Finite Group Databasebeta

← #14914699

Subgroups — #14914699

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic
3C2×C4×D4×D11C211yesmaximal, characteristic
4#13071525C211yesmaximal, characteristic, complemented
5#13071524C211yesmaximal, characteristic, complemented
6#13071523C212yesmaximal, complemented
7#13071522C212yesmaximal, complemented
8#13071521C211yesmaximal, characteristic, complemented
9C4⋊C4×D44C211yesmaximal, characteristic, complemented
10D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11#13071517C211yesmaximal, characteristic, complemented
12#13071514C212yesmaximal, complemented
13D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14#13071512C212yesmaximal, complemented
15#13071241C211yesmaximal, characteristic, complemented
16#13071238C211yesmaximal, characteristic, complemented
17#13071229C212yesmaximal, complemented
18#13071227C212yesmaximal, complemented
19#13071097C211yesmaximal, characteristic, complemented
20#13071096C211yesmaximal, characteristic, complemented
21C2×#10622281C212yesmaximal, complemented
22D11×#385C212yesmaximal, complemented
23C11×#2349C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C22×(C2×D11)⋊C4C2212yes—
36C22×(C2×D11)⋊C4C2212yes—
37C22×C4⋊Dic11C2212yescomplemented
38C22×Dic11⋊C4C2212yescomplemented
39#10623076—28no—
40#10623076C4116yescomplemented
41C4×D4×D11—28no—
42C2×#66946C2211yescharacteristic
43C2×#66946C2211yescharacteristic
44C2×#66946C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2212yescomplemented
49C2×C4⋊C4×D11C2212yescomplemented
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×C22⋊C4×D11C2212yes—
56C2×C4×D44C2211yescharacteristic
57C2×C4×D44C2211yescharacteristic
58C2×C4×D44C2211yescharacteristic
59C2×#66925C2211yescharacteristic
60C2×#66925C2211yescharacteristic
61C2×C42×D11C2211yescharacteristic
62C11×#389C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#385C2212yescomplemented
65C11×#385C2212yescomplemented
66C11×#382C2211yescharacteristic, complemented
67C11×#380C2212yescomplemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C2×C11×#95C2212yescomplemented
70#10622825C2212yescomplemented
71#10622823C2212yescomplemented
72#10622823C2212yescomplemented
73C2×C11⋊#95C2212yescomplemented
74#10622602C2211yescharacteristic
75#10622602C2212yes—
76#10622602C2212yes—
77#10622602C2211yescharacteristic
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622600C2212yescomplemented
81#10622600C2212yescomplemented
82#10622598C2211yescharacteristic, complemented
83#10622598C2211yescharacteristic, complemented
84#10622590C2211yescharacteristic, complemented
85#10622589C2212yescomplemented
86#10622589C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2212yescomplemented
88#10622586C2211yescharacteristic, complemented
89#10622586C2211yescharacteristic, complemented
90#10622585C2211yescharacteristic, complemented
91#10622585C2211yescharacteristic, complemented
92#10622563C2212yescomplemented
93#10622563C2212yescomplemented
94#10622559C2212yescomplemented
95#10622559C2212yescomplemented
96#10622555C2212yescomplemented
97#10622555C2212yescomplemented
98#10622548C2211yescharacteristic, complemented
99C4×C4⋊Dic11C2211yescharacteristic, complemented
100C4×Dic11⋊C4C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2211yescharacteristic, complemented
102#10622541C2211yescharacteristic, complemented
