Finite Group Databasebeta

← #14960710

Subgroups — #14960710

Order 2816.

3034 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3#13076910C211yesmaximal, characteristic, complemented
4#13076906C211yesmaximal, characteristic, complemented
5#13075235C212yesmaximal, complemented
6#13075231C212yesmaximal, complemented
7#13075206C212yesmaximal, complemented
8#13075204C212yesmaximal, complemented
9#13074984C212yesmaximal, complemented
10#13074983C212yesmaximal, complemented
11#13074943C212yesmaximal, complemented
12#13074934C212yesmaximal, complemented
13#13074328C211yesmaximal, characteristic, complemented
14#13072895C211yesmaximal, characteristic, complemented
15#13072025C211yesmaximal, characteristic, complemented
16#13072019C211yesmaximal, characteristic, complemented
17#13072003C211yesmaximal, characteristic, complemented
18#13071997C211yesmaximal, characteristic, complemented
19#13071941C211yesmaximal, characteristic, complemented
20#13071940C211yesmaximal, characteristic, complemented
21#13071927C211yesmaximal, characteristic, complemented
22#13071197C211yesmaximal, characteristic, complemented
23C11×#2613C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic, complemented
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic, complemented
28C22×D4×D11C2211yescharacteristic
29C2×C11×#123C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C2×C11×#120C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C2×#67006C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic, complemented
35C2×#66992—28no—
36C2×#66992C2212yes—
37C2×#66992C2212yes—
38C2×#66992C2212yescomplemented
39C2×#66992C2212yescomplemented
40C2×#66991C2211yescharacteristic, complemented
41C2×#66991C2211yescharacteristic, complemented
42C2×#66990C2211yescharacteristic, complemented
43C2×#66990C2211yescharacteristic, complemented
44C2×#66990C2212yescomplemented
45C2×#66988C2211yescharacteristic
46C2×#66988C2212yescomplemented
47C2×#66982C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50#10623120—28no—
51C2×#66939C2211yescharacteristic
52C2×#66939C2212yescomplemented
53C2×#66937C2211yescharacteristic, complemented
54C2×#66937C2211yescharacteristic, complemented
55C2×#66936C2211yescharacteristic, complemented
56C2×#66936C2211yescharacteristic, complemented
57C2×#66936C2212yescomplemented
58C2×C22⋊C4×D11C2211yescharacteristic
59C2×#66930C2211yescharacteristic, complemented
60C2×#66930C2211yescharacteristic, complemented
61C11×#394C2212yescomplemented
62C11×#394C2212yescomplemented
63C11×#392C2212yescomplemented
64C11×#392C2212yescomplemented
65C11×#381C2211yescharacteristic, complemented
66C11×#379C2211yescharacteristic, complemented
67C11×#379C2211yescharacteristic, complemented
68#10622860C2211yescharacteristic, complemented
69#10622860C2211yescharacteristic, complemented
70#10622836C2212yescomplemented
71#10622836C2212yescomplemented
72#10622836C2212yescomplemented
73#10622835C2212yescomplemented
74#10622835C2212yescomplemented
75#10622835C2212yescomplemented
76#10622834C2212yescomplemented
77#10622833C2211yescharacteristic
78#10622833C2211yescharacteristic
79#10622833C2212yescomplemented
80#10622824C2211yescharacteristic, complemented
81#10622604C2212yescomplemented
82#10622602C2212yescomplemented
83#10622593C2212yescomplemented
84#10622586C2212yescomplemented
85#10622574C2212yescomplemented
86#10622573C2212yescomplemented
87#10622572C2212yescomplemented
88#10622572C2212yescomplemented
89#10622572C2212yescomplemented
90#10622571C2211yescharacteristic
91#10622571C2211yescharacteristic
