Finite Group Databasebeta

← C2×D4×#4339 #15660733

Subgroups — C2×D4×#4339 #15660733

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×#4339C212yesmaximal, complemented
2D4×#4339C2132yesmaximal, direct product factor
3C2×#10623084C211yesmaximal, characteristic, complemented
4C2×D4×Dic22C211yesmaximal, characteristic, complemented
5C2×#10623083C212yesmaximal, complemented
6C2×#10623082C211yesmaximal, characteristic, complemented
7C2×#10623038C212yesmaximal, complemented
8C2×#10623081C212yesmaximal, complemented
9C2×#10623021C214yesmaximal, complemented
10C2×D4×D44C211yesmaximal, characteristic, complemented
11C2×D4×C22⋊D11C212yesmaximal, complemented
12C2×#10623008C211yesmaximal, characteristic, complemented
13C2×#10623079C212yesmaximal, complemented
14C2×#10623322C212yesmaximal, complemented
15C2×#10623078C214yesmaximal, complemented
16C2×C4×#4339C211yesmaximal, characteristic, complemented
17C2×C4×D4×D11C212yesmaximal, complemented
18C22×C4×D4×C11C211yesmaximal, characteristic, complemented
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2212yescomplemented
21C23×C22⋊D11C2214yescomplemented
22C22×D4×D11C2212yes—
23C22×#4339—232no—
24C22×#4339C2211yescharacteristic
25C22×#4339C2214yescomplemented
26C22×#4339C2212yescomplemented
27C22×#4339C2214yescomplemented
28C22×#4339C2212yescomplemented
29C22×#4339C2212yescomplemented
30C22×#4339C22132yescomplemented
31C23×D44C2212yescomplemented
32C23×C4×D11C2214yescomplemented
33C23×Dic22C2212yescomplemented
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2212yescomplemented
37C2×C4×D4×C11C2211yescharacteristic, complemented
38C2×C4×D4×C11C2212yescomplemented
39C2×C4×D4×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C22116yescomplemented
41C22×C11×C4⋊C4C2211yescharacteristic, complemented
42C22×C11×C22⋊C4C2212yescomplemented
43C22×C42×C11C2211yescharacteristic, complemented
44C2×#67006C2214yescomplemented
45C2×#66993C2212yescomplemented
46C2×#66992C2214yescomplemented
47D4×C22⋊D11C22132yescomplemented
48C2×#66991C2212yescomplemented
49C2×#66990C2214yescomplemented
50C2×D4×Dic11C2212yes—
51#10623322C22132yescomplemented
52C2×#66983C2212yescomplemented
53C2×#66983C2212yescomplemented
54C2×#66983C2212yescomplemented
55C2×#66983C2212yescomplemented
56C2×#66982C2214yescomplemented
57C2×C4×C22⋊D11C2214yescomplemented
58C2×C4×C22⋊D11C2214yescomplemented
59C2×C4×C22⋊D11C2212yescomplemented
60C2×C4×C22⋊D11C2212yescomplemented
61C2×#66979C2211yescharacteristic, complemented
62C2×#66977C2212yescomplemented
63C2×#66977C2212yescomplemented
64#10623084C22116yescomplemented
65#10623083C22132yescomplemented
66#10623082C22116yescomplemented
67#10623081C22132yescomplemented
68D4×D44C22116yescomplemented
69#10623079C22132yescomplemented
70#10623078C22164yescomplemented
71C4×D4×D11C22132yescomplemented
72D4×Dic22C22116yescomplemented
73C2×#66949C2214yescomplemented
74#10623038C22132yescomplemented
75C2×#66948C2212yescomplemented
76C2×#66947C2214yescomplemented
77C2×#66946C2212yescomplemented
78C2×C4⋊C4×D11C2212yescomplemented
79C2×#66941C2212yescomplemented
80C2×#66938C2214yescomplemented
81#10623021C22164yescomplemented
82C2×#66937C2214yescomplemented
83C2×#66937C2214yescomplemented
84C2×#66936C2214yescomplemented
85C2×#66935C2214yescomplemented
86C2×(C22⋊D11)⋊C4C2214yescomplemented
87C2×C22⋊C4×D11C2214yescomplemented
88C2×#66931C2214yescomplemented
89#10623008C22116yescomplemented
90C2×#66928C2212yescomplemented
91C2×#66927C2211yescharacteristic, complemented
92C4×#4339C22116yescomplemented
93C2×C4×D44C2212yescomplemented
