Finite Group Databasebeta

← D4×#66901 #14769447

Subgroups — D4×#66901 #14769447

Order 2816.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic, complemented
2C22×#66901C212yesmaximal, complemented
3C4×D4×Dic11C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic, complemented
5#13069445C211yesmaximal, characteristic, complemented
6#13069060C212yesmaximal, complemented
7#13068919C212yesmaximal, complemented
8#13068636C211yesmaximal, characteristic, complemented
9#13068560C212yesmaximal, complemented
10C4×#66901C211yesmaximal, characteristic, complemented
11D4×C11×#41C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#550C411yescharacteristic, complemented
14D4×Q8×C11C411yescharacteristic, complemented
15C11×#548C412yescomplemented
16C11×#547—21no—
17C11×#547C411yescharacteristic, complemented
18C11×#546—22no—
19C11×#546C412yescomplemented
20D42×C11—21no—
21D42×C11C411yescharacteristic, complemented
22C11×#532—21no—
23C11×#532C2211yescharacteristic
24C11×#525—22no—
25C11×#525C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×D4×Dic11—21no—
30C22×C4×Dic11C2212yescomplemented
31C22×#4318C2212yescomplemented
32C2×#66901—28no—
33C2×#66901C2211yescharacteristic
34C2×#66901C2212yes—
35C2×#66901C2211yescharacteristic
36C2×#66901C2212yescomplemented
37C2×#66901C2212yescomplemented
38C2×#66901C2212yescomplemented
39C2×#66901C2212yescomplemented
40C4×C22⋊Dic11C2212yescomplemented
41#10622820C2212yescomplemented
42#10622625—21no—
43#10622624—22no—
44D4×C11⋊C8—21no—
45C4⋊C4×Dic11—21no—
46C22⋊C4×Dic11—22no—
47C4×C4⋊Dic11C2211yescharacteristic, complemented
48C42×Dic11C2211yescharacteristic, complemented
49#10622537C2211yescharacteristic, complemented
50C4×#4318C2211yescharacteristic, complemented
51#10622170C2211yescharacteristic, complemented
52#10622170C2212yescomplemented
53#10622170C2211yescharacteristic, complemented
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41—42no—
59C2×C11×#41—42no—
60C2×C11×#41C2×C412yescomplemented
61C2×C11×#41C2×C412yescomplemented
62C2×C11×#41C2312yes—
63C2×C11×#41C2311yescharacteristic
64C22×Q8×C11C2×C412yescomplemented
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11C2×C412yescomplemented
68C22×D4×C11D411yescharacteristic
69C23×C4×C11—22no—
70C23×C4×C11C2312yes—
71C23×Dic11—22no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2×C411yescharacteristic, complemented
74C11×#127—21no—
75C11×#127C2×C411yescharacteristic, complemented
76C11×#124—22no—
77C11×#124C2×C412yescomplemented
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8C2×C412yescomplemented
84C11×C22⋊Q8C2×C412yescomplemented
85C11×#121—22no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121C2×C412yescomplemented
93C11×#121C2×C412yescomplemented
94C11×#120—22no—
95C11×#120—22no—
96C11×#120—22no—
97C4×Q8×C11C2×C411yescharacteristic, complemented
98C4×Q8×C11C2×C411yescharacteristic, complemented
99C4×D4×C11—21no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—22no—
104C4×D4×C11—21no—
105C4×D4×C11—22no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11C2×C411yescharacteristic
109C4×D4×C11C2×C412yes—
110C4×D4×C11C2×C411yescharacteristic
111C4×D4×C11C2×C411yescharacteristic, complemented
112C4×D4×C11C2×C411yescharacteristic, complemented
113C4×D4×C11D411yescharacteristic
114C4×D4×C11D412yes—
115C4×D4×C11D411yescharacteristic
116C11×#117—21no—
117C11×#117C2311yescharacteristic
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4D412yes—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—22no—
125D4×Dic11—28no—
126C2×C4⋊Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—42no—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×#4318—22no—
