Finite Group Databasebeta

← C2×#13077472 #15617906

Subgroups — C2×#13077472 #15617906

Order 2816.

2870 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D11C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic, complemented
3C2×#10623076C211yesmaximal, characteristic
4#13077472C2116yesmaximal, direct product factor
5C2×#10622323C211yesmaximal, characteristic, complemented
6C2×#10622777C211yesmaximal, characteristic, complemented
7C2×#10622502C211yesmaximal, characteristic, complemented
8C2×#10622371C211yesmaximal, characteristic, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×C4×#4324C211yesmaximal, characteristic, complemented
11C2×#10622401C211yesmaximal, characteristic, complemented
12C2×#10622493C211yesmaximal, characteristic, complemented
13C2×#10622415C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic, complemented
23C22×#4325C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×C4×C22⋊D11—21no—
27C22×(C2×D11)⋊C4—21no—
28C2×SD16×D11C4116yescomplemented
29C2×SD16×D11C2218yes—
30C22×#4314C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623103—24no—
34#10623103C2218yescomplemented
35#10623076—24no—
36#10623076C2218yes—
37C2×#66946C2211yescharacteristic
38C2×#66945—21no—
39C2×#66945C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66940—21no—
42C2×#66940C2211yescharacteristic, complemented
43C2×(C22⋊D11)⋊C4—21no—
44C2×C22⋊C4×D11—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925—21no—
47C2×#66925C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#440C2218yescomplemented
51C2×C11×#107C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic, complemented
55C2×#66899C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic
57#10622777C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic, complemented
60C2×#66880C2211yescharacteristic, complemented
61C2×#66879C2211yescharacteristic, complemented
62C2×C8×Dic11C2211yescharacteristic, complemented
63C4×#4325C2218yescomplemented
64C4×#4324C2218yescomplemented
65C2×#66874C2211yescharacteristic, complemented
66C2×#66873C2211yescharacteristic
67C2×#66872C2211yescharacteristic, complemented
68C2×#66872C2211yescharacteristic, complemented
69C2×C4×C11⋊C8C2211yescharacteristic, complemented
70#10622502C2218yescomplemented
71#10622493C2218yescomplemented
72#10622415C2218yescomplemented
73#10622401C2218yescomplemented
74#10622383C2218yes—
75#10622371C2218yescomplemented
76#10622323C2218yescomplemented
77#10622321C2218yescomplemented
78C24×D11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11C2×C418yescomplemented
87C2×Q8×D11C2314yes—
88C2×D4×D11—22no—
89C2×D4×D11—24no—
90C2×D4×D11C2×C418yes—
91C2×D4×D11C2314yes—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22C2311yescharacteristic
99C2×C11×SD16C2×C418yescomplemented
100C2×C11×SD16C2314yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×Q8×C11—22no—
104C4×Q8×C11C2314yescomplemented
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C22⋊Dic11—21no—
114Q8×Dic11—22no—
115Q8×Dic11C2314yescomplemented
116C2×#4325C2×C418yescomplemented
117C2×#4325C2314yes—
118D4×Dic11—22no—
119D4×Dic11C2314yes—
120C2×#4324C2×C418yescomplemented
121C2×#4324C2314yes—
122C4×C22⋊D11—28no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—28no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4D411yescharacteristic
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11—21no—
142C2×C4×Dic11C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145SD16×D11C2×C4164yescomplemented
146C2×#4314C2×C418yescomplemented
147C2×#4314C2314yes—
148C2×#4313—24no—
149C2×#4313C2314yes—
