Finite Group Databasebeta

← C2×#13071989 #14921187

Subgroups — C2×#13071989 #14921187

Order 2816.

8730 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×#66935C211yesmaximal, characteristic, complemented
5C22×#66935C211yesmaximal, characteristic, complemented
6C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13071989C2116yesmaximal, direct product factor
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622284C211yesmaximal, characteristic, complemented
11C2×#10622573C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C25×D11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic, complemented
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic, complemented
24C23×C22⋊D11C2211yescharacteristic, complemented
25C24×Dic11C2211yescharacteristic, complemented
26C22×D4×D11—28no—
27C22×D4×D11—28no—
28C22×D4×D11—28no—
29C22×D4×D11C2218yescomplemented
30C23×D44C2211yescharacteristic
31C23×D44C2211yescharacteristic
32C23×D44C2211yescharacteristic, complemented
33C23×D44C2211yescharacteristic, complemented
34C23×C4×D11C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic, complemented
36C22×C11×C22⋊C4C2211yescharacteristic, complemented
37C22×C11×C22⋊C4C2211yescharacteristic, complemented
38C22×C22⋊Dic11C2211yescharacteristic, complemented
39C2×#66992—28no—
40C2×#66992C2218yescomplemented
41C2×#66983—28no—
42C2×#66983C2218yescomplemented
43C22×(C2×D11)⋊C4—28no—
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2218yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
51C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
52C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
53C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
54C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
55C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
56C22×C4⋊Dic11C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C2×#66935—28no—
59C2×#66935—28no—
60C2×#66935C2218yescomplemented
61C2×#66935C2218yescomplemented
62C11×#386C2218yescomplemented
63C2×C11×#95C2211yescharacteristic, complemented
64C2×C11×#95C2211yescharacteristic, complemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67#10622574C2218yescomplemented
68#10622573C2218yescomplemented
69#10622571C2218yescomplemented
70#10622568C2218yescomplemented
71#10622285C2218yescomplemented
72#10622284C2218yescomplemented
73#10622281C2218yescomplemented
74#10622278C2218yescomplemented
75C25×C11C2311yescharacteristic
76C25×C11C2311yescharacteristic
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—24no—
81C24×D11—24no—
82C24×D11—24no—
83C24×D11—24no—
84C24×D11—24no—
85C24×D11—24no—
86C24×D11—42no—
87C24×D11—42no—
88C24×D11—42no—
89C24×D11—42no—
90C24×D11D418yescomplemented
91C24×D11C2311yescharacteristic
92C24×D11C2311yescharacteristic
93C24×D11C2311yescharacteristic
94C24×D11C2314yes—
95C24×D11C2314yes—
96C24×D11C2311yescharacteristic
97C22×D4×C11—24no—
98C22×D4×C11—24no—
99C22×D4×C11D418yescomplemented
100C22×D4×C11C2314yes—
101C23×C4×C11—24no—
102C23×C4×C11—24no—
103C23×C4×C11—42no—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2314yescomplemented
110C22×C22⋊D11—24no—
111C22×C22⋊D11—24no—
112C22×C22⋊D11—24no—
113C22×C22⋊D11—24no—
114C22×C22⋊D11—24no—
115C22×C22⋊D11—24no—
116C22×C22⋊D11—24no—
