Finite Group Databasebeta

← #14816780

Subgroups — #14816780

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622371C211yesmaximal, characteristic
2#13072451C211yesmaximal, characteristic, complemented
3#13071521C211yesmaximal, characteristic
4#13070161C211yesmaximal, characteristic, complemented
5#13070100C211yesmaximal, characteristic, complemented
6#13070010C211yesmaximal, characteristic, complemented
7#13069946C211yesmaximal, characteristic, complemented
8#13069347C211yesmaximal, characteristic, complemented
9#13069170C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic
11#13068948C211yesmaximal, characteristic
12#13068875C211yesmaximal, characteristic
13#13068867C211yesmaximal, characteristic, complemented
14#13068865C211yesmaximal, characteristic
15C2×C11×#474C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C11×#474—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843—21no—
29#10622842—21no—
30C2×#66896C2211yescharacteristic
31#10622823—21no—
32C2×C11⋊#95—21no—
33C2×#66882C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622597—21no—
39#10622591—21no—
40#10622590C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622559—21no—
48#10622555—21no—
49C4×Dic11⋊C4C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622371—24no—
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—41no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—41no—
85C2×#4324—22no—
86C2×#4324—22no—
87C2×#4324Q814yescomplemented
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4D411yescharacteristic
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66940—22no—
104#66940—41no—
105C11×#107—22no—
106C11×#107—22no—
107C11×C4⋊C8—22no—
108C11×#102—22no—
109C11×#102D414yes—
110#66896—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66882—22no—
124#66880—22no—
125#66880—22no—
126C8×Dic11—22no—
127#66874—41no—
128#66872—22no—
129#66872—41no—
130#26372—111nomaximal, Sylow
131C24×C11—21no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—81no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×Q812yes—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—81no—
158C22×Dic11—81no—
159C22×Dic11—81no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C2×Q812yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—42no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188#4324—28no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—81no—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—22no—
197Dic11⋊C4—22no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×Q812yes—
213C2×#474D1111yescharacteristic
214C2×C4×SD16—111no—
215#2451—111no—
216#2349—111no—
217#2097—111no—
218#2085—111no—
219#2068—111no—
220#2058—111no—
221#1942—111no—
222#1916—111no—
223#1877—111no—
224#1877—111no—
225#1864—111no—
226#1863—111no—
227#1862—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—84no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11C22⋊Q814yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—84no—
256C2×C4×C11#13512yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
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—84no—
287C2×Dic11—84no—
288C2×Dic11#13712yes—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293C8×C11—22no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×SD16—111no—
298C2×C4⋊Q8C2×D1111yescharacteristic
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4C2×D1111yescharacteristic
303#474—24no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107C2×D1111yescharacteristic
307C2×#107C2×D1111yescharacteristic
308C2×#106—111no—
309C2×#106—111no—
310C2×C4⋊C8C2×D1111yescharacteristic
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#102—111no—
315C2×#102C2×D1111yescharacteristic
316C2×#102C2×D1111yescharacteristic
317C2×C4×C8—111no—
318#398—221no—
319#395—221no—
320#391—111no—
321#391—111no—
322#391—221no—
323#389—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#387—221no—
328#385—221no—
329#385—221no—
330#382—111no—
331#380—221no—
332C4×C4⋊C4—111no—
333C2×#95—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11#52511yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11D4×Q811yescharacteristic
352C22×C11C2×#13511yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57611yescharacteristic
355C22×C11#57711yescharacteristic
356C4×C11—22no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11C2×C22⋊Q811yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#55411yescharacteristic
365Dic11—22no—
366Dic11—41no—
367Dic11—41no—
368Dic11—42no—
369Dic11—42no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—21no—
374C22×Q8—111no—
375C22×D4C22×D1111yescharacteristic
376C23×C4—21no—
377C23×C4—221no—
378C23×C4—221no—
379C2×SD16—114no—
380C2×SD16—222no—
381C2×SD16—222no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—22no—
387C4⋊Q8—41no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—22no—
391C4×D4—41no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—22no—
418#107—22no—
419#107—222no—
420#106—222no—
421#106—441no—
422C4⋊C8—22no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—22no—
427#102—222no—
428#102C22⋊D1114yes—
429C4×C8—222no—
430#95—111no—
431#95—111no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—44no—
443C2×C11#244911yescharacteristic
444C2×C11#310711yescharacteristic
445C2×C11#311811yescharacteristic
446C2×C11#326611yescharacteristic
447C2×C11#328011yescharacteristic
448C2×C11#338111yescharacteristic
449C2×C11#338511yescharacteristic
450C24—21no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8—112no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4Q8×D1112yes—
464C2×D4#434312yes—
465C2×D4C2×C22⋊D1112yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8C2×C22⋊D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—112no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4C2×C22⋊D1112yes—
522C22⋊C4—42no—
523C22⋊C4—224no—
524C22⋊C4—442no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C11#2637211yescharacteristic, complemented, Sylow
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×D4×D1111yescharacteristic
541Q8—84no—
542Q8—222no—
543Q8—222no—
544Q8—441no—
545Q8—441no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4#6699914yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—112no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4—884no—
591C2×C4#6696512yes—
592C2×C4#6703711yescharacteristic
593C2×C4C2×Q8×D1111yescharacteristic
594C2×C4C2×#434311yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—22no—
599C8—41no—
600C8—222no—
601C8—441no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22#1062315811yescharacteristic
610C22#1062316311yescharacteristic
611C22C2×#6696511yescharacteristic
612C22#1062328811yescharacteristic
613C22D11×#13711yescharacteristic
614C22#1062330911yescharacteristic
615C22D4×C22⋊D1111yescharacteristic
616C4—22no—
617C4—41no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—222no—
622C4—441no—
623C4—442no—
624C4—442no—
625C4—441no—
626C4—441no—
627C4—881no—
628C4—881no—
629C4#1062316711yescharacteristic
630C4#1062317611yescharacteristic
631C4C2×#6699911yescharacteristic
632C4#1062335511yescharacteristic
633C2—44no—
634C2#1307242111yescharacteristic
635C2#1307868911yescharacteristic
636C2#1307880711yescharacteristic
637C2#1308012011yescharacteristic
638C2#1308030111yescharacteristic
639C2#1308149511yescharacteristic
640C2#1308152111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11#26372
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. #13072451C2semidirect
4. #13070161C2semidirect
5. #13070100C2semidirect
6. #13070010C2semidirect
7. #13069946C2semidirect
8. #13069347C2semidirect
9. #13069170C2semidirect
13. #13068867C2semidirect
87. C2×#4324Q8semidirect
532. C11#26372semidirect

Maximal subgroups

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

subgroupindex
C2×#106223712
#130724512
#130715212
#130701612
#130701002
#130700102
#130699462
#130693472
#130691702
#130689502
#130689482
#130688752
#130688672
#130688652
C2×C11×#4742
#2637211