103#10622541C2211yescharacteristic, complemented
104#10622281C2212yes—
105#10622281C2212yes—
106#10622281C2211yescharacteristic
107#10622281C2212yes—
108#10622281C2212yes—
109#10622281C2211yescharacteristic
110#10622281C2212yescomplemented
111#10622281C2212yescomplemented
112#10622281C2212yescomplemented
113#10622281C2212yescomplemented
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622280C2212yescomplemented
117#10622280C2212yescomplemented
118D11×#95C2212yescomplemented
119D11×#95C2212yescomplemented
120#10622263C2212yescomplemented
121#10622262C2212yescomplemented
122#10622260C2212yescomplemented
123#10622260C2212yescomplemented
124#10622260C2211yescharacteristic, complemented
125#10622260C2211yescharacteristic, complemented
126C24×D11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C23×Dic11C2312yes—
133C23×Dic11C2312yes—
134C23×Dic11C2312yes—
135C2×D4×D11C2×C418yes—
136C2×D4×D11D418yes—
137C2×D4×D11Q818yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11—28no—
140C22×C4×D11—44no—
141C22×C4×D11—44no—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C4×D4×C11—24no—
153C4×D4×C11—24no—
154C4×D4×C11C2×C418yescomplemented
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171D4×Dic11—24no—
172D4×Dic11—24no—
173D4×Dic11C2×C418yescomplemented
174C4×C22⋊D11—28no—
175C4×C22⋊D11—28no—
176C4×C22⋊D11C2×C4116yescomplemented
177C2×(C2×D11)⋊C4—28no—
178C2×(C2×D11)⋊C4C2×C4116yescomplemented
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×C4⋊Dic11—44no—
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×Dic11⋊C4—44no—
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224#66946—24no—
225#66946—24no—
226#66946C2×C418yescomplemented
227#66945—24no—
228#66945C2×C418yescomplemented
229C4⋊C4×D11—24no—
230C4⋊C4×D11—44no—
231C4⋊C4×D11—44no—
232(C22⋊D11)⋊C4—28no—
233(C22⋊D11)⋊C4—28no—
234(C22⋊D11)⋊C4C2×C4116yescomplemented
235C22⋊C4×D11—28no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11C2×C4116yescomplemented
238C4×D44—24no—
239C4×D44—24no—
240C4×D44C2×C418yescomplemented
241#66925—24no—
242#66925C2×C418yescomplemented
243C42×D11—24no—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2312yes—
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264#34248—111nomaximal, Sylow
265C24×C11C2412yes—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11C22×C418yes—
271C23×D11C2×D418yes—
272C23×D11C2×Q818yes—
273C23×D11C2411yescharacteristic
274C23×D11C2412yes—
275C2×D4×C11C22×C414yes—
276C2×D4×C11C2×D414yes—
277C2×D4×C11C2×Q814yes—
278C22×C4×C11—24no—
279C22×C4×C11—24no—
280C22×C4×C11—24no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C418yescomplemented
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11C22×C418yes—
298C2×C22⋊D11C2×D418yes—
299C2×C22⋊D11C2×Q818yes—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—24no—
303C22×Dic11—42no—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11C22×C418yescomplemented
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319D4×D11C4⋊C4164yescomplemented
320C2×D44C22×C414yes—
321C2×D44C2×D414yes—
322C2×D44C2×Q814yes—
323C2×C4×D11—22no—
324C2×C4×D11—24no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—432no—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C418yescomplemented
351C2×C4×D11C22×C418yescomplemented
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×Q814yes—
