Finite Group Databasebeta

← C2×D4×#4341 #15660727

Subgroups — C2×D4×#4341 #15660727

Order 2816.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C212yesmaximal, complemented
2D4×#4341C2132yesmaximal, direct product factor
3C2×#10623249C211yesmaximal, characteristic, complemented
4C2×D4×Dic22C211yesmaximal, characteristic, complemented
5C2×#10623129C212yesmaximal, complemented
6C2×#10623086C211yesmaximal, characteristic, complemented
7C2×#10623142C212yesmaximal, complemented
8C2×#10623337C212yesmaximal, complemented
9C2×#10623122C214yesmaximal, complemented
10C2×D4×C22⋊D11C212yesmaximal, complemented
11C2×#10623247C211yesmaximal, characteristic, complemented
12C2×#10623127C212yesmaximal, complemented
13C2×#10623137C212yesmaximal, complemented
14C2×#10623117C214yesmaximal, complemented
15C2×C4×#4341C211yesmaximal, characteristic, complemented
16C22×D4×Dic11C212yesmaximal, complemented
17C2×C4×D4×D11C211yesmaximal, characteristic, complemented
18C2×D42×C11C211yesmaximal, characteristic, complemented
19C23×D4×C11C2212yes—
20C23×D4×C11C2212yescomplemented
21C23×C22⋊D11C2214yescomplemented
22C24×Dic11C2214yescomplemented
23C22×#4341—232no—
24C22×#4341C2211yescharacteristic
25C22×#4341C2212yescomplemented
26C22×#4341C2214yescomplemented
27C22×#4341C2214yescomplemented
28C22×#4341C2212yescomplemented
29C22×#4341C2212yescomplemented
30C22×#4341C22132yescomplemented
31C22×D4×D11C2211yescharacteristic
32C23×C4×D11C2212yescomplemented
33C23×Dic22C2212yescomplemented
34D42×C11C22116yescomplemented
35C2×C11×#127C2211yescharacteristic, complemented
36C2×C11×#121C2212yescomplemented
37C2×C11×#121C2212yescomplemented
38C2×C11×#120C2214yescomplemented
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2211yescharacteristic, complemented
41C2×#67006C2214yescomplemented
42C22×C22⋊Dic11C2214yescomplemented
43#10623337C22132yescomplemented
44C2×#66993C2212yescomplemented
45C2×#66992C2214yescomplemented
46C2×#66992C2214yescomplemented
47C2×#66992C2214yescomplemented
48D4×C22⋊D11C22132yescomplemented
49C2×#66991C2212yescomplemented
50C2×#66991C2212yescomplemented
51C2×#66991C2212yescomplemented
52C2×#66990C2214yescomplemented
53C2×#66989C2212yescomplemented
54C2×#66988C2214yescomplemented
55C2×D4×Dic11C2211yescharacteristic
56C2×D4×Dic11C2212yes—
57C2×D4×Dic11C2214yescomplemented
58C2×D4×Dic11C2212yescomplemented
59C2×D4×Dic11C2212yescomplemented
60C2×D4×Dic11C2214yescomplemented
61C2×D4×Dic11C2212yescomplemented
62C2×D4×Dic11C2211yescharacteristic, complemented
63C2×D4×Dic11C22132yescomplemented
64C2×#66983C2212yescomplemented
65C2×C4×C22⋊D11C2212yescomplemented
66C2×C4×C22⋊D11C2212yescomplemented
67C22×C4⋊Dic11C2212yescomplemented
68C2×#66977C2212yescomplemented
69C22×C4×Dic11C2212yescomplemented
70#10623249C22116yescomplemented
71#10623247C22116yescomplemented
72#10623142C22132yescomplemented
73#10623137C22132yescomplemented
74#10623129C22132yescomplemented
75#10623127C22132yescomplemented
76#10623122C22164yescomplemented
77#10623117C22164yescomplemented
78#10623086C22116yescomplemented
79C4×D4×D11C22116yescomplemented
80D4×Dic22C22116yescomplemented
81C4×#4341C22116yescomplemented
82C2×#66950C2212yescomplemented
83C2×#66946C2211yescharacteristic, complemented
84C2×#66945C2211yescharacteristic, complemented
85C2×C4⋊C4×D11C2211yescharacteristic, complemented
86C2×#66941C2212yescomplemented
87C2×#66940C2211yescharacteristic, complemented
88C2×#66939C2214yescomplemented
89C2×#66938C2214yescomplemented
90C2×#66936C2214yescomplemented
91C2×(C22⋊D11)⋊C4C2214yescomplemented
92C2×(C22⋊D11)⋊C4C2212yescomplemented
