Finite Group Databasebeta

← #14921949

Subgroups — #14921949

Order 2816.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic, complemented
2#13072858C212yesmaximal, complemented
3#13072678C212yesmaximal, complemented
4#13072519C212yesmaximal, complemented
5#13072484C211yesmaximal, characteristic, complemented
6#13072399C211yesmaximal, characteristic, complemented
7#13072336C211yesmaximal, characteristic, complemented
8#13072264C211yesmaximal, characteristic, complemented
9#13072189C211yesmaximal, characteristic, complemented
10#13072104C211yesmaximal, characteristic, complemented
11#13072075C212yesmaximal, complemented
12#13072063C211yesmaximal, characteristic, complemented
13#13071968C211yesmaximal, characteristic
14#13071873C212yesmaximal, complemented
15#13071858C212yesmaximal, complemented
16C4×#67000C211yesmaximal, characteristic, complemented
17C4×#66999C211yesmaximal, characteristic, complemented
18C4×#66983C211yesmaximal, characteristic, complemented
19C4×#66990C212yesmaximal, complemented
20#13071081C211yesmaximal, characteristic, complemented
21#13070995C212yesmaximal, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C2×C11×#529C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C11×#529—28no—
27C2×C11×#126C2212yescomplemented
28C2×C11×#125C2211yescharacteristic, complemented
29C2×C11×#124C2211yescharacteristic
30C2×C11×#123C2212yescomplemented
31C2×C11×C22⋊Q8C2211yescharacteristic, complemented
32C2×C11×#121C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic, complemented
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2212yescomplemented
36C2×C11×#117C2212yescomplemented
37C22×C42×C11C2211yescharacteristic, complemented
38C2×#67000C2211yescharacteristic
39C2×#66999C2211yescharacteristic
40C2×#66990C2212yes—
41C2×D4×Dic11C2211yescharacteristic
42C2×#66983C2211yescharacteristic
43C2×C4×C22⋊D11C2212yes—
44C2×C4×C22⋊D11C2211yescharacteristic
45C2×C4×C22⋊D11C2211yescharacteristic
46C2×C4×C22⋊D11C2211yescharacteristic
47C2×C4×C22⋊D11C2212yescomplemented
48C2×#66979C2212yescomplemented
49C4×D4×D11—28no—
50C2×#66946C2211yescharacteristic
51C2×C4⋊C4×D11C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56#10622843C2211yescharacteristic, complemented
57#10622843C2211yescharacteristic, complemented
58#10622836C2212yes—
59#10622835C2212yescomplemented
60#10622834C2211yescharacteristic
61#10622834C2211yescharacteristic
62#10622833C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic, complemented
65C4×C22⋊Dic11C2212yescomplemented
66C4×C22⋊Dic11C2211yescharacteristic, complemented
67C4×C22⋊Dic11C2211yescharacteristic, complemented
68C4×C22⋊Dic11C2211yescharacteristic, complemented
69#10622607C2212yescomplemented
70#10622606C2212yescomplemented
71#10622605C2212yescomplemented
72#10622603C2212yescomplemented
73#10622603C2212yescomplemented
74#10622602C2212yes—
75#10622602C2212yes—
76#10622602C2212yescomplemented
77#10622601C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2212yes—
80#10622600C2212yes—
81#10622600C2212yescomplemented
82#10622600C2212yescomplemented
83#10622598C2211yescharacteristic, complemented
84#10622598C2211yescharacteristic, complemented
85#10622597C2212yescomplemented
86#10622595C2212yescomplemented
87#10622593C2212yescomplemented
88#10622591C2212yescomplemented
89#10622590C2211yescharacteristic, complemented
90#10622586C2211yescharacteristic, complemented
91#10622574C2212yescomplemented
92#10622572C2212yes—
93#10622572C2212yes—
94#10622572C2212yes—
95#10622569C2212yes—
