Finite Group Databasebeta

← #14764166

Subgroups — #14764166

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622731C211yesmaximal, characteristic
2#13071018C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069387C211yesmaximal, characteristic, complemented
5#13069385C211yesmaximal, characteristic, complemented
6#13069383C211yesmaximal, characteristic, complemented
7#13069381C211yesmaximal, characteristic, complemented
8#13069378C211yesmaximal, characteristic, complemented
9#13069376C211yesmaximal, characteristic, complemented
10#13069373C211yesmaximal, characteristic, complemented
11#13069371C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic
13#13068647C211yesmaximal, characteristic
14#13068647C211yesmaximal, characteristic
15C11×#1809C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66930—21no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C11×#380C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25#10622825C2211yescharacteristic
26#10622731C418yescomplemented
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622590C2211yescharacteristic
35#10622589C2211yescharacteristic
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622556—21no—
46#10622555—21no—
47C22⋊C4×Dic11—21no—
48#10622264—21no—
49#10622263—21no—
50#10622262—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11D411yescharacteristic
62C23×Dic11D411yescharacteristic
63C2×C11×M16—41no—
64C2×C11×M16—41no—
65C2×C11×M16C2×C414yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2×C414yes—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11Q814yes—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318—41no—
95C2×#4318—41no—
96C2×#4318C2×C414yes—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66930—44no—
100C11×#107—41no—
101C11×#106—41no—
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66882—41no—
115#66881—41no—
116Dic11⋊C8C2×C414yes—
117Dic11⋊C8C2×C414yes—
118Dic11⋊C8C2×C414yes—
119Dic11⋊C8C2×C414yes—
120#66872—41no—
121#66872—41no—
122#66871—41no—
123#66871—41no—
124#21963—111nomaximal, Sylow
125C24×C11C2×D411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11C4⋊C414yes—
147C22×Dic11C4⋊C414yes—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C11×M16—44no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C22⋊Dic11—42no—
170C22⋊Dic11—42no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186C4×Dic11—42no—
187C4×Dic11C4⋊C414yes—
188C4×Dic11C4⋊C414yes—
189C4×Dic11C22×C412yes—
190C4×Dic11C22×C412yes—
191C4×Dic11C2×Q812yes—
192C4×Dic11C2×Q812yes—
193#4318—44no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C22×C412yes—
199C2×C11⋊C8C22×C412yes—
200C2×#423—111no—
201#2285—111no—
202#2283—111no—
203#1949—111no—
204#1949—111no—
205#1949—111no—
206#1949—111no—
207#1948—111no—
208#1948—111no—
209#1947—111no—
210#1947—111no—
211#1809—111no—
212#1809—111no—
213#1809—111no—
214#1809D1111yescharacteristic
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11C2×C4⋊C412yes—
222C23×C11C22×D411yescharacteristic
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C2×C4⋊C412yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×Q811yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—28no—
255C2×Dic11—44no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11C2×C4⋊C412yes—
269C2×Dic11C2×C4⋊C412yes—
270C2×Dic11C2×C4⋊C412yes—
271C2×Dic11C2×C4⋊C412yes—
272C2×Dic11AGL(1,ℤ/8)12yes—
273C2×Dic11#13712yes—
274C8×C11—22no—
275C8×C11—22no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C22×M16—111no—
279C22×M16C2×D1111yescharacteristic
280C2×#117—221no—
281C22×C42—111no—
282C2×#107—111no—
283C2×#107—111no—
284C2×#107—111no—
285C2×#107C2×D1111yescharacteristic
286C2×#106—111no—
287C2×#106—111no—
288C2×#106—111no—
289C2×#106C2×D1111yescharacteristic
290#423—118no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295#384—111no—
296#384—111no—
297#383—221no—
298#382—111no—
299#382—111no—
300#382—221no—
301#381—221no—
302#380—111no—
303#380—111no—
304#380—221no—
305#380C2×D1111yescharacteristic
306#380C2×D1111yescharacteristic
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—221no—