150C2×C8×D11C2×C418yescomplemented
151C2×C8×D11C2314yes—
152#66946—22no—
153#66946C2314yes—
154#66945—22no—
155#66945—22no—
156#66945—28no—
157#66945C2314yes—
158#66945C2314yes—
159#66940—28no—
160#66940—22no—
161#66940C2314yescomplemented
162(C22⋊D11)⋊C4—28no—
163C22⋊C4×D11—28no—
164C4×D44—22no—
165C4×D44C2314yes—
166#66925—28no—
167#66925D414yes—
168#66925C2314yes—
169C4×Dic22—22no—
170C4×Dic22—28no—
171C4×Dic22C2314yescomplemented
172C11×#107C2314yescomplemented
173C11×#103C2314yescomplemented
174C11×#102C2314yes—
175C11×#97C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yes—
178#66885C2314yes—
179#66882C2314yescomplemented
180#66880C2314yescomplemented
181#66879C2314yescomplemented
182C8×Dic11C2314yescomplemented
183#66874C2314yescomplemented
184#66873C2314yes—
185#66872C2314yescomplemented
186#66872C2314yescomplemented
187C4×C11⋊C8C2314yescomplemented
188C2×#2949—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11—28no—
192C23×D11—24no—
193C23×D11—82no—
194C23×D11—82no—
195C23×D11C2×D411yescharacteristic
196C2×Q8×C11—21no—
197C2×Q8×C11—22no—
198C2×Q8×C11C22×C414yes—
199C2×Q8×C11C2412yes—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11C22×C414yes—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—82no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—28no—
213C2×C22⋊D11—24no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—82no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222Q8×D11—216no—
223Q8×D11—28no—
224Q8×D11C22×C4116yescomplemented
225D4×D11—216no—
226D4×D11—28no—
227D4×D11C22×C4116yes—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44C22×C414yes—
231C2×D44C2412yes—
232C2×C4×D11—24no—
233C2×C4×D11—28no—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—82no—
237C2×C4×D11—82no—
238C2×C4×D11C22×C414yes—
239C2×C4×D11C2×D412yes—
240C2×C4×D11#4114yes—
241C2×C4×D11C2412yes—
242C2×Dic22—28no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22C22×C414yes—
247C2×Dic22C2412yes—
248C11×SD16C22×C4116yescomplemented
249C2×C8×C11—22no—
250C2×C8×C11C22×C414yes—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C42×C11—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263#4325C22×C4116yescomplemented
264#4324C22×C4116yescomplemented
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4C2×D414yes—
270(C2×D11)⋊C4C2×D414yes—
271C4⋊Dic11—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4C2×D414yes—
279Dic11⋊C4C2×D414yes—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C4×Dic11C2×D412yes—
286C4×Dic11C2412yes—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C22×C414yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291#4314C22×C4116yescomplemented
292#4313—28no—
293C8×D11C22×C4116yescomplemented
294C23×SD16—111no—
295C2×#519—111no—
296C2×#518—111no—
297#2949—1116no—
298C2×#440—111no—
299C2×#440—111no—
300C2×#440—111no—
301C2×#440D1111yescharacteristic, complemented
302C2×C4×SD16—111no—
303C2×C4×SD16—111no—
304C2×C4×SD16—111no—
305C2×C4×SD16—111no—
306C2×#427—111no—
307C2×#419—111no—
308C2×#418—111no—
309C2×#405—111no—
310C23×C11—24no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11C22×D411yescharacteristic
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—216no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—816no—
323C22×D11—84no—
324C22×D11—84no—
325C22×D11C4×D414yes—
326C22×D11C22×D412yes—
327Q8×C11—24no—
328Q8×C11—22no—
329Q8×C11C23×C414yes—
330D4×C11—24no—
331D4×C11—22no—
332D4×C11C23×C414yes—
333C2×C4×C11—24no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—84no—