92#10622571C2212yescomplemented
93#10622570C2212yescomplemented
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622570C2212yescomplemented
98#10622569C2212yescomplemented
99#10622569C2212yescomplemented
100#10622568C2211yescharacteristic
101#10622568C2211yescharacteristic
102#10622568C2212yescomplemented
103#10622564C2212yescomplemented
104#10622563C2212yescomplemented
105#10622563C2211yescharacteristic, complemented
106#10622563C2211yescharacteristic, complemented
107#10622561C2212yescomplemented
108#10622561C2212yescomplemented
109#10622561C2212yescomplemented
110#10622559C2212yescomplemented
111#10622559C2211yescharacteristic, complemented
112#10622559C2211yescharacteristic, complemented
113#10622557C2212yescomplemented
114#10622557C2212yescomplemented
115#10622556C2212yescomplemented
116#10622556C2212yescomplemented
117#10622289C2212yescomplemented
118#10622288C2212yescomplemented
119#10622287C2212yescomplemented
120#10622282C2212yescomplemented
121#10622281C2212yescomplemented
122#10622277C2212yescomplemented
123#10622270C2212yescomplemented
124#10622260C2212yescomplemented
125C25×C11C2311yescharacteristic
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11—24no—
130C22×D4×C11—42no—
131C22×D4×C11—42no—
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2312yes—
136C22×D4×C11C2312yes—
137C22×D4×C11C2312yes—
138C23×C4×C11C2311yescharacteristic
139C22×C22⋊D11—24no—
140C22×C22⋊D11—44no—
141C22×C22⋊D11—42no—
142C22×C22⋊D11—42no—
143C22×C22⋊D11D418yescomplemented
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2312yes—
147C22×C22⋊D11C2311yescharacteristic
148C22×C22⋊D11C2311yescharacteristic
149C22×C22⋊D11C2311yescharacteristic
150C22×C22⋊D11C2312yes—
151C22×C22⋊D11C2311yescharacteristic
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2311yescharacteristic
154C22×C22⋊D11C2311yescharacteristic
155C23×Dic11—24no—
156C23×Dic11—44no—
157C23×Dic11C2311yescharacteristic
158C23×Dic11C2312yes—
159C23×Dic11C2312yes—
160C23×Dic11C2311yescharacteristic
161C23×Dic11C2311yescharacteristic
162C2×D4×D11—24no—
163C2×D4×D11—42no—
164C2×D4×D11—42no—
165C22×D44C2311yescharacteristic
166C22×C4×D11C2311yescharacteristic
167C22×C4×D11C2311yescharacteristic
168C22×C4×D11C2311yescharacteristic
169C11×#123—42no—
170C11×#120—24no—
171C11×#120—42no—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184#67006—24no—
185#67006—42no—
186C2×C22⋊Dic11—24no—
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2311yescharacteristic
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2311yescharacteristic
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203#66992—28no—
204#66992—28no—
205#66992—28no—
206#66992—28no—
207#66991—24no—
208#66991—24no—
209#66990—24no—
210#66990—24no—
211#66990—44no—
212#66988—24no—
213#66988—44no—
214#66982—42no—
215C2×(C2×D11)⋊C4—24no—
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2312yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2312yes—
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×(C2×D11)⋊C4C2312yes—
229C2×C4⋊Dic11C2311yescharacteristic
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2312yes—
232C2×C4⋊Dic11C2312yes—
233C2×Dic11⋊C4—24no—
234C2×Dic11⋊C4C2311yescharacteristic
235C2×Dic11⋊C4C2311yescharacteristic
236C2×Dic11⋊C4C2312yes—
237C2×Dic11⋊C4C2312yes—
238C2×Dic11⋊C4C2312yes—
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2312yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×C4×Dic11C2312yes—
244C2×C4×Dic11C2312yes—
245#66939—24no—
246#66939—44no—
247#66937—24no—
248#66937—24no—
249#66936—24no—