93C2×(C22⋊D11)⋊C4C2212yescomplemented
94C2×C22⋊C4×D11C2212yescomplemented
95C2×#66931C2214yescomplemented
96C2×#66931C2214yescomplemented
97C2×#66930C2212yescomplemented
98C2×C4×D44C2211yescharacteristic, complemented
99C2×C42×D11C2211yescharacteristic, complemented
100C2×#66922C2211yescharacteristic, complemented
101C2×C4×Dic22C2211yescharacteristic, complemented
102C25×C11C2314yes—
103C24×D11C2312yes—
104C22×D4×C11—216no—
105C22×D4×C11—216no—
106C22×D4×C11C2314yes—
107C22×D4×C11C2312yes—
108C22×D4×C11C23116yes—
109C22×D4×C11C2314yes—
110C22×D4×C11C2312yes—
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C22×D4×C11C2311yescharacteristic
114C22×D4×C11C23116yescomplemented
115C23×C4×C11C2312yes—
116C23×C4×C11C2312yes—
117C22×C22⋊D11—232no—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2314yes—
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2314yes—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C23132yescomplemented
125C23×Dic11—232no—
126C23×Dic11C2314yes—
127C23×Dic11C2314yes—
128C23×Dic11C2312yes—
129C23×Dic11C2314yes—
130C23×Dic11C2314yes—
131C23×Dic11C2312yes—
132C23×Dic11C2312yes—
133C23×Dic11C23132yescomplemented
134C2×#4341—216no—
135C2×#4341—232no—
136C2×#4341—232no—
137C2×#4341—2256no—
138C2×#4341—216no—
139C2×#4341—216no—
140C2×#4341D4116yesdirect product factor
141C2×#4341C2318yes—
142C2×#4341C23116yescomplemented
143C2×#4341C23116yescomplemented
144C2×#4341C23116yescomplemented
145C2×#4341C23132yescomplemented
146C2×#4341C23132yescomplemented
147C2×D4×D11—28no—
148C2×D4×D11C2318yes—
149C22×D44C2311yescharacteristic
150C22×C4×D11—216no—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C23116yescomplemented
158C22×Dic22—216no—
159C22×Dic22C2312yes—
160C22×Dic22C2314yes—
161C22×Dic22C2311yescharacteristic
162C22×Dic22C23116yescomplemented
163C11×#127C2318yescomplemented
164C11×#121C23116yescomplemented
165C11×#121C23116yescomplemented
166C11×#120C23132yescomplemented
167C4×D4×C11C2318yes—
168C4×D4×C11C2318yescomplemented
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2314yes—
174C2×C42×C11C2311yescharacteristic
175#67006C23132yescomplemented
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2314yes—
178C2×C22⋊Dic11C2314yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2314yes—
181C2×C22⋊Dic11C2314yes—
182C2×C22⋊Dic11C23132yescomplemented
183#66993C23116yescomplemented
184#66992C23132yescomplemented
185#66992C23132yescomplemented
186#66992C23132yescomplemented
187#66991C23116yescomplemented
188#66991C23116yescomplemented
189#66991C23116yescomplemented
190#66990C23132yescomplemented
191#66989C23116yescomplemented
192#66988C23132yescomplemented
193D4×Dic11C23116yes—
194D4×Dic11C2318yes—
195D4×Dic11C23116yescomplemented
196D4×Dic11C23116yescomplemented
197D4×Dic11C23116yescomplemented
198D4×Dic11C2318yescomplemented
199D4×Dic11C23132yescomplemented
200D4×Dic11C23132yescomplemented
201#66983C23116yescomplemented
202C4×C22⋊D11C23116yescomplemented
203C4×C22⋊D11C23116yescomplemented
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2314yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2314yes—
213C2×C4⋊Dic11C23116yescomplemented
214#66977C23116yescomplemented
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2314yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C23116yescomplemented
226#66950C23116yescomplemented
227#66946C2318yescomplemented
228#66945C2318yescomplemented
229C4⋊C4×D11C2318yescomplemented
230#66941C23116yescomplemented
231#66940C2318yescomplemented
232#66939C23132yescomplemented
233#66938C23132yescomplemented
234#66936C23132yescomplemented