136C2×#4318—24no—
137C2×#4318—42no—
138C2×#4318C2311yescharacteristic
139C2×#4318C2312yes—
140C2×#4318C2311yescharacteristic
141C22×C11⋊C8—22no—
142#66901—24no—
143#66901—22no—
144#66901—24no—
145#66901—24no—
146#66901—42no—
147#66901—42no—
148#66901D414yesdirect product factor
149C11⋊#95—21no—
150C11⋊#95—22no—
151C22⋊(C11⋊C8)—22no—
152C22⋊(C11⋊C8)—22no—
153C4⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155#66867—21no—
156C4×C11⋊C8—21no—
157D4×#104—111nomaximal, Sylow
158C24×C11—22no—
159C24×C11C2×D412yes—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—24no—
163C11×#41—24no—
164C11×#41—22no—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—22no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—42no—
171C11×#41—42no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41C2×D412yes—
175C11×#41#4112yes—
176C2×Q8×C11—22no—
177C2×Q8×C11—24no—
178C2×Q8×C11—42no—
179C2×Q8×C11C22×C412yes—
180C2×Q8×C11C22×C411yescharacteristic
181C2×D4×C11—21no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—42no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11C22⋊C412yes—
197C2×D4×C11C22⋊C411yescharacteristic
198C2×D4×C11C22⋊C411yescharacteristic
199C2×D4×C11C22×C412yes—
200C2×D4×C11C22×C411yescharacteristic
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—44no—
213C22×C4×C11—44no—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C22×C412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2411yescharacteristic
222C22×Dic11—28no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—22no—
226C22×Dic11—44no—
227C22×Dic11—44no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4C22⋊C411yescharacteristic
235C11×C4⋊C4C22⋊C411yescharacteristic
236C11×C4⋊C4C22⋊C412yes—
237C11×C4⋊C4C22×C411yescharacteristic
238C11×C4⋊C4C22×C411yescharacteristic
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4C22⋊C412yes—
249C11×C22⋊C4C22⋊C412yes—
250C11×C22⋊C4C22⋊C412yes—
251C11×C22⋊C4C22⋊C412yes—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11C22×C411yescharacteristic
256C42×C11C22×C411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C22⋊Dic11—28no—
260C4⋊Dic11—24no—
261C4×Dic11—24no—
262C4×Dic11—22no—
263C4×Dic11—21no—
264C4×Dic11—21no—
265C4×Dic11—21no—
266C4×Dic11—22no—
267C4×Dic11—44no—
268C4×Dic11—42no—
269C4×Dic11C2×D412yescomplemented
270#4318—22no—
271#4318—21no—
272#4318—21no—
273#4318—21no—
274#4318—22no—
275#4318—44no—
276#4318C2×D412yescomplemented
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—44no—
281D4×#41D1111yescharacteristic
282D4×M16—111no—
283C22×#104—112no—
284C42×D4—111no—
285#1980—111no—
286#1962—111no—
287#1896—112no—
288#1871—112no—
289#1806—111no—
290#1789—112no—
291C4×#104—111no—
292C23×C11—21no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—42no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—82no—
301C23×C11C2×C22⋊C412yes—
302C23×C11C2×C22⋊C412yes—
303C23×C11C22×D411yescharacteristic
304Q8×C11—21no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—44no—
308Q8×C11C4×D412yescomplemented
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—24no—
312D4×C11—22no—
313D4×C11—21no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—44no—
317D4×C11—44no—
318D4×C11—44no—
319D4×C11—42no—
320D4×C11—42no—
321D4×C11—44no—
322D4×C11—42no—
323D4×C11—81no—
324D4×C11—82no—
325D4×C11#10414yescomplemented
326D4×C11C4×D412yescomplemented
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—22no—
344C2×C4×C11—41no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—81no—
352C2×C4×C11C2×C22⋊C411yescharacteristic
353C2×C4×C11C2×C22⋊C411yescharacteristic