117C22×C22⋊D11—24no—
118C22×C22⋊D11—24no—
119C22×C22⋊D11—24no—
120C22×C22⋊D11—42no—
121C22×C22⋊D11D418yescomplemented
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2314yes—
124C22×C22⋊D11C2314yescomplemented
125C22×C22⋊D11C2314yescomplemented
126C23×Dic11—24no—
127C23×Dic11—24no—
128C23×Dic11—42no—
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2314yescomplemented
134C2×D4×D11—2128no—
135C2×D4×D11—232no—
136C2×D4×D11—232no—
137C2×D4×D11—232no—
138C22×D44—24no—
139C22×D44—24no—
140C22×D44—24no—
141C22×D44—24no—
142C22×D44—24no—
143C22×D44—24no—
144C22×D44—24no—
145C22×D44—24no—
146C22×D44—24no—
147C22×D44—42no—
148C22×D44—42no—
149C22×D44—42no—
150C22×D44C2314yes—
151C22×D44C2314yes—
152C22×D44C2314yescomplemented
153C22×D44C2314yescomplemented
154C22×C4×D11—24no—
155C22×C4×D11—24no—
156C22×C4×D11—24no—
157C22×C4×D11C2314yes—
158C2×C11×C22⋊C4—24no—
159C2×C11×C22⋊C4—24no—
160C2×C11×C22⋊C4—42no—
161C2×C11×C22⋊C4C2314yescomplemented
162C2×C11×C22⋊C4C2314yescomplemented
163C2×C11×C22⋊C4C2314yescomplemented
164C2×C22⋊Dic11—24no—
165C2×C22⋊Dic11C2314yescomplemented
166#66992—232no—
167#66983—232no—
168C2×(C2×D11)⋊C4—24no—
169C2×(C2×D11)⋊C4—24no—
170C2×(C2×D11)⋊C4—24no—
171C2×(C2×D11)⋊C4—24no—
172C2×(C2×D11)⋊C4—24no—
173C2×(C2×D11)⋊C4—24no—
174C2×(C2×D11)⋊C4—24no—
175C2×(C2×D11)⋊C4—24no—
176C2×(C2×D11)⋊C4—24no—
177C2×(C2×D11)⋊C4—232no—
178C2×(C2×D11)⋊C4—42no—
179C2×(C2×D11)⋊C4D418yescomplemented
180C2×(C2×D11)⋊C4C2314yes—
181C2×(C2×D11)⋊C4C2314yes—
182C2×(C2×D11)⋊C4C2314yes—
183C2×(C2×D11)⋊C4C2314yescomplemented
184C2×(C2×D11)⋊C4C2314yescomplemented
185C2×(C2×D11)⋊C4C2314yescomplemented
186C2×(C2×D11)⋊C4C2314yescomplemented
187C2×(C2×D11)⋊C4C2314yescomplemented
188C2×(C2×D11)⋊C4C2314yescomplemented
189C2×(C2×D11)⋊C4C2314yescomplemented
190C2×(C2×D11)⋊C4C2314yescomplemented
191C2×C4⋊Dic11—24no—
192C2×C4⋊Dic11C2314yescomplemented
193C2×Dic11⋊C4—24no—
194C2×Dic11⋊C4C2314yescomplemented
195#66935—232no—
196#66935—232no—
197C11×#95C2314yescomplemented
198C11×#95C2314yescomplemented
199C11⋊#95C2314yescomplemented
200C11⋊#95C2314yescomplemented
201C2×#2410—111nomaximal, Sylow
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11—22no—
207C24×C11—22no—
208C24×C11—22no—
209C24×C11—22no—
210C24×C11—22no—
211C24×C11—22no—
212C24×C11C2×D414yes—
213C24×C11C2×D414yes—
214C24×C11C2×D414yes—
215C24×C11C2×D414yes—
216C24×C11C2412yes—
217C24×C11C2412yes—
218C24×C11C2411yescharacteristic
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—232no—
224C23×D11—232no—
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—22no—
228C23×D11—22no—
229C23×D11—22no—
230C23×D11—22no—
231C23×D11—28no—
232C23×D11—28no—
233C23×D11—28no—
234C23×D11—22no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—22no—
238C23×D11—22no—
239C23×D11—22no—
240C23×D11—232no—
241C23×D11—28no—
242C23×D11—28no—
243C23×D11—28no—
244C23×D11—28no—
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—22no—
248C23×D11—22no—
249C23×D11—22no—
250C23×D11—22no—
251C23×D11—22no—
252C23×D11—28no—
253C23×D11—28no—
254C23×D11—416no—
255C23×D11—44no—
256C23×D11—44no—
257C23×D11—44no—
258C23×D11—44no—
259C23×D11—416no—
260C23×D11—416no—
261C23×D11—416no—
262C23×D11—416no—
263C23×D11—416no—
264C23×D11—416no—
265C23×D11—416no—
266C23×D11—416no—
