Finite Group Databasebeta

← #14816829

Subgroups — #14816829

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic
3#13072488C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic
5#13070098C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic
7#13069954C211yesmaximal, characteristic, complemented
8#13069341C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic
11#13068971C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic
15C11×#2351C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#389—21no—
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#382—21no—
27C11×#382C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C4×#4325—24no—
34#10622635—24no—
35#10622605—21no—
36#10622602—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622289—21no—
52#10622280—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
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⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325Q814yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×D44—22no—
106C4×D44—41no—
107#66923—22no—
108#66923—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66899—22no—
116#66899—22no—
117#66899D414yes—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66873—22no—
121#66873—22no—
122#66873—41no—
123#66872—22no—
124#66872—22no—
125#66872—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26375—111nomaximal, Sylow
131C23×D11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×Q812yes—
137C2×Q8×C11#4112yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C2×Q812yes—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4#4112yes—
174C42×C11—24no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—42no—
183#4325—28no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D412yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
210C2×C11⋊C8C2×Q812yes—
211C2×#479—111no—
212C2×C4×SD16—111no—
213#2454—111no—
214#2351D1111yescharacteristic, complemented
215#2092—111no—
216#2085—111no—
217#2065—111no—
218#2059—111no—
219#1941—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1865—111no—
224#1863—111no—
225#1862—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11C22⋊Q814yes—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
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×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11#13512yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q811yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—22no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—84no—
288C11⋊C8—22no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×SD16—111no—
293C2×#125—111no—
294C2×C4×Q8C2×D1111yescharacteristic
295C2×C4×Q8C2×D1111yescharacteristic
296C2×C4×Q8C2×D1111yescharacteristic
297C2×C4×D4—111no—
298#479—224no—
299C4×SD16—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C4×C8—111no—
313#399—221no—
314#396—221no—
315#390—111no—
316#390—111no—
317#389—21no—
318#389—21no—
319#389—111no—
320#389—111no—
321#389C2×D1111yescharacteristic
322#389C2×D1111yescharacteristic
323#385—221no—
324#382—21no—
325#382C2×D1111yescharacteristic
326#380—221no—
327C4×C4⋊C4—21no—
328C4×C4⋊C4C2×D1111yescharacteristic
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337C22×C11#52511yescharacteristic
338C22×C11D4211yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11C2×#13511yescharacteristic
341C22×C11#57511yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57711yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—24no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11C2×C22⋊Q811yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#55411yescharacteristic
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4—111no—
370C23×C4—221no—
371C2×SD16—114no—
372C2×SD16—222no—
373C2×SD16—222no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—111no—
378#125—222no—
379#125—441no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—41no—
385C4×Q8—41no—
386C4×D4—222no—
387C4×D4—441no—
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—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22⋊D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#107—441no—
418#106—222no—
419#106—222no—
420#106—222no—
421C4⋊C8—222no—
422#103—114no—
423#103—222no—
424#103—222no—
425#102—222no—
426#102—222no—
427#102—441no—
428C4×C8—222no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—221no—
434#95—221no—
435#95C22⋊D1111yescharacteristic
436#95C22⋊D1111yescharacteristic
437C2×C11#244911yescharacteristic
438C2×C11#310211yescharacteristic
439C2×C11#312611yescharacteristic
440C2×C11#327111yescharacteristic
441C2×C11#328211yescharacteristic
442C2×C11#338111yescharacteristic
443C2×C11#338811yescharacteristic
444D11—82no—
445C24—221no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8#433912yes—
450C2×Q8D4×D1112yes—
451C2×Q8Q8×D1112yes—
452C2×D4—112no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—881no—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476C2×C8—112no—
477C2×C8—112no—
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—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—112no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4#433912yes—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—24no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—42no—
525C11#2637511yescharacteristic, complemented, Sylow
526C23—222no—
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23C22×C22⋊D1111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8#6694914yes—
538D4—222no—
539D4—222no—
540D4—441no—
541D4—441no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—222no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—884no—
581C2×C4#6700312yes—
582C2×C4C2×#433911yescharacteristic
583C2×C4C2×#433911yescharacteristic
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4#6703711yescharacteristic
586C2×C4C2×Q8×D1111yescharacteristic
587C2×C4#6704011yescharacteristic
588C8—222no—
589C8—222no—
590C8—441no—
591C8—441no—
592C22—442no—
593C22—442no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22#1062332211yescharacteristic
600C22D4×C22⋊D1111yescharacteristic
601C22Q8×C22⋊D1111yescharacteristic
602C22C2×#6700311yescharacteristic
603C22#1062335311yescharacteristic
604C22#1062336811yescharacteristic
605C22#1062336811yescharacteristic
606C4—22no—
607C4—24no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—442no—
617C4—881no—
618C4—881no—
619C4#1062303811yescharacteristic
620C4C2×#6694911yescharacteristic
621C4#1062304211yescharacteristic
622C4#1062304611yescharacteristic
623C2—882no—
624C2#1307242511yescharacteristic
625C2#1307863411yescharacteristic
626C2#1307890711yescharacteristic
627C2#1308020211yescharacteristic
628C2#1308032411yescharacteristic
629C2#1308148711yescharacteristic
630C2#1308155511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2351D11
hypocenterC11#26375
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
5. #13070098C2semidirect
7. #13069954C2semidirect
8. #13069341C2semidirect
9. #13069175C2semidirect
12. #13068884C2semidirect
13. #13068870C2semidirect
15. C11×#2351C2semidirect
214. #2351D11semidirect
525. C11#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×C4×#43252
#130724882
#130701402
#130700982
#130699872
#130699542
#130693412
#130691752
#130689712
#130688842
#130688702
#130688622
C11×#23512
#2637511