250#66936—24no—
251#66936—44no—
252C22⋊C4×D11—24no—
253#66930—42no—
254#66930—42no—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#36715—111nomaximal, Sylow
268C24×C11—22no—
269C24×C11—22no—
270C24×C11—22no—
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—42no—
274C24×C11—42no—
275C24×C11—42no—
276C24×C11—42no—
277C24×C11C2×D414yes—
278C24×C11C2411yescharacteristic
279C24×C11C2412yes—
280C24×C11C2411yescharacteristic
281C24×C11C2411yescharacteristic
282C24×C11C2411yescharacteristic
283C23×D11—22no—
284C23×D11—22no—
285C23×D11—22no—
286C23×D11—41no—
287C23×D11—41no—
288C23×D11—42no—
289C23×D11—42no—
290C23×D11—42no—
291C23×D11—42no—
292C23×D11C2×D414yes—
293C23×D11C2411yescharacteristic
294C23×D11C2411yescharacteristic
295C23×D11C2411yescharacteristic
296C2×D4×C11—22no—
297C2×D4×C11—24no—
298C2×D4×C11—24no—
299C2×D4×C11—22no—
300C2×D4×C11—22no—
301C2×D4×C11—22no—
302C2×D4×C11—22no—
303C2×D4×C11—42no—
304C2×D4×C11—42no—
305C2×D4×C11—42no—
306C2×D4×C11—42no—
307C2×D4×C11—42no—
308C2×D4×C11—42no—
309C2×D4×C11—42no—
310C2×D4×C11—42no—
311C2×D4×C11—42no—
312C2×D4×C11—416no—
313C22×C4×C11—22no—
314C22×C4×C11—22no—
315C22×C4×C11—22no—
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2412yes—
319C22×C4×C11C2412yes—
320C22×C4×C11C2412yes—
321C22×C4×C11C2411yescharacteristic
322C2×C22⋊D11—24no—
323C2×C22⋊D11—24no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—22no—
326C2×C22⋊D11—22no—
327C2×C22⋊D11—22no—
328C2×C22⋊D11—22no—
329C2×C22⋊D11—22no—
330C2×C22⋊D11—24no—
331C2×C22⋊D11—24no—
332C2×C22⋊D11—41no—
333C2×C22⋊D11—41no—
334C2×C22⋊D11—416no—
335C2×C22⋊D11—42no—
336C2×C22⋊D11—42no—
337C2×C22⋊D11—41no—
338C2×C22⋊D11—41no—
339C2×C22⋊D11—41no—
340C2×C22⋊D11—41no—
341C2×C22⋊D11—41no—
342C2×C22⋊D11—41no—
343C2×C22⋊D11—41no—
344C2×C22⋊D11—41no—
345C2×C22⋊D11—42no—
346C2×C22⋊D11—42no—
347C2×C22⋊D11—42no—
348C2×C22⋊D11—42no—
349C2×C22⋊D11—42no—
350C2×C22⋊D11—416no—
351C2×C22⋊D11C2×D414yes—
352C2×C22⋊D11C2×D414yes—
353C2×C22⋊D11C2×D414yes—
354C2×C22⋊D11C2×D414yes—
355C22×Dic11—24no—
356C22×Dic11—24no—
357C22×Dic11—24no—
358C22×Dic11—22no—
359C22×Dic11—22no—
360C22×Dic11—24no—
361C22×Dic11—24no—
362C22×Dic11—22no—
363C22×Dic11—22no—
364C22×Dic11—42no—
365C22×Dic11—42no—
366C22×Dic11—42no—
367C22×Dic11—416no—
368C22×Dic11C2×D414yes—
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2412yes—
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2412yes—
373C22×Dic11C2412yes—
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2412yes—
378D4×D11—416no—
379C2×D44—22no—
380C2×D44—41no—
381C2×D44—41no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—41no—
386C2×C4×D11—41no—
387C2×C4×D11—42no—
388C2×C4×D11—42no—
389C11×C4⋊C4—42no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—22no—
394C11×C22⋊C4—22no—
395C11×C22⋊C4—42no—
396C11×C22⋊C4—42no—
397C11×C22⋊C4—42no—
398C11×C22⋊C4—42no—
399C11×C22⋊C4—42no—
400C11×C22⋊C4—42no—
401C22⋊Dic11—22no—
402C22⋊Dic11—22no—
403C22⋊Dic11—24no—
404C22⋊Dic11—24no—
405C22⋊Dic11—24no—
406C22⋊Dic11—22no—
407C22⋊Dic11—22no—
408C22⋊Dic11—22no—
409C22⋊Dic11—22no—
410C22⋊Dic11—22no—
411C22⋊Dic11—42no—
412C22⋊Dic11—42no—
413C22⋊Dic11—42no—
414C22⋊Dic11—42no—
415C22⋊Dic11—42no—
416C22⋊Dic11—42no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—24no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—22no—
422(C2×D11)⋊C4—24no—
423(C2×D11)⋊C4—24no—
424(C2×D11)⋊C4—42no—
425(C2×D11)⋊C4—42no—
426(C2×D11)⋊C4—42no—
427(C2×D11)⋊C4—42no—
428(C2×D11)⋊C4—42no—
429(C2×D11)⋊C4—42no—
430C4⋊Dic11—22no—
431C4⋊Dic11—22no—
432C4⋊Dic11—24no—