267C23×D11—416no—
268C23×D11—416no—
269C23×D11C2×D414yes—
270C23×D11C2×D414yes—
271C23×D11C2×D414yes—
272C23×D11C2×D414yes—
273C23×D11C2×D4116yescomplemented
274C23×D11#4114yes—
275C23×D11C2412yes—
276C23×D11C2412yes—
277C23×D11C2412yes—
278C23×D11C2412yes—
279C2×D4×C11—232no—
280C2×D4×C11—28no—
281C2×D4×C11—28no—
282C2×D4×C11C2×D4116yescomplemented
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—28no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—28no—
298C22×C4×C11—44no—
299C22×C4×C11—416no—
300C22×C4×C11C2×D414yes—
301C22×C4×C11C2×D414yescomplemented
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C2×C22⋊D11—232no—
308C2×C22⋊D11—28no—
309C2×C22⋊D11—28no—
310C2×C22⋊D11—232no—
311C2×C22⋊D11—28no—
312C2×C22⋊D11—28no—
313C2×C22⋊D11—28no—
314C2×C22⋊D11—28no—
315C2×C22⋊D11—28no—
316C2×C22⋊D11—28no—
317C2×C22⋊D11—28no—
318C2×C22⋊D11—28no—
319C2×C22⋊D11—44no—
320C2×C22⋊D11—416no—
321C2×C22⋊D11—416no—
322C2×C22⋊D11C2×D4116yescomplemented
323C22×Dic11—28no—
324C22×Dic11—22no—
325C22×Dic11—22no—
326C22×Dic11—22no—
327C22×Dic11—22no—
328C22×Dic11—22no—
329C22×Dic11—22no—
330C22×Dic11—22no—
331C22×Dic11—22no—
332C22×Dic11—28no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—44no—
336C22×Dic11—416no—
337C22×Dic11C2×D414yes—
338C22×Dic11C2×D414yescomplemented
339C22×Dic11C2412yes—
340C22×Dic11C2412yes—
341C22×Dic11C2412yes—
342C22×Dic11C2412yes—
343D4×D11—2256no—
344C2×D44—232no—
345C2×D44—28no—
346C2×D44—28no—
347C2×D44—28no—
348C2×D44—28no—
349C2×D44—28no—
350C2×D44—28no—
351C2×D44—28no—
352C2×D44—28no—
353C2×D44—28no—
354C2×D44—44no—
355C2×D44—44no—
356C2×D44—44no—
357C2×D44—416no—
358C2×D44—416no—
359C2×D44—416no—
360C2×C4×D11—232no—
361C2×C4×D11—28no—
362C2×C4×D11—28no—
363C2×C4×D11—28no—
364C11×C22⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—44no—
367C22⋊Dic11—28no—
368(C2×D11)⋊C4—28no—
369(C2×D11)⋊C4—28no—
370(C2×D11)⋊C4—28no—
371(C2×D11)⋊C4—28no—
372(C2×D11)⋊C4—28no—
373(C2×D11)⋊C4—28no—
374(C2×D11)⋊C4—28no—
375(C2×D11)⋊C4—28no—
376(C2×D11)⋊C4—28no—
377(C2×D11)⋊C4—44no—
378(C2×D11)⋊C4C2×D4116yescomplemented
379C4⋊Dic11—28no—
380Dic11⋊C4—28no—
381C24×D4—111no—
382C22×#121—111no—
383C22×#121—111no—
384C22×#120—111no—
385C22×#120—111no—
386C23×C22⋊C4—111no—
387#2410—1116no—
388C2×#394—111no—
389C2×#394—111no—
390C2×#392—111no—
391C2×#392—111no—
392C2×#386—111no—
393C2×#386—111no—
394C2×#386D1111yescharacteristic, complemented
395C2×#385—111no—
396C2×#379—111no—
397C23×C11—28no—
398C23×C11—28no—
399C23×C11—28no—
400C23×C11—28no—
401C23×C11—28no—
402C23×C11—28no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—28no—
408C23×C11—28no—
409C23×C11—28no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—44no—
417C23×C11—44no—
418C23×C11—44no—
419C23×C11—44no—
420C23×C11#120116yescomplemented
421C23×C11C22×D414yes—
422C23×C11C22×D414yes—
423C23×C11C22×D412yes—
424C23×C11C22×D414yes—
425C23×C11C22×D414yes—
426C23×C11C22×D412yes—
427C23×C11C22×D412yes—
428C23×C11C22×D412yes—
429C23×C11C2×#4112yes—
430C23×C11H(5,𝔽2)12yes—
431C23×C11H(5,𝔽2)12yes—
432C23×C11C2511yescharacteristic
433C22×D11—28no—
434C22×D11—28no—
435C22×D11—28no—
436C22×D11—28no—
437C22×D11—28no—
438C22×D11—28no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—232no—
444C22×D11—28no—