354C2×C4×C11C2×C22⋊C411yescharacteristic
355C2×C4×C11C2×C22⋊C412yes—
356C2×C4×C11C2×C22⋊C412yes—
357C2×C4×C11C2×C22⋊C411yescharacteristic
358C2×C4×C11C23×C411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4111yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—24no—
369C2×Dic11—416no—
370C2×Dic11—41no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—41no—
374C11⋊C8—22no—
375C11⋊C8—42no—
376C11⋊C8—41no—
377C22×#41C2×D1112yes—
378C22×M16—112no—
379#550Dic1111yescharacteristic, complemented
380D4×Q8Dic1111yescharacteristic, complemented
381#548Dic1112yescomplemented
382#547—21no—
383#547Dic1111yescharacteristic, complemented
384#546—22no—
385#546Dic1112yescomplemented
386D42—21no—
387D42Dic1111yescharacteristic, complemented
388#532—21no—
389#532C2×D1111yescharacteristic
390#525—22no—
391#525C2×D1112yes—
392C4×#41C2×D1111yescharacteristic
393C2×C4×D4—21no—
394C2×C4×D4—221no—
395C2×C4×D4C2×D1111yescharacteristic
396C22×C42—112no—
397#436—221no—
398#435—222no—
399C8×D4—221no—
400#423—111no—
401C2×#104—111no—
402C2×#104—112no—
403C2×#104—112no—
404C2×#104—112no—
405C2×#104—111no—
406C2×#104—112no—
407C2×#104—112no—
408C2×#104—228no—
409#407—112no—
410C4×M16—111no—
411C4×C4⋊C4—111no—
412C4×C4⋊C4—221no—
413C4×C22⋊C4—112no—
414C4×C22⋊C4—222no—
415C43—111no—
416#339—112no—
417#339—111no—
418#339—111no—
419C22×C11—22no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—44no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—88no—
435C22×C11C2×#10414yescomplemented
436C22×C11C22×C22⋊C411yescharacteristic
437C22×C11D4211yescharacteristic
438C22×C11#54611yescharacteristic
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—21no—
443C4×C11—21no—
444C4×C11—21no—
445C4×C11—42no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11C2×#10412yescomplemented
449C4×C11C2×C4×D411yescharacteristic
450C4×C11#51811yescharacteristic
451C4×C11D4211yescharacteristic
452C4×C11#54611yescharacteristic
453Dic11—24no—
454Dic11—42no—
455Dic11—44no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—24no—
459C2×#41—24no—
460C2×#41—42no—
461C2×#41—42no—
462C2×#41C2×Dic1112yescomplemented
463C2×#41C2×Dic1112yescomplemented
464C2×#41C22×D1112yes—
465C2×#41C22×D1111yescharacteristic
466C22×Q8C2×Dic1112yescomplemented
467C22×D4—22no—
468C22×D4—21no—
469C22×D4C2×Dic1112yescomplemented
470C22×D4C22⋊D1111yescharacteristic
471C23×C4—22no—
472C23×C4—222no—
473C23×C4C22×D1112yes—
474C2×M16—111no—
475C2×M16—112no—
476C2×M16—111no—
477C2×M16—222no—
478C2×M16—224no—
479C2×M16—442no—
480C22×C8—222no—
481C4⋊Q8—21no—
482C4⋊Q8C2×Dic1111yescharacteristic, complemented
483#127—21no—
484#127C2×Dic1111yescharacteristic, complemented
485#124—22no—
486#124C2×Dic1112yescomplemented
487#123—22no—
488#123—22no—
489#123—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8C2×Dic1112yescomplemented
493C22⋊Q8C2×Dic1112yescomplemented
494#121—22no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—22no—
500#121—22no—
501#121C2×Dic1112yescomplemented
502#121C2×Dic1112yescomplemented
503#120—22no—
504#120—22no—
505#120—22no—
506C4×Q8C2×Dic1111yescharacteristic, complemented
507C4×Q8C2×Dic1111yescharacteristic, complemented
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—228no—
518C4×D4C2×Dic1111yescharacteristic
519C4×D4C2×Dic1112yes—
520C4×D4C2×Dic1111yescharacteristic
521C4×D4C2×Dic1111yescharacteristic, complemented
522C4×D4C2×Dic1111yescharacteristic, complemented
523C4×D4C22⋊D1111yescharacteristic
524C4×D4C22⋊D1112yes—
525C4×D4C22⋊D1111yescharacteristic
526#117—21no—
527#117C22×D1111yescharacteristic
528C2×C4⋊C4—21no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4C22⋊D1111yescharacteristic