94C2×C4×D44C2212yescomplemented
95C2×C4×D44C2211yescharacteristic, complemented
96C2×C4×D44C2211yescharacteristic, complemented
97C2×#66925C2212yescomplemented
98C2×C42×D11C2212yescomplemented
99C2×#66922C2211yescharacteristic, complemented
100C2×C4×Dic22C2211yescharacteristic, complemented
101C2×C4×Dic22C2211yescharacteristic, complemented
102C25×C11C2312yes—
103C24×D11C2314yes—
104C22×D4×C11—28no—
105C22×D4×C11C2312yes—
106C22×D4×C11C2311yescharacteristic
107C22×D4×C11C2318yes—
108C22×D4×C11C2311yescharacteristic
109C23×C4×C11—216no—
110C23×C4×C11C2312yes—
111C23×C4×C11C2312yes—
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2312yes—
114C23×C4×C11C2312yes—
115C23×C4×C11C2312yes—
116C23×C4×C11C2311yescharacteristic
117C23×C4×C11C2311yescharacteristic
118C23×C4×C11C23116yescomplemented
119C22×C22⋊D11—232no—
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2314yes—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2314yes—
124C22×C22⋊D11C2314yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C23132yescomplemented
127C23×Dic11C2314yes—
128C2×D4×D11—216no—
129C2×D4×D11C23116yes—
130C2×#4339—216no—
131C2×#4339—232no—
132C2×#4339—2256no—
133C2×#4339—216no—
134C2×#4339—232no—
135C2×#4339—216no—
136C2×#4339D4116yesdirect product factor
137C2×#4339C2318yes—
138C2×#4339C23116yescomplemented
139C2×#4339C23132yescomplemented
140C2×#4339C23132yescomplemented
141C2×#4339C23116yescomplemented
142C2×#4339C23116yescomplemented
143C22×D44—216no—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×D44C2314yes—
147C22×D44C2312yes—
148C22×D44C2311yescharacteristic
149C22×D44C23116yescomplemented
150C22×C4×D11—232no—
151C22×C4×D11C2312yes—
152C22×C4×D11C2314yes—
153C22×C4×D11C2314yes—
154C22×C4×D11C2314yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C23132yescomplemented
158C22×Dic22—216no—
159C22×Dic22C2312yes—
160C22×Dic22C2314yes—
161C22×Dic22C2311yescharacteristic
162C22×Dic22C23116yescomplemented
163C4×D4×C11C2318yes—
164C4×D4×C11C2318yes—
165C4×D4×C11C23116yescomplemented
166C4×D4×C11C2318yescomplemented
167C4×D4×C11C23116yescomplemented
168C4×D4×C11C2318yescomplemented
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2318yescomplemented
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C23116yescomplemented
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2311yescharacteristic
180C2×C42×C11C2311yescharacteristic
181C2×C42×C11C2311yescharacteristic
182C2×C42×C11C2318yescomplemented
183#67006C23132yescomplemented
184C2×C22⋊Dic11C2314yes—
185C2×C22⋊Dic11C2314yes—
186C2×C22⋊Dic11C2312yes—
187#66993C23116yescomplemented
188#66992C23132yescomplemented
189#66991C23116yescomplemented
190#66990C23132yescomplemented
191D4×Dic11C23116yes—
192#66983C23116yescomplemented
193#66983C23116yescomplemented
194#66983C23116yescomplemented
195#66983C23116yescomplemented
196#66982C23132yescomplemented
197C4×C22⋊D11C23116yescomplemented
198C4×C22⋊D11C23116yescomplemented
199C4×C22⋊D11C23132yescomplemented
200C4×C22⋊D11C23132yescomplemented
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2314yes—
204C2×(C2×D11)⋊C4C2314yes—
205C2×(C2×D11)⋊C4C2314yes—
206C2×(C2×D11)⋊C4C2314yes—
207#66979C2318yescomplemented
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212#66977C23116yescomplemented
213#66977C23116yescomplemented
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2314yes—
217C2×Dic11⋊C4C2314yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66949C23132yescomplemented
222#66948C23116yescomplemented
223#66947C23132yescomplemented
