Finite Group Databasebeta

← #14804215

Subgroups — #14804215

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079016C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic
4#13070064C211yesmaximal, characteristic, complemented
5#13070059C211yesmaximal, characteristic, complemented
6#13069912C211yesmaximal, characteristic, complemented
7#13069912C211yesmaximal, characteristic, complemented
8#13069608C211yesmaximal, characteristic, complemented
9#13069389C211yesmaximal, characteristic, complemented
10#13069133C211yesmaximal, characteristic, complemented
11#13069133C211yesmaximal, characteristic, complemented
12#13068678C211yesmaximal, characteristic, complemented
13#13068673C211yesmaximal, characteristic, complemented
14C4×#66900C211yesmaximal, characteristic, complemented
15C11×#3037C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C11×#464—21no—
24C11×#464—21no—
25C11×#462—21no—
26C11×#460—21no—
27C11×#423C2211yescharacteristic
28C11×#417C2211yescharacteristic
29C11×#417C2211yescharacteristic
30#10622847C2211yescharacteristic
31#10622847C2211yescharacteristic
32#10622845C2211yescharacteristic
33#10622845C2211yescharacteristic
34#10622845C2211yescharacteristic
35#10622845C2211yescharacteristic
36C2×#66900C2211yescharacteristic
37C2×#66900C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41C2×#66886C2211yescharacteristic
42#10622695—21no—
43#10622684—21no—
44#10622669—21no—
45#10622669—21no—
46#10622635—21no—
47#10622635—21no—
48#10622635—21no—
49#10622635—21no—
50#10622625—21no—
51#10622624—21no—
52#10622624—21no—
53D4×C11⋊C8—21no—
54C2×#66872C2211yescharacteristic
55C2×#66871C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57C4×#4318C2211yescharacteristic
58C4×#4318C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C11×#137—22no—
71C11×#137—22no—
72C11×#137—41no—
73C11×#137—41no—
74C2×C11×Q16—21no—
75C2×C11×Q16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C11×C4⋊Q8D411yescharacteristic
81C11×#127D411yescharacteristic
82C11×#124D411yescharacteristic
83C11×#124D411yescharacteristic
84C11×#121—21no—
85C11×#121—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#67001—22no—
97#67001—22no—
98#67001—41no—
99#67001—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318C2311yescharacteristic
107C2×#4318C2311yescharacteristic
108C2×#4318C2311yescharacteristic
109C2×#4318C2311yescharacteristic
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114#66923—21no—
115#66923—21no—
116#66923—21no—
117#66923—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#102—21no—
123C11×#102—21no—
124#66900—22no—
125#66900—22no—
126#66899—21no—
127#66899—21no—
128#66899—21no—
129#66899—21no—
130#66899—21no—
131#66899—21no—
132#66899—21no—
133#66899—21no—
134#66896—21no—
135#66896—21no—
136#66896—21no—
137#66896—21no—
138C22⋊(C11⋊C8)—21no—
139C22⋊(C11⋊C8)—21no—
140C22⋊(C11⋊C8)—21no—
141C22⋊(C11⋊C8)—21no—
142#66886—41no—
143#66886—41no—
144#66872—21no—
145#66872—21no—
146#66871—21no—
147#66871—21no—
148C4⋊(C11⋊C8)D411yescharacteristic
149C4⋊(C11⋊C8)D411yescharacteristic
150C4⋊(C11⋊C8)D411yescharacteristic
151C4⋊(C11⋊C8)D411yescharacteristic
152#66867—21no—
153#66867—21no—
154C4×C11⋊C8—21no—
155C4×C11⋊C8—21no—
156#25363—111nomaximal, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—21no—
163C11×#41—21no—
164C11×#41—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11C2×D411yescharacteristic
171C2×Q8×C11C2×D411yescharacteristic
172C2×Q8×C11#4112yes—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11C2×D411yescharacteristic
178C2×D4×C11C2×D411yescharacteristic
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11#4111yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C11×Q16—42no—
189C11×Q16—42no—
190C11×SD16—42no—
191C11×SD16—42no—
192C11×M16—21no—
193C11×M16—21no—
194C11×M16—21no—
195C11×M16—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C42×C11—41no—