445C22×D11—28no—
446C22×D11—232no—
447C22×D11—28no—
448C22×D11—28no—
449C22×D11—28no—
450C22×D11—28no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—232no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—416no—
472C22×D11—416no—
473C22×D11—416no—
474C22×D11—4128no—
475C22×D11—416no—
476C22×D11—416no—
477C22×D11—416no—
478C22×D11—416no—
479C22×D11—416no—
480C22×D11—416no—
481C22×D11—4128no—
482C22×D11—416no—
483C22×D11—44no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11—44no—
487C22×D11—44no—
488C22×D11—44no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—416no—
492C22×D11—44no—
493C22×D11—44no—
494C22×D11—44no—
495C22×D11—44no—
496C22×D11—44no—
497C22×D11—44no—
498C22×D11—44no—
499C22×D11#121116yescomplemented
500C22×D11C22×D414yes—
501C22×D11C22×D414yes—
502C22×D11C22×D414yes—
503C22×D11C22×D414yes—
504C22×D11C2×#4114yes—
505D4×C11—232no—
506C2×C4×C11—28no—
507C2×C4×C11—28no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—416no—
522C2×C4×C11—44no—
523C2×C4×C11—44no—
524C2×C4×C11—44no—
525C2×C4×C11C22×D414yes—
526C2×C4×C11C22×D414yescomplemented
527C22⋊D11—232no—
528C22⋊D11—232no—
529C22⋊D11—416no—
530C22⋊D11—416no—
531C2×Dic11—28no—
532C2×Dic11—28no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—416no—
544C2×Dic11—44no—
545C2×Dic11—44no—
546C2×Dic11C22×D414yes—
547C2×Dic11C22×D414yescomplemented
548D44—232no—
549D44—416no—
550D44—416no—
551D44—416no—
552C4×D11—232no—
553C26—111no—
554C26—111no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4—111no—
558C23×D4—111no—
559C23×D4—118no—
560C23×D4—111no—
561C23×D4—111no—
562C23×D4—111no—
563C23×D4—111no—
564C23×D4—228no—
565C23×D4—228no—
566C23×D4—228no—
567C23×D4C2×D1111yescharacteristic
568C24×C4—111no—
569C24×C4—111no—
570C24×C4C2×D1111yescharacteristic, complemented
571C2×#121—118no—
572C2×#121—118no—
573C2×#121—228no—
574C2×#121—228no—
575C2×#120—118no—
576C2×#120—118no—
577C2×#120—228no—
578C2×#120—228no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—118no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—228no—
595C22×C22⋊C4C2×D1111yescharacteristic, complemented
596C22×C22⋊C4C2×D1111yescharacteristic, complemented
597C22×C22⋊C4C2×D1111yescharacteristic, complemented
598#394—118no—
599#394—118no—
600#392—118no—
601#392—118no—
602#386—118no—
603#386—118no—
604#386C2×D1118yescomplemented
605#385—118no—
606#379—118no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95C2×D1111yescharacteristic, complemented
610C2×#95C2×D1111yescharacteristic, complemented
611C22×C11—24no—
612C22×C11—232no—
613C22×C11—24no—
614C22×C11—24no—
615C22×C11—24no—
616C22×C11—24no—
617C22×C11—24no—
618C22×C11—24no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—42no—
622C22×C11—416no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11C2×#12014yes—
627C22×C11C2×#12018yescomplemented
628C22×C11C2×#12114yes—
629C22×C11#53414yes—
630C22×C11D4214yes—
631C22×C11D4214yes—
632C22×C11#54614yes—
633C22×C11#54614yes—
634C22×C11C23×D411yescharacteristic
635C22×C11C23×D411yescharacteristic
636C22×C11C23×D411yescharacteristic
637C22×C11C23×D411yescharacteristic
638C22×C11C22×#4111yescharacteristic
639C22×C11C2×H(5,𝔽2)11yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C2×D11—24no—
642C2×D11—232no—