531C2×C22⋊C4—22no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4C22⋊D1112yes—
534C2×C42—21no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—112no—
538C2×C42—224no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—222no—
542C2×C42—442no—
543C2×C42C22×D1111yescharacteristic
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—114no—
547#104—224no—
548#104—224no—
549#104—224no—
550#104—222no—
551#104—442no—
552#104—442no—
553C22⋊C8—222no—
554C22⋊C8—222no—
555#97—221no—
556C4×C8—221no—
557#95—222no—
558#95—221no—
559C2×C11—21no—
560C2×C11—21no—
561C2×C11—24no—
562C2×C11—42no—
563C2×C11—42no—
564C2×C11—82no—
565C2×C11D4×C22⋊C411yescharacteristic
566C2×C11C22×#10411yescharacteristic
567C2×C11#290111yescharacteristic
568C24—22no—
569C24C2×C22⋊D1112yes—
570#41—21no—
571#41—21no—
572#41—24no—
573#41—24no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—44no—
579#41—44no—
580#41—42no—
581#41—42no—
582#41—44no—
583#41—44no—
584#41D4×D1112yes—
585#41#434112yes—
586C2×Q8—22no—
587C2×Q8—24no—
588C2×Q8—42no—
589C2×Q8C22×Dic1112yes—
590C2×Q8C22×Dic1111yescharacteristic
591C2×D4—21no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—42no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4C22⋊Dic1112yes—
607C2×D4C22⋊Dic1111yescharacteristic
608C2×D4C22⋊Dic1111yescharacteristic
609C2×D4C22×Dic1112yes—
610C2×D4C22×Dic1111yescharacteristic
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—221no—
625C22×C4—228no—
626C22×C4—221no—
627C22×C4—222no—
628C22×C4—444no—
629C22×C4—444no—
630C22×C4C22×Dic1112yes—
631C22×C4C22×Dic1112yes—
632C22×C4C2×C22⋊D1112yes—
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C2×C22⋊D1112yes—
635C22×C4C2×C22⋊D1112yes—
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638M16—112no—
639M16—221no—
640M16—222no—
641M16—221no—
642M16—221no—
643M16—222no—
644M16—444no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—222no—
648C2×C8—444no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—224no—
656C4⋊C4C22⋊Dic1111yescharacteristic
657C4⋊C4C22⋊Dic1111yescharacteristic
658C4⋊C4C22⋊Dic1112yes—
659C4⋊C4C22×Dic1111yescharacteristic
660C4⋊C4C22×Dic1111yescharacteristic
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—228no—
671C22⋊C4C22⋊Dic1112yes—
672C22⋊C4C22⋊Dic1112yes—
673C22⋊C4C22⋊Dic1112yes—
674C22⋊C4C22⋊Dic1112yes—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—112no—
679C42—224no—
680C42—221no—
681C42—222no—
682C42—221no—
683C42—221no—
684C42—222no—
685C42—444no—
686C42—442no—
687C42C22×Dic1111yescharacteristic
688C42C22×Dic1111yescharacteristic
689C42C2×C22⋊D1111yescharacteristic
690C42C2×C22⋊D1111yescharacteristic
691C11D4×#10411yescharacteristic, complemented, Sylow
692C23—22no—
693C23—22no—
694C23—24no—
695C23—21no—
696C23—22no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—82no—
701C23C2×C22⋊Dic1112yes—
702C23C2×C22⋊Dic1112yes—
703C23C22×C22⋊D1111yescharacteristic
704Q8—21no—
705Q8—22no—
706Q8—22no—
707Q8—44no—
708Q8D4×Dic1112yescomplemented
709D4—22no—
710D4—22no—
711D4—24no—
712D4—22no—
713D4—21no—
714D4—22no—
715D4—22no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—42no—
720D4—42no—
721D4—44no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4#6690114yesdirect product factor
726D4D4×Dic1112yescomplemented
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—81no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—4416no—
758C2×C4—441no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—441no—
762C2×C4C2×C22⋊Dic1111yescharacteristic
763C2×C4C2×C22⋊Dic1111yescharacteristic
764C2×C4C2×C22⋊Dic1111yescharacteristic
765C2×C4C2×C22⋊Dic1112yes—
