Finite Group Databasebeta

← C2×#13071987 #14921183

Subgroups — C2×#13071987 #14921183

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×#66992C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4C22×#66990C211yesmaximal, characteristic, complemented
5C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13071987C2116yesmaximal, direct product factor
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C25×D11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic, complemented
21C23×D4×C11C2211yescharacteristic, complemented
22C24×C4×C11C2211yescharacteristic, complemented
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic, complemented
27C23×C22⋊D11C2211yescharacteristic, complemented
28C24×Dic11C2211yescharacteristic, complemented
29C22×D4×D11—28no—
30C22×D4×D11—28no—
31C22×D4×D11—28no—
32C22×D4×D11C2218yescomplemented
33C23×D44C2211yescharacteristic
34C23×C4×D11C2211yescharacteristic
35C2×C11×#121—28no—
36C2×C11×#121C2218yescomplemented
37C22×C11×C4⋊C4C2211yescharacteristic, complemented
38C22×C11×C22⋊C4C2211yescharacteristic, complemented
39C22×C11×C22⋊C4C2211yescharacteristic, complemented
40C22×C22⋊Dic11C2211yescharacteristic, complemented
41C22×C22⋊Dic11C2211yescharacteristic, complemented
42C22×C22⋊Dic11C2211yescharacteristic, complemented
43C22×C22⋊Dic11C2211yescharacteristic, complemented
44C2×#66992—28no—
45C2×#66992C2218yescomplemented
46C2×#66990—28no—
47C2×#66990—28no—
48C2×#66990C2218yescomplemented
49C2×#66990C2218yescomplemented
50C22×(C2×D11)⋊C4—28no—
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×(C2×D11)⋊C4C2211yescharacteristic
54C22×(C2×D11)⋊C4C2218yescomplemented
55C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
56C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
57C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
58C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
59C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
60C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
61C22×Dic11⋊C4C2211yescharacteristic, complemented
62#10622836C2218yescomplemented
63#10622833C2218yescomplemented
64#10622826C2218yescomplemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67C2×C11⋊#95C2211yescharacteristic, complemented
68C2×C11⋊#95C2211yescharacteristic, complemented
69#10622604C2218yescomplemented
70#10622602C2218yescomplemented
71#10622573C2218yescomplemented
72#10622572C2218yescomplemented
73#10622569C2218yescomplemented
74#10622568C2218yescomplemented
75C25×C11C2311yescharacteristic
76C25×C11C2311yescharacteristic
77C25×C11C2311yescharacteristic
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—24no—
87C24×D11—42no—
88C24×D11—42no—
89C24×D11—42no—
90C24×D11—42no—
91C24×D11D418yescomplemented
92C24×D11C2311yescharacteristic
93C24×D11C2311yescharacteristic
94C24×D11C2314yes—
95C24×D11C2314yes—
96C24×D11C2311yescharacteristic
97C22×D4×C11—24no—
98C22×D4×C11—24no—
99C22×D4×C11—24no—
100C22×D4×C11—24no—
101C22×D4×C11—24no—
102C22×D4×C11—24no—
103C22×D4×C11—24no—