643C2×D11—24no—
644C2×D11—24no—
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—464no—
655C2×D11—464no—
656C2×D11—42no—
657C2×D11—416no—
658C2×D11—416no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—88no—
674C2×D11C2×#12118yescomplemented
675C4×C11—24no—
676C4×C11—24no—
677C4×C11—42no—
678C4×C11—42no—
679C4×C11—42no—
680Dic11—24no—
681Dic11—24no—
682Dic11—42no—
683Dic11—42no—
684C25—111no—
685C25—111no—
686C25—111no—
687C25—118no—
688C25—114no—
689C25—111no—
690C25—114no—
691C25—224no—
692C25—224no—
693C25—224no—
694C25—224no—
695C25—224no—
696C25—224no—
697C25—224no—
698C25—224no—
699C25—224no—
700C25—442no—
701C25—442no—
702C25—442no—
703C25—442no—
704C25C22×D1111yescharacteristic
705C25C22×D1111yescharacteristic
706C22×D4—24no—
707C22×D4—24no—
708C22×D4—118no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—114no—
712C22×D4—114no—
713C22×D4—114no—
714C22×D4—114no—
715C22×D4—114no—
716C22×D4—114no—
717C22×D4—224no—
718C22×D4—224no—
719C22×D4—224no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4—224no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—224no—
726C22×D4—2232no—
727C22×D4—2232no—
728C22×D4—22128no—
729C22×D4—224no—
730C22×D4—224no—
731C22×D4—224no—
732C22×D4—224no—
733C22×D4—2232no—
734C22×D4—224no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—224no—
739C22×D4—224no—
740C22×D4—442no—
741C22×D4—442no—
742C22×D4—442no—
743C22×D4—442no—
744C22×D4D4418yescomplemented
745C22×D4C22×D1114yes—
746C23×C4—24no—
747C23×C4—24no—
748C23×C4—42no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—114no—
754C23×C4—114no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4—224no—
758C23×C4—224no—
759C23×C4—224no—
760C23×C4—442no—
761C23×C4C22×D1111yescharacteristic
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1114yescomplemented
767#121—2232no—
768#121—2232no—
769#120—2232no—
770#120—2232no—
771C2×C4⋊C4—114no—
772C2×C4⋊C4—114no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4—224no—
775C2×C22⋊C4—24no—
776C2×C22⋊C4—24no—
777C2×C22⋊C4—42no—
778C2×C22⋊C4—118no—
779C2×C22⋊C4—114no—
780C2×C22⋊C4—114no—
781C2×C22⋊C4—114no—
782C2×C22⋊C4—114no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—114no—
785C2×C22⋊C4—114no—
786C2×C22⋊C4—114no—
787C2×C22⋊C4—114no—
788C2×C22⋊C4—114no—
789C2×C22⋊C4—114no—
790C2×C22⋊C4—114no—
791C2×C22⋊C4—2232no—
792C2×C22⋊C4—224no—
793C2×C22⋊C4—224no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—224no—
796C2×C22⋊C4—224no—
797C2×C22⋊C4—224no—
798C2×C22⋊C4—224no—
799C2×C22⋊C4—224no—
800C2×C22⋊C4—224no—
801C2×C22⋊C4—224no—
802C2×C22⋊C4—442no—
803C2×C22⋊C4C22×D1114yescomplemented
804C2×C22⋊C4C22×D1114yescomplemented
805C2×C22⋊C4C22×D1114yescomplemented
806#95—114no—
807#95—114no—
808#95C22×D1114yescomplemented
809#95C22×D1114yescomplemented
810C2×C11—28no—
811C2×C11—44no—
812C2×C11#241018yescomplemented
813C2×C11C22×#12011yescharacteristic
814C2×C11C22×#12111yescharacteristic
815C2×C11C2×#53411yescharacteristic
816C2×C11C2×D4211yescharacteristic
817C2×C11C2×D4211yescharacteristic
818C2×C11C2×#54611yescharacteristic
819C2×C11C2×#54611yescharacteristic
820D11—28no—
821D11—44no—
822D11—44no—
823D11—82no—
824C24—22no—
825C24—22no—
826C24—22no—
827C24—22no—
828C24—22no—
829C24—22no—
830C24—22no—
831C24—22no—
