Finite Group Databasebeta

← #14823544

Subgroups — #14823544

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×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622323C211yesmaximal, characteristic
3#13072466C211yesmaximal, characteristic
4#13072392C211yesmaximal, characteristic, complemented
5#13070010C211yesmaximal, characteristic, complemented
6#13069945C211yesmaximal, characteristic, complemented
7#13069934C211yesmaximal, characteristic
8#13069701C211yesmaximal, characteristic
9#13069497C211yesmaximal, characteristic
10#13069306C211yesmaximal, characteristic, complemented
11#13069306C211yesmaximal, characteristic, complemented
12#13069299C211yesmaximal, characteristic
13#13068949C211yesmaximal, characteristic
14#13068873C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66949—21no—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622607—21no—
39#10622597—21no—
40#10622594—21no—
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622323—24no—
50#10622294—24no—
51#10622286—21no—
52#10622281—21no—
53#10622273—21no—
54#10622268—21no—
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314—41no—
99#66949—44no—
100C4×D44—22no—
101C4×D44—41no—
102#66922—22no—
103#66922—22no—
104#66922—41no—
105#66922—41no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×C4⋊C8—22no—
109C11×#97—22no—
110C11×#97—22no—
111C4×C8×C11—22no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66885—22no—
124#66885—22no—
125#66882—22no—
126#66882—41no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880D414yes—
133#26836—111nomaximal, Sylow
134C23×D11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44#4112yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×Dic22—81no—
172C2×Dic22C2×D412yes—
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—
184C2×C8×C11#4112yes—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—81no—
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⋊Dic11—21no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11C2×D412yes—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215C4×Dic11—42no—
216#4314—28no—
217#4314—44no—
218C2×#487—111no—
219C2×#440—111no—
220#2452—111no—
221#2446—111no—
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#1771D1111yescharacteristic, complemented
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
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×C11AGL(1,ℤ/8)12yes—
258C2×C4×C11#13712yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
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—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290C4×D11—84no—
291Dic22—22no—
292Dic22—22no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—84no—
300C8×C11—22no—
301C8×C11—22no—
302C8×C11—22no—
303C8×C11—41no—
304C22×SD16—111no—
305C22×SD16—111no—
306C2×C4⋊Q8—111no—
307C2×C4⋊Q8—111no—
308C2×C22⋊Q8—221no—
309C2×C4×Q8—111no—
310C2×C4×D4—111no—
311#487—224no—
312#440—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
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×#97C2×D1111yescharacteristic
325C2×#97C2×D1111yescharacteristic
326C2×C4×C8C2×D1111yescharacteristic
327#400—221no—
328#398—221no—
329#396—221no—
330#393—221no—
331#391—111no—
332#391—111no—
333#391—111no—
334#390—111no—
335#390—111no—
336#389—111no—
337#389—111no—
338#389—111no—
339#387—221no—
340#387—221no—
341#385—221no—
342C4×C4⋊C4C2×D1111yescharacteristic
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336C2×D1111yescharacteristic
348#336C2×D1111yescharacteristic
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—41no—
368C4×C11—41no—
369C4×C11#52511yescharacteristic
370C4×C11#54211yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55111yescharacteristic
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×Q8—111no—
382C22×Q8—221no—
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×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8—222no—
396C4⋊Q8—222no—
397C4⋊Q8—441no—
398C4⋊Q8—441no—
399C22⋊Q8—444no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4D4411yescharacteristic
417C2×C4⋊C4D4411yescharacteristic
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427#107—222no—
428#107—441no—
429C4⋊C8—22no—
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—22no—
439#97—22no—
440C4×C8—22no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95D4411yescharacteristic
451#95D4411yescharacteristic
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—112no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—881no—
476C2×D4—112no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C2×D4411yescharacteristic
496C22×C4C2×D4411yescharacteristic
497C22×C4C2×D4411yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—228no—
500SD16—444no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8#433912yes—
511C2×C8#433912yes—
512C2×C8D4×D1112yes—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—442no—
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—442no—
544C11#2683611yescharacteristic, complemented, Sylow
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C22×D4411yescharacteristic
553Q8—222no—
554Q8—222no—
555Q8—441no—
556Q8—441no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
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—21no—
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—222no—
583C2×C4—222no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
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#6696112yes—
605C2×C4#6696212yes—
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4#6704011yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704211yescharacteristic
612C8—22no—
613C8—22no—
614C8—22no—
615C8—41no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22#1062300811yescharacteristic
624C22D4×D4411yescharacteristic
625C22#1062310711yescharacteristic
626C22C2×#6696111yescharacteristic
627C22C2×#6696211yescharacteristic
628C22#1062328211yescharacteristic
629C22#1062328411yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—442no—
637C4—442no—
638C4—881no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062303811yescharacteristic
644C4#1062305811yescharacteristic
645C4#1062307811yescharacteristic
646C4#1062311311yescharacteristic
647C2—882no—
648C2#1307258311yescharacteristic
649C2#1307928411yescharacteristic
650C2#1307933411yescharacteristic
651C2#1308011611yescharacteristic
652C2#1308019111yescharacteristic
653C2#1308133611yescharacteristic
654C2#1308139911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1771C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1771D11
hypocenterC11#26836
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
4. #13072392C2semidirect
5. #13070010C2semidirect
6. #13069945C2semidirect
10. #13069306C2semidirect
11. #13069306C2semidirect
14. #13068873C2semidirect
15. C11×#1771C2semidirect
232. #1771D11semidirect
544. C11#26836semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106223232
#130724662
#130723922
#130700102
#130699452
#130699342
#130697012
#130694972
#130693062
#130692992
#130689492
#130688732
C11×#17712
#2683611