224#66946C23116yescomplemented
225C4⋊C4×D11C23116yescomplemented
226#66941C23116yescomplemented
227#66938C23132yescomplemented
228#66937C23132yescomplemented
229#66937C23132yescomplemented
230#66936C23132yescomplemented
231#66935C23132yescomplemented
232(C22⋊D11)⋊C4C23132yescomplemented
233C22⋊C4×D11C23132yescomplemented
234#66931C23132yescomplemented
235#66928C23116yescomplemented
236#66927C2318yescomplemented
237C4×D44C2318yescomplemented
238C4×D44C2318yescomplemented
239C4×D44C23116yescomplemented
240C4×D44C23116yescomplemented
241#66925C23116yescomplemented
242C42×D11C23116yescomplemented
243#66922C2318yescomplemented
244C4×Dic22C2318yescomplemented
245C4×Dic22C2318yescomplemented
246C2×D4×#41—111nomaximal, Sylow
247C24×C11—28no—
248C24×C11—28no—
249C24×C11—44no—
250C24×C11C2412yes—
251C24×C11C2418yes—
252C24×C11C2411yescharacteristic
253C24×C11C2412yes—
254C23×D11—216no—
255C23×D11—216no—
256C23×D11—48no—
257C23×D11C2414yes—
258C23×D11C24116yes—
259C23×D11C2412yes—
260C2×D4×C11—28no—
261C2×D4×C11—232no—
262C2×D4×C11—24no—
263C2×D4×C11#4118yescomplemented
264C2×D4×C11C2418yes—
265C2×D4×C11C2414yes—
266C2×D4×C11C2414yes—
267C22×C4×C11—28no—
268C22×C4×C11—28no—
269C22×C4×C11—28no—
270C22×C4×C11—28no—
271C22×C4×C11—28no—
272C22×C4×C11—264no—
273C22×C4×C11—24no—
274C22×C4×C11—42no—
275C22×C4×C11C2×D418yescomplemented
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2418yes—
282C22×C4×C11C2418yes—
283C22×C4×C11C2414yes—
284C22×C4×C11C2418yes—
285C22×C4×C11C2418yes—
286C22×C4×C11C2418yes—
287C22×C4×C11C2414yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2414yes—
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—2128no—
293C2×C22⋊D11—216no—
294C2×C22⋊D11—216no—
295C2×C22⋊D11—216no—
296C2×C22⋊D11—216no—
297C2×C22⋊D11—48no—
298C2×C22⋊D11C2×D4116yescomplemented
299C2×C22⋊D11C24116yes—
300C2×C22⋊D11C24116yes—
301C2×C22⋊D11C24116yes—
302C2×C22⋊D11C24116yes—
303C2×C22⋊D11C24116yes—
304C2×C22⋊D11C2418yes—
305C22×Dic11—216no—
306C22×Dic11C24116yes—
307C22×Dic11C2412yes—
308C22×Dic11C2412yes—
309C22×Dic11C2414yes—
310C22×Dic11C2412yes—
311D4×D11—264no—
312#4339—2128no—
313#4339—264no—
314#4339—2128no—
315#4339—264no—
316#4339—264no—
317#4339C2×D4164yesdirect product factor
318C2×D44—264no—
319C2×D44—216no—
320C2×D44—28no—
321C2×D44—28no—
322C2×D44—44no—
323C2×D44C2×D418yescomplemented
324C2×D44C2418yes—
325C2×D44C2418yes—
326C2×D44C24116yes—
327C2×D44C2418yes—
328C2×D44C2414yes—
329C2×C4×D11—216no—
330C2×C4×D11—2128no—
331C2×C4×D11—216no—
332C2×C4×D11—216no—
333C2×C4×D11—28no—
334C2×C4×D11—44no—
335C2×C4×D11C2×D4116yescomplemented
336C2×C4×D11C2418yes—
337C2×C4×D11C24116yes—
338C2×C4×D11C24116yes—
339C2×C4×D11C24116yes—
340C2×C4×D11C2418yes—
341C2×C4×D11C2418yes—
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×C4⋊C4C2418yes—
352C11×C22⋊C4C2418yes—
353C11×C22⋊C4C2418yes—
354C11×C22⋊C4C2418yes—
355C11×C22⋊C4C2418yes—
356C42×C11C2414yes—
357C42×C11C2414yes—
358C42×C11C2414yes—
359C42×C11C2414yes—
360C22⋊Dic11C24116yes—
361C22⋊Dic11C24116yes—
362C22⋊Dic11C2418yes—
363(C2×D11)⋊C4C2418yes—
364(C2×D11)⋊C4C2418yes—
365(C2×D11)⋊C4C24116yes—
366(C2×D11)⋊C4C24116yes—
367(C2×D11)⋊C4C24116yes—
368(C2×D11)⋊C4C24116yes—
369C4⋊Dic11C2414yes—
370C4⋊Dic11C2414yes—
371C4⋊Dic11C2418yes—
372C4⋊Dic11C2418yes—
373Dic11⋊C4C2418yes—
374Dic11⋊C4C2418yes—
375Dic11⋊C4C24116yes—
376Dic11⋊C4C24116yes—
377C4×Dic11C2418yes—
378C4×Dic11C2418yes—
379C4×Dic11C2418yes—
380C23×#41—112no—
381D4×#41—1132no—
382C2×#550—111no—
383C2×D4×Q8—111no—
384C2×#548—112no—
385C2×#547—111no—
386C2×#547—112no—