104C22×D4×C11—42no—
105C22×D4×C11D418yescomplemented
106C22×D4×C11C2314yes—
107C22×D4×C11C2314yescomplemented
108C22×D4×C11C2314yescomplemented
109C23×C4×C11—24no—
110C23×C4×C11—24no—
111C23×C4×C11—42no—
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2314yescomplemented
117C22×C22⋊D11—24no—
118C22×C22⋊D11—24no—
119C22×C22⋊D11—24no—
120C22×C22⋊D11—24no—
121C22×C22⋊D11—24no—
122C22×C22⋊D11—24no—
123C22×C22⋊D11—24no—
124C22×C22⋊D11—24no—
125C22×C22⋊D11—24no—
126C22×C22⋊D11—24no—
127C22×C22⋊D11—24no—
128C22×C22⋊D11—42no—
129C22×C22⋊D11—42no—
130C22×C22⋊D11—42no—
131C22×C22⋊D11D418yescomplemented
132C22×C22⋊D11C2314yes—
133C22×C22⋊D11C2314yes—
134C22×C22⋊D11C2314yes—
135C22×C22⋊D11C2314yescomplemented
136C22×C22⋊D11C2314yescomplemented
137C23×Dic11—24no—
138C23×Dic11—24no—
139C23×Dic11—42no—
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2314yescomplemented
146C2×D4×D11—2128no—
147C2×D4×D11—232no—
148C2×D4×D11—232no—
149C2×D4×D11—232no—
150C22×D44—24no—
151C22×D44—24no—
152C22×D44—24no—
153C22×D44C2314yes—
154C22×C4×D11—24no—
155C22×C4×D11—24no—
156C22×C4×D11—24no—
157C22×C4×D11C2314yes—
158C11×#121—232no—
159C2×C11×C4⋊C4—24no—
160C2×C11×C4⋊C4C2314yescomplemented
161C2×C11×C22⋊C4—24no—
162C2×C11×C22⋊C4—24no—
163C2×C11×C22⋊C4C2314yescomplemented
164C2×C11×C22⋊C4C2314yescomplemented
165C2×C22⋊Dic11—24no—
166C2×C22⋊Dic11—24no—
167C2×C22⋊Dic11—24no—
168C2×C22⋊Dic11—42no—
169C2×C22⋊Dic11C2314yescomplemented
170C2×C22⋊Dic11C2314yescomplemented
171C2×C22⋊Dic11C2314yescomplemented
172C2×C22⋊Dic11C2314yescomplemented
173#66992—232no—
174#66990—232no—
175#66990—232no—
176C2×(C2×D11)⋊C4—24no—
177C2×(C2×D11)⋊C4—24no—
178C2×(C2×D11)⋊C4—24no—
179C2×(C2×D11)⋊C4—24no—
180C2×(C2×D11)⋊C4—24no—
181C2×(C2×D11)⋊C4—24no—
182C2×(C2×D11)⋊C4—24no—
183C2×(C2×D11)⋊C4—232no—
184C2×(C2×D11)⋊C4—42no—
185C2×(C2×D11)⋊C4D418yescomplemented
186C2×(C2×D11)⋊C4C2314yes—
187C2×(C2×D11)⋊C4C2314yes—
188C2×(C2×D11)⋊C4C2314yes—
189C2×(C2×D11)⋊C4C2314yescomplemented
190C2×(C2×D11)⋊C4C2314yescomplemented
191C2×(C2×D11)⋊C4C2314yescomplemented
192C2×(C2×D11)⋊C4C2314yescomplemented
193C2×(C2×D11)⋊C4C2314yescomplemented
194C2×(C2×D11)⋊C4C2314yescomplemented
195C2×Dic11⋊C4—24no—
196C2×Dic11⋊C4C2314yescomplemented
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×C11—22no—
213C24×C11—22no—
214C24×C11—22no—
215C24×C11—22no—
216C24×C11—22no—
217C24×C11—22no—
218C24×C11—22no—
219C24×C11C2×D414yes—
220C24×C11C2×D414yes—
221C24×C11C2×D414yes—
222C24×C11C2×D414yes—
223C24×C11C2412yes—
224C24×C11C2412yes—
225C24×C11C2412yes—
226C24×C11C2411yescharacteristic
227C23×D11—22no—
228C23×D11—22no—
229C23×D11—22no—
230C23×D11—22no—
231C23×D11—232no—
232C23×D11—232no—
233C23×D11—22no—
234C23×D11—22no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—22no—
238C23×D11—22no—
239C23×D11—28no—
240C23×D11—28no—
241C23×D11—28no—
242C23×D11—22no—
243C23×D11—22no—
244C23×D11—22no—
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—22no—
248C23×D11—232no—
249C23×D11—28no—