96#10622569C2212yescomplemented
97#10622568C2212yes—
98#10622568C2212yes—
99#10622568C2212yes—
100#10622565C2212yescomplemented
101#10622565C2212yescomplemented
102#10622565C2212yescomplemented
103#10622564C2212yescomplemented
104#10622564C2212yescomplemented
105#10622561C2212yescomplemented
106#10622559C2212yescomplemented
107#10622556C2212yescomplemented
108#10622556C2212yescomplemented
109#10622553C2212yescomplemented
110#10622552C2211yescharacteristic
111C4×(C2×D11)⋊C4C2212yes—
112C4×(C2×D11)⋊C4C2211yescharacteristic
113C4×(C2×D11)⋊C4C2211yescharacteristic
114C4×(C2×D11)⋊C4C2211yescharacteristic
115C4×(C2×D11)⋊C4C2212yescomplemented
116C4×(C2×D11)⋊C4C2212yescomplemented
117C4×(C2×D11)⋊C4C2212yescomplemented
118C4×C4⋊Dic11C2211yescharacteristic, complemented
119C4×Dic11⋊C4C2211yescharacteristic, complemented
120C4×Dic11⋊C4C2212yescomplemented
121C4×Dic11⋊C4C2211yescharacteristic, complemented
122C4×Dic11⋊C4C2211yescharacteristic, complemented
123C42×Dic11C2211yescharacteristic, complemented
124#10622541C2211yescharacteristic, complemented
125C24×D11C2312yes—
126C22×Q8×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2312yes—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×D4×D11—24no—
140C22×D44C2311yescharacteristic
141C22×C4×D11—28no—
142C22×C4×D11—28no—
143C22×C4×D11—44no—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C11×#126—28no—
151C11×#125—24no—
152C11×#124—24no—
153C11×#123—28no—
154C11×C22⋊Q8—24no—
155C11×#121—24no—
156C4×Q8×C11—24no—
157C4×D4×C11—28no—
158C4×D4×C11D418yescomplemented
159C11×#117—28no—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C42×C11—24no—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186#67000—24no—
187#66999—24no—
188#66990—28no—
189D4×Dic11—24no—
190#66983—24no—
191C4×C22⋊D11—28no—
192C4×C22⋊D11—24no—
193C4×C22⋊D11—24no—
194C4×C22⋊D11—24no—
195C4×C22⋊D11—44no—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210#66979—44no—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2311yescharacteristic
233#66946—24no—
234C4⋊C4×D11—24no—
235(C22⋊D11)⋊C4—28no—
236C22⋊C4×D11—28no—
237C4×D44—24no—
238C42×D11—24no—
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#34700—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C2×Q8×C11—22no—
271C2×Q8×C11—22no—
272C2×Q8×C11—22no—
273C2×D4×C11—24no—
274C2×D4×C11—24no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—42no—
278C2×D4×C11C2×D414yes—
279C22×C4×C11—24no—
280C22×C4×C11—24no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
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—41no—
290C22×C4×C11C2×D418yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11#4114yes—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—42no—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322D4×D11—232no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44#4114yes—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—41no—
342C2×C4×D11—432no—
343C2×C4×D11#4114yes—
344C2×C4×D11#4114yes—
345C11×C4⋊C4—24no—
346C11×C4⋊C4—24no—
347C11×C4⋊C4—24no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—24no—
350C11×C4⋊C4C2×D414yes—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4C2×D418yes—
356C42×C11—22no—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—24no—
360C42×C11C2×D414yes—
361C22⋊Dic11—22no—
362C22⋊Dic11—22no—
363C22⋊Dic11—24no—
364C22⋊Dic11—24no—
365C22⋊Dic11—22no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11—42no—
369C22⋊Dic11—42no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11—22no—