832C24—22no—
833C24—22no—
834C24—114no—
835C24—114no—
836C24—114no—
837C24—112no—
838C24—114no—
839C24—114no—
840C24—112no—
841C24—112no—
842C24—1116no—
843C24—112no—
844C24—228no—
845C24—228no—
846C24—228no—
847C24—2232no—
848C24—228no—
849C24—228no—
850C24—228no—
851C24—2232no—
852C24—222no—
853C24—222no—
854C24—222no—
855C24—222no—
856C24—2232no—
857C24—228no—
858C24—228no—
859C24—222no—
860C24—222no—
861C24—222no—
862C24—222no—
863C24—228no—
864C24—222no—
865C24—222no—
866C24—222no—
867C24—222no—
868C24—222no—
869C24—222no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24—222no—
877C24—222no—
878C24—222no—
879C24—4416no—
880C24—444no—
881C24—444no—
882C24—444no—
883C24—444no—
884C24—4416no—
885C24—4416no—
886C24—4416no—
887C24—4416no—
888C24—4416no—
889C24—4416no—
890C24—4416no—
891C24—4416no—
892C24—4416no—
893C24—4416no—
894C24C2×D4414yes—
895C24C2×D4414yes—
896C24D4×D1114yes—
897C24D4×D1114yes—
898C24C23×D1112yes—
899C24C23×D1112yes—
900C24C23×D1111yescharacteristic
901C2×D4—232no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—1116no—
905C2×D4—228no—
906C2×D4—228no—
907C2×D4—2232no—
908C2×D4—228no—
909C2×D4—228no—
910C2×D4—228no—
911C2×D4—228no—
912C2×D4—228no—
913C2×D4—228no—
914C2×D4—228no—
915C2×D4—22256no—
916C2×D4—228no—
917C2×D4—2232no—
918C2×D4—2232no—
919C2×D4—228no—
920C2×D4—228no—
921C2×D4—228no—
922C2×D4—228no—
923C2×D4—228no—
924C2×D4—228no—
925C2×D4—228no—
926C2×D4—228no—
927C2×D4—228no—
928C2×D4—444no—
929C2×D4—444no—
930C2×D4—444no—
931C2×D4—4416no—
932C2×D4—4416no—
933C2×D4—4416no—
934C2×D4—444no—
935C2×D4—4416no—
936C2×D4—4416no—
937C2×D4C2×D44116yescomplemented
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—28no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—28no—
953C22×C4—44no—
954C22×C4—416no—
955C22×C4—114no—
956C22×C4—114no—
957C22×C4—112no—
958C22×C4—112no—
959C22×C4—112no—
960C22×C4—112no—
961C22×C4—228no—
962C22×C4—228no—
963C22×C4—2232no—
964C22×C4—228no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—228no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—228no—
973C22×C4—222no—
974C22×C4—222no—
975C22×C4—222no—
976C22×C4—222no—
977C22×C4—444no—
978C22×C4—4416no—
979C22×C4C2×D4414yes—
980C22×C4D4×D1114yescomplemented
981C22×C4C23×D1112yes—
982C22×C4C23×D1112yes—
983C22×C4C23×D1112yes—
984C22×C4C23×D1112yes—
985C22×C4C23×D1112yes—
986C4⋊C4—228no—
987C4⋊C4—228no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—1116no—
992C22⋊C4—228no—
993C22⋊C4—228no—
994C22⋊C4—228no—
995C22⋊C4—228no—
996C22⋊C4—228no—
997C22⋊C4—228no—
998C22⋊C4—228no—
999C22⋊C4—228no—
1000C22⋊C4—228no—
1001C22⋊C4—228no—
1002C22⋊C4—444no—
1003C11C2×#241011yescharacteristic, complemented, Sylow
1004C23—28no—
1005C23—28no—
1006C23—28no—
1007C23—28no—
1008C23—28no—
1009C23—28no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—28no—
1015C23—28no—
1016C23—28no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—44no—
1024C23—44no—
1025C23—44no—
1026C23—44no—
1027C23—1116no—
1028C23—114no—
1029C23—114no—
1030C23—114no—
1031C23—114no—
1032C23—114no—
1033C23—2232no—
1034C23—2232no—
1035C23—228no—
1036C23—228no—
1037C23—228no—
1038C23—228no—
1039C23—228no—
1040C23—228no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—228no—
1046C23—228no—