354C11×C4⋊C4—22no—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—42no—
358C11×C4⋊C4—41no—
359C11×C4⋊C4—42no—
360C11×C4⋊C4C22×C414yescomplemented
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4C22×C418yescomplemented
364C42×C11—22no—
365C42×C11—22no—
366C42×C11C22×C414yescomplemented
367C22⋊Dic11—24no—
368C22⋊Dic11—24no—
369C22⋊Dic11C22×C418yescomplemented
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C418yes—
380(C2×D11)⋊C4C22×C418yescomplemented
381(C2×D11)⋊C4C22×C418yescomplemented
382C4⋊Dic11—24no—
383C4⋊Dic11—22no—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11—42no—
387C4⋊Dic11—42no—
388C4⋊Dic11—42no—
389C4⋊Dic11—41no—
390C4⋊Dic11C22×C414yescomplemented
391Dic11⋊C4—22no—
392Dic11⋊C4—22no—
393Dic11⋊C4—24no—
394Dic11⋊C4—22no—
395Dic11⋊C4—24no—
396Dic11⋊C4—22no—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401Dic11⋊C4—41no—
402Dic11⋊C4—42no—
403Dic11⋊C4—41no—
404Dic11⋊C4C22×C414yescomplemented
405Dic11⋊C4C22×C414yescomplemented
406C4×Dic11—22no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11C22×C414yescomplemented
412C4×Dic11C22×C418yescomplemented
413C2×#518—111no—
414C2×#518—111no—
415C22×C4×D4—111no—
416#2349—111no—
417#2349—112no—
418#2349—111no—
419#2349—112no—
420#2349—111no—
421#2349D1111yescharacteristic, complemented
422D4×C4⋊C4—111no—
423D4×C4⋊C4—112no—
424D4×C4⋊C4—112no—
425D4×C4⋊C4—111no—
426D4×C4⋊C4—111no—
427D4×C4⋊C4—111no—
428#2317—111no—
429#2317—111no—
430#2315—112no—
431#2315—112no—
432#2296—111no—
433#2296—111no—
434C2×#385—112no—
435C2×#385—112no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11C23×C414yes—
441C23×C11C22×D414yes—
442C23×C11C22×Q814yes—
443C23×C11C2511yescharacteristic
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—48no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11—48no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11C2×C4⋊C4132yescomplemented
459C22×D11C23×C412yes—
460C22×D11C23×C414yes—
461C22×D11C22×D412yes—
462C22×D11C22×D414yes—
463C22×D11C22×Q812yes—
464C22×D11C22×Q814yes—
465D4×C11C2×C4⋊C4116yescomplemented
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—48no—
490C2×C4×C11—48no—
491C2×C4×C11—84no—
492C2×C4×C11C23×C414yes—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C22×D412yes—
497C2×C4×C11C22×Q812yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C22⋊D11C2×C4⋊C4132yescomplemented
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—48no—
524C2×Dic11—48no—
525C2×Dic11—84no—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C414yes—
529C2×Dic11C23×C412yes—
530C2×Dic11C22×D412yes—
531C2×Dic11C22×Q812yes—
532C2×Dic11H(5,𝔽2)12yes—
533D44C2×C4⋊C4116yescomplemented
534C4×D11—28no—
535C4×D11—48no—
536C4×D11—48no—
537C4×D11—48no—
538C4×D11—48no—
539C4×D11—44no—
540C4×D11—48no—
541C4×D11—84no—
542C4×D11—84no—
543C4×D11C2×C4⋊C4116yescomplemented
544C23×D4—111no—
545C24×C4—112no—
546#518—1116no—
547#518—228no—
548C2×C4×D4—111no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—112no—
558C2×C4×D4—112no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—228no—
564C2×C4×D4C2×D1111yescharacteristic
565C2×C4×D4C2×D1111yescharacteristic
566C2×C4×D4C2×D1111yescharacteristic
567C2×#117—111no—
568C2×#117—111no—
569C2×#117—111no—
570C2×#117—111no—
571C22×C4⋊C4—112no—
572C22×C4⋊C4—112no—
573C22×C4⋊C4—111no—
574C22×C4⋊C4—112no—
575C22×C4⋊C4—112no—
576C22×C22⋊C4—112no—
577C22×C22⋊C4—112no—
