Finite Group Databasebeta

← #14913221

Subgroups — #14913221

Order 2816.

3142 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2#13071585C212yesmaximal, complemented
3#13071555C214yesmaximal, complemented
4#13071525C212yesmaximal, complemented
5#13071493C211yesmaximal, characteristic, complemented
6#13071468C212yesmaximal, complemented
7#13071462C212yesmaximal, complemented
8C22⋊C4×D44C211yesmaximal, characteristic
9#13071436C211yesmaximal, characteristic
10#13071074C212yesmaximal, complemented
11#13071054C214yesmaximal, complemented
12#13071011C211yesmaximal, characteristic, complemented
13#13070998C212yesmaximal, complemented
14C4×#66946C212yesmaximal, complemented
15C4×#66930C211yesmaximal, characteristic, complemented
16C4×C22⋊C4×D11C212yesmaximal, complemented
17C11×#2345C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C23×C4×D11C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66946C4116yescomplemented
24C2×#66946C2212yes—
25C2×#66946C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×#66946C2212yes—
28C2×#66946C2212yes—
29C2×#66946C2211yescharacteristic
30C2×#66946C2211yescharacteristic
31C2×#66945C2214yescomplemented
32C2×C22⋊C4×D11C2212yes—
33C2×C22⋊C4×D11C2212yes—
34C2×#66930C2211yescharacteristic
35C2×#66930C2211yescharacteristic
36C2×C4×D44C2212yes—
37C2×C42×D11C2214yescomplemented
38C11×#389C2212yescomplemented
39C11×#387C2214yescomplemented
40C11×#380C2211yescharacteristic
41C11×#380C2212yes—
42C4×C11×C4⋊C4C2212yescomplemented
43C4×C11×C22⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4C2212yes—
45#10622825C2211yescharacteristic
46#10622825C2212yes—
47C4×C22⋊Dic11C2211yescharacteristic
48C4×C22⋊Dic11C2212yes—
49#10622603C2214yescomplemented
50#10622602C2214yescomplemented
51#10622601C2212yes—
52#10622600C2214yescomplemented
53#10622598C2212yescomplemented
54#10622594C2214yescomplemented
55#10622590C2212yescomplemented
56C4⋊C4×Dic11C2212yescomplemented
57C4⋊C4×Dic11C2212yescomplemented
58#10622568C2212yes—
59#10622568C2212yes—
60#10622556C2212yes—
61C22⋊C4×Dic11C2211yescharacteristic
62C22⋊C4×Dic11C2212yes—
63C22⋊C4×Dic11C2211yescharacteristic
64#10622553C2214yescomplemented
65#10622552C2212yes—
66C4×(C2×D11)⋊C4C2214yescomplemented
67C4×(C2×D11)⋊C4C2214yescomplemented
68C4×Dic11⋊C4C2212yescomplemented
69C42×Dic11C2212yescomplemented
70#10622283C2214yescomplemented
71#10622282C2214yescomplemented
72#10622281C2214yescomplemented
73#10622279C2214yescomplemented
74#10622279C2214yescomplemented
75#10622279C2214yescomplemented
76#10622278C2214yes—
77#10622278C2214yes—
78#10622277C2214yescomplemented
79D11×#95C2214yescomplemented
80#10622264C2212yescomplemented
81#10622262C2212yescomplemented
82#10622261C2212yescomplemented
83#10622261C2212yescomplemented
84C24×D11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×D44—28no—
90C22×D44C2×C418yes—
91C22×D44C2312yes—
92C22×D44C2311yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—48no—
95C22×C4×D11C2×C4116yescomplemented
96C22×C4×D11C2314yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C22×C4×D11C2312yes—
102C2×C11×C4⋊C4C2×C418yescomplemented
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2311yescharacteristic
111C2×C42×C11C2312yes—
112C2×C42×C11C2314yes—
113C2×C22⋊Dic11C2311yescharacteristic