433C4⋊Dic11—42no—
434Dic11⋊C4—22no—
435Dic11⋊C4—22no—
436Dic11⋊C4—24no—
437Dic11⋊C4—24no—
438Dic11⋊C4—24no—
439Dic11⋊C4—42no—
440Dic11⋊C4—42no—
441Dic11⋊C4—42no—
442Dic11⋊C4—42no—
443C4×Dic11—42no—
444C4×Dic11—42no—
445C2×#534—111no—
446C22×#121—111no—
447#2849—111no—
448#2849—111no—
449#2701—112no—
450#2701—112no—
451#2699—112no—
452#2699—112no—
453#2682—112no—
454#2682—112no—
455#2678—112no—
456#2678—112no—
457#2613—111no—
458#2613D1111yescharacteristic, complemented
459#2483—111no—
460#2413—111no—
461#2413—111no—
462#2411—111no—
463#2411—111no—
464#2405—111no—
465#2405—111no—
466#2403—111no—
467#2309—111no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—28no—
471C23×C11—22no—
472C23×C11—22no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—21no—
476C23×C11—21no—
477C23×C11—22no—
478C23×C11—22no—
479C23×C11—22no—
480C23×C11—21no—
481C23×C11—22no—
482C23×C11—22no—
483C23×C11—22no—
484C23×C11—21no—
485C23×C11—22no—
486C23×C11—22no—
487C23×C11—21no—
488C23×C11—22no—
489C23×C11—22no—
490C23×C11—22no—
491C23×C11—44no—
492C23×C11—44no—
493C23×C11—48no—
494C23×C11—48no—
495C23×C11—44no—
496C23×C11—44no—
497C23×C11—44no—
498C23×C11—84no—
499C23×C11—84no—
500C23×C11C22×D412yes—
501C23×C11C22×D412yes—
502C23×C11C22×D412yes—
503C23×C11H(5,𝔽2)12yes—
504C23×C11H(5,𝔽2)12yes—
505C23×C11C2511yescharacteristic
506C22×D11—22no—
507C22×D11—22no—
508C22×D11—21no—
509C22×D11—21no—
510C22×D11—21no—
511C22×D11—21no—
512C22×D11—22no—
513C22×D11—22no—
514C22×D11—28no—
515C22×D11—21no—
516C22×D11—22no—
517C22×D11—21no—
518C22×D11—21no—
519C22×D11—22no—
520C22×D11—44no—
521C22×D11—44no—
522C22×D11—44no—
523C22×D11—82no—
524C22×D11—82no—
525C22×D11—84no—
526C22×D11—84no—
527C22×D11—84no—
528C22×D11—84no—
529C22×D11C22×D412yes—
530C22×D11C22×D412yes—
531D4×C11—48no—
532D4×C11—48no—
533D4×C11—44no—
534D4×C11—82no—
535D4×C11—82no—
536D4×C11—84no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—22no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—21no—
548C2×C4×C11—22no—
549C2×C4×C11—21no—
550C2×C4×C11—22no—
551C2×C4×C11—22no—
552C2×C4×C11—22no—
553C2×C4×C11—44no—
554C22⋊D11—44no—
555C22⋊D11—44no—
556C22⋊D11—44no—
557C22⋊D11—44no—
558C22⋊D11—48no—
559C22⋊D11—48no—
560C22⋊D11—44no—
561C22⋊D11—44no—
562C22⋊D11—82no—
563C22⋊D11—82no—
564C22⋊D11—84no—
565C2×Dic11—28no—
566C2×Dic11—28no—
567C2×Dic11—22no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571C2×Dic11—21no—
572C2×Dic11—22no—
573C2×Dic11—21no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—22no—
580C2×Dic11—21no—
581C2×Dic11—22no—
582C2×Dic11—22no—
583C2×Dic11—22no—
584C2×Dic11—22no—
585C2×Dic11—21no—
586C2×Dic11—22no—
587C2×Dic11—22no—
588C2×Dic11—22no—
589C2×Dic11—48no—
590C2×Dic11—48no—
591C2×Dic11—44no—
592C2×Dic11C22×D412yes—
593C2×Dic11C22×D412yes—
594C2×Dic11H(5,𝔽2)14yes—
595D44—44no—
596C4×D11—44no—
597C4×D11—82no—
598C4×D11—82no—
599C23×D4—111no—
600C23×D4—111no—
601C23×D4—111no—
602C23×D4C2×D1111yescharacteristic, complemented
603C24×C4—111no—
604#534—228no—
605C2×#123—111no—
606C2×#123—112no—
607C2×#123—111no—
608C2×#123—111no—
609C2×#123—111no—
610C2×#123—111no—
611C2×#123—112no—
612C2×#123—112no—
613C2×#123C2×D1111yescharacteristic
614C2×#121—111no—
615C2×#121—111no—
616C2×#121—112no—
617C2×#121—112no—
618C2×#121—112no—
619C2×#121—112no—
620C2×#121—111no—
621C2×#121—111no—
622C2×#121—228no—
623C2×#120—111no—
624C2×#120—111no—
625C2×#120—111no—
626C2×#120—111no—
627C2×#120—112no—
628C2×#120C2×D1111yescharacteristic
629C2×#120C2×D1111yescharacteristic
630C2×#117—111no—
631C2×#117—111no—
632C22×C4⋊C4—111no—
