Finite Group Databasebeta

← #14813945

Subgroups — #14813945

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622644C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic
3#13072392C211yesmaximal, characteristic
4#13070155C211yesmaximal, characteristic
5#13070112C211yesmaximal, characteristic
6#13070025C211yesmaximal, characteristic
7#13069862C211yesmaximal, characteristic
8#13069291C211yesmaximal, characteristic
9#13069175C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic
11#13068957C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic
14#13068869C211yesmaximal, characteristic
15Q8×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#389—21no—
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#384—21no—
28C11×#384C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622644—24no—
34C4×#4326—24no—
35#10622597—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622273—21no—
52#10622268—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
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⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4326—22no—
89C2×#4326—22no—
90C2×#4326—22no—
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326D414yes—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66922—22no—
106#66922—41no—
107C4×Dic22—22no—
108C4×Dic22—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66899—22no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874—22no—
126#66874—22no—
127#66874—41no—
128#66871—22no—
129#66871—41no—
130C4⋊(C11⋊C8)—22no—
131C4×C11⋊C8—22no—
132#26171—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11#4112yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4Q1614yescomplemented
180C11×C4⋊C4#4112yes—
181C42×C11—24no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C42×C11—42no—
190#4326—28no—
191#4326—44no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
213C2×#462—111no—
214C2×C4×Q16—111no—
215#2446—111no—
216Q8×C4⋊C4D1111yescharacteristic
217#2095—111no—
218#2087—111no—
219#2072—111no—
220#2043—111no—
221#1933—111no—
222#1916—111no—
223#1878—111no—
224#1878—111no—
225#1878—111no—
226#1863—111no—
227#1863—111no—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11#12314yes—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
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—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C2×Q1612yes—
261C2×C4×C11C2×Q1612yes—
262C2×C4×C11C2×Q1612yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—22no—
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—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C22×Q16—111no—
294C22×Q16—111no—
295C2×C4⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8C2×D1111yescharacteristic
298C2×C4×Q8C2×D1111yescharacteristic
299C2×C4×Q8C2×D1111yescharacteristic
300#462—224no—
301C4×Q16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×C4⋊C8—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×C4×C8—111no—
314#400—221no—
315#398—221no—
316#391—111no—
317#391—111no—
318#391—111no—
319#389—21no—
320#389—21no—
321#389—111no—
322#389C2×D1111yescharacteristic
323#389C2×D1111yescharacteristic
324#387—221no—
325#387—221no—
326#384—21no—
327#384C2×D1111yescharacteristic
328C4×C4⋊C4—21no—
329C4×C4⋊C4C2×D1111yescharacteristic
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338C22×C11#52511yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54811yescharacteristic
341C22×C11C22×Q1611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57811yescharacteristic
345C4×C11—22no—
346C4×C11—24no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C2×#12311yescharacteristic
356C4×C11#53911yescharacteristic
357C4×C11#54711yescharacteristic
358C4×C11#55311yescharacteristic
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C22×Q8—111no—
365C22×Q8C22×D1111yescharacteristic
366C2×Q16—114no—
367C2×Q16—222no—
368C2×Q16—222no—
369C2×Q16—222no—
370C2×Q16—222no—
371C2×Q16—222no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C4⋊Q8—222no—
377C4⋊Q8—441no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×Q8—41no—
384C4×Q8—222no—
385C4×Q8—441no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22⋊D1111yescharacteristic
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—441no—
413C4⋊C8—222no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422C4×C8—222no—
423#95—21no—
424#95—21no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95C22⋊D1111yescharacteristic
433#95C22⋊D1111yescharacteristic
434C2×C11#244311yescharacteristic
435C2×C11#310411yescharacteristic
436C2×C11#312011yescharacteristic
437C2×C11#327111yescharacteristic
438C2×C11D4×Q1611yescharacteristic
439C2×C11#336311yescharacteristic
440C2×C11#337711yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—112no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8#433912yes—
457C2×Q8D4×D1112yes—
458C2×Q8#434312yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474Q16—228no—
475Q16—444no—
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4#432614yescomplemented
510C4⋊C4#433912yes—
511C42—24no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—42no—
520C42—442no—
521C11#2617111yescharacteristic, complemented, Sylow
522C23C22×C22⋊D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—222no—
527Q8—222no—
528Q8—441no—
529Q8—441no—
530Q8—441no—
531Q8—441no—
532Q8—441no—
533Q8—441no—
534Q8#6694714yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—222no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4C2×#432612yes—
575C2×C4C2×#432612yes—
576C2×C4C2×#432612yes—
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×#433911yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4#6703711yescharacteristic
581C2×C4C2×#434311yescharacteristic
582C2×C4#6704011yescharacteristic
583C8—222no—
584C8—441no—
585C8—441no—
586C8—441no—
587C22#1062332211yescharacteristic
588C22D4×C22⋊D1111yescharacteristic
589C22C22×#432611yescharacteristic
590C22#1062334811yescharacteristic
591C22#1062335311yescharacteristic
592C22#1062336711yescharacteristic
593C22#1062336911yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—24no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4C2×#6694711yescharacteristic
609C4#1062303811yescharacteristic
610C4#1062304511yescharacteristic
611C4#1062304611yescharacteristic
612C2#1307235111yescharacteristic
613C2#1307865511yescharacteristic
614C2#1307883011yescharacteristic
615C2#1308019711yescharacteristic
616C2D4×#432611yescharacteristic
617C2#1308129411yescharacteristic
618C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socle, prime radicalC23×C11C22×D4
hypercenterQ8×C4⋊C4D11
hypocenterC11#26171
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
179. C11×C4⋊C4Q16semidirect
509. C4⋊C4#4326semidirect
521. C11#26171semidirect

Maximal subgroups

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

subgroupindex
C2×#106226442
C2×C4×#43262
#130723922
#130701552
#130701122
#130700252
#130698622
#130692912
#130691752
#130689572
#130688702
#130688692
Q8×C11×C4⋊C42
#2617111