578C22×C22⋊C4—112no—
579C22×C22⋊C4—112no—
580C22×C22⋊C4—112no—
581C22×C42—111no—
582#389—111no—
583#389—111no—
584#389—111no—
585#389—111no—
586#389—111no—
587#389—111no—
588#389—111no—
589#389—111no—
590#389—112no—
591#389—112no—
592#389—111no—
593#389—111no—
594#389C2×D1111yescharacteristic, complemented
595#389C2×D1111yescharacteristic, complemented
596#385—112no—
597#385—112no—
598#385—112no—
599#385—111no—
600#385—112no—
601#385—112no—
602#385—112no—
603#385—111no—
604#385—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—111no—
609#385—112no—
610#385—112no—
611#385—112no—
612#385—112no—
613#385—112no—
614#385—112no—
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—111no—
620#385C2×D1112yescomplemented
621#385C2×D1112yescomplemented
622#384—112no—
623#384—111no—
624#384—111no—
625#382—111no—
626#382—112no—
627#382C2×D1111yescharacteristic, complemented
628#380—112no—
629#380—112no—
630#380—112no—
631#380—112no—
632#380—112no—
633#380—112no—
634#380—112no—
635#380C2×D1112yescomplemented
636C4×C4⋊C4—112no—
637C4×C4⋊C4—111no—
638C4×C4⋊C4—111no—
639C4×C4⋊C4—111no—
640C4×C4⋊C4—112no—
641C4×C4⋊C4C2×D1111yescharacteristic, complemented
642C2×#95—112no—
643C2×#95—112no—
644C2×#95—112no—
645C2×#95C2×D1112yescomplemented
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—24no—
652C22×C11C22×C4⋊C418yes—
653C22×C11C24×C411yescharacteristic
654C22×C11C23×D411yescharacteristic
655C22×C11C23×Q811yescharacteristic
656C22×C11C2×H(5,𝔽2)11yescharacteristic
657C22×C11C2×H(5,𝔽2)11yescharacteristic
658C22×C11#58511yescharacteristic
659C22×C11#58511yescharacteristic
660C2×D11—22no—
661C2×D11—22no—
662C2×D11—24no—
663C2×D11—24no—
664C2×D11—22no—
665C2×D11—24no—
666C2×D11—22no—
667C2×D11—24no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—24no—
671C2×D11—24no—
672C2×D11—432no—
673C2×D11C22×C4⋊C414yes—
674C2×D11C22×C4⋊C418yes—
675C4×C11—22no—
676C4×C11—24no—
677C4×C11—22no—
678C4×C11—22no—
679C4×C11—42no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11—41no—
684C4×C11C22×C4⋊C414yes—
685Dic11—22no—
686Dic11—24no—
687Dic11—22no—
688Dic11—22no—
689Dic11—42no—
690Dic11—42no—
691Dic11—41no—
692Dic11—41no—
693Dic11—41no—
694Dic11C22×C4⋊C414yes—
695C25—112no—
696C22×D4—112no—
697C22×D4—118no—
698C22×D4—118no—
699C22×D4—118no—
700C22×D4—111no—
701C22×D4C22×D1111yescharacteristic
702C23×C4—111no—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—112no—
715C23×C4—228no—
716C23×C4—444no—
717C23×C4—444no—
718C23×C4C22×D1112yes—
719C23×C4C22×D1112yes—
720C23×C4C22×D1112yes—
721C4×D4—24no—
722C4×D4—24no—
723C4×D4—118no—
724C4×D4—1116no—
725C4×D4—118no—
726C4×D4—1116no—
727C4×D4—118no—
728C4×D4—224no—
729C4×D4—224no—
730C4×D4—228no—
731C4×D4—228no—
732C4×D4—224no—
733C4×D4—224no—
734C4×D4—228no—
735C4×D4—228no—
736C4×D4—224no—
737C4×D4—224no—
738C4×D4C4×D1118yescomplemented
739#117—118no—
740#117—118no—
741#117—224no—
742#117—224no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—224no—
768C2×C4⋊C4—444no—
769C2×C4⋊C4—444no—
770C2×C4⋊C4—444no—
771C2×C4⋊C4—444no—
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1112yes—
777C2×C4⋊C4C22×D1111yescharacteristic
778C2×C4⋊C4C22×D1111yescharacteristic
779C2×C22⋊C4—112no—
780C2×C22⋊C4—1116no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—1116no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—228no—
797C2×C22⋊C4—228no—