633C22×C22⋊C4—111no—
634C22×C22⋊C4—111no—
635C22×C22⋊C4—111no—
636#398—112no—
637#398—112no—
638#397—112no—
639#397—112no—
640#396—112no—
641#396—112no—
642#396—112no—
643#396—112no—
644#394—112no—
645#394—112no—
646#394—112no—
647#394—112no—
648#394—112no—
649#394—112no—
650#394—112no—
651#394—112no—
652#394C2×D1112yescomplemented
653#394C2×D1112yescomplemented
654#392—112no—
655#392—112no—
656#392—112no—
657#392—112no—
658#392C2×D1112yescomplemented
659#392C2×D1112yescomplemented
660#390—112no—
661#390—112no—
662#390—112no—
663#390—112no—
664#390—112no—
665#390—112no—
666#389—112no—
667#389—112no—
668#388—112no—
669#388—112no—
670#388—112no—
671#388—112no—
672#386—111no—
673#386—111no—
674#386—112no—
675#386—111no—
676#386—111no—
677#386—112no—
678#386—112no—
679#386—112no—
680#385—112no—
681#385—111no—
682#385—111no—
683#385—112no—
684#385—111no—
685#385—111no—
686#385—112no—
687#385—112no—
688#381—111no—
689#381—112no—
690#381—112no—
691#381—112no—
692#381C2×D1111yescharacteristic, complemented
693#379—111no—
694#379—111no—
695#379—111no—
696#379—111no—
697#379—112no—
698#379C2×D1111yescharacteristic, complemented
699#379C2×D1111yescharacteristic, complemented
700C22×C11—22no—
701C22×C11—22no—
702C22×C11—24no—
703C22×C11—24no—
704C22×C11—22no—
705C22×C11—22no—
706C22×C11—22no—
707C22×C11—22no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—416no—
711C22×C11—42no—
712C22×C11—42no—
713C22×C11—42no—
714C22×C11—42no—
715C22×C11—42no—
716C22×C11—41no—
717C22×C11—41no—
718C22×C11—42no—
719C22×C11—41no—
720C22×C11—42no—
721C22×C11—42no—
722C22×C11—42no—
723C22×C11—42no—
724C22×C11—42no—
725C22×C11—42no—
726C22×C11—42no—
727C22×C11—88no—
728C22×C11#53414yes—
729C22×C11C23×D411yescharacteristic
730C22×C11C2×H(5,𝔽2)11yescharacteristic
731C22×C11C2×H(5,𝔽2)11yescharacteristic
732C22×C11C2×H(5,𝔽2)12yes—
733C22×C11#58512yes—
734C2×D11—22no—
735C2×D11—22no—
736C2×D11—22no—
737C2×D11—22no—
738C2×D11—22no—
739C2×D11—22no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—42no—
744C2×D11—41no—
745C2×D11—41no—
746C2×D11—41no—
747C2×D11—42no—
748C2×D11—42no—
749C2×D11—88no—
750C2×D11—88no—
751C4×C11—42no—
752C4×C11—41no—
753C4×C11—41no—
754C4×C11—41no—
755C4×C11—42no—
756C4×C11—42no—
757Dic11—22no—
758Dic11—22no—
759Dic11—24no—
760Dic11—41no—
761Dic11—41no—
762Dic11—42no—
763Dic11—41no—
764Dic11—42no—
765Dic11—42no—
766C25—111no—
767C25—111no—
768C25C22×D1111yescharacteristic
769C25C22×D1111yescharacteristic
770C22×D4—24no—
771C22×D4—42no—
772C22×D4—42no—
773C22×D4—118no—
774C22×D4—111no—
775C22×D4—111no—
776C22×D4—111no—
777C22×D4—111no—
778C22×D4—111no—
779C22×D4—112no—
780C22×D4—112no—
781C22×D4—111no—
782C22×D4—111no—
783C22×D4—111no—
784C22×D4—112no—
785C22×D4—111no—
786C22×D4—224no—
787C22×D4—224no—
788C22×D4—444no—
789C22×D4—442no—
790C22×D4—442no—
791C22×D4—442no—
792C22×D4—442no—
793C22×D4C22×D1111yescharacteristic
794C22×D4C22×D1111yescharacteristic
795C22×D4C22×D1111yescharacteristic
796C22×D4C22×D1112yes—
797C22×D4C22×D1112yes—
798C22×D4C22×D1112yes—
799C23×C4—111no—
800C23×C4—111no—
801C23×C4—112no—
802C23×C4—112no—
803C23×C4—111no—
804C23×C4—111no—
805C23×C4—111no—
806C23×C4—111no—
807C23×C4—224no—
808C23×C4—444no—
809C23×C4C22×D1111yescharacteristic
810#123—42no—
811#123—224no—
812#123—224no—
813#123—224no—
814#123—224no—
815#123—444no—
816#123—444no—
817#123—444no—
818#123—442no—
819#121—224no—
820#121—224no—
821#121—228no—
822#121—228no—
823#121—228no—
824#121—228no—
825#121—224no—
826#121—224no—
827#120—24no—
828#120—42no—
829#120—224no—
830#120—224no—