342C2×C4×C11C23×C412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11C2511yescharacteristic
348C22⋊D11—216no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—84no—
358C2×Dic11C4×D414yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362D44—24no—
363D44—22no—
364D44C23×C414yes—
365C4×D11—216no—
366C4×D11—84no—
367C4×D11—84no—
368C4×D11C4×D418yes—
369C4×D11C23×C414yes—
370C4×D11C2×#4114yes—
371Dic22—24no—
372Dic22—22no—
373Dic22—216no—
374Dic22C23×C414yes—
375C8×C11—22no—
376C8×C11C23×C414yes—
377C11⋊C8—22no—
378C11⋊C8C23×C414yes—
379C23×Q8—111no—
380C23×D4—111no—
381C22×SD16—111no—
382C22×SD16—111no—
383C22×SD16—118no—
384C22×SD16—1116no—
385C22×SD16—111no—
386C22×SD16C2×D1111yescharacteristic
387C22×M16—111no—
388C23×C8—111no—
389#519—118no—
390#519—224no—
391#518—118no—
392#518—224no—
393C2×C4×Q8—111no—
394C2×C4×Q8—111no—
395C2×C4×Q8—111no—
396C2×C4×Q8—221no—
397C2×C4×Q8—221no—
398C2×C4×Q8C2×D1111yescharacteristic, complemented
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×C4×D4—221no—
403C2×C4×D4—221no—
404C2×C4×D4C2×D1111yescharacteristic
405C2×#117—111no—
406C2×#117—111no—
407C2×#117—111no—
408C2×#117—221no—
409C2×#117—221no—
410C22×C22⋊C4—221no—
411C22×C22⋊C4—221no—
412#440—118no—
413#440—118no—
414#440—118no—
415#440C2×D1118yescomplemented
416C4×SD16—118no—
417C4×SD16—118no—
418C4×SD16—118no—
419C4×SD16—118no—
420#427—118no—
421C2×#107—111no—
422C2×#107C2×D1111yescharacteristic, complemented
423C2×#106—111no—
424C2×#106—111no—
425#419—118no—
426#418—118no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103C2×D1111yescharacteristic, complemented
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102C2×D1111yescharacteristic
435#405—118no—
436C2×#97—111no—
437C2×#97C2×D1111yescharacteristic, complemented
438C2×C4×C8—111no—
439C2×C4×C8—111no—
440C22×C11—24no—
441C22×C11—48no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11C2×C4×D412yes—
445C22×C11#57712yes—
446C22×C11#57712yes—
447C22×C11C23×D411yescharacteristic
448C2×D11—28no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—24no—
452C2×D11—48no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—816no—
456C2×D11C2×C4×D414yes—
457C4×C11—24no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11C2×C4×D412yes—
463C4×C11C24×C411yescharacteristic
464C4×C11C22×#4111yescharacteristic
465Dic11—24no—
466Dic11—22no—
467Dic11—22no—
468Dic11—42no—
469Dic11—42no—
470Dic11C2×C4×D414yes—
471C25—221no—
472C22×Q8—118no—
473C22×Q8—114no—
474C22×Q8—111no—
475C22×Q8—221no—
476C22×Q8—222no—
477C22×Q8—224no—
478C22×Q8C22×D1111yescharacteristic
479C22×D4—118no—
480C22×D4—114no—
481C22×D4—111no—
482C22×D4—222no—
483C22×D4—224no—
484C22×D4—221no—
485C22×D4C22×D1111yescharacteristic
486C23×C4—21no—
487C23×C4—111no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4—221no—
491C23×C4—221no—
492C2×SD16—118no—
493C2×SD16—114no—
494C2×SD16—118no—
495C2×SD16—114no—
496C2×SD16—1164no—
497C2×SD16—118no—
498C2×SD16—114no—
499C2×SD16C4×D1118yescomplemented
500C2×SD16C22×D1114yes—
501C2×M16—114no—
502C2×M16—224no—
503C22×C8—111no—
504C22×C8—118no—
505C22×C8—114no—
506C22×C8—111no—
507C22×C8C22×D1111yescharacteristic
508C22×C8C22×D1111yescharacteristic
509C4×Q8—22no—
510C4×Q8—114no—
511C4×Q8—114no—
512C4×Q8—114no—
513C4×Q8—228no—
514C4×Q8—222no—
515C4×Q8—222no—
516C4×Q8—228no—
517C4×Q8—222no—
518C4×Q8C22×D1114yescomplemented
519C4×D4—22no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—222no—
524C4×D4—222no—
525C4×D4—228no—
526C4×D4—228no—
527C4×D4—222no—
528C4×D4C22×D1114yes—
529#117—114no—
530#117—114no—
531#117—114no—
532#117—114no—
533#117—228no—
534#117—228no—