312C4×C22⋊C4—221no—
313#376—221no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C22×C4⋊C411yescharacteristic
330C22×C11#53711yescharacteristic
331C22×C11#53711yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57511yescharacteristic
335C22×C11#57511yescharacteristic
336C4×C11—22no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#51811yescharacteristic
342C4×C11#51911yescharacteristic
343C4×C11#54411yescharacteristic
344C4×C11#54411yescharacteristic
345Dic11—22no—
346Dic11—22no—
347Dic11—22no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352Dic11#42814yes—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4C22×D1111yescharacteristic
356C2×M16—41no—
357C2×M16—41no—
358C2×M16—114no—
359C2×M16—441no—
360C2×M16—441no—
361C2×M16C4×D1114yes—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366#117—444no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—114no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—114no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42—221no—
392C2×C42—221no—
393#107—41no—
394#107—441no—
395#107—441no—
396#107—441no—
397#106—41no—
398#106—441no—
399#106—441no—
400#106—441no—
401C4⋊C8—114no—
402C4⋊C8—114no—
403C4⋊C8—114no—
404C4⋊C8—114no—
405#95—21no—
406#95—21no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11—42no—
418C2×C11#231611yescharacteristic
419C2×C11C2×#42811yescharacteristic
420C2×C11#291111yescharacteristic
421C2×C11#325111yescharacteristic
422C2×C11#325111yescharacteristic
423C2×C11#325211yescharacteristic
424C2×C11#325211yescharacteristic
425C24D4×D1111yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—111no—
435C22×C4—114no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—114no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4C2×C4×D1112yes—
449C22×C4D4×D1111yescharacteristic
450C22×C4Q8×D1112yes—
451C22×C4C23×D1111yescharacteristic
452M16—44no—
453M16—444no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×C4×D1112yes—
465C2×C8C2×C4×D1112yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C42—114no—
491C42—114no—
492C42—112no—
493C42—112no—
494C42—112no—
495C42—112no—
496C42—442no—
497C42—442no—
498C42—442no—
499C42—442no—
500C11#2196311yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23C4⋊C4×D1112yes—
508C23C2×D4×D1111yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—228no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—444no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4C4⋊C4×D1112yes—
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#6703711yescharacteristic
557C2×C4C2×Q8×D1111yescharacteristic
558C2×C4#6704311yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—22no—
561C8—22no—
562C8—222no—
563C8—222no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C2×C4⋊C4×D1111yescharacteristic
572C22#1062312811yescharacteristic
573C22#1062312811yescharacteristic
574C22D11×AGL(1,ℤ/8)11yescharacteristic
575C22#1062330411yescharacteristic
576C22D11×#13711yescharacteristic
577C22#1062330811yescharacteristic
578C4—22no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—114no—
584C4—222no—
585C4—222no—
586C4—222no—
587C4—881no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062301711yescharacteristic
592C4#1062304711yescharacteristic
593C4#1062315411yescharacteristic
594C4#1062315411yescharacteristic
595C2—42no—
596C2#1307123311yescharacteristic
597C2D11×#42811yescharacteristic
598C2#1307720311yescharacteristic
599C2#1307997111yescharacteristic
600C2#1307997311yescharacteristic
601C2#1307998211yescharacteristic
602C2#1307998411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #13069387C2semidirect
5. #13069385C2semidirect
6. #13069383C2semidirect
7. #13069381C2semidirect
8. #13069378C2semidirect
9. #13069376C2semidirect
10. #13069373C2semidirect
11. #13069371C2semidirect
26. #10622731C4semidirect
500. C11#21963semidirect

Maximal subgroups

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

subgroupindex
C2×#106227312
#130710182
#130710112
#130693872
#130693852
#130693832
#130693812
#130693782
#130693762
#130693732
#130693712
#130686492
#130686472
C11×#18092
#2196311