Finite Group Databasebeta

← C2×#13080834 #15630588

Subgroups — C2×#13080834 #15630588

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2C2×#10623081C211yesmaximal, characteristic
3#13080834C2116yesmaximal, direct product factor
4C2×#10622310C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622336C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622458C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622344C211yesmaximal, characteristic, complemented
13C2×C4×#4314C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622744C211yesmaximal, characteristic, complemented
16C2×C11×#436C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66990—21no—
23C2×#66988—21no—
24C2×#66983C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic, complemented
27C2×#66977C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic, complemented
30C22×Dic44C2211yescharacteristic, complemented
31C22×#4314C2211yescharacteristic
32C22×#4314C2211yescharacteristic
33#10623081—24no—
34#10623081C2218yes—
35#10623072—24no—
36#10623072C2218yescomplemented
37C2×#66947—21no—
38C2×#66942—21no—
39C2×#66937—21no—
40C2×C22⋊C4×D11—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66923C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#436C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52#10622750C2218yescomplemented
53#10622747C2218yescomplemented
54#10622746C2218yescomplemented
55#10622744C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66881C2211yescharacteristic, complemented
65C2×#66880C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66880C2211yescharacteristic, complemented
69#10622460C2218yescomplemented
70#10622458C2218yescomplemented
71#10622348C2218yescomplemented
72#10622346C2218yescomplemented
73#10622344C2218yescomplemented
74#10622336C2218yescomplemented
75#10622310C2218yescomplemented
76C4×#4314C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11D411yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×#4339—22no—
85C2×#4339—24no—
86C2×#4339—42no—
87C2×#4339C2314yes—
88C22×D44—24no—
89C22×D44—21no—
90C22×D44—22no—
91C22×D44—42no—
92C22×D44C2311yescharacteristic
93C22×D44C2314yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×M16—42no—
100C2×C11×M16—42no—
101C2×C11×M16C2314yes—
102C2×C11×M16C2314yescomplemented
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C4×D4×C11D414yes—
108C4×D4×C11C2314yes—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66990—28no—
118#66988—28no—
119#66983—22no—
120#66983C2314yes—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125#66979—22no—
126#66979C2314yes—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yescomplemented
134#66977—22no—
135#66977—22no—
136#66977—22no—
137#66977C2314yes—
138#66977C2314yes—
139#66977C2314yescomplemented
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×Dic44—42no—
149C2×Dic44C2314yescomplemented
150C2×#4314—24no—
151C2×#4314—42no—
152C2×#4314C2314yes—
153C2×#4314C2314yes—
154#66947—28no—
155#66942—28no—
156#66937—28no—
157C22⋊C4×D11—28no—
158#66932—28no—
159#66930—28no—
160#66928—22no—
161#66928C2314yes—
162C4×D44—22no—
163C4×D44C2314yes—
164#66923—22no—
165#66923C2314yescomplemented
166C4×Dic22—22no—
167C4×Dic22C2314yescomplemented
168C11×C4⋊C8C2314yescomplemented
169C11×C22⋊C8C2314yes—
170C11×C22⋊C8C2314yescomplemented
171C4×C8×C11C2314yescomplemented
172#66885C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178#66882C2314yescomplemented
179#66881C2314yescomplemented
180#66881C2314yescomplemented
181#66880C2314yescomplemented
182#66880C2314yescomplemented
183#66880C2314yescomplemented
184#66880C2314yescomplemented
185C2×#3323—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C2×D4×C11—42no—
195C2×D4×C11C2×D414yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—82no—
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—44no—
221#4339—28no—
222#4339—44no—
223#4339—48no—
224C2×D44—28no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—24no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44—48no—
234C2×D44#4114yes—
235C2×D44C2412yes—
236C2×D44C2412yes—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—44no—
240C2×C4×D11—82no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22C2412yes—
248C2×Dic22C2412yes—
249C11×M16—44no—
250C11×M16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C11×C4⋊C4C2×D414yes—
260C11×C22⋊C4C2×D414yes—
261C11×C22⋊C4C2×D414yes—
262C42×C11C2×D412yes—
263C42×C11C2412yes—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—24no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289Dic44—44no—
290#4314—28no—
291#4314—44no—
292C2×#552—111no—
293C2×#546—111no—