535#117—222no—
536#117—222no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C4⋊C4C22×D1111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—228no—
551C2×C22⋊C4—228no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C42—21no—
558C2×C42—111no—
559C2×C42—221no—
560C2×C42—221no—
561C2×C42—221no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566#107C22×D1114yescomplemented
567#106—114no—
568#106—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103C22×D1114yescomplemented
573#102—114no—
574#102—114no—
575#102—114no—
576#102C22×D1114yes—
577#97—114no—
578#97C22×D1114yescomplemented
579C4×C8—114no—
580C4×C8—114no—
581C2×C11—44no—
582C2×C11#294914yescomplemented
583C2×C11C22×C4×D411yescharacteristic
584C2×C11C2×#57711yescharacteristic
585C2×C11C2×#57711yescharacteristic
586D11—24no—
587D11—44no—
588C24—21no—
589C24—111no—
590C24—224no—
591C24—228no—
592C24—221no—
593C24—882no—
594C24—882no—
595C2×Q8—21no—
596C2×Q8—22no—
597C2×Q8—1116no—
598C2×Q8—114no—
599C2×Q8—112no—
600C2×Q8—224no—
601C2×Q8—228no—
602C2×Q8—2216no—
603C2×Q8—228no—
604C2×Q8—221no—
605C2×Q8—222no—
606C2×Q8C2×C4×D1114yes—
607C2×Q8C23×D1112yes—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—1116no—
611C2×D4—114no—
612C2×D4—112no—
613C2×D4—2216no—
614C2×D4—228no—
615C2×D4—224no—
616C2×D4—228no—
617C2×D4—221no—
618C2×D4—222no—
619C2×D4C2×C4×D1114yes—
620C2×D4C23×D1112yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—82no—
626C22×C4—111no—
627C22×C4—114no—
628C22×C4—112no—
629C22×C4—114no—
630C22×C4—112no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—224no—
634C22×C4—224no—
635C22×C4—228no—
636C22×C4—224no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—224no—
641C22×C4—882no—
642C22×C4—882no—
643C22×C4—882no—
644C22×C4D4×D1111yescharacteristic
645C22×C4D4×D1111yescharacteristic
646C22×C4C23×D1111yescharacteristic
647SD16—1116no—
648SD16—1116no—
649SD16—1116no—
650SD16C2×C4×D11116yescomplemented
651M16—228no—
652C2×C8—22no—
653C2×C8—114no—
654C2×C8—112no—
655C2×C8—1116no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8C2×C4×D1114yes—
659C2×C8C23×D1112yes—
660C2×C8C23×D1112yes—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—114no—
665C4⋊C4—114no—
666C4⋊C4—112no—
667C4⋊C4—112no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—224no—
673C4⋊C4C23×D1112yes—
674C4⋊C4C23×D1112yes—
675C22⋊C4—24no—
676C22⋊C4—114no—
677C22⋊C4—114no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—24no—
684C42—112no—
685C42—112no—
686C42—224no—
687C42—224no—
688C42—224no—
689C42—224no—
690C42—224no—
691C42D4×D1112yes—
692C42C23×D1112yes—
693C11C2×#294911yescharacteristic, complemented, Sylow
694C23—24no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—114no—
699C23—112no—
700C23—2216no—
701C23—222no—
702C23—222no—
703C23—224no—
704C23—222no—
705C23—442no—
706C23—442no—
707C23—8816no—
708C23—884no—
709C23—884no—
710C23C2×D4×D1111yescharacteristic
711Q8—24no—
712Q8—22no—
713Q8—114no—
714Q8—2216no—
715Q8—224no—
716Q8—222no—
717Q8C22×C4×D1114yes—
718D4—24no—
719D4—22no—
720D4—114no—
721D4—2216no—
722D4—224no—
723D4—222no—
724D4C22×C4×D1114yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—114no—
735C2×C4—112no—
736C2×C4—118no—
737C2×C4—114no—
738C2×C4—114no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—2216no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—224no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—884no—
751C2×C4—884no—
752C2×C4—884no—
753C2×C4C22×C4×D1112yes—
754C2×C4C2×D4×D1112yes—
755C2×C4C2×D4×D1112yes—
756C2×C4C2×D4×D1111yescharacteristic
757C2×C4#41×D1112yes—