250C23×D11—28no—
251C23×D11—28no—
252C23×D11—28no—
253C23×D11—28no—
254C23×D11—28no—
255C23×D11—416no—
256C23×D11—44no—
257C23×D11—44no—
258C23×D11—44no—
259C23×D11—44no—
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×D11—416no—
270C23×D11C2×D414yes—
271C23×D11C2×D414yes—
272C23×D11C2×D414yes—
273C23×D11C2×D414yes—
274C23×D11C2×D4116yescomplemented
275C23×D11#4114yes—
276C23×D11C2412yes—
277C23×D11C2412yes—
278C23×D11C2412yes—
279C2×D4×C11—232no—
280C2×D4×C11—28no—
281C2×D4×C11—28no—
282C2×D4×C11—28no—
283C2×D4×C11—28no—
284C2×D4×C11—28no—
285C2×D4×C11—28no—
286C2×D4×C11—28no—
287C2×D4×C11—44no—
288C2×D4×C11—416no—
289C2×D4×C11—416no—
290C2×D4×C11C2×D4116yescomplemented
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—22no—
298C22×C4×C11—22no—
299C22×C4×C11—22no—
300C22×C4×C11—28no—
301C22×C4×C11—22no—
302C22×C4×C11—28no—
303C22×C4×C11—44no—
304C22×C4×C11—416no—
305C22×C4×C11C2×D414yes—
306C22×C4×C11C2×D414yescomplemented
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2412yes—
310C22×C4×C11C2412yes—
311C2×C22⋊D11—232no—
312C2×C22⋊D11—28no—
313C2×C22⋊D11—28no—
314C2×C22⋊D11—232no—
315C2×C22⋊D11—28no—
316C2×C22⋊D11—28no—
317C2×C22⋊D11—28no—
318C2×C22⋊D11—28no—
319C2×C22⋊D11—28no—
320C2×C22⋊D11—28no—
321C2×C22⋊D11—28no—
322C2×C22⋊D11—28no—
323C2×C22⋊D11—28no—
324C2×C22⋊D11—44no—
325C2×C22⋊D11—44no—
326C2×C22⋊D11—44no—
327C2×C22⋊D11—416no—
328C2×C22⋊D11—416no—
329C2×C22⋊D11—416no—
330C2×C22⋊D11C2×D4116yescomplemented
331C22×Dic11—28no—
332C22×Dic11—22no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—22no—
336C22×Dic11—22no—
337C22×Dic11—22no—
338C22×Dic11—22no—
339C22×Dic11—22no—
340C22×Dic11—28no—
341C22×Dic11—22no—
342C22×Dic11—22no—
343C22×Dic11—22no—
344C22×Dic11—22no—
345C22×Dic11—22no—
346C22×Dic11—44no—
347C22×Dic11—416no—
348C22×Dic11C2×D414yes—
349C22×Dic11C2×D414yescomplemented
350C22×Dic11C2412yes—
351C22×Dic11C2412yes—
352C22×Dic11C2412yes—
353C22×Dic11C2412yes—
354C22×Dic11C2412yes—
355D4×D11—2256no—
356C2×D44—232no—
357C2×D44—28no—
358C2×D44—28no—
359C2×D44—28no—
360C2×C4×D11—232no—
361C2×C4×D11—28no—
362C2×C4×D11—28no—
363C2×C4×D11—28no—
364C11×C4⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—28no—
367C22⋊Dic11—28no—
368C22⋊Dic11—28no—
369C22⋊Dic11—28no—
370C22⋊Dic11—44no—
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—28no—
378(C2×D11)⋊C4—44no—
379(C2×D11)⋊C4C2×D4116yescomplemented
380Dic11⋊C4—28no—
381C24×D4—111no—
382C22×#121—111no—
383C22×#121D1111yescharacteristic, complemented
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×#386—111no—
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—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—44no—
424C23×C11—44no—
425C23×C11—44no—
426C23×C11—44no—
427C23×C11—44no—
428C23×C11—44no—
429C23×C11—44no—
430C23×C11—44no—
431C23×C11—44no—
432C23×C11—44no—
433C23×C11—44no—
434C23×C11#120116yescomplemented
435C23×C11C22×D414yes—
436C23×C11C22×D414yes—
437C23×C11C22×D412yes—
438C23×C11C22×D412yes—
439C23×C11C22×D412yes—