209C42×C11—41no—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218Dic11⋊C4—41no—
219Dic11⋊C4—41no—
220Dic11⋊C4—41no—
221Dic11⋊C4—41no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—21no—
227#4318—21no—
228#4318—21no—
229#4318—42no—
230#4318—42no—
231#4318#4112yes—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—42no—
241C2×C11⋊C8—42no—
242C2×C11⋊C8C2×D411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
244C2×C11⋊C8C2×D411yescharacteristic
245C2×C11⋊C8C2×D411yescharacteristic
246#3142—111no—
247C2×#479—111no—
248#3037D1111yescharacteristic
249#2935—111no—
250#2079—111no—
251#2078—111no—
252#2052—111no—
253#2052—111no—
254#1998—111no—
255#1950—111no—
256#1908—111no—
257#1908—111no—
258#1816—111no—
259#1815—111no—
260C4×#101—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C2×#4111yescharacteristic
264Q8×C11—22no—
265Q8×C11—21no—
266Q8×C11—21no—
267Q8×C11—21no—
268Q8×C11—21no—
269Q8×C11—22no—
270Q8×C11—41no—
271Q8×C11—41no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—21no—
275D4×C11—21no—
276D4×C11—42no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—81no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—81no—
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11#12111yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—81no—
308C2×Dic11—81no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—21no—
312C11⋊C8—21no—
313C11⋊C8—21no—
314C11⋊C8—21no—
315C11⋊C8—22no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C2×#137C2×D1111yescharacteristic
320C2×#137C2×D1111yescharacteristic
321C2×#131—111no—
322C2×#131—111no—
323#532C2×D1111yescharacteristic
324C2×#125—111no—
325C2×C4×Q8C2×D1111yescharacteristic
326#491—221no—
327#490—221no—
328#488—221no—
329#488—221no—
330#479—221no—
331#479—221no—
332#479—221no—
333#479—221no—
334#464—21no—
335#464—21no—
336#462—21no—
337#460—21no—
338#436—221no—
339#435—221no—
340#435—221no—
341C8×D4—221no—
342C2×#108—111no—
343C2×#108—111no—
344C2×#107—111no—
345C2×#106—111no—
346#423C2×D1111yescharacteristic
347C2×C4⋊C8—111no—
348#417—111no—
349#417—111no—
350#417—111no—
351#417—111no—
352#417C2×D1111yescharacteristic
353#417C2×D1111yescharacteristic
354C2×#103—111no—
355C2×#103—111no—
356C2×#101—111no—
357C2×#101—111no—
358#408—111no—
359#408—111no—
360C4×M16—111no—
361C4×M16—111no—
362#343—111no—
363#343—111no—
364#343—111no—
365#343—111no—
366#343—111no—
367#343—111no—
368#341—111no—
369#341—111no—
370C22×C11—21no—
371C22×C11—21no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11C2×#12111yescharacteristic
379C22×C11#52911yescharacteristic
380C22×C11#54211yescharacteristic
381C4×C11—21no—
382C4×C11—21no—
383C4×C11—21no—
384C4×C11—21no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—42no—
388C4×C11—81no—
389C4×C11#54611yescharacteristic
390C4×C11#54611yescharacteristic
391C4×C11#54711yescharacteristic
392C4×C11#54811yescharacteristic
393Dic11—81no—
394Dic11—81no—
395C2×#41C22×D1111yescharacteristic
396C2×#41C22×D1111yescharacteristic
397C22×Q8C22×D1111yescharacteristic
398#137—22no—
399#137—22no—
400#137—41no—
401#137—41no—
402C2×Q16—21no—
403C2×Q16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406#131—222no—
407#131—222no—
408#131—441no—
409#131—441no—
410C2×M16—111no—
411C2×M16—111no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—221no—
415C2×M16—221no—
416C2×M16C22×D1111yescharacteristic
417C2×M16C22×D1111yescharacteristic
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—221no—
421C22×C8—221no—
422C4⋊Q8C22⋊D1111yescharacteristic
423#127C22⋊D1111yescharacteristic
424#125—221no—
425#125—221no—
426#125—221no—
427#125—221no—
428#124C22⋊D1111yescharacteristic
429#124C22⋊D1111yescharacteristic
430#121—21no—
431#121—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×D4—21no—
437C4×D4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C42—21no—
445C2×C42C22×D1111yescharacteristic
446#108—441no—