1047C23—2232no—
1048C23—228no—
1049C23—228no—
1050C23—228no—
1051C23—228no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—4416no—
1072C23—44128no—
1073C23—4416no—
1074C23—4416no—
1075C23—4416no—
1076C23—4416no—
1077C23—4416no—
1078C23—4416no—
1079C23—4416no—
1080C23—4416no—
1081C23—4416no—
1082C23—4416no—
1083C23—44128no—
1084C23—444no—
1085C23—444no—
1086C23—444no—
1087C23—444no—
1088C23—444no—
1089C23—444no—
1090C23—444no—
1091C23—444no—
1092C23—444no—
1093C23—444no—
1094C23—444no—
1095C23—444no—
1096C23—444no—
1097C23—444no—
1098C23—444no—
1099C23#66935116yescomplemented
1100C23C22×D4414yes—
1101C23C22×D4414yes—
1102C23C22×D4412yes—
1103C23C2×D4×D1114yes—
1104C23C2×D4×D1114yes—
1105C23C2×D4×D1112yes—
1106C23C2×D4×D1112yes—
1107C23C2×D4×D1112yes—
1108C23#6703712yes—
1109C23#41×D1112yes—
1110C23#6704212yes—
1111C23C24×D1111yescharacteristic
1112D4—232no—
1113D4—2232no—
1114D4—2232no—
1115D4—2232no—
1116D4—4416no—
1117D4—4416no—
1118D4—4416no—
1119D4—4416no—
1120D4—4416no—
1121C2×C4—28no—
1122C2×C4—28no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—416no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—114no—
1141C2×C4—114no—
1142C2×C4—2232no—
1143C2×C4—228no—
1144C2×C4—228no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—4416no—
1156C2×C4—444no—
1157C2×C4—444no—
1158C2×C4C22×D4414yes—
1159C2×C4C2×D4×D1114yescomplemented
1160C22—24no—
1161C22—232no—
1162C22—24no—
1163C22—24no—
1164C22—24no—
1165C22—24no—
1166C22—24no—
1167C22—24no—
1168C22—24no—
1169C22—24no—
1170C22—42no—
1171C22—416no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—118no—
1176C22—224no—
1177C22—2232no—
1178C22—224no—
1179C22—224no—
1180C22—224no—
1181C22—224no—
1182C22—224no—
1183C22—224no—
1184C22—224no—
1185C22—224no—
1186C22—224no—
1187C22—224no—
1188C22—224no—
1189C22—4464no—
1190C22—4464no—
1191C22—442no—
1192C22—4416no—
1193C22—4416no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—442no—
1207C22—442no—
1208C22—888no—
1209C22C2×#6693514yes—
1210C22C2×#6693518yescomplemented
1211C22D4×D4414yes—
1212C22#1062308514yes—
1213C22#1062312114yes—
1214C22D11×#12114yes—
1215C22#1062313614yes—
1216C22#1062318514yes—
1217C22C23×D4411yescharacteristic
1218C22C22×D4×D1111yescharacteristic
1219C22C22×D4×D1111yescharacteristic
1220C22C22×D4×D1111yescharacteristic
1221C22C2×#6703711yescharacteristic
1222C22C2×#41×D1111yescharacteristic
1223C22C2×#6704211yescharacteristic
1224C4—24no—
1225C4—24no—
1226C4—42no—
1227C4—42no—
1228C4—42no—
1229C4—224no—
1230C4—224no—
1231C4—442no—
1232C4—442no—
1233C2—28no—
1234C2—44no—
1235C2—228no—
1236C2—444no—
1237C2—444no—
1238C2—882no—
1239C2#1307198918yesdirect product factor
1240C2C22×#6693511yescharacteristic
1241C2C2×D11×#12111yescharacteristic
1242C2C2×#1062313611yescharacteristic
1243C2C2×#1062312111yescharacteristic
1244C2C2×D4×D4411yescharacteristic
1245C2C2×#1062318511yescharacteristic
1246C2C2×#1062308511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C22×#66983C2semidirect
3. C22×#66992C2semidirect
4. C22×#66935C2semidirect
5. C22×#66935C2semidirect
6. C23×(C2×D11)⋊C4C2semidirect
7. #13071989C2direct (N × H)
8. C2×#10622285C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622284C2semidirect
11. C2×#10622573C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#386C2semidirect