235(C22⋊D11)⋊C4C23116yescomplemented
236(C22⋊D11)⋊C4C23116yescomplemented
237(C22⋊D11)⋊C4C23132yescomplemented
238C22⋊C4×D11C23116yescomplemented
239#66931C23132yescomplemented
240#66931C23132yescomplemented
241#66930C23116yescomplemented
242C4×D44C2318yescomplemented
243C42×D11C2318yescomplemented
244#66922C2318yescomplemented
245C4×Dic22C2318yescomplemented
246C2×D4×#41—111nomaximal, Sylow
247C24×C11—216no—
248C24×C11—216no—
249C24×C11—48no—
250C24×C11C2414yes—
251C24×C11C24116yes—
252C24×C11C2412yes—
253C24×C11C2412yes—
254C23×D11—28no—
255C23×D11—28no—
256C23×D11—44no—
257C23×D11C2412yes—
258C23×D11C2418yes—
259C23×D11C2411yescharacteristic
260C2×D4×C11—216no—
261C2×D4×C11—216no—
262C2×D4×C11—264no—
263C2×D4×C11—264no—
264C2×D4×C11—28no—
265C2×D4×C11—28no—
266C2×D4×C11—44no—
267C2×D4×C11C2×D418yescomplemented
268C2×D4×C11#4118yescomplemented
269C2×D4×C11C24116yes—
270C2×D4×C11C2418yes—
271C2×D4×C11C24116yes—
272C2×D4×C11C2418yes—
273C2×D4×C11C2418yes—
274C2×D4×C11C2414yes—
275C2×D4×C11C2414yes—
276C22×C4×C11—28no—
277C22×C4×C11—28no—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2418yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2418yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C2×C22⋊D11—2128no—
286C2×C22⋊D11—216no—
287C2×C22⋊D11—216no—
288C2×C22⋊D11—28no—
289C2×C22⋊D11—216no—
290C2×C22⋊D11—48no—
291C2×C22⋊D11C2×D4116yescomplemented
292C2×C22⋊D11C2418yes—
293C2×C22⋊D11C24116yes—
294C2×C22⋊D11C24116yes—
295C2×C22⋊D11C24116yes—
296C2×C22⋊D11C24116yes—
297C2×C22⋊D11C2418yes—
298C22×Dic11—216no—
299C22×Dic11—28no—
300C22×Dic11—216no—
301C22×Dic11—216no—
302C22×Dic11—2128no—
303C22×Dic11—216no—
304C22×Dic11—44no—
305C22×Dic11C2×D4116yescomplemented
306C22×Dic11C24116yes—
307C22×Dic11C24116yes—
308C22×Dic11C2418yes—
309C22×Dic11C24116yes—
310C22×Dic11C24116yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2414yes—
315C22×Dic11C2412yes—
316C22×Dic11C2418yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2418yes—
320#4341—2128no—
321#4341—2128no—
322#4341—264no—
323#4341—264no—
324#4341—264no—
325#4341C2×D4164yesdirect product factor
326D4×D11—232no—
327C2×D44—24no—
328C2×D44C2414yes—
329C2×C4×D11—28no—
330C2×C4×D11—264no—
331C2×C4×D11—28no—
332C2×C4×D11—28no—
333C2×C4×D11—24no—
334C2×C4×D11—42no—
335C2×C4×D11C2×D418yescomplemented
336C2×C4×D11C2414yes—
337C2×C4×D11C2418yes—
338C2×C4×D11C2418yes—
339C2×C4×D11C2418yes—
340C2×C4×D11C2414yes—
341C2×C4×D11C2414yes—
342C2×Dic22—216no—
343C2×Dic22—264no—
344C2×Dic22—28no—
345C2×Dic22C2×D418yescomplemented
346C2×Dic22C2418yes—
347C2×Dic22C24116yes—
348C2×Dic22C2414yes—
349C11×C4⋊C4C2414yes—
350C11×C4⋊C4C2414yes—
351C11×C22⋊C4C2418yes—
352C11×C22⋊C4C2418yes—
353C11×C22⋊C4C24116yes—
354C42×C11C2414yes—
355C22⋊Dic11C2418yes—
356C22⋊Dic11C24116yes—
357C22⋊Dic11C24116yes—
358C22⋊Dic11C2418yes—
359C22⋊Dic11C24116yes—
360C22⋊Dic11C24116yes—
361(C2×D11)⋊C4C2418yes—
362(C2×D11)⋊C4C2418yes—
363(C2×D11)⋊C4C2418yes—
364(C2×D11)⋊C4C24116yes—
365C4⋊Dic11C2414yes—
366C4⋊Dic11C2418yes—
367C4⋊Dic11C2418yes—
368C4⋊Dic11C2414yes—
369C4⋊Dic11C24116yes—
370Dic11⋊C4C2418yes—
371Dic11⋊C4C2418yes—
372Dic11⋊C4C2418yes—
373Dic11⋊C4C24116yes—
374C4×Dic11C2418yes—
375C4×Dic11C2414yes—
376C4×Dic11C2414yes—
377C4×Dic11C2414yes—
378C4×Dic11C2418yes—
379C4×Dic11C2418yes—
380C23×#41—112no—
381D4×#41—1132no—
382C2×#550—111no—
383C2×D4×Q8—111no—
384C2×#548—112no—
385C2×#547—112no—
386C2×#547—111no—
387C2×#546—112no—
388C2×#546—114no—
389C2×D42—112no—
390C2×D42D1111yescharacteristic, complemented
391C2×#532—111no—
392C2×#532—112no—
393C2×#525—112no—
394C2×#525—114no—
395C2×C4×#41—111no—