387C2×#546—112no—
388C2×#546—114no—
389C2×D42—112no—
390C2×D42—111no—
391C2×#532—111no—
392C2×#532—112no—
393C2×#525—112no—
394C2×#525—114no—
395C2×C4×#41—111no—
396C22×C4×D4—112no—
397C22×C4×D4D1111yescharacteristic, complemented
398C23×C11—24no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—24no—
402C23×C11—216no—
403C23×C11—24no—
404C23×C11—24no—
405C23×C11—216no—
406C23×C11—24no—
407C23×C11—48no—
408C23×C11—432no—
409C23×C11C22×D414yes—
410C23×C11C2×#4118yescomplemented
411C23×C11C2514yes—
412C23×C11C2512yes—
413C23×C11C2514yes—
414C23×C11C2511yescharacteristic
415C22×D11—24no—
416C22×D11—24no—
417C22×D11—28no—
418C22×D11—28no—
419C22×D11—232no—
420C22×D11—28no—
421C22×D11—232no—
422C22×D11—416no—
423C22×D11—464no—
424C22×D11C22×D418yes—
425C22×D11C2518yes—
426C22×D11C2514yes—
427D4×C11—216no—
428D4×C11—28no—
429D4×C11C2×#41116yescomplemented
430C2×C4×C11—24no—
431C2×C4×C11—24no—
432C2×C4×C11—216no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—216no—
437C2×C4×C11—216no—
438C2×C4×C11—216no—
439C2×C4×C11—216no—
440C2×C4×C11—28no—
441C2×C4×C11—44no—
442C2×C4×C11C22×D414yes—
443C2×C4×C11C22×D414yes—
444C2×C4×C11C22×D4116yescomplemented
445C2×C4×C11C2×#4114yescomplemented
446C2×C4×C11C2512yes—
447C2×C4×C11C2512yes—
448C2×C4×C11C2512yes—
449C2×C4×C11C2514yes—
450C2×C4×C11C2514yes—
451C2×C4×C11C2512yes—
452C2×C4×C11C2512yes—
453C2×C4×C11C2512yes—
454C22⋊D11—232no—
455C22⋊D11—232no—
456C22⋊D11—232no—
457C22⋊D11—232no—
458C22⋊D11—416no—
459C22⋊D11C22×D4132yescomplemented
460C2×Dic11—28no—
461C2×Dic11—24no—
462C2×Dic11—24no—
463C2×Dic11—232no—
464C2×Dic11C22×D418yes—
465C2×Dic11C2514yes—
466C2×Dic11C2514yes—
467C2×Dic11C2518yes—
468C2×Dic11C2514yes—
469D44—232no—
470D44—216no—
471D44—216no—
472D44—48no—
473D44C22×D4116yescomplemented
474C4×D11—232no—
475C4×D11—232no—
476C4×D11—216no—
477C4×D11—232no—
478C4×D11—48no—
479C4×D11C22×D4132yescomplemented
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—112no—
494C23×D4—112no—
495C23×D4C2×D1111yescharacteristic
496C24×C4—114no—
497C24×C4C2×D1112yescomplemented
498#550—1116no—
499D4×Q8—1116no—
500#548—1132no—
501#547—1116no—
502#547—1132no—
503#546—1132no—
504#546—1164no—
505D42—1132no—
506D42—1116no—
507#532—1132no—
508#532—1116no—
509C2×C4⋊Q8—112no—
510C2×C4⋊Q8—111no—
511C2×#127—112no—
512C2×#127—111no—
513C2×#124—114no—
514C2×#124—112no—
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—114no—
526C2×#121—112no—
527C2×#121—112no—
528C2×#121—112no—
529C2×#121—112no—
530C2×#121—112no—
531C2×#121—114no—
532C2×#121—114no—
533C2×#120—114no—
534C2×#120—114no—
535C2×#120—114no—
536C4×#41—1116no—
537C2×C4×Q8—111no—
538C2×C4×Q8—111no—
539C2×C4×D4—112no—
540C2×C4×D4—114no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4—114no—
544C2×C4×D4—1132no—
545C2×C4×D4—112no—
546C2×C4×D4—114no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4C2×D1111yescharacteristic
552C2×C4×D4C2×D1111yescharacteristic
553C2×C4×D4C2×D1112yescomplemented
554C2×C4×D4C2×D1111yescharacteristic, complemented
555C2×C4×D4C2×D1112yescomplemented
556C2×C4×D4C2×D1111yescharacteristic, complemented
557C2×C4×D4C2×D11116yescomplemented
558C2×#117—111no—
559C2×#117—112no—
560C22×C4⋊C4—112no—
561C22×C4⋊C4C2×D1111yescharacteristic, complemented
562C22×C22⋊C4—114no—
563C22×C22⋊C4C2×D1112yescomplemented
564C22×C42—112no—
565C22×C42C2×D1111yescharacteristic, complemented
566C22×C11—24no—
567C22×C11—22no—
568C22×C11—22no—
569C22×C11—24no—
570C22×C11—216no—
571C22×C11—28no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—24no—
575C22×C11—432no—