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2311yescharacteristic
116C2×(C2×D11)⋊C4C2×C4116yescomplemented
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2314yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×C4×Dic11C2×C418yescomplemented
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143#66946—28no—
144#66946C2×C418yes—
145#66946C2×C418yes—
146#66946C2×C418yescomplemented
147#66946C2×C418yescomplemented
148#66946C2×C4116yescomplemented
149#66946C2×C4116yescomplemented
150#66945—48no—
151C22⋊C4×D11—28no—
152C22⋊C4×D11—28no—
153#66930—24no—
154#66930—24no—
155C4×D44—28no—
156C42×D11—48no—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170#34126—111nomaximal, Sylow
171C24×C11C2411yescharacteristic
172C23×D11—24no—
173C23×D11—24no—
174C23×D11—28no—
175C23×D11—44no—
176C23×D11C22×C418yes—
177C23×D11C2412yes—
178C23×D11C2412yes—
179C22×C4×C11—24no—
180C22×C4×C11—44no—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C22×C418yes—
183C22×C4×C11C2414yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—24no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11C22×C414yes—
194C22×Dic11C22×C414yes—
195C22×Dic11C2414yes—
196C22×Dic11C2412yes—
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2411yescharacteristic
199C22×Dic11C2411yescharacteristic
200C22×Dic11C2412yes—
201C22×Dic11C2411yescharacteristic
202C2×D44—232no—
203C2×D44—28no—
204C2×D44—24no—
205C2×D44C22×C418yes—
206C2×D44C22×C414yes—
207C2×D44C22×C414yes—
208C2×D44#4118yes—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—28no—
214C2×C4×D11—28no—
215C2×C4×D11—44no—
216C2×C4×D11—44no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—432no—
220C2×C4×D11C22×C418yes—
221C2×C4×D11C22×C418yes—
222C2×C4×D11C22×C418yes—
223C2×C4×D11C22×C418yes—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—44no—
226C11×C4⋊C4C22×C414yes—
227C11×C4⋊C4C22×C414yes—
228C11×C4⋊C4C22×C418yes—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4#4114yes—
232C42×C11—24no—
233C42×C11—44no—
234C22⋊Dic11—22no—
235C22⋊Dic11—24no—
236C22⋊Dic11#4114yes—
237(C2×D11)⋊C4—28no—
238(C2×D11)⋊C4—28no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4—44no—
243(C2×D11)⋊C4C22×C418yes—
244(C2×D11)⋊C4C22×C418yes—
245(C2×D11)⋊C4C22×C418yes—
246(C2×D11)⋊C4C22×C418yes—
247C4⋊Dic11—24no—
248C4⋊Dic11—44no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—28no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—24no—
257C4×Dic11—44no—
258C4×Dic11C22×C414yes—
259C4×Dic11C22×C414yes—
260C4×Dic11C22×C414yes—
261C4×Dic11C22×C414yes—
262C22×C4×D4—111no—
263#2357—112no—
264#2353—114no—
265#2349—112no—
266#2345—111no—
267#2345D1111yescharacteristic, complemented
268#2342—112no—
269#2342—112no—
270D4×C22⋊C4—111no—
271D4×C22⋊C4—111no—
272#2293—112no—
273#2290—114no—
274#2283—111no—
275#2280—112no—
276C42×D4—112no—
277C4×#117—111no—
278C2×C4×C22⋊C4—112no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11C23×C412yes—
282C23×C11C2×#4112yes—
283C23×C11C2×#4112yes—
284C23×C11C2511yescharacteristic
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—24no—
288C22×D11—216no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—216no—
294C22×D11—48no—
295C22×D11—416no—
296C22×D11—416no—
297C22×D11C23×C414yes—
298C22×D11C23×C414yes—