396C22×C4×D4—112no—
397C22×C4×D4—111no—
398C23×C11—24no—
399C23×C11—24no—
400C23×C11—24no—
401C23×C11—24no—
402C23×C11—232no—
403C23×C11—28no—
404C23×C11—28no—
405C23×C11—232no—
406C23×C11—28no—
407C23×C11—416no—
408C23×C11—464no—
409C23×C11C22×D418yes—
410C23×C11C2×#4118yescomplemented
411C23×C11C2518yes—
412C23×C11C2514yes—
413C23×C11C2514yes—
414C23×C11C2511yescharacteristic
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—24no—
418C22×D11—24no—
419C22×D11—216no—
420C22×D11—24no—
421C22×D11—216no—
422C22×D11—48no—
423C22×D11—432no—
424C22×D11C22×D414yes—
425C22×D11C2514yes—
426C22×D11C2512yes—
427D4×C11—232no—
428D4×C11—232no—
429D4×C11—216no—
430D4×C11—216no—
431D4×C11—48no—
432D4×C11C22×D4116yescomplemented
433D4×C11C2×#41116yescomplemented
434C2×C4×C11—24no—
435C2×C4×C11—24no—
436C2×C4×C11—22no—
437C2×C4×C11—216no—
438C2×C4×C11—216no—
439C2×C4×C11C22×D414yes—
440C2×C4×C11C2×#4114yescomplemented
441C2×C4×C11C2514yes—
442C2×C4×C11C2512yes—
443C2×C4×C11C2514yes—
444C2×C4×C11C2512yes—
445C2×C4×C11C2512yes—
446C22⋊D11—232no—
447C22⋊D11—216no—
448C22⋊D11—232no—
449C22⋊D11—232no—
450C22⋊D11—416no—
451C22⋊D11C22×D4132yescomplemented
452C2×Dic11—28no—
453C2×Dic11—24no—
454C2×Dic11—232no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—24no—
458C2×Dic11—232no—
459C2×Dic11—216no—
460C2×Dic11—232no—
461C2×Dic11—232no—
462C2×Dic11—48no—
463C2×Dic11C22×D418yes—
464C2×Dic11C22×D414yes—
465C2×Dic11C22×D4132yescomplemented
466C2×Dic11C2512yes—
467C2×Dic11C2512yes—
468C2×Dic11C2514yes—
469C2×Dic11C2518yes—
470C2×Dic11C2514yes—
471C2×Dic11C2512yes—
472C2×Dic11C2514yes—
473D44—28no—
474C4×D11—216no—
475C4×D11—216no—
476C4×D11—28no—
477C4×D11—216no—
478C4×D11—44no—
479C4×D11C22×D4116yescomplemented
480Dic22—216no—
481Dic22—232no—
482Dic22C22×D4116yescomplemented
483C22×#41—111no—
484C22×#41—114no—
485C22×#41—112no—
486C22×#41—112no—
487C22×#41—114no—
488C22×#41—112no—
489C22×#41—1132no—
490C22×#41—2232no—
491C23×Q8—112no—
492C23×D4—114no—
493C23×D4—111no—
494C23×D4C2×D1112yes—
495C23×D4C2×D1112yescomplemented
496C24×C4—114no—
497C24×C4—112no—
498#550—1116no—
499D4×Q8—1116no—
500#548—1132no—
501#547—1132no—
502#547—1116no—
503#546—1132no—
504#546—1164no—
505D42—1132no—
506D42C2×D11116yescomplemented
507#532—1116no—
508#532—1132no—
509C2×C4⋊Q8—112no—
510C2×C4⋊Q8—111no—
511C2×#127—112no—
512C2×#127C2×D1111yescharacteristic, complemented
513C2×#124—112no—
514C2×#124—114no—
515#525—1132no—
516#525—1164no—
517C2×#123—114no—
518C2×#123—114no—
519C2×#123—114no—
520C2×C22⋊Q8—112no—
521C2×C22⋊Q8—112no—
522C2×C22⋊Q8—114no—
523C2×C22⋊Q8—114no—
524C2×#121—112no—
525C2×#121—112no—
526C2×#121—112no—
527C2×#121—114no—
528C2×#121—114no—
529C2×#121—114no—
530C2×#121—112no—
531C2×#121C2×D1112yescomplemented
532C2×#121C2×D1112yescomplemented
533C2×#120—114no—
534C2×#120—114no—
535C2×#120C2×D1114yescomplemented
536C4×#41—1116no—
537C2×C4×Q8—111no—
538C2×C4×Q8—111no—
539C2×C4×D4—111no—
540C2×C4×D4—112no—
541C2×C4×D4—114no—
542C2×C4×D4—112no—
543C2×C4×D4—114no—
544C2×C4×D4—112no—
545C2×C4×D4—1132no—
546C2×C4×D4—111no—
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—1116no—
551C2×C4×D4—111no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—114no—
555C2×C4×D4—111no—
556C2×C4×D4C2×D1111yescharacteristic
557C2×C4×D4C2×D1111yescharacteristic, complemented
558C2×#117—111no—
559C2×#117—112no—
560C22×C4⋊C4—112no—
561C22×C4⋊C4—111no—
562C22×C22⋊C4—114no—
563C22×C22⋊C4—112no—
564C22×C42—112no—
565C22×C42—111no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—24no—
569C22×C11—24no—
570C22×C11—216no—
571C22×C11—216no—
572C22×C11—28no—
