Finite Group Databasebeta

← #14922691

Subgroups — #14922691

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic
3#13072489C212yesmaximal, complemented
4#13072478C212yesmaximal, complemented
5#13072467C212yesmaximal, complemented
6#13072456C212yesmaximal, complemented
7#13072442C214yesmaximal, complemented
8#13072427C214yesmaximal, complemented
9#13071892C214yesmaximal, complemented
10C4×#66949C214yesmaximal, complemented
11#13071104C211yesmaximal, characteristic
12#13071104C211yesmaximal, characteristic
13#13071098C211yesmaximal, characteristic, complemented
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C11×#2296C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C2×C4×C22⋊D11C2214yes—
21C2×#66979C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25#10623048—28no—
26C2×#66949C2214yes—
27C2×#66943C2212yes—
28C2×#66941C2212yes—
29C2×#66931C2214yes—
30C4×#4339—28no—
31C2×C4×D44C2212yes—
32C2×#66925C2212yes—
33C2×C42×D11C2212yes—
34C2×C4×Dic22C2214yes—
35C2×C4×Dic22C2212yes—
36C11×#389C2212yes—
37C11×#389C2212yes—
38C11×#385C2214yes—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2212yes—
41C2×C11⋊#95C2212yes—
42#10622607C2214yes—
43#10622605C2214yes—
44#10622602C2214yes—
45#10622601C2211yescharacteristic
46#10622601C2212yes—
47#10622601C2211yescharacteristic
48#10622594C2214yes—
49#10622593C2214yes—
50#10622592C2214yes—
51#10622587C2211yescharacteristic
52#10622587C2212yes—
53#10622587C2211yescharacteristic
54#10622586C2212yes—
55#10622586C2212yes—
56#10622585C2214yes—
57#10622571C2212yes—
58#10622571C2214yes—
59#10622571C2212yes—
60#10622559C2212yes—
61#10622559C2212yes—
62C4×(C2×D11)⋊C4C2214yes—
63C4×(C2×D11)⋊C4C2214yes—
64C4×Dic11⋊C4C2212yes—
65C4×Dic11⋊C4C2214yes—
66C4×Dic11⋊C4C2212yes—
67C4×Dic11⋊C4C2212yes—
68C4×Dic11⋊C4C2212yes—
69#10622289C2214yes—
70#10622286C2214yes—
71#10622281C2214yes—
72#10622280C2214yes—
73#10622271C2214yes—
74#10622270C2214yes—
75#10622265C2214yes—
76#10622259C2214yes—
77C23×C4×C11C2312yes—
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11C2312yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2312yes—
82C23×Dic11C2311yescharacteristic
83C2×#4339—24no—
84C2×#4339—24no—
85C2×#4339Q818yescomplemented
86C22×D44C2311yescharacteristic
87C22×C4×D11C2314yes—
88C22×C4×D11C2312yes—
89C22×Dic22C2314yes—
90C22×Dic22C2311yescharacteristic
91C11×#117—24no—
92C11×#117—24no—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C42×C11—24no—
101C2×C42×C11C2312yes—
102C2×C42×C11C2312yes—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2312yes—
106C2×C22⋊Dic11C2312yes—
107C4×C22⋊D11—216no—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113#66979D418yes—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4—28no—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2312yes—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135#66949—216no—
136#66943—28no—
137#66941—28no—
138#66931—216no—
139C4×D44—28no—
140#66925—28no—
141C42×D11—28no—
142C4×Dic22—28no—
143C4×Dic22—216no—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2312yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156#34745—111nomaximal, Sylow
157C24×C11C2411yescharacteristic
158C23×D11C2412yes—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×Q814yes—
164C22×C4×C11#4114yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11C2×Q818yes—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2414yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188#4339—232no—
189C2×D44—22no—
190C2×D44—22no—
191C2×D44C2×Q814yes—
192C2×C4×D11—28no—
193C2×C4×D11—24no—
194C2×C4×D11—24no—
195C2×C4×D11—28no—
196C2×C4×D11—44no—
197C2×C4×D11C2×Q818yes—
198C2×Dic22—28no—
199C2×Dic22—28no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—44no—
203C2×Dic22C2×Q814yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—44no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C42×C11—24no—
212C42×C11—24no—
213C42×C11—22no—
214C42×C11—22no—
215C42×C11—24no—
216C22⋊Dic11C2×D418yes—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—44no—
221(C2×D11)⋊C4—44no—
222C4⋊Dic11—28no—