576C22×C11—48no—
577C22×C11C23×D414yes—
578C22×C11C23×D412yes—
579C22×C11C22×#4112yes—
580C22×C11C22×#4118yescomplemented
581C22×C11#58512yes—
582C22×C11C2611yescharacteristic
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—216no—
586C2×D11—28no—
587C2×D11—28no—
588C2×D11—28no—
589C2×D11—464no—
590C2×D11—416no—
591C2×D11C23×D418yes—
592C4×C11—24no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11C23×D414yes—
598C4×C11C23×D414yes—
599C4×C11C22×#4114yescomplemented
600Dic11—28no—
601Dic11—24no—
602Dic11—24no—
603Dic11C23×D418yes—
604C25—114no—
605C25C22×D1112yes—
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—2232no—
615C2×#41—2216no—
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—28no—
625C22×D4—112no—
626C22×D4—114no—
627C22×D4—114no—
628C22×D4—114no—
629C22×D4—114no—
630C22×D4—1132no—
631C22×D4—114no—
632C22×D4—1116no—
633C22×D4—111no—
634C22×D4—112no—
635C22×D4—114no—
636C22×D4—112no—
637C22×D4—1116no—
638C22×D4—112no—
639C22×D4—2216no—
640C22×D4—2232no—
641C22×D4—2216no—
642C22×D4C22×D1112yes—
643C22×D4C22×D1111yescharacteristic
644C22×D4C22×D1118yes—
645C22×D4C22×D1111yescharacteristic
646C23×C4—216no—
647C23×C4—112no—
648C23×C4—114no—
649C23×C4—114no—
650C23×C4—112no—
651C23×C4—114no—
652C23×C4—1132no—
653C23×C4—114no—
654C23×C4—112no—
655C23×C4—2232no—
656C23×C4C22×D1112yes—
657C23×C4C22×D1111yescharacteristic
658C23×C4C22×D1112yes—
659C23×C4C22×D1112yes—
660C23×C4C22×D1112yes—
661C23×C4C22×D1112yes—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D11116yescomplemented
665C4⋊Q8—1116no—
666C4⋊Q8—118no—
667#127—1116no—
668#127—118no—
669#124—1132no—
670#124—1116no—
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—1116no—
681#121—1116no—
682#121—1116no—
683#121—1116no—
684#121—1116no—
685#121—1132no—
686#121—1132no—
687#120—1132no—
688#120—1132no—
689#120—1132no—
690C4×Q8—118no—
691C4×Q8—118no—
692C4×D4—1116no—
693C4×D4—1132no—
694C4×D4—1116no—
695C4×D4—1116no—
696C4×D4—1132no—
697C4×D4—1116no—
698C4×D4—1132no—
699C4×D4—1116no—
700C4×D4—118no—
701C4×D4—118no—
702C4×D4—1116no—
703C4×D4C22×D1118yes—
704C4×D4C22×D1118yes—
705C4×D4C22×D11116yescomplemented
706C4×D4C22×D1118yescomplemented
707C4×D4C22×D11116yescomplemented
708C4×D4C22×D1118yescomplemented
709#117—118no—
710#117—1116no—
711C2×C4⋊C4—112no—
712C2×C4⋊C4—114no—
713C2×C4⋊C4—112no—
714C2×C4⋊C4—112no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—111no—
717C2×C4⋊C4—114no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—1116no—
720C2×C4⋊C4C22×D1111yescharacteristic
721C2×C4⋊C4C22×D1111yescharacteristic
722C2×C4⋊C4C22×D1112yes—
723C2×C4⋊C4C22×D1118yescomplemented
724C2×C22⋊C4—114no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—114no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—114no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—112no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—1132no—
734C2×C22⋊C4C22×D1112yes—
735C2×C22⋊C4C22×D1112yes—
736C2×C22⋊C4C22×D1112yes—
737C2×C22⋊C4C22×D1112yes—
738C2×C22⋊C4C22×D11116yescomplemented
739C2×C42—112no—
740C2×C42—112no—
741C2×C42—112no—
742C2×C42—1116no—
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1111yescharacteristic
746C2×C42C22×D1111yescharacteristic
747C2×C42C22×D1118yescomplemented
748C2×C11—28no—
749C2×C11—24no—
750C2×C11—44no—
751C2×C11D4×#4114yescomplemented
752C2×C11C24×D411yescharacteristic
753C2×C11C23×#4111yescharacteristic
754C2×C11C2×#58511yescharacteristic
755D11—28no—
756D11—48no—
757C24—28no—
758C24—28no—
759C24—44no—
760C24—112no—
761C24—114no—
762C24—1116no—
763C24—2216no—
