Finite Group Databasebeta

← C4×#10623050 #14912932

Subgroups — C4×#10623050 #14912932

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2#13071364C212yesmaximal, complemented
3#13071360C212yesmaximal, complemented
4#13071357C212yesmaximal, complemented
5#13071353C212yesmaximal, complemented
6#13071344C214yesmaximal
7#13071239C211yesmaximal, characteristic
8#13071236C211yesmaximal, characteristic
9#13071232C211yesmaximal, characteristic
10C4×#66922C212yesmaximal, complemented
11C4×#66941C212yesmaximal, complemented
12C4×#66923C212yesmaximal, complemented
13C4×#66943C212yesmaximal, complemented
14C4×#66931C214yesmaximal
15C4×#66979C211yesmaximal, characteristic
16C2×C4×C4⋊Dic11C211yesmaximal, characteristic
17C4×C11×#117C211yesmaximal, characteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26#10623050C4116yesdirect product factor
27C2×#66943C2212yes—
28C2×#66941C2212yes—
29C2×#66931C2214yes—
30C2×#66923C2212yes—
31C2×#66922C2212yes—
32C2×C4×Dic22C2214yes—
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4C2212yes—
38C4×C11×C22⋊C4C2212yes—
39C11×#376C2212yes—
40C43×C11C2212yes—
41C4×C22⋊Dic11C2212yes—
42C4×C22⋊Dic11C2212yes—
43C2×C11⋊#95C2212yes—
44#10622598C2212yes—
45#10622598C2212yes—
46#10622590C2212yes—
47#10622589C2212yes—
48#10622586C2212yes—
49#10622586C2212yes—
50#10622563C2214yes—
51#10622559C2214yes—
52#10622555C2214yes—
53#10622549C2212yes—
54#10622548C2212yes—
55C4×C4⋊Dic11C2212yes—
56C4×C4⋊Dic11C2211yescharacteristic
57C4×C4⋊Dic11C2212yes—
58C4×C4⋊Dic11C2214yes—
59C4×C4⋊Dic11C2212yes—
60C4×C4⋊Dic11C2211yescharacteristic
61C4×C4⋊Dic11C2212yes—
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2211yescharacteristic
64#10622546C2214yes—
65#10622546C2214yes—
66#10622545C2212yes—
67C4×Dic11⋊C4C2214yes—
68C4×Dic11⋊C4C2214yes—
69C42×Dic11C2212yes—
70#10622542C2214yes—
71#10622541C2212yes—
72#10622541C2212yes—
73#10622541C2212yes—
74#10622541C2212yes—
75#10622541C2214yes—
76#10622268C2214yes—
77#10622268C2214yes—
78#10622267C2214yes—
79#10622267C2214yes—
80#10622260C2214yes—
81#10622260C2214yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×Dic11C2312yes—
88C23×Dic11C2312yes—
89C22×Dic22C2314yes—
90C11×#117—24no—
91C11×#117C2×C418yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11Q818yescomplemented
99C2×C42×C11C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2312yes—
103C2×C42×C11C2312yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2312yes—
111#66979—24no—
112#66979C2×C418yes—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2×C418yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2314yes—
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2312yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×C4×Dic11—44no—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141#66943C2×C4116yescomplemented
142#66941C2×C4116yescomplemented
143#66931C2×C4132yes—
144#66923C2×C4116yescomplemented
145#66922C2×C4116yescomplemented
146C4×Dic22—48no—
147C11×#95C2312yes—
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2312yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C4×#544—111nomaximal, Sylow
164C24×C11C2411yescharacteristic
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11C22×C414yes—