440C23×C11C22×D414yes—
441C23×C11C22×D414yes—
442C23×C11C22×D412yes—
443C23×C11C2×#4112yes—
444C23×C11H(5,𝔽2)12yes—
445C23×C11H(5,𝔽2)12yes—
446C23×C11C2511yescharacteristic
447C22×D11—28no—
448C22×D11—28no—
449C22×D11—28no—
450C22×D11—28no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—232no—
458C22×D11—28no—
459C22×D11—28no—
460C22×D11—232no—
461C22×D11—28no—
462C22×D11—28no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—232no—
478C22×D11—416no—
479C22×D11—416no—
480C22×D11—416no—
481C22×D11—4128no—
482C22×D11—416no—
483C22×D11—416no—
484C22×D11—416no—
485C22×D11—416no—
486C22×D11—416no—
487C22×D11—416no—
488C22×D11—4128no—
489C22×D11—416no—
490C22×D11—44no—
491C22×D11—44no—
492C22×D11—44no—
493C22×D11—44no—
494C22×D11—44no—
495C22×D11—44no—
496C22×D11—44no—
497C22×D11—44no—
498C22×D11—416no—
499C22×D11#121116yescomplemented
500C22×D11C22×D414yes—
501C22×D11C22×D414yes—
502C22×D11C22×D414yes—
503C22×D11C22×D414yes—
504C22×D11C2×#4114yes—
505D4×C11—232no—
506D4×C11—416no—
507D4×C11—416no—
508C2×C4×C11—28no—
509C2×C4×C11—28no—
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—416no—
521C2×C4×C11—44no—
522C2×C4×C11—44no—
523C2×C4×C11C22×D414yes—
524C2×C4×C11C22×D414yescomplemented
525C22⋊D11—232no—
526C22⋊D11—232no—
527C22⋊D11—416no—
528C22⋊D11—416no—
529C22⋊D11—416no—
530C2×Dic11—28no—
531C2×Dic11—28no—
532C2×Dic11—22no—
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—22no—
544C2×Dic11—22no—
545C2×Dic11—416no—
546C2×Dic11—44no—
547C2×Dic11—44no—
548C2×Dic11—44no—
549C2×Dic11C22×D414yes—
550C2×Dic11C22×D414yescomplemented
551D44—232no—
552C4×D11—232no—
553C26—111no—
554C26—111no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4—111no—
558C23×D4—111no—
559C23×D4—111no—
560C23×D4—118no—
561C23×D4—111no—
562C23×D4—228no—
563C23×D4—228no—
564C23×D4—228no—
565C23×D4C2×D1111yescharacteristic
566C23×D4C2×D1111yescharacteristic, complemented
567C23×D4C2×D1111yescharacteristic, complemented
568C24×C4—111no—
569C24×C4—111no—
570C24×C4C2×D1111yescharacteristic, complemented
571C2×#121—28no—
572C2×#121—118no—
573C2×#121—228no—
574C2×#121C2×D1118yescomplemented
575C2×#120—118no—
576C2×#120—118no—
577C2×#120—228no—
578C2×#120—228no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
595C22×C22⋊C4—228no—
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#386—118no—
605#385—118no—
606#379—118no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
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×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—88no—
634C22×C11C2×#12014yes—
635C22×C11C2×#12018yescomplemented
636C22×C11C2×#12114yes—
637C22×C11#53414yes—
638C22×C11D4214yes—
639C22×C11D4214yes—
640C22×C11#54614yes—
641C22×C11#54614yes—
642C22×C11C23×D411yescharacteristic
643C22×C11C23×D411yescharacteristic
644C22×C11C23×D411yescharacteristic
645C22×C11C23×D411yescharacteristic
646C22×C11C22×#4111yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C2×D11—24no—
650C2×D11—232no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—24no—