764C24—2216no—
765C24—448no—
766C24C23×D1112yes—
767C24C23×D1118yes—
768C24C23×D1112yes—
769C24C23×D1111yescharacteristic
770#41—1164no—
771#41—22128no—
772#41—22128no—
773#41—2264no—
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—28no—
784C2×D4—232no—
785C2×D4—24no—
786C2×D4—1116no—
787C2×D4—118no—
788C2×D4—1116no—
789C2×D4—1116no—
790C2×D4—1116no—
791C2×D4—1116no—
792C2×D4—1116no—
793C2×D4—118no—
794C2×D4—114no—
795C2×D4—118no—
796C2×D4—1116no—
797C2×D4—118no—
798C2×D4—118no—
799C2×D4—2264no—
800C2×D4—2216no—
801C2×D4—2216no—
802C2×D4—22128no—
803C2×D4—2216no—
804C2×D4—2216no—
805C2×D4—2216no—
806C2×D4—2264no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—444no—
810C2×D4—448no—
811C2×D4#433918yesdirect product factor
812C2×D4C23×D1118yes—
813C2×D4C23×D1114yes—
814C2×D4C23×D1114yes—
815C22×C4—28no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—264no—
822C22×C4—42no—
823C22×C4—112no—
824C22×C4—1116no—
825C22×C4—118no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—114no—
829C22×C4—1116no—
830C22×C4—118no—
831C22×C4—1116no—
832C22×C4—1116no—
833C22×C4—1116no—
834C22×C4—118no—
835C22×C4—2216no—
836C22×C4—22128no—
837C22×C4—2216no—
838C22×C4—2216no—
839C22×C4—228no—
840C22×C4—2216no—
841C22×C4—444no—
842C22×C4D4×D1118yescomplemented
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1114yes—
847C22×C4C23×D1112yes—
848C22×C4C23×D1112yes—
849C22×C4C23×D1118yes—
850C22×C4C23×D1118yes—
851C22×C4C23×D1118yes—
852C22×C4C23×D1118yes—
853C22×C4C23×D1118yes—
854C22×C4C23×D1114yes—
855C22×C4C23×D1111yescharacteristic
856C22×C4C23×D1111yescharacteristic
857C22×C4C23×D1114yes—
858C22×C4C23×D1111yescharacteristic
859C4⋊C4—118no—
860C4⋊C4—1116no—
861C4⋊C4—118no—
862C4⋊C4—118no—
863C4⋊C4—114no—
864C4⋊C4—114no—
865C4⋊C4—1116no—
866C4⋊C4—118no—
867C4⋊C4C23×D1114yes—
868C4⋊C4C23×D1114yes—
869C4⋊C4C23×D1118yes—
870C22⋊C4—1116no—
871C22⋊C4—118no—
872C22⋊C4—1116no—
873C22⋊C4—1116no—
874C22⋊C4—1116no—
875C22⋊C4—118no—
876C22⋊C4—118no—
877C22⋊C4—1116no—
878C22⋊C4—1116no—
879C22⋊C4C23×D1118yes—
880C22⋊C4C23×D1118yes—
881C22⋊C4C23×D1118yes—
882C22⋊C4C23×D1118yes—
883C42—118no—
884C42—118no—
885C42—118no—
886C42C23×D1114yes—
887C42C23×D1114yes—
888C42C23×D1114yes—
889C42C23×D1114yes—
890C11C2×D4×#4111yescharacteristic, complemented, Sylow
891C23—22no—
892C23—24no—
893C23—22no—
894C23—24no—
895C23—24no—
896C23—216no—
897C23—216no—
898C23—24no—
899C23—24no—
900C23—48no—
901C23—432no—
902C23—118no—
903C23—114no—
904C23—118no—
905C23—2232no—
906C23—224no—
907C23—224no—
908C23—228no—
909C23—2232no—
910C23—228no—
911C23—228no—
912C23—4416no—
913C23—4464no—
914C23C2×#433918yescomplemented
915C23C2×D4×D1114yes—
916C23C24×D1114yes—
917C23C24×D1114yes—
918C23C24×D1112yes—
919C23C24×D1111yescharacteristic
920Q8—1116no—
921Q8—2232no—
922Q8—2216no—
923D4—216no—
924D4—28no—
925D4—1132no—
926D4—1116no—
927D4—2232no—
928D4—2232no—
929D4—2232no—
930D4—2232no—
931D4—2232no—
932D4—2216no—
933D4—2216no—
934D4—448no—
935D4—4416no—
936D4C2×#4339116yesdirect product factor
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—216no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—216no—
945C2×C4—216no—
946C2×C4—216no—
947C2×C4—216no—
948C2×C4—44no—
949C2×C4—118no—
950C2×C4—114no—
951C2×C4—1132no—
952C2×C4—114no—
953C2×C4—114no—
954C2×C4—118no—
955C2×C4—2232no—
956C2×C4—2232no—
957C2×C4—2232no—
958C2×C4—224no—
959C2×C4—228no—
960C2×C4—224no—
961C2×C4—2216no—
962C2×C4—2232no—
963C2×C4—448no—
964C2×C4C2×#433914yescomplemented
965C2×C4C2×D4×D1114yes—
966C2×C4C2×D4×D1114yes—