387C4⋊Dic11—42no—
388C4⋊Dic11—42no—
389Dic11⋊C4—22no—
390Dic11⋊C4—22no—
391Dic11⋊C4—22no—
392Dic11⋊C4—24no—
393Dic11⋊C4—24no—
394Dic11⋊C4—42no—
395Dic11⋊C4—42no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—24no—
405C4×Dic11—41no—
406C2×#529D1111yescharacteristic, complemented
407C22×C4×D4—111no—
408#2480—112no—
409#2468—112no—
410#2457—112no—
411#2454—111no—
412#2447—111no—
413#2442—111no—
414#2435—111no—
415#2427—111no—
416#2420—111no—
417#2418—112no—
418#2417—111no—
419#2408—111no—
420#2395—112no—
421#2392—112no—
422C4×#124—111no—
423C4×C22⋊Q8—111no—
424C4×#121—111no—
425C4×#120—112no—
426#2293—111no—
427#2280—112no—
428C42×D4—111no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—21no—
441C23×C11C22×D414yes—
442C23×C11C2×#4112yes—
443C23×C11C2511yescharacteristic
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—216no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—48no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11—48no—
459C22×D11—48no—
460C22×D11—48no—
461C22×D11C2×#4114yes—
462C22×D11C2×#4112yes—
463C22×D11C2×#4112yes—
464C22×D11C2×#4112yes—
465Q8×C11—44no—
466D4×C11—28no—
467D4×C11—48no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—216no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—44no—
489C2×C4×C11—44no—
490C2×C4×C11—44no—
491C2×C4×C11C22×D412yes—
492C2×C4×C11C22×D414yes—
493C2×C4×C11C22×D412yes—
494C2×C4×C11C22×D412yes—
495C2×C4×C11C2×#4112yes—
496C2×C4×C11C2×#4112yes—
497C2×C4×C11C2×#4112yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C22⋊D11—216no—
500C22⋊D11—28no—
501C22⋊D11—48no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—48no—
530C2×Dic11C2×#4112yes—
531C2×Dic11C2×#4112yes—
532C2×Dic11C2×#4112yes—
533D44—28no—
534C4×D11—28no—
535C4×D11—28no—
536C4×D11—48no—
537C4×D11—44no—
538C4×D11—48no—
539C4×D11—48no—
540C23×D4—111no—
541C24×C4—112no—
542#529—28no—
543C2×#126C2×D1112yescomplemented
544C2×#125C2×D1111yescharacteristic, complemented
545C2×#124—111no—
546C2×#124C2×D1111yescharacteristic
547C2×#123C2×D1112yescomplemented
548C2×C22⋊Q8—111no—
549C2×C22⋊Q8C2×D1111yescharacteristic, complemented
550C2×#121—111no—
551C2×#121C2×D1111yescharacteristic
552C2×#120—112no—
553C2×C4×Q8C2×D1111yescharacteristic, complemented
554C2×C4×D4—111no—
555C2×C4×D4—112no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4—228no—
564C2×C4×D4C2×D1111yescharacteristic
565C2×C4×D4C2×D1112yescomplemented
566C2×#117—112no—
567C2×#117C2×D1112yescomplemented
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C42—111no—
571C22×C42C2×D1111yescharacteristic, complemented
572#400—112no—
573#399—112no—
574#398—112no—
575#398—112no—
576#397—112no—
577#397—112no—
578#397—112no—
579#397—112no—
580#396—112no—
581#396—112no—
582#394—112no—
583#394—112no—
584#394—112no—
585#394—112no—
586#394—112no—
587#392—112no—
588#391—111no—
589#391—111no—
590#390—111no—
591#390—111no—
592#390—111no—
593#390—111no—
594#389—111no—
595#389—111no—
596#389—111no—
597#389—111no—
598#388—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#387—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#385—112no—
612#382—111no—
613#381—112no—
614#381—112no—
615#380—111no—
616#380—111no—
617#380—112no—
618#380—112no—
619#380—112no—
620#380—112no—
621#379—112no—
622#379—112no—
623#379—112no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—111no—
629C4×C22⋊C4—111no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—111no—
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C43—111no—