170C22×C4×C11C2×Q814yes—
171C22×C4×C11C2×Q814yes—
172C22×C4×C11C2×Q814yes—
173C22×C4×C11#4114yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—24no—
185C22×Dic11—42no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C22×Dic11—42no—
189C22×Dic11C22×C418yes—
190C22×Dic11C2412yes—
191C22×Dic11C2414yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C22×Dic11C2414yes—
196C2×Dic22—44no—
197C2×Dic22—44no—
198C2×Dic22C22×C4116yes—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C22×C414yes—
202C11×C4⋊C4C22×C414yes—
203C11×C22⋊C4—24no—
204C11×C22⋊C4C22×C418yes—
205C42×C11—24no—
206C42×C11—24no—
207C42×C11—24no—
208C42×C11—42no—
209C42×C11—42no—
210C42×C11C22×C418yes—
211C42×C11C2×Q814yes—
212C42×C11C2×Q814yes—
213C42×C11C2×Q814yes—
214C42×C11C2×Q814yes—
215C22⋊Dic11—24no—
216C22⋊Dic11C22×C418yes—
217C4⋊Dic11—24no—
218C4⋊Dic11—24no—
219C4⋊Dic11—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11—44no—
222C4⋊Dic11—44no—
223C4⋊Dic11C22×C414yes—
224C4⋊Dic11C22×C418yes—
225C4⋊Dic11C22×C4116yes—
226C4⋊Dic11C22×C414yes—
227C4⋊Dic11C22×C418yes—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4C22×C4116yes—
233Dic11⋊C4C22×C4116yes—
234C4×Dic11—24no—
235C4×Dic11—24no—
236C4×Dic11—28no—
237C4×Dic11—24no—
238C4×Dic11—44no—
239C4×Dic11—42no—
240C4×Dic11—42no—
241C4×Dic11C22×C418yes—
242C2×#544—111no—
243#2331—112no—
244#2331—112no—
245#2330—112no—
246#2330—112no—
247#2329—114no—
248#2317—111no—
249#2317—111no—
250#2316—111no—
251C4×C4⋊Q8—112no—
252C4×C4⋊Q8—112no—
253C4×#125—112no—
254C4×#125—112no—
255C4×C22⋊Q8—114no—
256C4×#117—111no—
257C4×#117D1111yescharacteristic
258C2×C4×C4⋊C4—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C23×C412yes—
264C23×C11C22×Q812yes—
265C23×C11C2×#4112yes—
266C23×C11C2511yescharacteristic
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—28no—
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—44no—
285C2×C4×C11C4×Q8116yescomplemented
286C2×C4×C11C23×C414yes—
287C2×C4×C11C23×C414yes—
288C2×C4×C11C23×C412yes—
289C2×C4×C11C23×C412yes—
290C2×C4×C11C22×Q812yes—
291C2×C4×C11C22×Q812yes—
292C2×C4×C11C22×Q812yes—
293C2×C4×C11C22×Q812yes—
294C2×C4×C11C22×Q812yes—
295C2×C4×C11C22×Q812yes—
296C2×C4×C11C2×#4112yes—
297C2×C4×C11C2×#4112yes—
298C2×C4×C11H(5,𝔽2)12yes—
299C2×C4×C112−1+412yes—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—48no—
316C2×Dic11—48no—
317C2×Dic11C23×C414yes—
318C2×Dic11C23×C414yes—
319C2×Dic11C23×C418yes—
320Dic22—416no—
321#544—1116no—
322C2×C4⋊Q8—112no—
323C2×C4⋊Q8—112no—
324C2×#125—112no—
325C2×#125—112no—
326C2×C22⋊Q8—114no—
327C2×C4×Q8—114no—
328C2×#117—111no—
329C2×#117—111no—
330C2×#117C2×D1111yescharacteristic
331C2×#117C2×D1111yescharacteristic
332C22×C4⋊C4—111no—
333C22×C4⋊C4—111no—
334C22×C42—112no—
335C22×C42C2×D1111yescharacteristic
336#391—114no—
337#391—114no—
338#391—114no—
339#389—112no—
340#389—112no—
341#389—112no—
342#389—112no—
343#389—112no—
344#389—112no—
345#389—112no—
346#389—112no—
347#389—114no—
348#389—114no—
349#389—114no—
350#387—114no—
351#387—114no—
352#387—114no—
353#387—114no—
354#387—114no—
355#387—114no—
356#385—114no—
357#385—114no—
358#384—112no—
359#384—112no—
360#382—112no—
361#382—112no—
362#380—114no—