967C2×C4C2×D4×D11116yescomplemented
968C2×C4C24×D1112yes—
969C2×C4C24×D1112yes—
970C2×C4C24×D1112yes—
971C2×C4C24×D1114yes—
972C2×C4C24×D1114yes—
973C2×C4C24×D1112yes—
974C2×C4C24×D1112yes—
975C2×C4C24×D1112yes—
976C22—24no—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—28no—
981C22—216no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—432no—
986C22—48no—
987C22—118no—
988C22—224no—
989C22—224no—
990C22—2216no—
991C22—228no—
992C22—228no—
993C22—228no—
994C22—4464no—
995C22—4416no—
996C22C22×#433912yes—
997C22C22×#433918yescomplemented
998C22C22×D4×D1114yes—
999C22C22×D4×D1112yes—
1000C22#1062345312yes—
1001C22C25×D1111yescharacteristic
1002C4—24no—
1003C4—24no—
1004C4—22no—
1005C4—22no—
1006C4—22no—
1007C4—118no—
1008C4—228no—
1009C4—224no—
1010C4—224no—
1011C4C22×#433914yescomplemented
1012C4C22×D4×D1114yes—
1013C4C22×D4×D1114yes—
1014C2—24no—
1015C2—28no—
1016C2—44no—
1017C2—228no—
1018C2—448no—
1019C2D4×#433914yesdirect product factor
1020C2C23×D4×D1111yescharacteristic
1021C2C23×#433911yescharacteristic
1022C2C2×#1062345311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×D4×C11C2
socleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×D4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. D4×#4339C2direct (N × H)
3. C2×#10623084C2semidirect
4. C2×D4×Dic22C2semidirect
5. C2×#10623083C2semidirect
6. C2×#10623082C2semidirect
7. C2×#10623038C2semidirect
8. C2×#10623081C2semidirect
9. C2×#10623021C2semidirect
10. C2×D4×D44C2semidirect
11. C2×D4×C22⋊D11C2semidirect
12. C2×#10623008C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623322C2semidirect
15. C2×#10623078C2semidirect
16. C2×C4×#4339C2semidirect
17. C2×C4×D4×D11C2semidirect
18. C22×C4×D4×C11C2semidirect
20. C24×C4×C11C22semidirect
21. C23×C22⋊D11C22semidirect
25. C22×#4339C22semidirect
26. C22×#4339C22semidirect
27. C22×#4339C22semidirect
28. C22×#4339C22semidirect
29. C22×#4339C22semidirect
30. C22×#4339C22semidirect
31. C23×D44C22semidirect
32. C23×C4×D11C22semidirect
33. C23×Dic22C22semidirect
36. C2×C4×D4×C11C22semidirect
37. C2×C4×D4×C11C22semidirect
38. C2×C4×D4×C11C22semidirect
39. C2×C4×D4×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. C22×C11×C4⋊C4C22semidirect
42. C22×C11×C22⋊C4C22semidirect
43. C22×C42×C11C22semidirect
44. C2×#67006C22semidirect
45. C2×#66993C22semidirect
46. C2×#66992C22semidirect
47. D4×C22⋊D11C22semidirect
48. C2×#66991C22semidirect
49. C2×#66990C22semidirect
51. #10623322C22semidirect
52. C2×#66983C22semidirect
53. C2×#66983C22semidirect
54. C2×#66983C22semidirect
55. C2×#66983C22semidirect
56. C2×#66982C22semidirect
57. C2×C4×C22⋊D11C22semidirect
58. C2×C4×C22⋊D11C22semidirect
59. C2×C4×C22⋊D11C22semidirect
60. C2×C4×C22⋊D11C22semidirect
61. C2×#66979C22semidirect
62. C2×#66977C22semidirect
63. C2×#66977C22semidirect
64. #10623084C22semidirect
65. #10623083C22semidirect
66. #10623082C22semidirect
67. #10623081C22semidirect
68. D4×D44C22semidirect
69. #10623079C22semidirect
70. #10623078C22semidirect
71. C4×D4×D11C22semidirect
72. D4×Dic22C22semidirect
73. C2×#66949C22semidirect
74. #10623038C22semidirect
75. C2×#66948C22semidirect
76. C2×#66947C22semidirect
77. C2×#66946C22semidirect
78. C2×C4⋊C4×D11C22semidirect
79. C2×#66941C22semidirect
80. C2×#66938C22semidirect
81. #10623021C22semidirect
82. C2×#66937C22semidirect
83. C2×#66937C22semidirect
84. C2×#66936C22semidirect
85. C2×#66935C22semidirect
86. C2×(C22⋊D11)⋊C4C22semidirect
87. C2×C22⋊C4×D11C22semidirect
88. C2×#66931C22semidirect
89. #10623008C22semidirect
90. C2×#66928C22semidirect