659C2×D11—24no—
660C2×D11—24no—
661C2×D11—24no—
662C2×D11—464no—
663C2×D11—464no—
664C2×D11—42no—
665C2×D11—416no—
666C2×D11—416no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11C2×#12118yescomplemented
675C4×C11—24no—
676C4×C11—24no—
677C4×C11—42no—
678C4×C11—42no—
679Dic11—24no—
680Dic11—24no—
681Dic11—42no—
682Dic11—42no—
683Dic11—42no—
684C25—111no—
685C25—111no—
686C25—111no—
687C25—118no—
688C25—114no—
689C25—114no—
690C25—224no—
691C25—224no—
692C25—224no—
693C25—224no—
694C25—224no—
695C25—224no—
696C25—224no—
697C25—224no—
698C25—224no—
699C25—442no—
700C25—442no—
701C25—442no—
702C25—442no—
703C25C22×D1111yescharacteristic
704C25C22×D1111yescharacteristic
705C25C22×D1111yescharacteristic
706C22×D4—24no—
707C22×D4—24no—
708C22×D4—24no—
709C22×D4—24no—
710C22×D4—24no—
711C22×D4—24no—
712C22×D4—24no—
713C22×D4—42no—
714C22×D4—118no—
715C22×D4—114no—
716C22×D4—114no—
717C22×D4—114no—
718C22×D4—114no—
719C22×D4—114no—
720C22×D4—114no—
721C22×D4—224no—
722C22×D4—224no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—2232no—
726C22×D4—2232no—
727C22×D4—22128no—
728C22×D4—224no—
729C22×D4—224no—
730C22×D4—224no—
731C22×D4—224no—
732C22×D4—2232no—
733C22×D4—224no—
734C22×D4—224no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—224no—
739C22×D4—442no—
740C22×D4—442no—
741C22×D4—442no—
742C22×D4C22⋊D1118yescomplemented
743C22×D4C22×D1114yes—
744C22×D4C22×D1114yescomplemented
745C22×D4C22×D1114yescomplemented
746C23×C4—24no—
747C23×C4—24no—
748C23×C4—42no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—114no—
755C23×C4—114no—
756C23×C4—224no—
757C23×C4—224no—
758C23×C4—224no—
759C23×C4—224no—
760C23×C4—224no—
761C23×C4—442no—
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1114yescomplemented
767#121—232no—
768#121—2232no—
769#120—2232no—
770#120—2232no—
771C2×C4⋊C4—24no—
772C2×C4⋊C4—114no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4C22×D1114yescomplemented
775C2×C22⋊C4—24no—
776C2×C22⋊C4—24no—
777C2×C22⋊C4—118no—
778C2×C22⋊C4—114no—
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⋊C4—442no—
804C2×C22⋊C4C22×D1114yescomplemented
805C2×C22⋊C4C22×D1114yescomplemented
806#95—114no—
807#95—114no—
808#95—114no—
809#95—114no—
810C2×C11—28no—
811C2×C11—44no—
812C2×C11—82no—
813C2×C11#241018yescomplemented
814C2×C11C22×#12011yescharacteristic
815C2×C11C22×#12111yescharacteristic
816C2×C11C2×#53411yescharacteristic
817C2×C11C2×D4211yescharacteristic
818C2×C11C2×D4211yescharacteristic
819C2×C11C2×#54611yescharacteristic
820C2×C11C2×#54611yescharacteristic
821D11—28no—
822D11—44no—
823D11—44no—
824C24—22no—
825C24—22no—
826C24—22no—
827C24—22no—
828C24—22no—
829C24—22no—
830C24—22no—
831C24—22no—
832C24—22no—
833C24—22no—
834C24—22no—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—22no—
839C24—22no—
840C24—22no—
841C24—114no—
842C24—114no—
843C24—114no—
844C24—112no—
845C24—114no—
846C24—114no—
847C24—112no—
848C24—112no—
849C24—1116no—
850C24—228no—
851C24—228no—