641C22×C11—24no—
642C22×C11—22no—
643C22×C11—24no—
644C22×C11—22no—
645C22×C11—24no—
646C22×C11—22no—
647C22×C11—41no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—42no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11C23×D411yescharacteristic
656C22×C11C22×#4111yescharacteristic
657C22×C11C22×#4111yescharacteristic
658C22×C11C22×#4111yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11#58511yescharacteristic
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—432no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11#52914yescomplemented
677C4×C11—24no—
678C4×C11—22no—
679C4×C11—41no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11#52514yes—
685C4×C11#54614yes—
686Dic11—22no—
687Dic11—22no—
688Dic11—22no—
689Dic11—41no—
690Dic11—42no—
691Dic11—42no—
692Dic11—41no—
693Dic11—41no—
694Dic11—41no—
695Dic11—42no—
696C25—112no—
697C22×Q8C22×D1111yescharacteristic
698C22×D4—111no—
699C22×D4—112no—
700C22×D4—112no—
701C22×D4—111no—
702C22×D4—224no—
703C22×D4—224no—
704C22×D4—224no—
705C22×D4C22×D1112yes—
706C22×D4C22×D1111yescharacteristic
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—228no—
715C23×C4—228no—
716C23×C4—444no—
717C23×C4C22×D1111yescharacteristic
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1112yes—
721#126—28no—
722#125—24no—
723#124—24no—
724#124—224no—
725#123—28no—
726C22⋊Q8—24no—
727C22⋊Q8—224no—
728#121—24no—
729#121—224no—
730#120—228no—
731C4×Q8—24no—
732C4×D4—28no—
733C4×D4—224no—
734C4×D4—224no—
735C4×D4—224no—
736C4×D4—224no—
737C4×D4—228no—
738C4×D4—224no—
739C4×D4—228no—
740C4×D4—224no—
741C4×D4—444no—
742C4×D4C22⋊D1118yescomplemented
743#117—28no—
744#117—444no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—111no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—224no—
758C2×C4⋊C4C22×D1112yes—
759C2×C4⋊C4C22×D1112yes—
760C2×C4⋊C4C22×D1112yes—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C22⋊C4—112no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—228no—
788C2×C22⋊C4C22×D1112yes—
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1112yes—
793C2×C42—24no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—111no—
797C2×C42—111no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—112no—
801C2×C42—111no—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—224no—
805C2×C42C22×D1111yescharacteristic
806C2×C42C22×D1111yescharacteristic
807C2×C42C22×D1111yescharacteristic
808C2×C42C22×D1112yes—
809C2×C42C22×D1111yescharacteristic
810#95—111no—
811#95—111no—
812#95—111no—
813#95—111no—
814#95—111no—
815#95—111no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829C2×C11—44no—
830C2×C11—42no—
831C2×C11C2×#52511yescharacteristic
832C2×C11C2×#52911yescharacteristic
833C2×C11#346011yescharacteristic
834C2×C11C2×#54611yescharacteristic
835C2×C11D4×#4111yescharacteristic
836C2×C11#347511yescharacteristic
837C2×C11#348111yescharacteristic
838D11—24no—
839D11—44no—
840C24—111no—
841C24—112no—
842C24—224no—
843C24—224no—
844C24—224no—
845C24—224no—
846C24—224no—
847C24—442no—
848C24—442no—
849C24C23×D1111yescharacteristic
850C24C23×D1112yes—
851C2×Q8—22no—
852C2×Q8—22no—
853C2×Q8—22no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—42no—
859C2×D4—114no—
860C2×D4—114no—
861C2×D4—224no—
862C2×D4—2232no—
863C2×D4—222no—
864C2×D4—222no—
865C2×D4—224no—
866C2×D4—224no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—222no—
870C2×D4—222no—
871C2×D4—442no—
872C2×D4C2×C22⋊D1114yes—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—41no—
