Finite Group Databasebeta

← #14776267

Subgroups — #14776267

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622795C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic
3#13071670C211yesmaximal, characteristic
4#13071534C211yesmaximal, characteristic
5#13069434C211yesmaximal, characteristic
6#13069381C211yesmaximal, characteristic
7#13069303C211yesmaximal, characteristic
8#13069292C211yesmaximal, characteristic
9#13068959C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic
11#13068884C211yesmaximal, characteristic
12#13068867C211yesmaximal, characteristic
13#13068490C211yesmaximal, characteristic
14#13068448C211yesmaximal, characteristic
15C2×C4×C11×Q16C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C4×C11×Q16—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622795C418yescomplemented
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622591—21no—
40#10622590—21no—
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586—21no—
44#10622586C2211yescharacteristic
45#10622585—21no—
46C2×#66874C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48#10622546—21no—
49C4×Dic11⋊C4—21no—
50C4×Dic11⋊C4—21no—
51C4×Dic11⋊C4C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541—21no—
54#10622541C2211yescharacteristic
55#10622402—24no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11—41no—
73C4×Q8×C11—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83Q8×Dic11—41no—
84Q8×Dic11C2×C414yes—
85#66997—22no—
86#66997C2×C414yes—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326C2×C414yes—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66940—22no—
111#66940—41no—
112C11×#107—22no—
113C11×#103—22no—
114C11×#103D414yes—
115C4×C8×C11—22no—
116#66899—22no—
117#66899—41no—
118#66899C2×C414yes—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66880—22no—
131#66880C2×C414yes—
132#66879—22no—
133#66879—22no—
134Dic11⋊C8C2×C414yes—
135#66874—41no—
136#66872—22no—
137#23014—111nomaximal, Sylow
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×C11C22×C412yes—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11#4112yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C11×Q16—28no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C22×C412yes—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C2×D412yes—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—42no—
187C42×C11—42no—
188#4326—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11C22×C412yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—22no—
200Dic11⋊C4—41no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—24no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11C22×C412yes—
211C4×Dic11#4112yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×#462—111no—
219C2×#441—111no—
220C2×C4×Q16D1111yescharacteristic
221#2365—111no—
222#2351—111no—
223#1960—111no—
224#1949—111no—
225#1935—111no—
226#1933—111no—
227#1878—111no—
228#1878—111no—
229#1865—111no—
230#1863—111no—
231#1771—111no—
232#1763—111no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11C4×D414yes—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
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#13712yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
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—41no—
287C2×Dic11—41no—
288C2×Dic11C4×D412yes—
289C2×Dic11C4×D412yes—
290Dic22—22no—
291Dic22—22no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—22no—
295C8×C11—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16—111no—
299C22×Q16C2×D1111yescharacteristic
300C2×C4⋊Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×C4×Q8C2×D1111yescharacteristic
306#462—118no—
307#441—224no—
308C4×Q16—24no—
309C2×#107C2×D1111yescharacteristic
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8C2×D1111yescharacteristic
323#391—111no—
324#391—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389—221no—
330#387—221no—
331#387—221no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—221no—
337C4×C4⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57811yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—24no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11C2×C4×D411yescharacteristic
358C4×C11#52011yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—22no—
362Dic11—22no—
363Dic11—42no—
364Dic11—42no—
365Dic11—41no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—111no—
370C22×Q8C22×D1111yescharacteristic
371C22×Q8C22×D1111yescharacteristic
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—114no—
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16C4×D1114yes—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—114no—
383C4⋊Q8—222no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×Q8—114no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—22no—
420#106—222no—
421C4⋊C8—114no—
422#103—22no—
423#103—114no—
424#103—114no—
425#103—222no—
426#103—222no—
427#103—441no—
428#103—441no—
429#103C22⋊D1114yes—
430#97—222no—
431#97—222no—
432C4×C8—22no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#236111yescharacteristic
445C2×C11C4×#13711yescharacteristic
446C2×C11#295011yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327011yescharacteristic
449C2×C11#337411yescharacteristic
450C2×C11#337711yescharacteristic
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—112no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8C2×C4×D1112yes—
466C2×Q8C2×C4×D1112yes—
467C2×Q8#433912yes—
468C2×Q8C2×C22⋊D1112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484Q16—28no—
485Q16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—112no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8C2×C4×D1112yes—
497C2×C8C2×C22⋊D1112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—112no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—224no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—441no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4C2×C22⋊D1112yes—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—42no—
523C42—112no—
524C42—112no—
525C42—224no—
526C42—221no—
527C42—221no—
528C42—442no—
529C42—442no—
530C42—442no—
531C11#2301411yescharacteristic, complemented, Sylow
532C23C2×D4×D1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540Q8—222no—
541Q8—222no—
542Q8—441no—
543Q8—441no—
544Q8C4×C22⋊D1114yes—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4#6697112yes—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704311yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—22no—
594C8—22no—
595C8—222no—
596C8—441no—
597C22C4×D4×D1111yescharacteristic
598C22#1062308311yescharacteristic
599C22C2×#6697111yescharacteristic
600C22#1062329711yescharacteristic
601C22#1062329911yescharacteristic
602C22#1062330211yescharacteristic
603C22D4×C22⋊D1111yescharacteristic
604C4—24no—
605C4—22no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—222no—
611C4—222no—
612C4—442no—
613C4—441no—
614C4—441no—
615C4—442no—
616C4—881no—
617C4—881no—
618C4#1062307111yescharacteristic
619C4#1062307711yescharacteristic
620C4C2×C4×C22⋊D1111yescharacteristic
621C4#1062335511yescharacteristic
622C2#1307163311yescharacteristic
623C2C4×#6697111yescharacteristic
624C2#1307747911yescharacteristic
625C2#1308017111yescharacteristic
626C2#1308018611yescharacteristic
627C2#1308141711yescharacteristic
628C2#1308145411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11#23014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
33. #10622795C4semidirect
531. C11#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#106227952
C2×#106224022
#130716702
#130715342
#130694342
#130693812
#130693032
#130692922
#130689592
#130689572
#130688842
#130688672
#130684902
#130684482
C2×C4×C11×Q162
#2301411