299C22×D11C2×#4118yes—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—28no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—48no—
313C2×C4×C11C23×C412yes—
314C2×C4×C11C23×C414yes—
315C2×C4×C11C23×C414yes—
316C2×C4×C11C23×C412yes—
317C2×C4×C11C2×#4114yes—
318C2×C4×C11C2×#4114yes—
319C2×Dic11—28no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—22no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—28no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11C23×C412yes—
335C2×Dic11C23×C412yes—
336C2×Dic11C23×C412yes—
337C2×Dic11C23×C412yes—
338C2×Dic11C2×#4114yes—
339C2×Dic11H(5,𝔽2)14yes—
340D44—216no—
341D44—28no—
342D44#117116yescomplemented
343C4×D11—216no—
344C4×D11—216no—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—416no—
348C4×D11—416no—
349C23×D4—111no—
350C24×C4—112no—
351C2×C4×D4—111no—
352C2×C4×D4—112no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—112no—
356C2×C4×D4—111no—
357C2×C4×D4—112no—
358C2×C4×D4—1116no—
359C2×C4×D4—112no—
360C2×#117—114no—
361C2×#117—111no—
362C2×#117—111no—
363C22×C4⋊C4C2×D1111yescharacteristic
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C22⋊C4—112no—
367C22×C42—111no—
368C22×C42—114no—
369#390—112no—
370#390—112no—
371#389—112no—
372#389C2×D1112yescomplemented
373#388—114no—
374#388—114no—
375#388—114no—
376#388—114no—
377#387—114no—
378#387C2×D1114yescomplemented
379#386—114no—
380#386—114no—
381#385—114no—
382#385—114no—
383#383—112no—
384#382—112no—
385#381—112no—
386#381—114no—
387#380—111no—
388#380—112no—
389#380—114no—
390#380C2×D1111yescharacteristic
391#380C2×D1112yes—
392#379—112no—
393#379—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4—112no—
398C4×C4⋊C4C2×D1112yescomplemented
399C4×C22⋊C4—111no—
400C4×C22⋊C4—112no—
401C4×C22⋊C4—111no—
402C4×C22⋊C4—112no—
403C4×C22⋊C4—111no—
404C4×C22⋊C4—114no—
405C4×C22⋊C4—114no—
406C4×C22⋊C4—114no—
407C4×C22⋊C4—114no—
408C4×C22⋊C4—114no—
409C4×C22⋊C4C2×D1111yescharacteristic
410C4×C22⋊C4C2×D1112yes—
411#376—112no—
412#376—112no—
413C2×#95—114no—
414C43—112no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11C4×#4114yes—
420C22×C11C24×C411yescharacteristic
421C22×C11C22×#4111yescharacteristic
422C22×C11C22×#4112yes—
423C22×C11C22×#4111yescharacteristic
424C22×C11C2×H(5,𝔽2)12yes—
425C2×D11—24no—
426C2×D11—24no—
427C2×D11—28no—
428C2×D11—28no—
429C2×D11—24no—
430C2×D11—24no—
431C2×D11—24no—
432C2×D11—432no—
433C2×D11—44no—
434C2×D11—44no—
435C2×D11C2×#11718yes—
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—24no—
439C4×C11—24no—
440C4×C11—42no—
441C4×C11—44no—
442C4×C11C2×#11714yes—
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—24no—
447Dic11—44no—
448Dic11—42no—
449Dic11#51814yes—
450C25—112no—
451C22×D4—118no—
452C22×D4—111no—
453C22×D4—112no—
454C22×D4—111no—
455C22×D4—228no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—112no—
459C23×C4—112no—
460C23×C4—1116no—
461C23×C4—112no—
462C23×C4—112no—
463C23×C4—114no—
464C23×C4—114no—
465C23×C4—448no—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1112yes—
468C4×D4—118no—
469C4×D4—118no—
470C4×D4—1116no—
471C4×D4—118no—
472C4×D4—1116no—
473C4×D4—118no—
474C4×D4—228no—
475C4×D4—228no—
476#117—224no—
477#117—224no—
478#117—448no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4C4×D1118yescomplemented