831#120—224no—
832#120—444no—
833#120—442no—
834#117—442no—
835#117—442no—
836C2×C4⋊C4—112no—
837C2×C4⋊C4—112no—
838C2×C4⋊C4—111no—
839C2×C4⋊C4—111no—
840C2×C4⋊C4—111no—
841C2×C4⋊C4—111no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4—112no—
847C2×C4⋊C4—112no—
848C2×C4⋊C4—112no—
849C2×C4⋊C4—224no—
850C2×C4⋊C4C22×D1112yes—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—111no—
855C2×C22⋊C4—111no—
856C2×C22⋊C4—111no—
857C2×C22⋊C4—111no—
858C2×C22⋊C4—111no—
859C2×C22⋊C4—111no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—111no—
862C2×C22⋊C4—111no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—111no—
866C2×C22⋊C4—111no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—112no—
872C2×C22⋊C4—112no—
873C2×C22⋊C4—112no—
874C2×C22⋊C4—112no—
875C2×C22⋊C4—112no—
876C2×C22⋊C4—112no—
877C2×C22⋊C4—112no—
878C2×C22⋊C4—112no—
879C2×C22⋊C4—112no—
880C2×C22⋊C4—224no—
881C2×C22⋊C4—224no—
882C2×C22⋊C4—224no—
883C2×C22⋊C4C22×D1111yescharacteristic
884C2×C22⋊C4C22×D1111yescharacteristic
885C2×C22⋊C4C22×D1111yescharacteristic
886C2×C22⋊C4C22×D1111yescharacteristic
887C2×C22⋊C4C22×D1111yescharacteristic
888C2×C22⋊C4C22×D1112yes—
889C2×C22⋊C4C22×D1112yes—
890C2×C22⋊C4C22×D1112yes—
891C2×C22⋊C4C22×D1112yes—
892C2×C22⋊C4C22×D1112yes—
893C2×C22⋊C4C22×D1112yes—
894C2×C42—112no—
895C2×C42—112no—
896#95—112no—
897#95—112no—
898#95—112no—
899#95—112no—
900#95—112no—
901#95—112no—
902#95—112no—
903#95—112no—
904#95—112no—
905#95—112no—
906#95C22×D1112yes—
907#95C22×D1112yes—
908C2×C11—24no—
909C2×C11—42no—
910C2×C11—42no—
911C2×C11—81no—
912C2×C11—82no—
913C2×C11C2×#53411yescharacteristic
914C2×C11#348411yescharacteristic
915C2×C11#348511yescharacteristic
916C2×C11#354212yes—
917C2×C11#354212yes—
918D11—42no—
919D11—42no—
920D11—81no—
921C24—22no—
922C24—22no—
923C24—22no—
924C24—22no—
925C24—22no—
926C24—42no—
927C24—42no—
928C24—42no—
929C24—42no—
930C24—111no—
931C24—111no—
932C24—114no—
933C24—111no—
934C24—222no—
935C24—222no—
936C24—222no—
937C24—442no—
938C24—441no—
939C24—441no—
940C24—442no—
941C24—442no—
942C24—442no—
943C24D4×D1114yes—
944C24C23×D1111yescharacteristic
945C24C23×D1112yes—
946C24C23×D1111yescharacteristic
947C24C23×D1111yescharacteristic
948C24C23×D1111yescharacteristic
949C2×D4—22no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—22no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—416no—
966C2×D4—114no—
967C2×D4—114no—
968C2×D4—114no—
969C2×D4—114no—
970C2×D4—222no—
971C2×D4—224no—
972C2×D4—224no—
973C2×D4—224no—
974C2×D4—224no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—441no—
982C2×D4—441no—
983C2×D4—4416no—
984C2×D4—441no—
985C2×D4—441no—
986C2×D4—441no—
987C2×D4—441no—
988C2×D4—441no—
989C2×D4—441no—
990C2×D4—441no—
991C2×D4—441no—
992C2×D4—442no—
993C2×D4—442no—
994C2×D4—441no—
995C2×D4—441no—
996C2×D4—4416no—
997C2×D4—442no—
998C2×D4—442no—
999C2×D4—442no—
1000C2×D4—442no—
1001C2×D4—442no—
1002C2×D4—4416no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—114no—
1007C22×C4—112no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—112no—
1012C22×C4—112no—
1013C22×C4—111no—
1014C22×C4—112no—
1015C22×C4—111no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—222no—
1019C22×C4—224no—
1020C22×C4—224no—
1021C22×C4—224no—
1022C22×C4—222no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—224no—
1027C22×C4—224no—
1028C22×C4—441no—
1029C22×C4—441no—
1030C22×C4—442no—
1031C22×C4—442no—
1032C22×C4—442no—
1033C22×C4—442no—
1034C22×C4—442no—
1035C22×C4—4416no—
1036C22×C4C23×D1111yescharacteristic