447#108—441no—
448#107—221no—
449#107—221no—
450#106—221no—
451#106—221no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—111no—
455C4⋊C8—111no—
456C4⋊C8—111no—
457C4⋊C8—111no—
458#103—21no—
459#103—21no—
460#103—221no—
461#103—221no—
462#103—221no—
463#103—221no—
464#103—221no—
465#103—221no—
466#103—221no—
467#103—221no—
468#102—21no—
469#102—21no—
470#102—221no—
471#102—221no—
472#102—221no—
473#102—221no—
474#101—222no—
475#101—222no—
476C22⋊C8—221no—
477C22⋊C8—221no—
478C22⋊C8—221no—
479C22⋊C8—221no—
480#97—221no—
481#97—221no—
482C4×C8—221no—
483C4×C8—221no—
484C2×C11—21no—
485C2×C11—21no—
486C2×C11—81no—
487C2×C11—81no—
488C2×C11#242711yescharacteristic
489C2×C11#306711yescharacteristic
490C2×C11#306911yescharacteristic
491#41—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8#434112yes—
505C2×Q8C2×C22⋊D1111yescharacteristic
506C2×Q8C2×C22⋊D1111yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×C22⋊D1111yescharacteristic
512C2×D4C2×C22⋊D1111yescharacteristic
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4#434111yescharacteristic
520C22×C4#434111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522Q16—42no—
523Q16—42no—
524SD16—42no—
525SD16—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—112no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—442no—
539M16—442no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—442no—
555C2×C8—442no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—441no—
567C4⋊C4—441no—
568C4⋊C4—441no—
569C4⋊C4—441no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C42—41no—
575C42—41no—
576C42D4×D1111yescharacteristic
577C42D4×D1111yescharacteristic
578C42C2×C22⋊D1111yescharacteristic
579C42C2×C22⋊D1111yescharacteristic
580C11#2536311yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23C2×#434111yescharacteristic
584Q8—22no—
585Q8—21no—
586Q8—21no—
587Q8—21no—
588Q8—21no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—21no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—42no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—81no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—81no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—881no—
618C2×C4—881no—
619C2×C4#6699211yescharacteristic
620C2×C4#6699211yescharacteristic
621C2×C4#6699211yescharacteristic
622C2×C4#6699211yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#6703711yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704311yescharacteristic
628C2×C4C22×C22⋊D1111yescharacteristic
629C8—41no—
630C8—41no—
631C8—221no—
632C8—221no—
633C8—221no—
634C8—221no—
635C8—222no—
636C8—441no—
637C8—441no—
638C8—441no—
639C22—21no—
640C22—21no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22#1062313111yescharacteristic
648C22#1062313411yescharacteristic
649C22C2×#6699211yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—41no—
655C4—41no—
656C4—42no—
657C4—81no—
658C4—881no—
659C4—881no—
660C4#1062312911yescharacteristic
661C4#1062314311yescharacteristic
662C4#1062333711yescharacteristic
663C4#1062335511yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2#1307219511yescharacteristic
669C2#1307833311yescharacteristic
670C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3037C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#25363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
4. #13070064C2semidirect
5. #13070059C2semidirect
6. #13069912C2semidirect
7. #13069912C2semidirect
8. #13069608C2semidirect
9. #13069389C2semidirect
10. #13069133C2semidirect
11. #13069133C2semidirect
12. #13068678C2semidirect
13. #13068673C2semidirect
14. C4×#66900C2semidirect
580. C11#25363semidirect

Maximal subgroups

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

subgroupindex
#130790162
C2×#106226352
#130773602
#130700642
#130700592
#130699122
#130696082
#130693892
#130691332
#130686782
#130686732
C4×#669002
C11×#30372
#2536311