852C24—228no—
853C24—2232no—
854C24—228no—
855C24—228no—
856C24—228no—
857C24—2232no—
858C24—222no—
859C24—222no—
860C24—222no—
861C24—222no—
862C24—2232no—
863C24—222no—
864C24—222no—
865C24—228no—
866C24—222no—
867C24—222no—
868C24—222no—
869C24—222no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—228no—
875C24—228no—
876C24—222no—
877C24—222no—
878C24—4416no—
879C24—444no—
880C24—444no—
881C24—444no—
882C24—444no—
883C24—4416no—
884C24—4416no—
885C24—4416no—
886C24—4416no—
887C24—4416no—
888C24—4416no—
889C24—4416no—
890C24—4416no—
891C24—4416no—
892C24—4416no—
893C24D4×D1114yes—
894C24D4×D1114yes—
895C24C2×C22⋊D1114yes—
896C24C2×C22⋊D1114yes—
897C24C23×D1112yes—
898C24C23×D1112yes—
899C24C23×D1112yes—
900C24C23×D1111yescharacteristic
901C2×D4—232no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—416no—
911C2×D4—416no—
912C2×D4—1116no—
913C2×D4—228no—
914C2×D4—228no—
915C2×D4—2232no—
916C2×D4—228no—
917C2×D4—228no—
918C2×D4—22256no—
919C2×D4—228no—
920C2×D4—2232no—
921C2×D4—2232no—
922C2×D4—228no—
923C2×D4—228no—
924C2×D4—228no—
925C2×D4—228no—
926C2×D4—228no—
927C2×D4—228no—
928C2×D4—228no—
929C2×D4—228no—
930C2×D4—228no—
931C2×D4—444no—
932C2×D4—444no—
933C2×D4—444no—
934C2×D4—4416no—
935C2×D4—4416no—
936C2×D4—4416no—
937C2×D4C2×C22⋊D11116yescomplemented
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—22no—
948C22×C4—28no—
949C22×C4—28no—
950C22×C4—44no—
951C22×C4—416no—
952C22×C4—114no—
953C22×C4—114no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—112no—
958C22×C4—112no—
959C22×C4—228no—
960C22×C4—228no—
961C22×C4—2232no—
962C22×C4—228no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—228no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—228no—
974C22×C4—222no—
975C22×C4—222no—
976C22×C4—222no—
977C22×C4—222no—
978C22×C4—444no—
979C22×C4—4416no—
980C22×C4D4×D1114yescomplemented
981C22×C4C2×C22⋊D1114yes—
982C22×C4C23×D1112yes—
983C22×C4C23×D1112yes—
984C22×C4C23×D1112yes—
985C22×C4C23×D1112yes—
986C4⋊C4—28no—
987C4⋊C4—228no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—1116no—
991C22⋊C4—228no—
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—444no—
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—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—44no—
1031C23—44no—
1032C23—44no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—44no—
1037C23—44no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—1116no—
1042C23—114no—
1043C23—114no—
1044C23—114no—
1045C23—114no—
1046C23—114no—
1047C23—2232no—
1048C23—2232no—
1049C23—228no—
1050C23—228no—
1051C23—228no—
1052C23—228no—
1053C23—228no—
1054C23—228no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—228no—
1060C23—228no—
1061C23—2232no—
1062C23—228no—
1063C23—228no—
1064C23—228no—
1065C23—228no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—4416no—
1079C23—44128no—
1080C23—4416no—
1081C23—4416no—
1082C23—4416no—
1083C23—4416no—
1084C23—4416no—
1085C23—4416no—
1086C23—4416no—
1087C23—4416no—
1088C23—4416no—
