Finite Group Databasebeta

← #14925873

Subgroups — #14925873

Order 2816.

1948 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074108C214yesmaximal, complemented
2#13073986C211yesmaximal, characteristic, complemented
3#13073855C211yesmaximal, characteristic, complemented
4#13073619C211yesmaximal, characteristic
5#13073215C212yesmaximal, complemented
6#13073211C212yesmaximal, complemented
7#13072417C212yesmaximal, complemented
8#13072410C212yesmaximal, complemented
9#13071872C214yesmaximal, complemented
10#127×Dic11C211yesmaximal, characteristic
11#13071163C212yesmaximal, complemented
12#124×Dic11C212yesmaximal, complemented
13#13071078C212yesmaximal, complemented
14#13071078C212yesmaximal, complemented
15C4×Q8×Dic11C211yesmaximal, characteristic, complemented
16C4×#66940C211yesmaximal, characteristic, complemented
17C11×#2548C211yesmaximal, characteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66989C2212yes—
24C2×D4×Dic11C2212yes—
25C2×D4×Dic11C2212yes—
26C2×D4×Dic11C2212yes—
27C2×#66940C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×#66930C2214yes—
30C2×C4×Dic22C2211yescharacteristic
31C11×#394C2214yes—
32C11×#390C2212yes—
33C11×#390C2212yes—
34C11×#390C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36#10622843C2212yes—
37#10622835C2214yes—
38#10622834C2212yes—
39#10622834C2212yes—
40#10622834C2212yes—
41#10622834C2212yes—
42#10622834C2212yes—
43#10622834C2212yes—
44#10622597C2214yes—
45#10622590C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2211yescharacteristic
52#10622586C2212yes—
53#10622586C2212yes—
54#10622566C2214yes—
55#10622565C2214yes—
56#10622565C2214yes—
57#10622564C2214yes—
58#10622564C2214yes—
59#10622562C2214yes—
60#10622558C2214yes—
61#10622558C2214yes—
62#10622557C2214yes—
63#10622557C2214yes—
64#10622557C2214yes—
65#10622557C2214yes—
66C22⋊C4×Dic11C2214yes—
67C22⋊C4×Dic11C2214yes—
68C22⋊C4×Dic11C2214yes—
69#10622549C2212yes—
70#10622548C2211yescharacteristic
71C4×C4⋊Dic11C2212yes—
72C4×C4⋊Dic11C2211yescharacteristic
73C4×Dic11⋊C4C2212yes—
74C42×Dic11C2212yes—
75C42×Dic11C2212yes—
76C42×Dic11C2211yescharacteristic
77#10622542C2212yes—
78#10622541C2212yes—
79#10622541C2212yes—
80#10622273C2214yes—
81#10622262C2212yes—
82#10622262C2212yes—
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11C2312yes—
85C22×D4×C11C2312yes—
86C22×D4×C11C2312yes—
87C23×Dic11C2314yes—
88C22×Dic22C2311yescharacteristic
89C11×#127—24no—
90C11×#124—28no—
91C4×Q8×C11—24no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2314yes—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110Q8×Dic11—24no—
111Q8×Dic11—24no—
112#66989—28no—
113D4×Dic11—28no—
114D4×Dic11—28no—
115D4×Dic11—44no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66940—24no—
146#66940—24no—
147#66930—48no—
148C4×Dic22—24no—
149C11×#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2312yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161#34954—111nomaximal, Sylow
162C24×C11C2414yes—
163C2×Q8×C11—22no—
164C2×Q8×C11—22no—
165C2×Q8×C11#4114yes—
166C2×D4×C11—24no—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—24no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—28no—
183C22×Dic11—28no—
184C22×Dic11—28no—
185C22×Dic11C2412yes—
186C22×Dic11C2414yes—
187C22×Dic11C2412yes—
188C22×Dic11C2411yescharacteristic
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2411yescharacteristic
192C22×Dic11C2411yescharacteristic
193C22×Dic11C2411yescharacteristic
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22#4114yes—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C22⋊C4—28no—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—44no—
204C11×C22⋊C4—44no—
205C42×C11—24no—
206C42×C11—24no—
207C42×C11#4114yes—
208C22⋊Dic11—28no—
209C22⋊Dic11—28no—
210C22⋊Dic11—28no—
211C22⋊Dic11—28no—
212C22⋊Dic11—44no—
213C22⋊Dic11—44no—
214C22⋊Dic11—44no—
215C4⋊Dic11—24no—
216C4⋊Dic11—22no—
217C4⋊Dic11—24no—
218C4⋊Dic11—24no—
219C4⋊Dic11—24no—
220C4⋊Dic11—22no—
221C4⋊Dic11—22no—
222C4⋊Dic11—42no—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226Dic11⋊C4—44no—