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1112yes—
1039C22×C4C23×D1112yes—
1040C22×C4C23×D1112yes—
1041C22×C4C23×D1111yescharacteristic
1042C4⋊C4—42no—
1043C4⋊C4—224no—
1044C4⋊C4—224no—
1045C4⋊C4—222no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—224no—
1050C4⋊C4—224no—
1051C4⋊C4—442no—
1052C4⋊C4—442no—
1053C4⋊C4—442no—
1054C4⋊C4—442no—
1055C4⋊C4—442no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—224no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—224no—
1073C22⋊C4—224no—
1074C22⋊C4—224no—
1075C22⋊C4—224no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C22⋊C4—224no—
1079C22⋊C4—222no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—442no—
1085C22⋊C4—442no—
1086C22⋊C4—442no—
1087C22⋊C4—442no—
1088C22⋊C4—442no—
1089C22⋊C4—442no—
1090C22⋊C4—442no—
1091C22⋊C4—442no—
1092C22⋊C4—442no—
1093C22⋊C4—442no—
1094C22⋊C4—442no—
1095C22⋊C4—442no—
1096C42—442no—
1097C42—442no—
1098C11#3671511yescharacteristic, complemented, Sylow
1099C23—22no—
1100C23—22no—
1101C23—28no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—21no—
1111C23—22no—
1112C23—21no—
1113C23—22no—
1114C23—22no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—44no—
1123C23—44no—
1124C23—48no—
1125C23—48no—
1126C23—44no—
1127C23—44no—
1128C23—44no—
1129C23—84no—
1130C23—84no—
1131C23—112no—
1132C23—112no—
1133C23—221no—
1134C23—221no—
1135C23—221no—
1136C23—221no—
1137C23—222no—
1138C23—222no—
1139C23—222no—
1140C23—222no—
1141C23—228no—
1142C23—221no—
1143C23—221no—
1144C23—221no—
1145C23—222no—
1146C23—222no—
1147C23—444no—
1148C23—444no—
1149C23—444no—
1150C23—884no—
1151C23—884no—
1152C23—882no—
1153C23—882no—
1154C23—884no—
1155C23—884no—
1156C23C2×D4×D1112yes—
1157C23C2×D4×D1112yes—
1158C23C2×D4×D1112yes—
1159C23#6703712yes—
1160C23#6703712yes—
1161C23C24×D1111yescharacteristic
1162D4—48no—
1163D4—48no—
1164D4—44no—
1165D4—82no—
1166D4—82no—
1167D4—84no—
1168D4—444no—
1169D4—444no—
1170D4—444no—
1171D4—444no—
1172D4—444no—
1173D4—448no—
1174D4—448no—
1175D4—444no—
1176D4—444no—
1177D4—882no—
1178D4—882no—
1179D4—884no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—44no—
1197C2×C4—112no—
1198C2×C4—112no—
1199C2×C4—114no—
1200C2×C4—228no—
1201C2×C4—228no—
1202C2×C4—222no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—221no—
1206C2×C4—221no—
1207C2×C4—222no—
1208C2×C4—221no—
1209C2×C4—221no—
1210C2×C4—222no—
1211C2×C4—221no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—222no—
1223C2×C4—222no—
1224C2×C4—444no—
1225C2×C4—448no—
1226C2×C4—448no—
1227C2×C4—444no—
1228C2×C4—882no—
1229C2×C4—882no—
1230C22—24no—
1231C22—24no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—416no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—41no—
1253C22—41no—
1254C22—42no—
1255C22—41no—
1256C22—42no—
1257C22—88no—
1258C22—222no—
1259C22—222no—
1260C22—222no—
1261C22—222no—
1262C22—222no—
1263C22—222no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—441no—
1271C22—441no—
1272C22—441no—
1273C22—888no—
1274C22—888no—
1275C22#1062312014yes—
1276C22C22×D4×D1111yescharacteristic
1277C22C2×#6703711yescharacteristic
1278C22C2×#6703711yescharacteristic
1279C22D11×H(5,𝔽2)12yes—
1280C22#1062345512yes—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—222no—
1288C4—222no—
1289C4—224no—
1290C4—442no—
1291C4—442no—
1292C4—441no—
1293C4—442no—
1294C4—441no—
1295C4—441no—
1296C2—24no—
1297C2—42no—
1298C2—42no—
1299C2—82no—
1300C2—81no—
1301C2—442no—
1302C2—442no—
1303C2—881no—
1304C2C2×#1062312011yescharacteristic
1305C2#1308224811yescharacteristic
1306C2#1308225711yescharacteristic