573C22×C11—28no—
574C22×C11—28no—
575C22×C11—464no—
576C22×C11—416no—
577C22×C11C23×D418yes—
578C22×C11C23×D412yes—
579C22×C11C22×#4112yes—
580C22×C11C22×#4118yescomplemented
581C22×C11#58512yes—
582C22×C11C2611yescharacteristic
583C2×D11—22no—
584C2×D11—22no—
585C2×D11—28no—
586C2×D11—24no—
587C2×D11—24no—
588C2×D11—24no—
589C2×D11—432no—
590C2×D11—48no—
591C2×D11C23×D414yes—
592C4×C11—24no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11C23×D414yes—
596C4×C11C22×#4114yescomplemented
597Dic11—28no—
598Dic11—24no—
599Dic11—22no—
600Dic11—22no—
601Dic11—24no—
602Dic11C23×D418yes—
603Dic11C23×D414yes—
604C25—112no—
605C25C22×D1114yes—
606C2×#41—1116no—
607C2×#41—118no—
608C2×#41—1132no—
609C2×#41—1116no—
610C2×#41—1116no—
611C2×#41—1132no—
612C2×#41—1116no—
613C2×#41—2232no—
614C2×#41—2216no—
615C2×#41—2232no—
616C2×#41—2216no—
617C2×#41—22256no—
618C2×#41—2216no—
619C22×Q8—111no—
620C22×Q8—114no—
621C22×Q8—112no—
622C22×Q8—1116no—
623C22×Q8—2216no—
624C22×D4—216no—
625C22×D4—216no—
626C22×D4—112no—
627C22×D4—112no—
628C22×D4—114no—
629C22×D4—114no—
630C22×D4—114no—
631C22×D4—1132no—
632C22×D4—114no—
633C22×D4—118no—
634C22×D4—111no—
635C22×D4—2232no—
636C22×D4—228no—
637C22×D4C22×D1114yes—
638C22×D4C22×D1112yes—
639C22×D4C22×D11116yes—
640C22×D4C22×D1114yes—
641C22×D4C22×D1112yes—
642C22×D4C22×D1112yes—
643C22×D4C22×D1111yescharacteristic
644C22×D4C22×D1111yescharacteristic
645C22×D4C22×D11116yescomplemented
646C23×C4—112no—
647C23×C4—111no—
648C23×C4—114no—
649C23×C4—112no—
650C23×C4—114no—
651C23×C4—114no—
652C23×C4—114no—
653C23×C4—1132no—
654C23×C4—112no—
655C23×C4—112no—
656C23×C4—111no—
657C23×C4—112no—
658C23×C4—112no—
659C23×C4—1116no—
660C23×C4—111no—
661C23×C4—2216no—
662C23×C4—2232no—
663C23×C4C22×D1112yes—
664C23×C4C22×D1112yes—
665C4⋊Q8—1116no—
666C4⋊Q8—118no—
667#127—1116no—
668#127C22×D1118yescomplemented
669#124—1116no—
670#124—1132no—
671#123—1132no—
672#123—1132no—
673#123—1132no—
674C22⋊Q8—1116no—
675C22⋊Q8—1116no—
676C22⋊Q8—1132no—
677C22⋊Q8—1132no—
678#121—1132no—
679#121—1116no—
680#121—1132no—
681#121—1116no—
682#121—1116no—
683#121—1132no—
684#121—1116no—
685#121C22×D11116yescomplemented
686#121C22×D11116yescomplemented
687#120—1132no—
688#120—1132no—
689#120C22×D11132yescomplemented
690C4×Q8—118no—
691C4×Q8—118no—
692C4×D4—118no—
693C4×D4—1132no—
694C4×D4—1116no—
695C4×D4—1116no—
696C4×D4—1132no—
697C4×D4—1116no—
698C4×D4—118no—
699C4×D4—1116no—
700C4×D4—1116no—
701C4×D4—1116no—
702C4×D4—118no—
703C4×D4—1116no—
704C4×D4—1116no—
705C4×D4—1132no—
706C4×D4—118no—
707C4×D4C22×D1118yes—
708C4×D4C22×D1118yescomplemented
709#117—118no—
710#117—1116no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—112no—
713C2×C4⋊C4—112no—
714C2×C4⋊C4—114no—
715C2×C4⋊C4—1116no—
716C2×C4⋊C4—112no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—111no—
719C2×C4⋊C4—114no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—118no—
722C2×C4⋊C4C22×D1111yescharacteristic
723C2×C4⋊C4C22×D1111yescharacteristic
724C2×C22⋊C4—112no—
725C2×C22⋊C4—114no—
726C2×C22⋊C4—114no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—1132no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4—112no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—114no—
735C2×C22⋊C4—1116no—
736C2×C22⋊C4C22×D1112yes—
737C2×C22⋊C4C22×D1112yes—
738C2×C22⋊C4C22×D1114yes—
739C2×C42—112no—
740C2×C42—111no—
741C2×C42—111no—
742C2×C42—112no—
743C2×C42—111no—
744C2×C42—112no—
745C2×C42—1116no—
746C2×C42—118no—
747C2×C42C22×D1111yescharacteristic
748C2×C11—28no—
749C2×C11—28no—
750C2×C11—48no—
751C2×C11D4×#4114yescomplemented