91. C2×#66927C22semidirect
92. C4×#4339C22semidirect
93. C2×C4×D44C22semidirect
94. C2×C4×D44C22semidirect
95. C2×C4×D44C22semidirect
96. C2×C4×D44C22semidirect
97. C2×#66925C22semidirect
98. C2×C42×D11C22semidirect
99. C2×#66922C22semidirect
100. C2×C4×Dic22C22semidirect
101. C2×C4×Dic22C22semidirect
118. C23×C4×C11C23semidirect
126. C22×C22⋊D11C23semidirect
136. C2×#4339D4direct (N × H)
138. C2×#4339C23semidirect
139. C2×#4339C23semidirect
140. C2×#4339C23semidirect
141. C2×#4339C23semidirect
142. C2×#4339C23semidirect
149. C22×D44C23semidirect
157. C22×C4×D11C23semidirect
162. C22×Dic22C23semidirect
165. C4×D4×C11C23semidirect
166. C4×D4×C11C23semidirect
167. C4×D4×C11C23semidirect
168. C4×D4×C11C23semidirect
172. C2×C11×C4⋊C4C23semidirect
177. C2×C11×C22⋊C4C23semidirect
182. C2×C42×C11C23semidirect
183. #67006C23semidirect
187. #66993C23semidirect
188. #66992C23semidirect
189. #66991C23semidirect
190. #66990C23semidirect
192. #66983C23semidirect
193. #66983C23semidirect
194. #66983C23semidirect
195. #66983C23semidirect
196. #66982C23semidirect
197. C4×C22⋊D11C23semidirect
198. C4×C22⋊D11C23semidirect
199. C4×C22⋊D11C23semidirect
200. C4×C22⋊D11C23semidirect
207. #66979C23semidirect
212. #66977C23semidirect
213. #66977C23semidirect
221. #66949C23semidirect
222. #66948C23semidirect
223. #66947C23semidirect
224. #66946C23semidirect
225. C4⋊C4×D11C23semidirect
226. #66941C23semidirect
227. #66938C23semidirect
228. #66937C23semidirect
229. #66937C23semidirect
230. #66936C23semidirect
231. #66935C23semidirect
232. (C22⋊D11)⋊C4C23semidirect
233. C22⋊C4×D11C23semidirect
234. #66931C23semidirect
235. #66928C23semidirect
236. #66927C23semidirect
237. C4×D44C23semidirect
238. C4×D44C23semidirect
239. C4×D44C23semidirect
240. C4×D44C23semidirect
241. #66925C23semidirect
242. C42×D11C23semidirect
243. #66922C23semidirect
244. C4×Dic22C23semidirect
245. C4×Dic22C23semidirect
263. C2×D4×C11#41semidirect
275. C22×C4×C11C2×D4semidirect
298. C2×C22⋊D11C2×D4semidirect
317. #4339C2×D4direct (N × H)
323. C2×D44C2×D4semidirect
335. C2×C4×D11C2×D4semidirect
345. C2×Dic22C2×D4semidirect
397. C22×C4×D4D11semidirect
410. C23×C11C2×#41semidirect
429. D4×C11C2×#41semidirect
444. C2×C4×C11C22×D4semidirect
445. C2×C4×C11C2×#41semidirect
459. C22⋊D11C22×D4semidirect
473. D44C22×D4semidirect
479. C4×D11C22×D4semidirect
482. Dic22C22×D4semidirect
497. C24×C4C2×D11semidirect
553. C2×C4×D4C2×D11semidirect
554. C2×C4×D4C2×D11semidirect
555. C2×C4×D4C2×D11semidirect
556. C2×C4×D4C2×D11semidirect
557. C2×C4×D4C2×D11semidirect
561. C22×C4⋊C4C2×D11semidirect
563. C22×C22⋊C4C2×D11semidirect
565. C22×C42C2×D11semidirect
580. C22×C11C22×#41semidirect
599. C4×C11C22×#41semidirect
664. C23×C4C22×D11semidirect
705. C4×D4C22×D11semidirect
706. C4×D4C22×D11semidirect
707. C4×D4C22×D11semidirect
708. C4×D4C22×D11semidirect
723. C2×C4⋊C4C22×D11semidirect
738. C2×C22⋊C4C22×D11semidirect
747. C2×C42C22×D11semidirect
751. C2×C11D4×#41semidirect
811. C2×D4#4339direct (N × H)
842. C22×C4D4×D11semidirect
890. C11C2×D4×#41semidirect
914. C23C2×#4339semidirect
936. D4C2×#4339direct (N × H)
964. C2×C4C2×#4339semidirect
967. C2×C4C2×D4×D11semidirect
997. C22C22×#4339semidirect
1011. C4C22×#4339semidirect
1019. C2D4×#4339direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
D4×#43392
C2×#106230842
C2×D4×Dic222
C2×#106230832
C2×#106230822
C2×#106230382
C2×#106230812
C2×#106230212
C2×D4×D442
C2×D4×C22⋊D112
C2×#106230082
C2×#106230792
C2×#106233222
C2×#106230782
C2×C4×#43392
C2×C4×D4×D112
C22×C4×D4×C112
C2×D4×#4111