363C4×C4⋊C4—114no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4—111no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—111no—
374C4×C4⋊C4C2×D1111yescharacteristic
375C4×C4⋊C4C2×D1111yescharacteristic
376C4×C4⋊C4C2×D1111yescharacteristic
377C4×C4⋊C4C2×D1111yescharacteristic
378C4×C22⋊C4—112no—
379C4×C22⋊C4—112no—
380C4×C22⋊C4C2×D1112yes—
381C4×C22⋊C4C2×D1112yes—
382#376—112no—
383#376C2×D1112yes—
384C2×#95—112no—
385C43—112no—
386C43C2×D1112yes—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11C2×C4×Q814yes—
394C22×C11C24×C411yescharacteristic
395C22×C11C23×Q811yescharacteristic
396C22×C11C22×#4111yescharacteristic
397C22×C11C2×H(5,𝔽2)11yescharacteristic
398C22×C11C2×2−1+411yescharacteristic
399C22×C11#58511yescharacteristic
400C22×C11#58511yescharacteristic
401C4×C11—24no—
402C4×C11—24no—
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11C2×C4×Q814yes—
409C4×C11C2×C4×Q814yes—
410C4×C11#54414yescomplemented
411Dic11—24no—
412Dic11—28no—
413Dic11—24no—
414Dic11—42no—
415Dic11—44no—
416Dic11—42no—
417C22×Q8—114no—
418C23×C4—112no—
419C23×C4—112no—
420C23×C4C22×D1111yescharacteristic
421C23×C4C22×D1111yescharacteristic
422C23×C4C22×D1111yescharacteristic
423C4⋊Q8—1116no—
424C4⋊Q8—1116no—
425#125—1116no—
426#125—1116no—
427C22⋊Q8—1132no—
428C4×Q8—448no—
429#117—24no—
430#117—118no—
431#117—224no—
432#117C4×D1118yes—
433C2×C4⋊C4—118no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C4⋊C4C22×D1111yescharacteristic
454C2×C4⋊C4C22×D1111yescharacteristic
455C2×C4⋊C4C22×D1111yescharacteristic
456C2×C22⋊C4—112no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4C22×D1112yes—
459C2×C22⋊C4C22×D1112yes—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—112no—
463C2×C42—114no—
464C2×C42—112no—
465C2×C42—112no—
466C2×C42—112no—
467C2×C42—114no—
468C2×C42—444no—
469C2×C42Dic2218yescomplemented
470C2×C42C22×D1112yes—
471C2×C42C22×D1112yes—
472C2×C42C22×D1112yes—
473C2×C42C22×D1112yes—
474C2×C42C22×D1112yes—
475C2×C42C22×D1111yescharacteristic
476C2×C42C22×D1111yescharacteristic
477C2×C42C22×D1111yescharacteristic
478C2×C42C22×D1111yescharacteristic
479C2×C42C22×D1112yes—
480#95—114no—
481#95—114no—
482#95—112no—
483#95—112no—
484#95—112no—
485#95—112no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95C22×D1112yes—
493#95C22×D1112yes—
494#95C22×D1112yes—
495#95C22×D1112yes—
496C2×C11—24no—
497C2×C11C22×C4×Q811yescharacteristic
498C2×C11C4×H(5,𝔽2)11yescharacteristic
499C2×C11C4×2−1+411yescharacteristic
500C2×C11C2×#54411yescharacteristic
501C2×C11#345811yescharacteristic
502C2×C11#346011yescharacteristic
503C2×C11#346111yescharacteristic
504C24C23×D1111yescharacteristic
505C2×Q8—1116no—
506C2×Q8—444no—
507C2×Q8—444no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—114no—
515C22×C4—118no—
516C22×C4—112no—
517C22×C4—114no—
518C22×C4—112no—
519C22×C4—224no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4C2×Dic2214yes—
525C22×C4C2×Dic2214yes—
526C22×C4C2×Dic2214yes—
527C22×C4C2×C4×D1114yes—
528C22×C4#433914yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1111yescharacteristic
532C22×C4C23×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C22×C4C23×D1112yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—118no—
542C4⋊C4—118no—
543C4⋊C4—114no—