1089C23—4416no—
1090C23—44128no—
1091C23—444no—
1092C23—444no—
1093C23—444no—
1094C23—444no—
1095C23—444no—
1096C23—444no—
1097C23—444no—
1098C23—444no—
1099C23#66990116yescomplemented
1100C23C2×D4×D1114yes—
1101C23C2×D4×D1114yes—
1102C23C2×D4×D1112yes—
1103C23C2×D4×D1112yes—
1104C23C2×D4×D1112yes—
1105C23#6703712yes—
1106C23#41×D1112yes—
1107C23#6704212yes—
1108C23C22×C22⋊D1114yes—
1109C23C22×C22⋊D1114yes—
1110C23C22×C22⋊D1112yes—
1111C23C24×D1111yescharacteristic
1112D4—232no—
1113D4—416no—
1114D4—416no—
1115D4—2232no—
1116D4—2232no—
1117D4—2232no—
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—416no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—114no—
1137C2×C4—114no—
1138C2×C4—2232no—
1139C2×C4—228no—
1140C2×C4—228no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
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—4416no—
1155C2×C4—444no—
1156C2×C4—444no—
1157C2×C4—444no—
1158C2×C4C2×D4×D1114yescomplemented
1159C2×C4C22×C22⋊D1114yes—
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—42no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—88no—
1183C22—118no—
1184C22—224no—
1185C22—2232no—
1186C22—224no—
1187C22—224no—
1188C22—224no—
1189C22—224no—
1190C22—224no—
1191C22—224no—
1192C22—224no—
1193C22—224no—
1194C22—224no—
1195C22—224no—
1196C22—224no—
1197C22—4464no—
1198C22—4464no—
1199C22—442no—
1200C22—4416no—
1201C22—4416no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—442no—
1207C22—442no—
1208C22—442no—
1209C22D11×#12114yes—
1210C22#1062313614yes—
1211C22#1062314014yes—
1212C22#1062314114yes—
1213C22C2×#6699014yes—
1214C22C2×#6699018yescomplemented
1215C22D4×C22⋊D1114yes—
1216C22#1062336014yes—
1217C22C22×D4×D1111yescharacteristic
1218C22C22×D4×D1111yescharacteristic
1219C22C22×D4×D1111yescharacteristic
1220C22C2×#6703711yescharacteristic
1221C22C2×#41×D1111yescharacteristic
1222C22C2×#6704211yescharacteristic
1223C22C23×C22⋊D1111yescharacteristic
1224C4—24no—
1225C4—24no—
1226C4—42no—
1227C4—42no—
1228C4—224no—
1229C4—224no—
1230C4—442no—
1231C4—442no—
1232C4—442no—
1233C2—28no—
1234C2—44no—
1235C2—82no—
1236C2—228no—
1237C2—444no—
1238C2—444no—
1239C2#1307198718yesdirect product factor
1240C2C22×#6699011yescharacteristic
1241C2C2×D11×#12111yescharacteristic
1242C2C2×#1062313611yescharacteristic
1243C2C2×D4×C22⋊D1111yescharacteristic
1244C2C2×#1062314011yescharacteristic
1245C2C2×#1062336011yescharacteristic
1246C2C2×#1062314111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C22×#66992C2semidirect
3. C22×#66990C2semidirect
4. C22×#66990C2semidirect
5. C23×(C2×D11)⋊C4C2semidirect
6. #13071987C2direct (N × H)
7. C2×#10622604C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C22×C11×#121C2semidirect
20. C23×D4×C11C22semidirect
21. C23×D4×C11C22semidirect
22. C24×C4×C11C22semidirect
26. C23×C22⋊D11C22semidirect
27. C23×C22⋊D11C22semidirect
28. C24×Dic11C22semidirect
32. C22×D4×D11C22semidirect
36. C2×C11×#121C22semidirect
37. C22×C11×C4⋊C4C22semidirect
38. C22×C11×C22⋊C4C22semidirect