758C2×C4C24×D1111yescharacteristic
759C8—22no—
760C8—114no—
761C8—222no—
762C8C22×C4×D1114yes—
763C22—24no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—114no—
768C22—228no—
769C22—222no—
770C22—222no—
771C22—224no—
772C22—448no—
773C22—442no—
774C22—442no—
775C22—8816no—
776C22C4×D4×D1112yes—
777C22#1062330612yes—
778C22#1062330912yes—
779C22C22×D4×D1111yescharacteristic
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—114no—
786C4—224no—
787C4—222no—
788C4—222no—
789C4—442no—
790C4—442no—
791C4C4×D4×D1112yes—
792C4C23×C4×D1111yescharacteristic
793C4C2×#41×D1111yescharacteristic
794C2—44no—
795C2—224no—
796C2—444no—
797C2#1307747214yesdirect product factor
798C2C2×C4×D4×D1111yescharacteristic
799C2C2×#1062330911yescharacteristic
800C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC2×C4×C11C25
hypercenterC2×#440D11
hypocenterC11C2×#2949
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#10623103C2semidirect
4. #13077472C2direct (N × H)
5. C2×#10622323C2semidirect
6. C2×#10622777C2semidirect
7. C2×#10622502C2semidirect
8. C2×#10622371C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×C4×#4324C2semidirect
11. C2×#10622401C2semidirect
12. C2×#10622493C2semidirect
13. C2×#10622415C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#440C2semidirect
20. C2×C4×Q8×C11C22semidirect
22. C2×Q8×Dic11C22semidirect
28. C2×SD16×D11C4semidirect
34. #10623103C22semidirect
42. C2×#66940C22semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#440C22semidirect
51. C2×C11×#107C22semidirect
52. C2×C11×#103C22semidirect
54. C2×C11×#97C22semidirect
55. C2×#66899C22semidirect
57. #10622777C22semidirect
59. C2×#66882C22semidirect
60. C2×#66880C22semidirect
61. C2×#66879C22semidirect
62. C2×C8×Dic11C22semidirect
63. C4×#4325C22semidirect
64. C4×#4324C22semidirect
65. C2×#66874C22semidirect
67. C2×#66872C22semidirect
68. C2×#66872C22semidirect
69. C2×C4×C11⋊C8C22semidirect
70. #10622502C22semidirect
71. #10622493C22semidirect
72. #10622415C22semidirect
73. #10622401C22semidirect
75. #10622371C22semidirect
76. #10622323C22semidirect
77. #10622321C22semidirect
86. C2×Q8×D11C2×C4semidirect
99. C2×C11×SD16C2×C4semidirect
104. C4×Q8×C11C23semidirect
115. Q8×Dic11C23semidirect
116. C2×#4325C2×C4semidirect
120. C2×#4324C2×C4semidirect
145. SD16×D11C2×C4semidirect
146. C2×#4314C2×C4semidirect
150. C2×C8×D11C2×C4semidirect
161. #66940C23semidirect
171. C4×Dic22C23semidirect
172. C11×#107C23semidirect
173. C11×#103C23semidirect
175. C11×#97C23semidirect
176. #66899C23semidirect
179. #66882C23semidirect
180. #66880C23semidirect
181. #66879C23semidirect
182. C8×Dic11C23semidirect
183. #66874C23semidirect
185. #66872C23semidirect
186. #66872C23semidirect
187. C4×C11⋊C8C23semidirect
224. Q8×D11C22×C4semidirect
248. C11×SD16C22×C4semidirect
263. #4325C22×C4semidirect
264. #4324C22×C4semidirect
291. #4314C22×C4semidirect
293. C8×D11C22×C4semidirect
301. C2×#440D11semidirect
398. C2×C4×Q8C2×D11semidirect
415. #440C2×D11semidirect
422. C2×#107C2×D11semidirect
430. C2×#103C2×D11semidirect
437. C2×#97C2×D11semidirect
499. C2×SD16C4×D11semidirect
518. C4×Q8C22×D11semidirect
566. #107C22×D11semidirect
572. #103C22×D11semidirect
578. #97C22×D11semidirect
582. C2×C11#2949semidirect
650. SD16C2×C4×D11semidirect
693. C11C2×#2949semidirect
797. C2#13077472direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D112
C2×#106231032
C2×#106230762
#130774722
C2×#106223232
C2×#106227772
C2×#106225022
C2×#106223712
C2×C4×#43252
C2×C4×#43242
C2×#106224012
C2×#106224932
C2×#106224152
C2×#106223832
C2×#106223212
C2×C11×#4402
C2×#294911