544C4⋊C4—114no—
545C4⋊C4—1116no—
546C4⋊C4—1116no—
547C4⋊C4—1116no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—222no—
551C4⋊C4—222no—
552C4⋊C4—444no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C4⋊C4—444no—
558C4⋊C4C2×C4×D1114yes—
559C4⋊C4C2×C4×D1114yes—
560C22⋊C4—24no—
561C22⋊C4—118no—
562C22⋊C4—224no—
563C22⋊C4C2×C4×D1118yes—
564C42—24no—
565C42—24no—
566C42—24no—
567C42—42no—
568C42—42no—
569C42—118no—
570C42—224no—
571C42—228no—
572C42—224no—
573C42—224no—
574C42—444no—
575C42—442no—
576C42—442no—
577C42C2×Dic2214yes—
578C42C2×Dic2214yes—
579C42C2×Dic2214yes—
580C42C2×Dic2214yes—
581C42C2×C4×D1118yes—
582C11C4×#54411yescharacteristic, complemented, Sylow
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23C22×Dic2212yes—
588C23C22×C4×D1112yes—
589C23C2×#433912yes—
590C23C24×D1111yescharacteristic
591Q8—4416no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—28no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—44no—
610C2×C4—114no—
611C2×C4—114no—
612C2×C4—118no—
613C2×C4—224no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—224no—
628C2×C4—448no—
629C2×C4—448no—
630C2×C4C4×Dic22116yescomplemented
631C2×C4C22×Dic2212yes—
632C2×C4C22×Dic2212yes—
633C2×C4C22×Dic2212yes—
634C2×C4C22×Dic2212yes—
635C2×C4C22×Dic2212yes—
636C2×C4C22×Dic2212yes—
637C2×C4C22×C4×D1114yes—
638C2×C4C22×C4×D1114yes—
639C2×C4C22×C4×D1112yes—
640C2×C4C22×C4×D1112yes—
641C2×C4C2×#433912yes—
642C2×C4C2×#433912yes—
643C2×C4#6704212yes—
644C2×C4#6704312yes—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22C2×C4×Dic2214yes—
652C22C23×Dic2211yescharacteristic
653C22C23×C4×D1111yescharacteristic
654C22C22×#433911yescharacteristic
655C22C2×#6704211yescharacteristic
656C22C2×#6704311yescharacteristic
657C22#1062345311yescharacteristic
658C22#1062345311yescharacteristic
659C4—22no—
660C4—22no—
661C4—22no—
662C4—24no—
663C4—24no—
664C4—42no—
665C4—42no—
666C4—228no—
667C4—224no—
668C4—224no—
669C4—444no—
670C4—442no—
671C4—442no—
672C4C2×C4×Dic2214yes—
673C4C2×C4×Dic2214yes—
674C4#1062305014yesdirect product factor
675C2—24no—
676C2C22×C4×Dic2211yescharacteristic
677C2C4×#6704211yescharacteristic
678C2C4×#6704311yescharacteristic
679C2C2×#1062305011yescharacteristic
680C2#1308202111yescharacteristic
681C2#1308203211yescharacteristic
682C2#1308204311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC4×#117D11
hypocenterC11C4×#544
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13071364C2semidirect
3. #13071360C2semidirect
4. #13071357C2semidirect
5. #13071353C2semidirect
10. C4×#66922C2semidirect
11. C4×#66941C2semidirect
12. C4×#66923C2semidirect
13. C4×#66943C2semidirect
26. #10623050C4direct (N × H)
98. C2×C42×C11Q8semidirect
141. #66943C2×C4semidirect
142. #66941C2×C4semidirect
144. #66923C2×C4semidirect
145. #66922C2×C4semidirect
285. C2×C4×C11C4×Q8semidirect
410. C4×C11#544semidirect
469. C2×C42Dic22semidirect
582. C11C4×#544semidirect
630. C2×C4C4×Dic22semidirect
674. C4#10623050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130713642
#130713602
#130713572
#130713532
#130713442
#130712392
#130712362
#130712322
C4×#669222
C4×#669412
C4×#669232
C4×#669432
C4×#669312
C4×#669792
C2×C4×C4⋊Dic112
C4×C11×#1172
C4×#54411