766C2×C4C2×C22⋊Dic1112yes—
767C2×C4C2×C22⋊Dic1111yescharacteristic
768C2×C4C2×D4×D1111yescharacteristic
769C2×C4C2×#434111yescharacteristic
770C2×C4#6703711yescharacteristic
771C2×C4#6703711yescharacteristic
772C2×C4C23×Dic1111yescharacteristic
773C2×C4C22×C22⋊D1111yescharacteristic
774C8—222no—
775C8—442no—
776C8—441no—
777C22—22no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—44no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—88no—
793C22C2×#6690114yescomplemented
794C22D4×C22⋊D1111yescharacteristic
795C22#1062333711yescharacteristic
796C22C22×C22⋊Dic1111yescharacteristic
797C4—22no—
798C4—22no—
799C4—22no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—224no—
807C4—444no—
808C4—442no—
809C4C2×#6690112yescomplemented
810C4C2×D4×Dic1111yescharacteristic
811C4#1062332911yescharacteristic
812C4D4×C22⋊D1111yescharacteristic
813C4#1062333711yescharacteristic
814C2—21no—
815C2—21no—
816C2—24no—
817C2—42no—
818C2—42no—
819C2—82no—
820C2D4×C22⋊Dic1111yescharacteristic
821C2C22×#6690111yescharacteristic
822C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalD4×C11×#41C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterD4×#41D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#4318C2semidirect
2. C22×#66901C2semidirect
3. C4×D4×Dic11C2semidirect
4. #13069536C2semidirect
5. #13069445C2semidirect
6. #13069060C2semidirect
7. #13068919C2semidirect
8. #13068636C2semidirect
9. #13068560C2semidirect
10. C4×#66901C2semidirect
13. C11×#550C4semidirect
14. D4×Q8×C11C4semidirect
15. C11×#548C4semidirect
17. C11×#547C4semidirect
19. C11×#546C4semidirect
21. D42×C11C4semidirect
30. C22×C4×Dic11C22semidirect
31. C22×#4318C22semidirect
36. C2×#66901C22semidirect
37. C2×#66901C22semidirect
38. C2×#66901C22semidirect
39. C2×#66901C22semidirect
40. C4×C22⋊Dic11C22semidirect
41. #10622820C22semidirect
47. C4×C4⋊Dic11C22semidirect
48. C42×Dic11C22semidirect
49. #10622537C22semidirect
50. C4×#4318C22semidirect
51. #10622170C22semidirect
52. #10622170C22semidirect
53. #10622170C22semidirect
60. C2×C11×#41C2×C4semidirect
61. C2×C11×#41C2×C4semidirect
64. C22×Q8×C11C2×C4semidirect
67. C22×D4×C11C2×C4semidirect
73. C11×C4⋊Q8C2×C4semidirect
75. C11×#127C2×C4semidirect
77. C11×#124C2×C4semidirect
83. C11×C22⋊Q8C2×C4semidirect
84. C11×C22⋊Q8C2×C4semidirect
92. C11×#121C2×C4semidirect
93. C11×#121C2×C4semidirect
97. C4×Q8×C11C2×C4semidirect
98. C4×Q8×C11C2×C4semidirect
111. C4×D4×C11C2×C4semidirect
112. C4×D4×C11C2×C4semidirect
148. #66901D4direct (N × H)
269. C4×Dic11C2×D4semidirect
276. #4318C2×D4semidirect
308. Q8×C11C4×D4semidirect
325. D4×C11#104semidirect
326. D4×C11C4×D4semidirect
379. #550Dic11semidirect
380. D4×Q8Dic11semidirect
381. #548Dic11semidirect
383. #547Dic11semidirect
385. #546Dic11semidirect
387. D42Dic11semidirect
435. C22×C11C2×#104semidirect
448. C4×C11C2×#104semidirect
462. C2×#41C2×Dic11semidirect
463. C2×#41C2×Dic11semidirect
466. C22×Q8C2×Dic11semidirect
469. C22×D4C2×Dic11semidirect
482. C4⋊Q8C2×Dic11semidirect
484. #127C2×Dic11semidirect
486. #124C2×Dic11semidirect
492. C22⋊Q8C2×Dic11semidirect
493. C22⋊Q8C2×Dic11semidirect
501. #121C2×Dic11semidirect
502. #121C2×Dic11semidirect
506. C4×Q8C2×Dic11semidirect
507. C4×Q8C2×Dic11semidirect
521. C4×D4C2×Dic11semidirect
522. C4×D4C2×Dic11semidirect
691. C11D4×#104semidirect
708. Q8D4×Dic11semidirect
725. D4#66901direct (N × H)
726. D4D4×Dic11semidirect
793. C22C2×#66901semidirect
809. C4C2×#66901semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
C22×#669012
C4×D4×Dic112
#130695362
#130694452
#130690602
#130689192
#130686362
#130685602
C4×#669012
D4×C11×#412
D4×#10411