39. C22×C11×C22⋊C4C22semidirect
40. C22×C22⋊Dic11C22semidirect
41. C22×C22⋊Dic11C22semidirect
42. C22×C22⋊Dic11C22semidirect
43. C22×C22⋊Dic11C22semidirect
45. C2×#66992C22semidirect
48. C2×#66990C22semidirect
49. C2×#66990C22semidirect
54. C22×(C2×D11)⋊C4C22semidirect
55. C22×(C2×D11)⋊C4C22semidirect
56. C22×(C2×D11)⋊C4C22semidirect
57. C22×(C2×D11)⋊C4C22semidirect
58. C22×(C2×D11)⋊C4C22semidirect
59. C22×(C2×D11)⋊C4C22semidirect
60. C22×(C2×D11)⋊C4C22semidirect
61. C22×Dic11⋊C4C22semidirect
62. #10622836C22semidirect
63. #10622833C22semidirect
64. #10622826C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. C2×C11⋊#95C22semidirect
68. C2×C11⋊#95C22semidirect
69. #10622604C22semidirect
70. #10622602C22semidirect
71. #10622573C22semidirect
72. #10622572C22semidirect
73. #10622569C22semidirect
74. #10622568C22semidirect
91. C24×D11D4semidirect
105. C22×D4×C11D4semidirect
107. C22×D4×C11C23semidirect
108. C22×D4×C11C23semidirect
116. C23×C4×C11C23semidirect
131. C22×C22⋊D11D4semidirect
135. C22×C22⋊D11C23semidirect
136. C22×C22⋊D11C23semidirect
145. C23×Dic11C23semidirect
160. C2×C11×C4⋊C4C23semidirect
163. C2×C11×C22⋊C4C23semidirect
164. C2×C11×C22⋊C4C23semidirect
169. C2×C22⋊Dic11C23semidirect
170. C2×C22⋊Dic11C23semidirect
171. C2×C22⋊Dic11C23semidirect
172. C2×C22⋊Dic11C23semidirect
185. C2×(C2×D11)⋊C4D4semidirect
189. C2×(C2×D11)⋊C4C23semidirect
190. C2×(C2×D11)⋊C4C23semidirect
191. C2×(C2×D11)⋊C4C23semidirect
192. C2×(C2×D11)⋊C4C23semidirect
193. C2×(C2×D11)⋊C4C23semidirect
194. C2×(C2×D11)⋊C4C23semidirect
196. C2×Dic11⋊C4C23semidirect
197. C11⋊#95C23semidirect
198. C11⋊#95C23semidirect
199. C11⋊#95C23semidirect
200. C11⋊#95C23semidirect
274. C23×D11C2×D4semidirect
290. C2×D4×C11C2×D4semidirect
306. C22×C4×C11C2×D4semidirect
330. C2×C22⋊D11C2×D4semidirect
349. C22×Dic11C2×D4semidirect
379. (C2×D11)⋊C4C2×D4semidirect
383. C22×#121D11semidirect
434. C23×C11#120semidirect
499. C22×D11#121semidirect
524. C2×C4×C11C22×D4semidirect
550. C2×Dic11C22×D4semidirect
566. C23×D4C2×D11semidirect
567. C23×D4C2×D11semidirect
570. C24×C4C2×D11semidirect
574. C2×#121C2×D11semidirect
580. C22×C4⋊C4C2×D11semidirect
596. C22×C22⋊C4C2×D11semidirect
597. C22×C22⋊C4C2×D11semidirect
635. C22×C11C2×#120semidirect
674. C2×D11C2×#121semidirect
742. C22×D4C22⋊D11semidirect
744. C22×D4C22×D11semidirect
745. C22×D4C22×D11semidirect
766. C23×C4C22×D11semidirect
774. C2×C4⋊C4C22×D11semidirect
804. C2×C22⋊C4C22×D11semidirect
805. C2×C22⋊C4C22×D11semidirect
813. C2×C11#2410semidirect
937. C2×D4C2×C22⋊D11semidirect
980. C22×C4D4×D11semidirect
1003. C11C2×#2410semidirect
1099. C23#66990semidirect
1158. C2×C4C2×D4×D11semidirect
1214. C22C2×#66990semidirect
1239. C2#13071987direct (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×#669922
C22×#669902
C23×(C2×D11)⋊C42
#130719872
C2×#106226042
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106228332
C2×#106228262
C2×#106225692
C2×#106226022
C2×#106225682
C22×C11×#1212
C2×#241011