223C4⋊Dic11C2×D418yes—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—28no—
227Dic11⋊C4—28no—
228Dic11⋊C4—24no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—44no—
232Dic11⋊C4#4118yescomplemented
233C4×Dic11—28no—
234C4×Dic11—24no—
235C4×Dic11—22no—
236C4×Dic11—22no—
237C4×Dic11—24no—
238C4×Dic11—24no—
239C4×Dic11C2×D418yes—
240C2×#533—111no—
241C2×C4×#41—111no—
242#2454—112no—
243#2453—112no—
244#2452—112no—
245#2451—112no—
246#2450—114no—
247#2449—114no—
248#2396—114no—
249C4×C22⋊Q8—114no—
250#2297—111no—
251#2297—111no—
252#2296—111no—
253#2296D1111yescharacteristic, complemented
254C2×C4×C4⋊C4—111no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11C22×D412yes—
258C23×C11C22×Q812yes—
259C23×C11C2×#4112yes—
260C23×C11C2511yescharacteristic
261C22×D11—22no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11—24no—
265C22×D11C22×Q814yes—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11—48no—
279C2×C4×C11C22⋊Q8116yescomplemented
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×Q812yes—
283C2×C4×C11C22×Q812yes—
284C2×C4×C11C2×#4112yes—
285C2×C4×C11C2×#4112yes—
286C2×C4×C11C2×#4114yes—
287C22⋊D11—216no—
288C2×Dic11—28no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—48no—
304C2×Dic11—44no—
305C2×Dic11C22×D418yes—
306C2×Dic11C22×Q814yes—
307C2×Dic11C2×#4114yes—
308C2×Dic11C2×#4114yes—
309D44—28no—
310C4×D11—216no—
311C4×D11—416no—
312Dic22—28no—
313Dic22—416no—
314C22×#41—111no—
315#533—228no—
316C2×C4⋊Q8—112no—
317C2×#125—112no—
318C2×C22⋊Q8—114no—
319C2×C22⋊Q8—114no—
320C4×#41—228no—
321C2×C4×Q8—114no—
322C2×C4×Q8—112no—
323C2×C4×D4—114no—
324C2×C4×D4—112no—
325C2×#117—111no—
326C2×#117—112no—
327C2×#117C2×D1111yescharacteristic
328C2×#117C2×D1111yescharacteristic
329C22×C4⋊C4—112no—
330C22×C42—111no—
331C22×C42—111no—
332C22×C42—112no—
333C22×C42C2×D1111yescharacteristic
334#400—114no—
335#399—114no—
336#398—114no—
337#398—114no—
338#396—114no—
339#396—114no—
340#395—114no—
341#393—114no—
342#391—111no—
343#391—112no—
344#391—111no—
345#391—114no—
346#390—111no—
347#390—112no—
348#390—111no—
349#389—114no—
350#389—112no—
351#389—112no—
352#389C2×D1112yes—
353#389C2×D1112yes—
354#387—114no—
355#387—114no—
356#386—112no—
357#386—114no—
358#386—112no—
359#385—114no—
360#385—112no—
361#385—112no—
362#385—114no—
363#385C2×D1114yes—
364#380—114no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—114no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—112no—
370C4×C4⋊C4C2×D1112yes—
371C4×C4⋊C4C2×D1112yes—
372C4×C22⋊C4—114no—
373C4×C22⋊C4—114no—
374C2×#95—112no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11C2×C22⋊Q814yes—
380C22×C11C23×D411yescharacteristic
381C22×C11C23×Q811yescharacteristic
382C22×C11C22×#4111yescharacteristic
383C22×C11C22×#4112yes—
384C22×C11#58512yes—
385C2×D11—24no—
386C2×D11—28no—
387C2×D11—42no—
388C2×D11—42no—
389C2×D11—44no—
390C4×C11—24no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—44no—
395C4×C11C2×C22⋊Q814yes—
396C4×C11C2×C22⋊Q814yes—
397Dic11—24no—
398Dic11—24no—
399Dic11—24no—
400Dic11—28no—
401Dic11—42no—
402Dic11—42no—
403C2×#41—118no—
404C2×#41—224no—
405C2×#41—224no—
406C22×Q8—111no—
407C22×Q8—114no—
408C22×D4—112no—
409C22×D4—111no—
410C23×C4—112no—
411C23×C4—111no—
412C23×C4—112no—
413C23×C4—111no—
414C23×C4—114no—
415C23×C4C22×D1112yes—
416C23×C4C22×D1111yescharacteristic
417C4⋊Q8—228no—
418#125—228no—
419C22⋊Q8—2216no—
420C22⋊Q8—2216no—
421C4×Q8—2216no—
422C4×Q8—228no—
423C4×D4—228no—
424C4×D4—2216no—
425#117—24no—
426#117—24no—
427#117—118no—
428#117—228no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—228no—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C4⋊C4C22×D1114yes—
445C2×C4⋊C4C22×D1114yes—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—114no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4C22×D1112yes—
453C2×C22⋊C4C22×D1112yes—
454C2×C42—24no—
455C2×C42—112no—
456C2×C42—114no—
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—112no—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—228no—
463C2×C42—224no—
464C2×C42—224no—
465C2×C42C22×D1112yes—