752C2×C11C24×D411yescharacteristic
753C2×C11C23×#4111yescharacteristic
754C2×C11C2×#58511yescharacteristic
755D11—24no—
756D11—44no—
757C24—216no—
758C24—216no—
759C24—48no—
760C24—111no—
761C24—112no—
762C24—118no—
763C24—228no—
764C24—228no—
765C24—444no—
766C24C23×D1114yes—
767C24C23×D11116yes—
768C24C23×D1112yes—
769C24C23×D1112yes—
770#41—1164no—
771#41—22128no—
772#41—2264no—
773#41—22128no—
774#41—2264no—
775#41—2264no—
776C2×Q8—118no—
777C2×Q8—114no—
778C2×Q8—1116no—
779C2×Q8—118no—
780C2×Q8—2216no—
781C2×Q8—2264no—
782C2×Q8—228no—
783C2×D4—216no—
784C2×D4—216no—
785C2×D4—264no—
786C2×D4—264no—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—44no—
790C2×D4—1116no—
791C2×D4—118no—
792C2×D4—118no—
793C2×D4—1116no—
794C2×D4—1116no—
795C2×D4—1116no—
796C2×D4—1116no—
797C2×D4—114no—
798C2×D4—2216no—
799C2×D4—22128no—
800C2×D4—2216no—
801C2×D4—2216no—
802C2×D4—228no—
803C2×D4—2232no—
804C2×D4—224no—
805C2×D4—448no—
806C2×D4D4×D1118yescomplemented
807C2×D4#434118yesdirect product factor
808C2×D4C23×D11116yes—
809C2×D4C23×D1118yes—
810C2×D4C23×D11116yes—
811C2×D4C23×D1118yes—
812C2×D4C23×D1118yes—
813C2×D4C23×D1114yes—
814C2×D4C23×D1114yes—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—1116no—
818C22×C4—118no—
819C22×C4—111no—
820C22×C4—112no—
821C22×C4—118no—
822C22×C4—114no—
823C22×C4—1116no—
824C22×C4—118no—
825C22×C4—1116no—
826C22×C4—1116no—
827C22×C4—1116no—
828C22×C4—111no—
829C22×C4—111no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—114no—
833C22×C4—118no—
834C22×C4—114no—
835C22×C4—118no—
836C22×C4—118no—
837C22×C4—118no—
838C22×C4—114no—
839C22×C4—228no—
840C22×C4—2264no—
841C22×C4—228no—
842C22×C4—228no—
843C22×C4—2216no—
844C22×C4—2216no—
845C22×C4—2216no—
846C22×C4—22128no—
847C22×C4—2216no—
848C22×C4—228no—
849C22×C4—224no—
850C22×C4—442no—
851C22×C4—444no—
852C22×C4C23×D1118yes—
853C22×C4C23×D1118yes—
854C22×C4C23×D1112yes—
855C22×C4C23×D1111yescharacteristic
856C22×C4C23×D1112yes—
857C22×C4C23×D1111yescharacteristic
858C22×C4C23×D1111yescharacteristic
859C4⋊C4—114no—
860C4⋊C4—118no—
861C4⋊C4—118no—
862C4⋊C4—1116no—
863C4⋊C4—118no—
864C4⋊C4—118no—
865C4⋊C4—114no—
866C4⋊C4—1116no—
867C4⋊C4—118no—
868C4⋊C4C23×D1114yes—
869C4⋊C4C23×D1114yes—
870C22⋊C4—118no—
871C22⋊C4—1116no—
872C22⋊C4—1116no—
873C22⋊C4—1116no—
874C22⋊C4—118no—
875C22⋊C4—1116no—
876C22⋊C4—118no—
877C22⋊C4—118no—
878C22⋊C4—118no—
879C22⋊C4—1116no—
880C22⋊C4C23×D1118yes—
881C22⋊C4C23×D1118yes—
882C22⋊C4C23×D11116yes—
883C42—114no—
884C42—118no—
885C42—114no—
886C42—118no—
887C42—114no—
888C42—118no—
889C42C23×D1114yes—
890C11C2×D4×#4111yescharacteristic, complemented, Sylow
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—232no—
896C23—28no—
897C23—28no—
898C23—232no—
899C23—28no—
900C23—416no—
901C23—464no—
902C23—114no—
903C23—112no—
904C23—114no—
905C23—2216no—
906C23—222no—
907C23—222no—
908C23—224no—
909C23—224no—
910C23—2216no—
911C23—224no—
912C23—448no—
913C23—4432no—
914C23C2×D4×D1118yes—
915C23C2×#434118yescomplemented
916C23C24×D1118yes—
917C23C24×D1114yes—
918C23C24×D1114yes—
919C23C24×D1111yescharacteristic
920Q8—1116no—
921Q8—2232no—
922Q8—2216no—
923D4—232no—
924D4—232no—
925D4—216no—
926D4—216no—
927D4—48no—
928D4—1132no—
929D4—2232no—
930D4—2232no—
931D4—2232no—
932D4—2216no—
933D4—228no—
934D4—4416no—
935D4C2×D4×D11116yescomplemented
936D4C2×#4341116yesdirect product factor
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—216no—
941C2×C4—216no—
942C2×C4—114no—
943C2×C4—118no—
944C2×C4—1132no—
945C2×C4—112no—
946C2×C4—114no—
947C2×C4—1116no—
948C2×C4—112no—
949C2×C4—112no—
950C2×C4—114no—
951C2×C4—114no—