20. C24×C4×C11C22semidirect
23. C23×C22⋊D11C22semidirect
24. C23×C22⋊D11C22semidirect
25. C24×Dic11C22semidirect
29. C22×D4×D11C22semidirect
32. C23×D44C22semidirect
33. C23×D44C22semidirect
35. C22×C11×C22⋊C4C22semidirect
36. C22×C11×C22⋊C4C22semidirect
37. C22×C11×C22⋊C4C22semidirect
38. C22×C22⋊Dic11C22semidirect
40. C2×#66992C22semidirect
42. C2×#66983C22semidirect
47. C22×(C2×D11)⋊C4C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
50. C22×(C2×D11)⋊C4C22semidirect
51. C22×(C2×D11)⋊C4C22semidirect
52. C22×(C2×D11)⋊C4C22semidirect
53. C22×(C2×D11)⋊C4C22semidirect
54. C22×(C2×D11)⋊C4C22semidirect
55. C22×(C2×D11)⋊C4C22semidirect
56. C22×C4⋊Dic11C22semidirect
57. C22×Dic11⋊C4C22semidirect
60. C2×#66935C22semidirect
61. C2×#66935C22semidirect
62. C11×#386C22semidirect
63. C2×C11×#95C22semidirect
64. C2×C11×#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. #10622574C22semidirect
68. #10622573C22semidirect
69. #10622571C22semidirect
70. #10622568C22semidirect
71. #10622285C22semidirect
72. #10622284C22semidirect
73. #10622281C22semidirect
74. #10622278C22semidirect
90. C24×D11D4semidirect
99. C22×D4×C11D4semidirect
109. C23×C4×C11C23semidirect
121. C22×C22⋊D11D4semidirect
124. C22×C22⋊D11C23semidirect
125. C22×C22⋊D11C23semidirect
133. C23×Dic11C23semidirect
152. C22×D44C23semidirect
153. C22×D44C23semidirect
161. C2×C11×C22⋊C4C23semidirect
162. C2×C11×C22⋊C4C23semidirect
163. C2×C11×C22⋊C4C23semidirect
165. C2×C22⋊Dic11C23semidirect
179. C2×(C2×D11)⋊C4D4semidirect
183. C2×(C2×D11)⋊C4C23semidirect
184. C2×(C2×D11)⋊C4C23semidirect
185. C2×(C2×D11)⋊C4C23semidirect
186. C2×(C2×D11)⋊C4C23semidirect
187. C2×(C2×D11)⋊C4C23semidirect
188. C2×(C2×D11)⋊C4C23semidirect
189. C2×(C2×D11)⋊C4C23semidirect
190. C2×(C2×D11)⋊C4C23semidirect
192. C2×C4⋊Dic11C23semidirect
194. C2×Dic11⋊C4C23semidirect
197. C11×#95C23semidirect
198. C11×#95C23semidirect
199. C11⋊#95C23semidirect
200. C11⋊#95C23semidirect
273. C23×D11C2×D4semidirect
282. C2×D4×C11C2×D4semidirect
301. C22×C4×C11C2×D4semidirect
322. C2×C22⋊D11C2×D4semidirect
338. C22×Dic11C2×D4semidirect
378. (C2×D11)⋊C4C2×D4semidirect
394. C2×#386D11semidirect
420. C23×C11#120semidirect
499. C22×D11#121semidirect
526. C2×C4×C11C22×D4semidirect
547. C2×Dic11C22×D4semidirect
570. C24×C4C2×D11semidirect
595. C22×C22⋊C4C2×D11semidirect
596. C22×C22⋊C4C2×D11semidirect
597. C22×C22⋊C4C2×D11semidirect
604. #386C2×D11semidirect
609. C2×#95C2×D11semidirect
610. C2×#95C2×D11semidirect
627. C22×C11C2×#120semidirect
674. C2×D11C2×#121semidirect
744. C22×D4D44semidirect
766. C23×C4C22×D11semidirect
803. C2×C22⋊C4C22×D11semidirect
804. C2×C22⋊C4C22×D11semidirect
805. C2×C22⋊C4C22×D11semidirect
808. #95C22×D11semidirect
809. #95C22×D11semidirect
812. C2×C11#2410semidirect
937. C2×D4C2×D44semidirect
980. C22×C4D4×D11semidirect
1003. C11C2×#2410semidirect
1099. C23#66935semidirect
1159. C2×C4C2×D4×D11semidirect
1210. C22C2×#66935semidirect
1239. C2#13071989direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D112
C22×#669832
C22×#669922
C22×#669352
C23×(C2×D11)⋊C42
#130719892
C2×#106222852
C2×#106225742
C2×#106222842
C2×#106225732
C2×#106222782
C2×#106225712
C2×#106222812
C2×#106225682
C2×C11×#3862
C2×#241011