294#3323—1116no—
295C2×#488—111no—
296C2×#481—111no—
297C2×#485—111no—
298C2×#478—111no—
299C2×#470—111no—
300C2×#468—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×C4×SD16—111no—
305C2×#436D1111yescharacteristic, complemented
306C2×#417—111no—
307C2×#418—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11C22×D412yes—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—48no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—48no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—84no—
328C22×D11—816no—
329D4×C11—44no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4112yes—
346C2×C4×C11H(5,𝔽2)12yes—
347C2×C4×C11C2511yescharacteristic
348C22⋊D11—48no—
349C22⋊D11—84no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—48no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363D44—24no—
364D44—22no—
365D44—22no—
366D44—22no—
367D44—48no—
368D44—42no—
369D44C2×#4114yes—
370C4×D11—48no—
371C4×D11—84no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—22no—
376Dic22—42no—
377Dic22—42no—
378C8×C11—22no—
379C8×C11—22no—
380C8×C11—22no—
381C8×C11—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16C2×D1111yescharacteristic
388C22×M16C2×D1111yescharacteristic, complemented
389#552—118no—
390#552—224no—
391#546—118no—
392#546—224no—
393C2×#126—221no—
394C2×#125—111no—
395C2×#125—221no—
396C2×#124—111no—
397C2×#123—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8—111no—
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—111no—
406C2×C4×D4—111no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—111no—
411C22×C22⋊C4—221no—
412#488—118no—
413#485—118no—
414#481—118no—
415#478—118no—
416#470—118no—
417#468—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421C4×SD16—118no—
422#436C2×D1118yescomplemented
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8C2×D1111yescharacteristic, complemented
427#418—118no—
428#417—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×C22⋊C8C2×D1111yescharacteristic
440C2×C22⋊C8C2×D1111yescharacteristic, complemented
441C2×C4×C8C2×D1111yescharacteristic, complemented
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—44no—
449C22×C11—44no—
450C22×C11#54612yes—
451C22×C11#57512yes—
452C22×C11#57712yes—
453C22×C11C23×D411yescharacteristic
454C2×D11—24no—
455C2×D11—48no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11#54612yes—
468C4×C11C22×#4111yescharacteristic
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—224no—
479C2×#41—222no—
480C2×#41—442no—
481C22×Q8—111no—
482C22×Q8—111no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—114no—
486C22×D4—224no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—222no—
491C22×D4—442no—
492C22×D4D4411yescharacteristic
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×M16—42no—
505C2×M16—42no—
506C2×M16C22×D1114yes—
507C2×M16C22×D1114yescomplemented
508C22×C8C22×D1111yescharacteristic
509C22×C8C22×D1111yescharacteristic
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#126—228no—
513#125—114no—
514#125—228no—
515#125—222no—
516#124—114no—
517#124—222no—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526#121—114no—
527#121—222no—
528#121—228no—
529#120—228no—
530C4×Q8—114no—
531C4×Q8—222no—
532C4×D4—114no—
533C4×D4—222no—
534C4×D4D4414yes—
535C4×D4C22×D1114yes—
536#117—114no—
537#117—222no—
538#117—228no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4D4411yescharacteristic
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4D4411yescharacteristic
563C2×C22⋊C4D4411yescharacteristic
564C2×C42—221no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8C22×D1114yescomplemented
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581C22⋊C8C22×D1114yes—
582C22⋊C8C22×D1114yescomplemented
583C4×C8C22×D1114yescomplemented
584C2×C11—42no—
585C2×C11—42no—
586C2×C11#332314yescomplemented
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#57511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590D11—44no—
591D11—82no—
592C24—221no—
593C24—221no—
594C24—224no—
595C24—444no—
596C24—444no—
597C24—882no—
598C24C2×D4411yescharacteristic
599C24C2×D4411yescharacteristic
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—112no—
604C2×Q8—112no—
605C2×Q8—221no—
606C2×Q8—221no—
607C2×Q8—222no—
608C2×Q8—222no—
609C2×Q8—222no—
610C2×Q8—222no—
611C2×D4—42no—
612C2×D4—114no—
613C2×D4—112no—
614C2×D4—112no—
615C2×D4—228no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—221no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—222no—
624C2×D4—444no—
625C2×D4—448no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—882no—
629C2×D4C2×D4414yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—224no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—444no—