484C2×C4⋊C4C22×D1112yes—
485C2×C4⋊C4C22×D1114yes—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1112yes—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C22⋊C4—111no—
490C2×C22⋊C4—1116no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—114no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—228no—
504C2×C22⋊C4—228no—
505C2×C22⋊C4C22×D1112yes—
506C2×C22⋊C4C22×D1111yescharacteristic
507C2×C22⋊C4C22×D1111yescharacteristic
508C2×C42—118no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—111no—
513C2×C42—112no—
514C2×C42—112no—
515C2×C42—112no—
516C2×C42—114no—
517C2×C42—112no—
518C2×C42—112no—
519C2×C42—114no—
520C2×C42—448no—
521C2×C42C22×D1112yes—
522C2×C42C22×D1114yes—
523#95—112no—
524#95—114no—
525#95—114no—
526#95—112no—
527#95—112no—
528#95—112no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95C22×D1114yes—
533#95C22×D1112yes—
534#95C22×D1112yes—
535#95C22×D1114yes—
536C2×C11—24no—
537C2×C11C22×#11711yescharacteristic
538C2×C11C2×C4×#4111yescharacteristic
539C2×C11C2×#51811yescharacteristic
540C2×C11#348112yes—
541C2×C11#348112yes—
542D11—28no—
543D11—44no—
544C24—112no—
545C24—112no—
546C24—118no—
547C24—228no—
548C24—224no—
549C24—224no—
550C24—444no—
551C24C23×D1111yescharacteristic
552C2×D4—114no—
553C2×D4—118no—
554C2×D4—114no—
555C2×D4—118no—
556C2×D4—2232no—
557C2×D4—228no—
558C2×D4—224no—
559C22×C4—24no—
560C22×C4—44no—
561C22×C4—111no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—112no—
567C22×C4—111no—
568C22×C4—118no—
569C22×C4—118no—
570C22×C4—118no—
571C22×C4—118no—
572C22×C4—114no—
573C22×C4—112no—
574C22×C4—228no—
575C22×C4—228no—
576C22×C4—228no—
577C22×C4—228no—
578C22×C4—228no—
579C22×C4—224no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—228no—
583C22×C4—444no—
584C22×C4—444no—
585C22×C4—444no—
586C22×C4—444no—
587C22×C4—4432no—
588C22×C4C2×C4×D1114yes—
589C22×C4C2×C4×D1118yes—
590C22×C4C23×D1114yes—
591C22×C4C23×D1112yes—
592C22×C4C23×D1111yescharacteristic
593C22×C4C23×D1112yes—
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597C4⋊C4—24no—
598C4⋊C4—44no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4—224no—
602C4⋊C4—444no—
603C4⋊C4C2×C4×D1118yes—
604C4⋊C4C2×C4×D1114yes—
605C4⋊C4C2×C4×D1114yes—
606C22⋊C4—24no—
607C22⋊C4—22no—
608C22⋊C4—114no—
609C22⋊C4—118no—
610C22⋊C4—118no—
611C22⋊C4—118no—
612C22⋊C4—118no—
613C22⋊C4—228no—
614C22⋊C4—228no—
615C22⋊C4—228no—
616C22⋊C4—224no—
617C22⋊C4—222no—
618C22⋊C4—228no—
619C22⋊C4—444no—
620C22⋊C4—444no—
621C22⋊C4#434314yes—
622C42—24no—
623C42—44no—
624C42—114no—
625C42—114no—
626C42—114no—
627C42—114no—
628C42—224no—
629C42—228no—
630C42—224no—
631C42—224no—
632C42—224no—
633C42—224no—
634C42—444no—
635C11#3412611yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—114no—
639C23—118no—
640C23—114no—
641C23—2216no—
642C23—222no—
643C23—222no—
644C23—224no—
645C23—2216no—
646C23—222no—
647C23—222no—
648C23—224no—
649C23—224no—
650C23—448no—
651C23—4416no—
652C23—4416no—
653C23C22×C4×D1112yes—
654C23C2×#434312yes—
655C23#41×D1112yes—
656C23C24×D1111yescharacteristic
657D4—1116no—
658D4—2216no—
659D4—228no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—48no—
673C2×C4—112no—
674C2×C4—114no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—114no—