952C2×C4—118no—
953C2×C4—2216no—
954C2×C4—2216no—
955C2×C4—2216no—
956C2×C4—2232no—
957C2×C4—2232no—
958C2×C4—2232no—
959C2×C4—224no—
960C2×C4—228no—
961C2×C4—2232no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—224no—
965C2×C4—2216no—
966C2×C4—228no—
967C2×C4—444no—
968C2×C4—448no—
969C2×C4C2×D4×D1114yes—
970C2×C4C2×#434114yescomplemented
971C2×C4C24×D1114yes—
972C2×C4C24×D1112yes—
973C2×C4C24×D1114yes—
974C2×C4C24×D1112yes—
975C2×C4C24×D1112yes—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—216no—
981C22—216no—
982C22—28no—
983C22—28no—
984C22—28no—
985C22—464no—
986C22—416no—
987C22—114no—
988C22—222no—
989C22—222no—
990C22—228no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22—4432no—
995C22—448no—
996C22C22×D4×D1118yes—
997C22C22×D4×D1112yes—
998C22C22×#434112yes—
999C22C22×#434118yescomplemented
1000C22#1062345512yes—
1001C22C25×D1111yescharacteristic
1002C4—24no—
1003C4—24no—
1004C4—22no—
1005C4—114no—
1006C4—118no—
1007C4—224no—
1008C4—228no—
1009C4—222no—
1010C4—222no—
1011C4—224no—
1012C4C22×D4×D1114yes—
1013C4C22×#434114yescomplemented
1014C2—28no—
1015C2—28no—
1016C2—48no—
1017C2—224no—
1018C2—444no—
1019C2D4×#434114yesdirect product factor
1020C2C23×D4×D1111yescharacteristic
1021C2C23×#434111yescharacteristic
1022C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×D42×C11C2
socleC23×C11C25
hypercenterC2×D42D11
hypocenterC11C2×D4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. D4×#4341C2direct (N × H)
3. C2×#10623249C2semidirect
4. C2×D4×Dic22C2semidirect
5. C2×#10623129C2semidirect
6. C2×#10623086C2semidirect
7. C2×#10623142C2semidirect
8. C2×#10623337C2semidirect
9. C2×#10623122C2semidirect
10. C2×D4×C22⋊D11C2semidirect
11. C2×#10623247C2semidirect
12. C2×#10623127C2semidirect
13. C2×#10623137C2semidirect
14. C2×#10623117C2semidirect
15. C2×C4×#4341C2semidirect
16. C22×D4×Dic11C2semidirect
17. C2×C4×D4×D11C2semidirect
18. C2×D42×C11C2semidirect
20. C23×D4×C11C22semidirect
21. C23×C22⋊D11C22semidirect
22. C24×Dic11C22semidirect
25. C22×#4341C22semidirect
26. C22×#4341C22semidirect
27. C22×#4341C22semidirect
28. C22×#4341C22semidirect
29. C22×#4341C22semidirect
30. C22×#4341C22semidirect
32. C23×C4×D11C22semidirect
33. C23×Dic22C22semidirect
34. D42×C11C22semidirect
35. C2×C11×#127C22semidirect
36. C2×C11×#121C22semidirect
37. C2×C11×#121C22semidirect
38. C2×C11×#120C22semidirect
40. C2×C4×D4×C11C22semidirect
41. C2×#67006C22semidirect
42. C22×C22⋊Dic11C22semidirect
43. #10623337C22semidirect
44. C2×#66993C22semidirect
45. C2×#66992C22semidirect
46. C2×#66992C22semidirect
47. C2×#66992C22semidirect
48. D4×C22⋊D11C22semidirect
49. C2×#66991C22semidirect
50. C2×#66991C22semidirect
51. C2×#66991C22semidirect
52. C2×#66990C22semidirect
53. C2×#66989C22semidirect
54. C2×#66988C22semidirect
57. C2×D4×Dic11C22semidirect
58. C2×D4×Dic11C22semidirect
59. C2×D4×Dic11C22semidirect
60. C2×D4×Dic11C22semidirect
61. C2×D4×Dic11C22semidirect
62. C2×D4×Dic11C22semidirect
63. C2×D4×Dic11C22semidirect
64. C2×#66983C22semidirect
65. C2×C4×C22⋊D11C22semidirect
66. C2×C4×C22⋊D11C22semidirect
67. C22×C4⋊Dic11C22semidirect
68. C2×#66977C22semidirect
69. C22×C4×Dic11C22semidirect
70. #10623249C22semidirect
71. #10623247C22semidirect
72. #10623142C22semidirect
73. #10623137C22semidirect
74. #10623129C22semidirect
75. #10623127C22semidirect
76. #10623122C22semidirect
77. #10623117C22semidirect
78. #10623086C22semidirect
79. C4×D4×D11C22semidirect
80. D4×Dic22C22semidirect
81. C4×#4341C22semidirect
82. C2×#66950C22semidirect
83. C2×#66946C22semidirect
84. C2×#66945C22semidirect