884C22×C4—111no—
885C22×C4—111no—
886C22×C4—111no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—111no—
890C22×C4—112no—
891C22×C4—112no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—224no—
897C22×C4—222no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—222no—
901C22×C4—222no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—224no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—441no—
914C22×C4—4432no—
915C22×C4—442no—
916C22×C4C2×C22⋊D1118yes—
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1112yes—
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1112yes—
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—224no—
935C4⋊C4—222no—
936C4⋊C4—222no—
937C4⋊C4—224no—
938C4⋊C4—222no—
939C4⋊C4—442no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4C2×C22⋊D1114yes—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—224no—
949C22⋊C4—222no—
950C22⋊C4—222no—
951C22⋊C4—222no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—224no—
957C22⋊C4—222no—
958C22⋊C4—222no—
959C22⋊C4—224no—
960C22⋊C4—222no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—224no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4—442no—
967C22⋊C4—442no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4C2×C22⋊D1118yes—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—24no—
976C42—222no—
977C42—222no—
978C42—222no—
979C42—222no—
980C42—222no—
981C42—224no—
982C42—222no—
983C42—222no—
984C42—222no—
985C42—441no—
986C42C2×C22⋊D1114yes—
987C11#3470011yescharacteristic, complemented, Sylow
988C23—21no—
989C23—21no—
990C23—22no—
991C23—22no—
992C23—21no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—22no—
998C23—21no—
999C23—21no—
1000C23—112no—
1001C23—112no—
1002C23—112no—
1003C23—114no—
1004C23—2216no—
1005C23—221no—
1006C23—221no—
1007C23—221no—
1008C23—221no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—448no—
1016C23—448no—
1017C23—448no—
1018C23—448no—
1019C23—448no—
1020C23—448no—
1021C23#41×D1112yes—
1022C23C22×C22⋊D1114yes—
1023C23C24×D1111yescharacteristic
1024Q8—44no—
1025D4—28no—
1026D4—48no—
1027D4—228no—
1028D4—2216no—
1029D4—228no—
1030D4—448no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—216no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—112no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—228no—
1064C2×C4—228no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—448no—
1087C2×C4—448no—
1088C2×C4—444no—
1089C2×C4—448no—
1090C2×C4—448no—
1091C2×C4#41×D1112yes—
1092C2×C4#41×D1112yes—
1093C2×C4#41×D1112yes—
1094C2×C4#6704212yes—
1095C2×C4C22×C22⋊D1112yes—
1096C2×C4C22×C22⋊D1114yes—
1097C2×C4C22×C22⋊D1112yes—
1098C2×C4C22×C22⋊D1112yes—
1099C22—22no—
1100C22—22no—
1101C22—24no—
1102C22—22no—
1103C22—24no—
1104C22—24no—
1105C22—42no—
1106C22—42no—
1107C22—41no—
1108C22—42no—
1109C22—42no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—114no—
1114C22—222no—
1115C22—222no—
1116C22—222no—
1117C22—222no—
1118C22—222no—
1119C22—222no—
1120C22—224no—
1121C22—224no—
1122C22—224no—
1123C22—4432no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22C2×#41×D1111yescharacteristic
1129C22C2×#41×D1111yescharacteristic
1130C22C2×#41×D1111yescharacteristic
1131C22C2×#41×D1111yescharacteristic
1132C22C2×#6704211yescharacteristic
1133C22#1062345311yescharacteristic
1134C22C23×C22⋊D1111yescharacteristic
1135C4—24no—
1136C4—22no—
1137C4—41no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—42no—
1142C4—222no—
1143C4—222no—
1144C4—222no—
1145C4—441no—