644C22×C4—444no—
645C22×C4—882no—
646C22×C4C2×D4412yes—
647C22×C4C2×D4412yes—
648C22×C4C2×D4411yescharacteristic
649C22×C4C2×D4411yescharacteristic
650C22×C4C2×D4411yescharacteristic
651C22×C4C2×D4411yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—228no—
657SD16—444no—
658M16—44no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8C23×D1112yes—
665C2×C8C23×D1112yes—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—112no—
669C4⋊C4—112no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—224no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4C2×D4414yes—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4C2×D4414yes—
693C22⋊C4C2×D4414yes—
694C42—224no—
695C42—224no—
696C42C2×D4412yes—
697C42C23×D1112yes—
698C11C2×#332311yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—224no—
706C23—222no—
707C23—222no—
708C23—448no—
709C23—448no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—884no—
716C23—8816no—
717C23C22×D4412yes—
718C23C22×D4412yes—
719C23C22×D4411yescharacteristic
720Q8—222no—
721Q8—222no—
722Q8—222no—
723Q8—222no—
724Q8—442no—
725Q8—442no—
726D4—44no—
727D4—114no—
728D4—224no—
729D4—222no—
730D4—222no—
731D4—222no—
732D4—448no—
733D4—448no—
734D4—442no—
735D4—884no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—448no—
753C2×C4—448no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—884no—
761C2×C4C22×D4412yes—
762C2×C4C22×D4412yes—
763C2×C4C22×D4412yes—
764C2×C4C22×D4412yes—
765C2×C4C22×D4411yescharacteristic
766C2×C4#6703712yes—
767C2×C4#41×D1112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—224no—
782C22—448no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—8816no—
789C22—884no—
790C22#1062308512yes—
791C22#1062327912yes—
792C22#1062328212yes—
793C22C23×D4411yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—442no—
799C4—442no—
800C4—442no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062308512yes—
805C4C2×#6703711yescharacteristic
806C4C2×#41×D1111yescharacteristic
807C2—42no—
808C2—42no—
809C2—444no—
810C2—882no—
811C2#1308083414yesdirect product factor
812C2C2×#1062308511yescharacteristic
813C2C2×#1062327911yescharacteristic
814C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
hypercenterC2×#436D11
hypocenterC11C2×#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
3. #13080834C2direct (N × H)
4. C2×#10622310C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622336C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622750C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622458C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622344C2semidirect
13. C2×C4×#4314C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622744C2semidirect
16. C2×C11×#436C2semidirect
20. C22×C11×M16C22semidirect
26. C22×C4⋊Dic11C22semidirect
29. C2×#66977C22semidirect
30. C22×Dic44C22semidirect
36. #10623072C22semidirect
45. C2×#66923C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#436C22semidirect
48. C2×C11×C4⋊C8C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C4×C8×C11C22semidirect
52. #10622750C22semidirect
53. #10622747C22semidirect
54. #10622746C22semidirect
55. #10622744C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66881C22semidirect
65. C2×#66880C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. C2×#66880C22semidirect
69. #10622460C22semidirect
70. #10622458C22semidirect
71. #10622348C22semidirect
72. #10622346C22semidirect
73. #10622344C22semidirect
74. #10622336C22semidirect
75. #10622310C22semidirect
76. C4×#4314C22semidirect
102. C2×C11×M16C23semidirect
133. C2×C4⋊Dic11C23semidirect
139. #66977C23semidirect
149. C2×Dic44C23semidirect
165. #66923C23semidirect
167. C4×Dic22C23semidirect
168. C11×C4⋊C8C23semidirect
170. C11×C22⋊C8C23semidirect
171. C4×C8×C11C23semidirect
178. #66882C23semidirect
179. #66881C23semidirect
180. #66881C23semidirect
181. #66880C23semidirect
182. #66880C23semidirect
183. #66880C23semidirect
184. #66880C23semidirect
305. C2×#436D11semidirect
388. C22×M16C2×D11semidirect
422. #436C2×D11semidirect
426. C2×C4⋊C8C2×D11semidirect
440. C2×C22⋊C8C2×D11semidirect
441. C2×C4×C8C2×D11semidirect
507. C2×M16C22×D11semidirect
570. C4⋊C8C22×D11semidirect
582. C22⋊C8C22×D11semidirect
583. C4×C8C22×D11semidirect
586. C2×C11#3323semidirect
698. C11C2×#3323semidirect
811. C2#13080834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106230812
#130808342
C2×#106223102
C2×#106223482
C2×#106223362
C2×#106224602
C2×#106227502
C2×#106227472
C2×#106224582
C2×#106223462
C2×#106223442
C2×C4×#43142
C2×#106227462
C2×#106227442
C2×C11×#4362
C2×#332311