466C2×C42C22×D1111yescharacteristic
467C2×C42C22×D1112yes—
468C2×C42C22×D1112yes—
469C2×C42C22×D1111yescharacteristic
470#95—112no—
471#95—112no—
472#95—112no—
473#95—112no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95C22×D1114yes—
481#95C22×D1114yes—
482C2×C11—24no—
483C2×C11C22×C22⋊Q811yescharacteristic
484C2×C11#344411yescharacteristic
485C2×C11#345511yescharacteristic
486C2×C11D4×#4112yes—
487C2×C11Q8×#4112yes—
488D11—44no—
489C24—112no—
490C24C23×D1111yescharacteristic
491#41—2232no—
492C2×Q8—114no—
493C2×Q8—228no—
494C2×Q8—228no—
495C2×Q8—222no—
496C2×Q8—222no—
497C2×Q8—444no—
498C2×D4—118no—
499C2×D4—114no—
500C2×D4—224no—
501C2×D4—224no—
502C2×D4—222no—
503C2×D4—222no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—42no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—114no—
511C22×C4—118no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—228no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—222no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—222no—
521C22×C4—224no—
522C22×C4—228no—
523C22×C4—444no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4#433914yes—
527C22×C4D4×D1114yes—
528C22×C4Q8×D1114yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535C22×C4C23×D1111yescharacteristic
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—28no—
540C4⋊C4—44no—
541C4⋊C4—118no—
542C4⋊C4—118no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—228no—
546C4⋊C4—228no—
547C4⋊C4—228no—
548C4⋊C4—228no—
549C4⋊C4—228no—
550C4⋊C4—224no—
551C4⋊C4—444no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—118no—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—228no—
558C22⋊C4—444no—
559C22⋊C4—444no—
560C42—24no—
561C42—22no—
562C42—22no—
563C42—24no—
564C42—24no—
565C42—118no—
566C42—228no—
567C42—224no—
568C42—224no—
569C42—224no—
570C42—222no—
571C42—222no—
572C11#3474511yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—114no—
576C23—222no—
577C23—222no—
578C23—224no—
579C23—224no—
580C23C2×#433912yes—
581C23C2×D4×D1112yes—
582C23C2×Q8×D1112yes—
583C23C24×D1111yescharacteristic
584Q8—228no—
585Q8—4416no—
586D4—2216no—
587D4—228no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—48no—
601C2×C4—118no—
602C2×C4—114no—
603C2×C4—114no—
604C2×C4—114no—
605C2×C4—228no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—2216no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—4416no—
622C2×C4—448no—
623C2×C4—444no—
624C2×C4#66949116yescomplemented
625C2×C4C2×#433912yes—
626C2×C4C2×#433912yes—
627C2×C4C2×D4×D1112yes—
628C2×C4C2×D4×D1112yes—
629C2×C4C2×Q8×D1112yes—
630C2×C4C2×Q8×D1112yes—
631C2×C4#41×D1114yes—
632C22—22no—
633C22—24no—
634C22—22no—
635C22—24no—
636C22—228no—
637C22—224no—
638C22—442no—
639C22—442no—
640C22—444no—
641C22C2×#6694914yes—
642C22C22×#433911yescharacteristic
643C22C22×D4×D1111yescharacteristic
644C22C22×Q8×D1111yescharacteristic
645C22C2×#41×D1112yes—
646C22#1062345312yes—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—44no—
652C4—224no—
653C4—224no—
654C4—224no—
655C4—228no—
656C4—442no—
657C4—442no—
658C4C2×#6694914yes—
659C4C2×#6694914yes—
660C2—24no—
661C2—444no—
662C2C22×#6694911yescharacteristic
663C2#1308190911yescharacteristic
664C2#1308200111yescharacteristic
665C2#1308209912yes—
666C2#1308219412yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2296C2
prime radicalC22×#4339C22
hypercenter#2296D11
hypocenterC11#34745
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13072489C2semidirect
4. #13072478C2semidirect
5. #13072467C2semidirect
6. #13072456C2semidirect
7. #13072442C2semidirect
8. #13072427C2semidirect
9. #13071892C2semidirect
10. C4×#66949C2semidirect
13. #13071098C2semidirect
14. C2×C4×Dic11⋊C4C2semidirect
15. C11×#2296C2semidirect
85. C2×#4339Q8semidirect
232. Dic11⋊C4#41semidirect
253. #2296D11semidirect
279. C2×C4×C11C22⋊Q8semidirect
572. C11#34745semidirect
624. C2×C4#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×C4×#43392
#130724892
#130724782
#130724672
#130724562
#130724422
#130724272
#130718922
C4×#669492
#130711042
#130710982
C2×C4×Dic11⋊C42
C11×#22962
#3474511