1146C4—442no—
1147C4—441no—
1148C4—441no—
1149C4—442no—
1150C4—442no—
1151C4—441no—
1152C4#1062335914yes—
1153C4#1062336014yes—
1154C2—44no—
1155C2—42no—
1156C2—224no—
1157C2—444no—
1158C2C2×#1062335911yescharacteristic
1159C2D11×#52911yescharacteristic
1160C2#1308203711yescharacteristic
1161C2C2×#1062336011yescharacteristic
1162C2#41×C22⋊D1111yescharacteristic
1163C2#1308217211yescharacteristic
1164C2#1308222211yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#529C2
prime radical#13071968C2
hypercenterC2×#529D11
hypocenterC11#34700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D11C2semidirect
2. #13072858C2semidirect
3. #13072678C2semidirect
4. #13072519C2semidirect
5. #13072484C2semidirect
6. #13072399C2semidirect
7. #13072336C2semidirect
8. #13072264C2semidirect
9. #13072189C2semidirect
10. #13072104C2semidirect
11. #13072075C2semidirect
12. #13072063C2semidirect
14. #13071873C2semidirect
15. #13071858C2semidirect
16. C4×#67000C2semidirect
17. C4×#66999C2semidirect
18. C4×#66983C2semidirect
19. C4×#66990C2semidirect
20. #13071081C2semidirect
21. #13070995C2semidirect
22. C42×C22⋊D11C2semidirect
23. C2×C11×#529C2semidirect
27. C2×C11×#126C22semidirect
28. C2×C11×#125C22semidirect
30. C2×C11×#123C22semidirect
31. C2×C11×C22⋊Q8C22semidirect
33. C2×C4×Q8×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
36. C2×C11×#117C22semidirect
37. C22×C42×C11C22semidirect
47. C2×C4×C22⋊D11C22semidirect
48. C2×#66979C22semidirect
56. #10622843C22semidirect
57. #10622843C22semidirect
59. #10622835C22semidirect
62. #10622833C22semidirect
63. #10622826C22semidirect
64. #10622825C22semidirect
65. C4×C22⋊Dic11C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. C4×C22⋊Dic11C22semidirect
68. C4×C22⋊Dic11C22semidirect
69. #10622607C22semidirect
70. #10622606C22semidirect
71. #10622605C22semidirect
72. #10622603C22semidirect
73. #10622603C22semidirect
76. #10622602C22semidirect
81. #10622600C22semidirect
82. #10622600C22semidirect
83. #10622598C22semidirect
84. #10622598C22semidirect
85. #10622597C22semidirect
86. #10622595C22semidirect
87. #10622593C22semidirect
88. #10622591C22semidirect
89. #10622590C22semidirect
90. #10622586C22semidirect
91. #10622574C22semidirect
96. #10622569C22semidirect
100. #10622565C22semidirect
101. #10622565C22semidirect
102. #10622565C22semidirect
103. #10622564C22semidirect
104. #10622564C22semidirect
105. #10622561C22semidirect
106. #10622559C22semidirect
107. #10622556C22semidirect
108. #10622556C22semidirect
109. #10622553C22semidirect
115. C4×(C2×D11)⋊C4C22semidirect
116. C4×(C2×D11)⋊C4C22semidirect
117. C4×(C2×D11)⋊C4C22semidirect
118. C4×C4⋊Dic11C22semidirect
119. C4×Dic11⋊C4C22semidirect
120. C4×Dic11⋊C4C22semidirect
121. C4×Dic11⋊C4C22semidirect
122. C4×Dic11⋊C4C22semidirect
123. C42×Dic11C22semidirect
124. #10622541C22semidirect
158. C4×D4×C11D4semidirect
406. C2×#529D11semidirect
543. C2×#126C2×D11semidirect
544. C2×#125C2×D11semidirect
547. C2×#123C2×D11semidirect
549. C2×C22⋊Q8C2×D11semidirect
553. C2×C4×Q8C2×D11semidirect
565. C2×C4×D4C2×D11semidirect
567. C2×#117C2×D11semidirect
571. C22×C42C2×D11semidirect
676. C2×D11#529semidirect
742. C4×D4C22⋊D11semidirect
987. C11#34700semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130728582
#130726782
#130725192
#130724842
#130723992
#130723362
#130722642
#130721892
#130721042
#130720752
#130720632
#130719682
#130718732
#130718582
C4×#670002
C4×#669992
C4×#669832
C4×#669902
#130710812
#130709952
C42×C22⋊D112
C2×C11×#5292
#3470011