no—
129Dic11⋊C8—22no—
130#66874—41no—
131#66872—41no—
132#26160—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11C2×D412yes—
145C2×D4×C11#4112yes—
146C2×D4×C11#4112yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11—81no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—24no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C11×D8—28no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C2×D412yes—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—24no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—81no—
199#4324—44no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—22no—
207Dic11⋊C4—41no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×#463—111no—
222C2×C4×D8D1111yescharacteristic
223#2447—111no—
224#2349—111no—
225#2097—111no—
226#2086—111no—
227#2073—111no—
228#2042—111no—
229#1933—111no—
230#1916—111no—
231#1879—111no—
232#1877—111no—
233#1877—111no—
234#1864—111no—
235#1864—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C22×D411yescharacteristic
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11#12314yes—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11—84no—
272C2×C4×C11#13512yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—84no—
304C2×Dic11—84no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—22no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C22×D8C2×D1111yescharacteristic
315C2×#124—111no—
316C2×C4×D4—111no—
317C2×C4×D4—111no—
318C2×C4×D4C2×D1111yescharacteristic
319C2×C4×D4C2×D1111yescharacteristic
320#463—224no—
321C4×D8—24no—
322C2×#107C2×D1111yescharacteristic
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102C2×D1111yescharacteristic
332C2×#102C2×D1111yescharacteristic
333C2×C4×C8C2×D1111yescharacteristic
334#397—221no—
335#397—221no—
336#391—111no—
337#391—111no—
338#390—111no—
339#389—111no—
340#389—111no—
341#389—111no—
342#385—221no—
343#385—221no—
344#385—221no—
345#382—111no—
346#381—221no—
347#380—221no—
348C4×C4⋊C4—111no—
349C2×#95—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336—111no—
355#336—111no—
356#336—111no—
357#336—111no—
358C22×C11—24no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11#52511yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54811yescharacteristic
375C22×C11C2×#13511yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57611yescharacteristic
378C22×C11#57711yescharacteristic
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11C2×#12311yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54711yescharacteristic
386C4×C11#55311yescharacteristic
387Dic11—41no—
388Dic11—41no—
389Dic11—42no—
390Dic11—41no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×D4C22×D1111yescharacteristic
397C22×D4C22×D1111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—221no—
401C23×C4—221no—
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—222no—
405C2×D8—22no—
406C2×D8—22no—
407C2×D8C22⋊D1114yes—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412#124—222no—
413#124—441no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—41no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42C22×D1111yescharacteristic
443#107—22no—
444#106—441no—
445C4⋊C8—222no—
446#103—222no—
447#103—222no—
448#103—441no—
449#102—22no—
450#102—22no—
451#102—222no—
452#102—222no—
453#102—222no—
454C4×C8—22no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—44no—
467C2×C11—82no—
468C2×C11#244311yescharacteristic
469C2×C11#310211yescharacteristic
470C2×C11#311811yescharacteristic
471C2×C11#326711yescharacteristic
472C2×C11#328011yescharacteristic
473C2×C11#336011yescharacteristic
474C2×C11#337011yescharacteristic
475C24—21no—
476C24—21no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4#433912yes—
492C2×D4#433912yes—
493C2×D4C2×C22⋊D1112yes—
494C2×D4C2×C22⋊D1112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—221no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—881no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520SD16—444no—
521D8—28no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8C2×C22⋊D1112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—112no—
539C4⋊C4—222no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—441no—
546C4⋊C4—881no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—224no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—881no—
557C42—21no—
558C42—21no—
559C42—221no—
560C42—221no—
561C42—221no—
562C42—221no—
563C11#2616011yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×D4×D1111yescharacteristic
579Q8—441no—
580Q8—441no—
581Q8—441no—
582Q8—441no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4—22no—
588D4—41no—
589D4—41no—
590D4#6698214yes—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—84no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—884no—
629C2×C4—884no—
630C2×C4#6696512yes—
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×#433911yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#6704311yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—22no—
638C8—41no—
639C8—441no—
640C8—441no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22#1062307811yescharacteristic
656C22#1062308311yescharacteristic
657C22C2×#6696511yescharacteristic
658C22#1062328811yescharacteristic
659C22#1062329911yescharacteristic
660C22#1062330111yescharacteristic
661C22D4×C22⋊D1111yescharacteristic
662C4—22no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—441no—
667C4—442no—
668C4—441no—
669C4—441no—
670C4—441no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4#1062307111yescharacteristic
675C4#1062309511yescharacteristic
676C4C2×#6698211yescharacteristic
677C4#1062335511yescharacteristic
678C2—44no—
679C2—82no—
680C2#1307234511yescharacteristic
681C2#1307863011yescharacteristic
682C2#1307879611yescharacteristic
683C2#1308014111yescharacteristic
684C2#1308030111yescharacteristic
685C2#1308126311yescharacteristic
686C2#1308136511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11#26160
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. #13072397C2semidirect
3. #13071521C2semidirect
4. #13070161C2semidirect
5. #13070105C2semidirect
6. #13070032C2semidirect
7. #13069855C2semidirect
8. #13069292C2semidirect
9. #13069173C2semidirect
11. #13068950C2semidirect
12. #13068948C2semidirect
13. #13068877C2semidirect
14. #13068875C2semidirect
563. C11#26160semidirect

Maximal subgroups

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

subgroupindex
C2×#106227662
#130723972
#130715212
#130701612
#130701052
#130700322
#130698552
#130692922
#130691732
#130689662
#130689502
#130689482
#130688772
#130688752
C2×C4×C11×D82
#2616011