Finite Group Databasebeta

← #14823197

Subgroups — #14823197

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622336C211yesmaximal, characteristic, complemented
2C2×#10622460C211yesmaximal, characteristic, complemented
3#13072957C211yesmaximal, characteristic, complemented
4#13071652C211yesmaximal, characteristic
5#13069996C211yesmaximal, characteristic, complemented
6#13069955C211yesmaximal, characteristic, complemented
7#13069806C211yesmaximal, characteristic
8#13069621C211yesmaximal, characteristic
9#13069497C211yesmaximal, characteristic, complemented
10#13069251C211yesmaximal, characteristic, complemented
11#13069244C211yesmaximal, characteristic, complemented
12#13068949C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068513C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622570—21no—
40#10622569—21no—
41#10622565—21no—
42#10622557—21no—
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622460—24no—
50#10622336—24no—
51#10622282—21no—
52#10622279—21no—
53#10622271—21no—
54#10622263—21no—
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66983—22no—
78#66983—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83#66979—22no—
84#66979—41no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977—41no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×#4314—22no—
101C2×#4314—22no—
102C2×#4314—41no—
103C4×D44—22no—
104C4×D44—41no—
105#66923—22no—
106#66923—41no—
107C11×C4⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—22no—
110C11×#97—22no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66885—22no—
122#66885—22no—
123#66885—22no—
124#66882—41no—
125#66882D414yescomplemented
126#66881—22no—
127#66881—22no—
128#66881—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#26813—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—24no—
148C2×C22⋊D11—81no—
149C2×C22⋊D11—81no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44#4112yes—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C2×C8×C11#4112yes—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2×D412yes—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11—81no—
216#4314—44no—
217C2×#485—111no—
218C2×#478—111no—
219#2489—111no—
220#2363—111no—
221#2066—111no—
222#2059—111no—
223#2034—111no—
224#2000—111no—
225#1973—111no—
226#1927—111no—
227#1926—111no—
228#1924D1111yescharacteristic, complemented
229#1877—111no—
230#1854—111no—
231#1776—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C22⋊D11—84no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294D44—22no—
295D44—22no—
296D44—41no—
297D44—41no—
298C4×D11—84no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—41no—
307C22×SD16—111no—
308C2×#125—111no—
309C2×C22⋊Q8—111no—
310C2×#121—111no—
311C2×C4×D4—111no—
312C2×#117—111no—
313#485—224no—
314#478—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×C22⋊C8C2×D1111yescharacteristic
329C2×#97C2×D1111yescharacteristic
330#400—221no—
331#397—221no—
332#391—111no—
333#391—111no—
334#390—111no—
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#382—221no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345C4×C22⋊C4C2×D1111yescharacteristic
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#336C2×D1111yescharacteristic
351#336C2×D1111yescharacteristic
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11#52511yescharacteristic
360C22×C11D4211yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57711yescharacteristic
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11#53211yescharacteristic
379C4×C11#54211yescharacteristic
380C4×C11#54811yescharacteristic
381C4×C11#55111yescharacteristic
382Dic11—42no—
383Dic11—42no—
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—111no—
390C22×D4—111no—
391C22×D4—221no—
392C23×C4—221no—
393C23×C4C22×D1111yescharacteristic
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—441no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401#125—222no—
402#125—441no—
403C22⋊Q8—222no—
404C22⋊Q8—441no—
405#121—222no—
406#121—222no—
407C4×D4—222no—
408C4×D4—441no—
409#117—222no—
410#117—441no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4D4411yescharacteristic
429C2×C22⋊C4D4411yescharacteristic
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435#107—114no—
436#107—441no—
437#106—222no—
438#106—222no—
439#106—222no—
440C4⋊C8—22no—
441#103—222no—
442#103—222no—
443#103—222no—
444#102—222no—
445#102—222no—
446#102—222no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449#97—22no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95D4411yescharacteristic
459#95D4411yescharacteristic
460C2×C11—81no—
461C2×C11#246111yescharacteristic
462C2×C11#311111yescharacteristic
463C2×C11#312311yescharacteristic
464C2×C11#326711yescharacteristic
465C2×C11#327111yescharacteristic
466C2×C11#334811yescharacteristic
467C2×C11#335111yescharacteristic
468D11—82no—
469C24—221no—
470C24C2×D4411yescharacteristic
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×D4—112no—
478C2×D4—224no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—881no—
485C2×D4—881no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C23×D1111yescharacteristic
508SD16—444no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8D4×D1112yes—
520C2×C8#434112yes—
521C4⋊C4—112no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—881no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—442no—
551C42—442no—
552C42—881no—
553C11#2681311yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—222no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23C22×D4411yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573D4—222no—
574D4—222no—
575D4—441no—
576D4—441no—
577D4—884no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×#434111yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#6704211yescharacteristic
624C2×C4#6704311yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22#1062305511yescharacteristic
644C22D4×D4411yescharacteristic
645C22#1062308611yescharacteristic
646C22#1062327911yescharacteristic
647C22#1062327911yescharacteristic
648C22#1062328211yescharacteristic
649C22#1062328211yescharacteristic
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—442no—
656C4—442no—
657C4—442no—
658C4—881no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4#1062312711yescharacteristic
663C4#1062318911yescharacteristic
664C4#1062320811yescharacteristic
665C4#1062324111yescharacteristic
666C2—81no—
667C2—882no—
668C2#1307258111yescharacteristic
669C2#1307872711yescharacteristic
670C2#1307886911yescharacteristic
671C2#1308014611yescharacteristic
672C2#1308020611yescharacteristic
673C2#1308113311yescharacteristic
674C2#1308117811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1924C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1924D11
hypocenterC11#26813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#10622336C2semidirect
2. C2×#10622460C2semidirect
3. #13072957C2semidirect
5. #13069996C2semidirect
6. #13069955C2semidirect
9. #13069497C2semidirect
10. #13069251C2semidirect
11. #13069244C2semidirect
12. #13068949C2semidirect
13. #13068817C2semidirect
14. #13068513C2semidirect
15. C11×#1924C2semidirect
125. #66882D4semidirect
228. #1924D11semidirect
553. C11#26813semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
C2×#106224602
#130729572
#130716522
#130699962
#130699552
#130698062
#130696212
#130694972
#130692512
#130692442
#130689492
#130688172
#130685132
C11×#19242
#2681311