227Dic11⋊C4—44no—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231C4×Dic11—24no—
232C4×Dic11—24no—
233C4×Dic11—22no—
234C4×Dic11—24no—
235C4×Dic11—22no—
236C4×Dic11—24no—
237C4×Dic11—24no—
238C4×Dic11—22no—
239C4×Dic11—41no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C4×Dic11#4114yes—
243C4×Dic11#4114yes—
244#2593—114no—
245#2582—111no—
246#2571—111no—
247#2548—111no—
248#2548D1111yescharacteristic
249#2513—112no—
250#2513—112no—
251#2448—112no—
252#2448—112no—
253#2395—114no—
254C4×#127—111no—
255C4×#124—112no—
256C4×#124—112no—
257#2293—112no—
258#2293—112no—
259C42×Q8—111no—
260C42×Q8—111no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11C2511yescharacteristic
269Q8×C11—28no—
270D4×C11—48no—
271D4×C11—48no—
272D4×C11—48no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11C2×#4114yes—
287C2×C4×C11C2×#4112yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4112yes—
290C2×C4×C11C2×#4112yes—
291C2×C4×C11C2×#4112yes—
292C2×C4×C11C2×#4112yes—
293C2×C4×C11C2×#4112yes—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—22no—
302C2×Dic11—21no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—21no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—416no—
316C2×Dic11C2×#4114yes—
317C2×Dic11C2×#4112yes—
318C2×Dic11C2×#4112yes—
319C2×Dic11C2×#4112yes—
320C2×Dic11C2×#4112yes—
321C2×Dic11H(5,𝔽2)12yes—
322Dic22—28no—
323C2×#127C2×D1111yescharacteristic
324C2×#124—112no—
325C2×#124C2×D1112yes—
326C2×C4×Q8—111no—
327C2×C4×Q8—111no—
328C2×C4×Q8—111no—
329C2×C4×Q8—111no—
330C2×C4×Q8—111no—
331C2×C4×Q8C2×D1111yescharacteristic
332C2×C4×D4—112no—
333C2×C4×D4—112no—
334C2×C4×D4—112no—
335C2×#117—114no—
336#400—114no—
337#399—114no—
338#398—114no—
339#397—114no—
340#397—114no—
341#397—114no—
342#394—114no—
343#394C2×D1114yes—
344#391—112no—
345#391—112no—
346#390—112no—
347#390—112no—
348#390—112no—
349#390—112no—
350#390—112no—
351#390—112no—
352#390C2×D1112yes—
353#390C2×D1112yes—
354#390C2×D1112yes—
355#389—112no—
356#389—112no—
357#389—112no—
358#389—112no—
359#388—114no—
360#388—114no—
361#388—114no—
362#388—114no—
363#388—114no—
364#388—114no—
365#388—114no—
366#388—114no—
367#384—111no—
368#382—112no—
369#382—112no—
370C4×C4⋊C4—112no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—111no—
373C4×C4⋊C4—111no—
374C4×C4⋊C4—111no—
375C4×C4⋊C4—111no—
376C4×C4⋊C4—111no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—112no—
379C4×C4⋊C4—112no—
380C4×C4⋊C4—112no—
381C4×C4⋊C4C2×D1111yescharacteristic
382C4×C22⋊C4—114no—
383C4×C22⋊C4—114no—
384C4×C22⋊C4—114no—
385C43—111no—
386C43—112no—
387C43—112no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11C22×#4111yescharacteristic
396C22×C11C22×#4111yescharacteristic
397C22×C11C22×#4111yescharacteristic
398C22×C11C22×#4111yescharacteristic
399C22×C11C22×#4111yescharacteristic
400C22×C11C2×H(5,𝔽2)11yescharacteristic
401C22×C11#58511yescharacteristic
402C4×C11—24no—
403C4×C11—22no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11#52914yes—
408C4×C11#52914yes—
409Dic11—24no—
410Dic11—22no—
411Dic11—22no—
412Dic11—42no—
413Dic11—44no—
414Dic11—42no—
415Dic11—41no—
416Dic11—42no—
417Dic11#55914yes—
418C22×Q8—111no—
419C22×Q8C22×D1111yescharacteristic
420C22×D4C22×D1112yes—
421C22×D4C22×D1112yes—
422C22×D4C22×D1112yes—
423C23×C4—114no—
424#127—24no—
425#124—28no—
426#124—228no—
427C4×Q8—24no—
428C4×Q8—224no—
429C4×Q8—224no—
430C4×Q8—224no—
431C4×Q8—224no—
432C4×Q8—224no—
433C4×D4—228no—
434C4×D4—228no—
435C4×D4—444no—
436#117—448no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C4⋊C4C22×D1112yes—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—114no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4C22×D1114yes—
462C2×C22⋊C4C22×D1114yes—
463C2×C22⋊C4C22×D1114yes—
464C2×C22⋊C4C22×D1114yes—
465C2×C42—111no—
466C2×C42—111no—
467C2×C42—112no—
468C2×C42—112no—
469C2×C42—111no—
470C2×C42—112no—
471C2×C42—112no—
472C2×C42—111no—
473C2×C42—111no—
474C2×C42—112no—
475C2×C42—112no—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—111no—
479C2×C42—112no—
480C2×C42—112no—
481C2×C42C22×D1112yes—
482C2×C42C22×D1112yes—