679C2×C4—2216no—
680C2×C4—2216no—
681C2×C4—228no—
682C2×C4—228no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—222no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—224no—
692C2×C4—222no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—448no—
697C2×C4—448no—
698C2×C4—4416no—
699C2×C4—4416no—
700C2×C4C22×C4×D1112yes—
701C2×C4C22×C4×D1114yes—
702C2×C4C22×C4×D1114yes—
703C2×C4C22×C4×D1112yes—
704C2×C4C2×#434314yes—
705C2×C4#41×D1114yes—
706C22—24no—
707C22—24no—
708C22—22no—
709C22—22no—
710C22—118no—
711C22—228no—
712C22—228no—
713C22—224no—
714C22—224no—
715C22—224no—
716C22—224no—
717C22—224no—
718C22—4432no—
719C22—444no—
720C22—444no—
721C22C4×#434314yes—
722C22C23×C4×D1111yescharacteristic
723C22C22×#434311yescharacteristic
724C22C2×#41×D1111yescharacteristic
725C22C2×#41×D1112yes—
726C22D11×H(5,𝔽2)12yes—
727C4—24no—
728C4—22no—
729C4—24no—
730C4—24no—
731C4—44no—
732C4—42no—
733C4—114no—
734C4—224no—
735C4—222no—
736C4—222no—
737C4—222no—
738C4—444no—
739C4—442no—
740C4D11×#11714yes—
741C2—24no—
742C2—228no—
743C2—444no—
744C2C2×D11×#11711yescharacteristic
745C2C2×C4×#434311yescharacteristic
746C2D11×#51811yescharacteristic
747C2#1308222312yes—
748C2#1308222712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2345C2
socle, cosocleC23×C11C25
prime radicalC23×D44C22
hypercenter#2345D11
hypocenterC11#34126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13071585C2semidirect
3. #13071555C2semidirect
4. #13071525C2semidirect
5. #13071493C2semidirect
6. #13071468C2semidirect
7. #13071462C2semidirect
10. #13071074C2semidirect
11. #13071054C2semidirect
12. #13071011C2semidirect
13. #13070998C2semidirect
14. C4×#66946C2semidirect
15. C4×#66930C2semidirect
16. C4×C22⋊C4×D11C2semidirect
17. C11×#2345C2semidirect
23. C2×#66946C4semidirect
31. C2×#66945C22semidirect
37. C2×C42×D11C22semidirect
38. C11×#389C22semidirect
39. C11×#387C22semidirect
42. C4×C11×C4⋊C4C22semidirect
49. #10622603C22semidirect
50. #10622602C22semidirect
52. #10622600C22semidirect
53. #10622598C22semidirect
54. #10622594C22semidirect
55. #10622590C22semidirect
56. C4⋊C4×Dic11C22semidirect
57. C4⋊C4×Dic11C22semidirect
64. #10622553C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. C42×Dic11C22semidirect
70. #10622283C22semidirect
71. #10622282C22semidirect
72. #10622281C22semidirect
73. #10622279C22semidirect
74. #10622279C22semidirect
75. #10622279C22semidirect
78. #10622277C22semidirect
79. D11×#95C22semidirect
80. #10622264C22semidirect
81. #10622262C22semidirect
82. #10622261C22semidirect
83. #10622261C22semidirect
95. C22×C4×D11C2×C4semidirect
102. C2×C11×C4⋊C4C2×C4semidirect
116. C2×(C2×D11)⋊C4C2×C4semidirect
131. C2×C4×Dic11C2×C4semidirect
146. #66946C2×C4semidirect
147. #66946C2×C4semidirect
148. #66946C2×C4semidirect
149. #66946C2×C4semidirect
267. #2345D11semidirect
342. D44#117semidirect
372. #389C2×D11semidirect
378. #387C2×D11semidirect
398. C4×C4⋊C4C2×D11semidirect
483. C2×C4⋊C4C4×D11semidirect
635. C11#34126semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
#130715852
#130715552
#130715252
#130714932
#130714682
#130714622
C22⋊C4×D442
#130714362
#130710742
#130710542
#130710112
#130709982
C4×#669462
C4×#669302
C4×C22⋊C4×D112
C11×#23452
#3412611