1307C2#1308291912yes—
1308C2#1308292712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2613C2
hypercenter#2613D11
hypocenterC11#36715
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2613

Complements

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

NH ≅ G/Ntype
1. C2×#10623120C2semidirect
2. C22×#66992C2semidirect
3. #13076910C2semidirect
4. #13076906C2semidirect
5. #13075235C2semidirect
6. #13075231C2semidirect
7. #13075206C2semidirect
8. #13075204C2semidirect
9. #13074984C2semidirect
10. #13074983C2semidirect
11. #13074943C2semidirect
12. #13074934C2semidirect
13. #13074328C2semidirect
14. #13072895C2semidirect
15. #13072025C2semidirect
16. #13072019C2semidirect
17. #13072003C2semidirect
18. #13071997C2semidirect
19. #13071941C2semidirect
20. #13071940C2semidirect
21. #13071927C2semidirect
22. #13071197C2semidirect
23. C11×#2613C2semidirect
24. C23×D4×C11C22semidirect
27. C24×Dic11C22semidirect
34. C22×C22⋊Dic11C22semidirect
38. C2×#66992C22semidirect
39. C2×#66992C22semidirect
40. C2×#66991C22semidirect
41. C2×#66991C22semidirect
42. C2×#66990C22semidirect
43. C2×#66990C22semidirect
44. C2×#66990C22semidirect
46. C2×#66988C22semidirect
49. C22×Dic11⋊C4C22semidirect
52. C2×#66939C22semidirect
53. C2×#66937C22semidirect
54. C2×#66937C22semidirect
55. C2×#66936C22semidirect
56. C2×#66936C22semidirect
57. C2×#66936C22semidirect
59. C2×#66930C22semidirect
60. C2×#66930C22semidirect
61. C11×#394C22semidirect
62. C11×#394C22semidirect
63. C11×#392C22semidirect
64. C11×#392C22semidirect
65. C11×#381C22semidirect
66. C11×#379C22semidirect
67. C11×#379C22semidirect
68. #10622860C22semidirect
69. #10622860C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
72. #10622836C22semidirect
73. #10622835C22semidirect
74. #10622835C22semidirect
75. #10622835C22semidirect
76. #10622834C22semidirect
79. #10622833C22semidirect
80. #10622824C22semidirect
81. #10622604C22semidirect
82. #10622602C22semidirect
83. #10622593C22semidirect
84. #10622586C22semidirect
85. #10622574C22semidirect
86. #10622573C22semidirect
87. #10622572C22semidirect
88. #10622572C22semidirect
89. #10622572C22semidirect
92. #10622571C22semidirect
93. #10622570C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622570C22semidirect
98. #10622569C22semidirect
99. #10622569C22semidirect
102. #10622568C22semidirect
103. #10622564C22semidirect
104. #10622563C22semidirect
105. #10622563C22semidirect
106. #10622563C22semidirect
107. #10622561C22semidirect
108. #10622561C22semidirect
109. #10622561C22semidirect
110. #10622559C22semidirect
111. #10622559C22semidirect
112. #10622559C22semidirect
113. #10622557C22semidirect
114. #10622557C22semidirect
115. #10622556C22semidirect
116. #10622556C22semidirect
117. #10622289C22semidirect
118. #10622288C22semidirect
119. #10622287C22semidirect
120. #10622282C22semidirect
121. #10622281C22semidirect
122. #10622277C22semidirect
123. #10622270C22semidirect
124. #10622260C22semidirect
143. C22×C22⋊D11D4semidirect
458. #2613D11semidirect
602. C23×D4C2×D11semidirect
652. #394C2×D11semidirect
653. #394C2×D11semidirect
658. #392C2×D11semidirect
659. #392C2×D11semidirect
692. #381C2×D11semidirect
698. #379C2×D11semidirect
699. #379C2×D11semidirect
1098. C11#36715semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C22×#669922
#130769102
#130769062
#130752352
#130752312
#130752062
#130752042
#130749842
#130749832
#130749432
#130749342
#130743282
#130728952
#130720252
#130720192
#130720032
#130719972
#130719412
#130719402
#130719272
#130711972
C11×#26132
#3671511