483C2×C42C22×D1111yescharacteristic
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—112no—
491#95—112no—
492#95—112no—
493#95—112no—
494#95—112no—
495#95C22×D1112yes—
496C2×C11—84no—
497C2×C11C2×#52911yescharacteristic
498C2×C11C2×#52911yescharacteristic
499C2×C11#346011yescharacteristic
500C2×C11C2×#55911yescharacteristic
501C2×C11#348011yescharacteristic
502C2×C11#348011yescharacteristic
503C2×C11#348311yescharacteristic
504C24C23×D1114yes—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—114no—
508C2×Q8—222no—
509C2×Q8—222no—
510C2×Q8#434114yes—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—42no—
519C2×D4—42no—
520C22×C4—111no—
521C22×C4—112no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—112no—
525C22×C4—114no—
526C22×C4—112no—
527C22×C4—111no—
528C22×C4—112no—
529C22×C4—228no—
530C22×C4—228no—
531C22×C4—228no—
532C22×C4C23×D1112yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1112yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539C4⋊C4—24no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—224no—
546C4⋊C4—224no—
547C4⋊C4—224no—
548C4⋊C4—222no—
549C4⋊C4—222no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—222no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—442no—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—228no—
561C22⋊C4—228no—
562C22⋊C4—228no—
563C22⋊C4—228no—
564C22⋊C4—444no—
565C22⋊C4—444no—
566C22⋊C4—444no—
567C42—24no—
568C42—24no—
569C42—114no—
570C42—114no—
571C42—224no—
572C42—224no—
573C42—222no—
574C42—224no—
575C42—224no—
576C42—224no—
577C42—224no—
578C42—222no—
579C42—224no—
580C42—222no—
581C42—224no—
582C42—441no—
583C42—442no—
584C42—442no—
585C42#434114yes—
586C11#3495411yescharacteristic, complemented, Sylow
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23C24×D1111yescharacteristic
595Q8—28no—
596Q8—228no—
597D4—48no—
598D4—48no—
599D4—48no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—114no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—221no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—221no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—221no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—224no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—4416no—
641C2×C4C2×#434114yes—
642C2×C4C2×#434112yes—
643C2×C4C2×#434112yes—
644C2×C4C2×#434112yes—
645C2×C4C2×#434112yes—
646C2×C4#41×D1112yes—
647C2×C4#41×D1112yes—
648C2×C4#41×D1112yes—
649C22—44no—
650C22—44no—
651C22—44no—
652C22—44no—
653C22—44no—
654C22—44no—
655C22—44no—
656C22C22×#434111yescharacteristic
657C22C22×#434111yescharacteristic
658C22C2×#41×D1111yescharacteristic
659C22C2×#41×D1111yescharacteristic
660C22C2×#41×D1111yescharacteristic
661C22D11×H(5,𝔽2)11yescharacteristic
662C22#1062345511yescharacteristic
663C4—24no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—114no—
669C4—224no—
670C4—222no—
671C4—222no—
672C4—444no—
673C4—442no—
674C4—442no—
675C4—441no—
676C4—442no—
677C4#1062313114yes—
678C4#1062321114yes—
679C2—84no—
680C2C2×#1062321111yescharacteristic
681C2C2×#1062313111yescharacteristic
682C2#1308202911yescharacteristic
683C2D11×#55911yescharacteristic
684C2#1308221211yescharacteristic
685C2#1308221511yescharacteristic
686C2#1308223911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2548C2
prime radicalC2×C11×#127C22
hypercenter#2548D11
hypocenterC11#34954
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #13074108C2semidirect
2. #13073986C2semidirect
3. #13073855C2semidirect
5. #13073215C2semidirect
6. #13073211C2semidirect
7. #13072417C2semidirect
8. #13072410C2semidirect
9. #13071872C2semidirect
11. #13071163C2semidirect
12. #124×Dic11C2semidirect
13. #13071078C2semidirect
14. #13071078C2semidirect
15. C4×Q8×Dic11C2semidirect
16. C4×#66940C2semidirect
586. C11#34954semidirect

Maximal subgroups

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

subgroupindex
#130741082
#130739862
#130738552
#130736192
#130732152
#130732112
#130724172
#130724102
#130718722
#127×Dic112
#130711632
#124×Dic112
#130710782
C4×Q8×Dic112
C4×#669402
C11×#25482
#3495411