85. C2×C4⋊C4×D11C22semidirect
86. C2×#66941C22semidirect
87. C2×#66940C22semidirect
88. C2×#66939C22semidirect
89. C2×#66938C22semidirect
90. C2×#66936C22semidirect
91. C2×(C22⋊D11)⋊C4C22semidirect
92. C2×(C22⋊D11)⋊C4C22semidirect
93. C2×(C22⋊D11)⋊C4C22semidirect
94. C2×C22⋊C4×D11C22semidirect
95. C2×#66931C22semidirect
96. C2×#66931C22semidirect
97. C2×#66930C22semidirect
98. C2×C4×D44C22semidirect
99. C2×C42×D11C22semidirect
100. C2×#66922C22semidirect
101. C2×C4×Dic22C22semidirect
114. C22×D4×C11C23semidirect
124. C22×C22⋊D11C23semidirect
133. C23×Dic11C23semidirect
140. C2×#4341D4direct (N × H)
142. C2×#4341C23semidirect
143. C2×#4341C23semidirect
144. C2×#4341C23semidirect
145. C2×#4341C23semidirect
146. C2×#4341C23semidirect
157. C22×C4×D11C23semidirect
162. C22×Dic22C23semidirect
163. C11×#127C23semidirect
164. C11×#121C23semidirect
165. C11×#121C23semidirect
166. C11×#120C23semidirect
168. C4×D4×C11C23semidirect
175. #67006C23semidirect
182. C2×C22⋊Dic11C23semidirect
183. #66993C23semidirect
184. #66992C23semidirect
185. #66992C23semidirect
186. #66992C23semidirect
187. #66991C23semidirect
188. #66991C23semidirect
189. #66991C23semidirect
190. #66990C23semidirect
191. #66989C23semidirect
192. #66988C23semidirect
195. D4×Dic11C23semidirect
196. D4×Dic11C23semidirect
197. D4×Dic11C23semidirect
198. D4×Dic11C23semidirect
199. D4×Dic11C23semidirect
200. D4×Dic11C23semidirect
201. #66983C23semidirect
202. C4×C22⋊D11C23semidirect
203. C4×C22⋊D11C23semidirect
213. C2×C4⋊Dic11C23semidirect
214. #66977C23semidirect
225. C2×C4×Dic11C23semidirect
226. #66950C23semidirect
227. #66946C23semidirect
228. #66945C23semidirect
229. C4⋊C4×D11C23semidirect
230. #66941C23semidirect
231. #66940C23semidirect
232. #66939C23semidirect
233. #66938C23semidirect
234. #66936C23semidirect
235. (C22⋊D11)⋊C4C23semidirect
236. (C22⋊D11)⋊C4C23semidirect
237. (C22⋊D11)⋊C4C23semidirect
238. C22⋊C4×D11C23semidirect
239. #66931C23semidirect
240. #66931C23semidirect
241. #66930C23semidirect
242. C4×D44C23semidirect
243. C42×D11C23semidirect
244. #66922C23semidirect
245. C4×Dic22C23semidirect
267. C2×D4×C11C2×D4semidirect
268. C2×D4×C11#41semidirect
291. C2×C22⋊D11C2×D4semidirect
305. C22×Dic11C2×D4semidirect
325. #4341C2×D4direct (N × H)
335. C2×C4×D11C2×D4semidirect
345. C2×Dic22C2×D4semidirect
390. C2×D42D11semidirect
410. C23×C11C2×#41semidirect
432. D4×C11C22×D4semidirect
433. D4×C11C2×#41semidirect
440. C2×C4×C11C2×#41semidirect
451. C22⋊D11C22×D4semidirect
465. C2×Dic11C22×D4semidirect
479. C4×D11C22×D4semidirect
482. Dic22C22×D4semidirect
495. C23×D4C2×D11semidirect
506. D42C2×D11semidirect
512. C2×#127C2×D11semidirect
531. C2×#121C2×D11semidirect
532. C2×#121C2×D11semidirect
535. C2×#120C2×D11semidirect
557. C2×C4×D4C2×D11semidirect
580. C22×C11C22×#41semidirect
596. C4×C11C22×#41semidirect
645. C22×D4C22×D11semidirect
668. #127C22×D11semidirect
685. #121C22×D11semidirect
686. #121C22×D11semidirect
689. #120C22×D11semidirect
708. C4×D4C22×D11semidirect
751. C2×C11D4×#41semidirect
806. C2×D4D4×D11semidirect
807. C2×D4#4341direct (N × H)
890. C11C2×D4×#41semidirect
915. C23C2×#4341semidirect
935. D4C2×D4×D11semidirect
936. D4C2×#4341direct (N × H)
970. C2×C4C2×#4341semidirect
999. C22C22×#4341semidirect
1013. C4C22×#4341semidirect
1019. C2D4×#4341direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
D4×#43412
C2×#106232492
C2×D4×Dic222
C2×#106231292
C2×#106230862
C2×#106231422
C2×#106233372
C2×#106231222
C2×D4×C22⋊D112
C2×#106232472
C2×#106231272
C2×#106231372
C2×#106231172
C2×C4×#43412
C22×D4×Dic112
C2×C4×D4×D112
C2×D42×C112
C2×D4×#4111