Finite Group Databasebeta

← #14823543

Subgroups — #14823543

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622694C211yesmaximal, characteristic, complemented
2C2×#10622639C211yesmaximal, characteristic
3#13072466C211yesmaximal, characteristic
4#13070011C211yesmaximal, characteristic, complemented
5#13069944C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic
7#13069699C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic
9#13069309C211yesmaximal, characteristic, complemented
10#13069309C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic
12#13068953C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic, complemented
14#13068491C211yesmaximal, characteristic, complemented
15C11×#2446C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66949—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#400—21no—
24C11×#398—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C11×#387—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622694—24no—
39#10622639—24no—
40#10622607—21no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622286—21no—
54#10622281—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4325—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66949—44no—
104C4×D44—22no—
105C4×D44—41no—
106#66922—22no—
107#66922—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117#66899—22no—
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899—22no—
122#66899D414yes—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66873—22no—
126#66873—22no—
127#66871—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26836—111nomaximal, Sylow
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44#4112yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22—81no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190#4325—28no—
191#4325—44no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
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—42no—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×C11⋊C8#4112yes—
218C2×#487—111no—
219C2×#440—111no—
220#2452—111no—
221#2446D1111yescharacteristic, complemented
222#2068—111no—
223#2057—111no—
224#2055—111no—
225#2013—111no—
226#1973—111no—
227#1935—111no—
228#1935—111no—
229#1934—111no—
230#1877—111no—
231#1863—111no—
232#1771—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
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—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11AGL(1,ℤ/8)12yes—
278C2×C4×C11#13712yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—22no—
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—84no—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C22×SD16—111no—
306C2×C4⋊Q8—111no—
307C2×C4⋊Q8C2×D1111yescharacteristic
308C2×C22⋊Q8—221no—
309C2×C4×Q8C2×D1111yescharacteristic
310C2×C4×D4—111no—
311#487—224no—
312#440—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8—111no—
327#400—21no—
328#398—21no—
329#396—221no—
330#393—221no—
331#391C2×D1111yescharacteristic
332#391C2×D1111yescharacteristic
333#391C2×D1111yescharacteristic
334#390—111no—
335#390—111no—
336#389—111no—
337#389—111no—
338#389C2×D1111yescharacteristic
339#387—21no—
340#387—21no—
341#385—221no—
342C4×C4⋊C4C2×D1111yescharacteristic
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11#53211yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57811yescharacteristic
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52511yescharacteristic
374C4×C11#54211yescharacteristic
375C4×C11#54711yescharacteristic
376C4×C11#55111yescharacteristic
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—221no—
381C22×Q8C22×D1111yescharacteristic
382C22×Q8C22×D1111yescharacteristic
383C22×D4—111no—
384C23×C4—221no—
385C2×SD16—222no—
386C2×SD16—222no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—222no—
390C2×SD16—441no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C4⋊Q8—22no—
396C4⋊Q8—41no—
397C4⋊Q8—222no—
398C4⋊Q8—441no—
399C22⋊Q8—444no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C4⋊C4C22⋊D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427#107—222no—
428#107—441no—
429C4⋊C8—222no—
430#103—114no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—222no—
435#103—222no—
436#102—222no—
437#102—222no—
438#97—222no—
439#97—222no—
440C4×C8—222no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—221no—
449#95—221no—
450#95C22⋊D1111yescharacteristic
451#95C22⋊D1111yescharacteristic
452C2×C11#246111yescharacteristic
453C2×C11#317811yescharacteristic
454C2×C11#318211yescharacteristic
455C2×C11#326511yescharacteristic
456C2×C11#327011yescharacteristic
457C2×C11#336711yescharacteristic
458C2×C11#337211yescharacteristic
459D11—82no—
460C24—221no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—442no—
473C2×Q8—442no—
474C2×Q8—881no—
475C2×Q8D4×D1112yes—
476C2×D4—112no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—228no—
500SD16—444no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C11#2683611yescharacteristic, complemented, Sylow
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C22×C22⋊D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—884no—
562D4—222no—
563D4—222no—
564D4—441no—
565D4—441no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4#6699512yes—
605C2×C4#6700212yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4#6703711yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—222no—
613C8—222no—
614C8—222no—
615C8—441no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22D4×C22⋊D1111yescharacteristic
624C22C2×#6699511yescharacteristic
625C22C2×#6700211yescharacteristic
626C22#1062336211yescharacteristic
627C22#1062336311yescharacteristic
628C22#1062336811yescharacteristic
629C22#1062336911yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4#1062318611yescharacteristic
644C4#1062318711yescharacteristic
645C4#1062319011yescharacteristic
646C4#1062319311yescharacteristic
647C2—882no—
648C2#1307258211yescharacteristic
649C2#1307928611yescharacteristic
650C2#1307933511yescharacteristic
651C2#1308011211yescharacteristic
652C2#1308018711yescharacteristic
653C2#1308133011yescharacteristic
654C2#1308139311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2446D11
hypocenterC11#26836
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2446

Complements

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

NH ≅ G/Ntype
1. C2×#10622694C2semidirect
4. #13070011C2semidirect
5. #13069944C2semidirect
9. #13069309C2semidirect
10. #13069309C2semidirect
13. #13068870C2semidirect
14. #13068491C2semidirect
15. C11×#2446C2semidirect
221. #2446D11semidirect
544. C11#26836semidirect

Maximal subgroups

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

subgroupindex
C2×#106226942
C2×#106226392
#130724662
#130700112
#130699442
#130699312
#130696992
#130695002
#130693092
#130692982
#130689532
#130688702
#130684912
C11×#24462
#2683611