798C2×C22⋊C4—228no—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C42—112no—
803C2×C42—111no—
804C2×C42—112no—
805C2×C42—111no—
806C2×C42—111no—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—224no—
810C2×C42C22×D1111yescharacteristic
811C2×C42C22×D1111yescharacteristic
812C2×C42C22×D1111yescharacteristic
813#95—112no—
814#95—111no—
815#95—111no—
816#95—111no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—111no—
823#95—111no—
824#95—112no—
825#95—112no—
826#95—111no—
827#95C22×D1112yes—
828#95C22×D1112yes—
829#95C22×D1111yescharacteristic
830#95C22×D1112yes—
831#95C22×D1112yes—
832#95C22×D1111yescharacteristic
833C2×C11—28no—
834C2×C11C23×C4⋊C411yescharacteristic
835C2×C11C4×H(5,𝔽2)11yescharacteristic
836C2×C11C4×H(5,𝔽2)11yescharacteristic
837C2×C11#348411yescharacteristic
838C2×C11#348511yescharacteristic
839C2×C11#350111yescharacteristic
840C2×C11#350111yescharacteristic
841D11—24no—
842D11—28no—
843C24—111no—
844C24—112no—
845C24—118no—
846C24—118no—
847C24—118no—
848C24—442no—
849C24—442no—
850C24—442no—
851C24—442no—
852C24C23×D1112yes—
853C2×D4—118no—
854C2×D4—118no—
855C2×D4—118no—
856C2×D4—1164no—
857C2×D4—114no—
858C2×D4—114no—
859C2×D4—114no—
860C2×D4C2×C4×D1114yes—
861C2×D4D4×D1114yes—
862C2×D4Q8×D1114yes—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—111no—
872C22×C4—114no—
873C22×C4—114no—
874C22×C4—114no—
875C22×C4—111no—
876C22×C4—112no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—118no—
880C22×C4—118no—
881C22×C4—118no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—112no—
885C22×C4—112no—
886C22×C4—111no—
887C22×C4—222no—
888C22×C4—224no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—224no—
892C22×C4—224no—
893C22×C4—224no—
894C22×C4—224no—
895C22×C4—224no—
896C22×C4—224no—
897C22×C4—222no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—441no—
910C22×C4—441no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—442no—
915C22×C4—4432no—
916C22×C4—442no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4C2×C4×D1118yescomplemented
922C22×C4C23×D1112yes—
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1112yes—
926C22×C4C23×D1111yescharacteristic
927C22×C4C23×D1112yes—
928C22×C4C23×D1111yescharacteristic
929C22×C4C23×D1111yescharacteristic
930C22×C4C23×D1111yescharacteristic
931C22×C4C23×D1111yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—42no—
936C4⋊C4—41no—
937C4⋊C4—42no—
938C4⋊C4—114no—
939C4⋊C4—114no—
940C4⋊C4—114no—
941C4⋊C4—224no—
942C4⋊C4—222no—
943C4⋊C4—224no—
944C4⋊C4—222no—
945C4⋊C4—222no—
946C4⋊C4—222no—
947C4⋊C4—222no—
948C4⋊C4—222no—
949C4⋊C4—224no—
950C4⋊C4—222no—
951C4⋊C4—442no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—441no—
959C4⋊C4—442no—
960C4⋊C4—441no—
961C4⋊C4—441no—
962C4⋊C4C2×C4×D1114yescomplemented
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—118no—
966C22⋊C4—118no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4C2×C4×D1118yescomplemented
981C42—22no—
982C42—22no—
983C42—118no—
984C42—114no—
985C42—222no—
986C42—222no—
987C42—224no—
988C42—222no—
989C42—222no—
990C42C2×C4×D1114yescomplemented
991C11#3424811yescharacteristic, complemented, Sylow
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—112no—
997C23—114no—
998C23—112no—
999C23—114no—
1000C23—112no—
1001C23—114no—
1002C23—1132no—
1003C23—222no—
1004C23—221no—
1005C23—222no—
1006C23—221no—
1007C23—222no—
1008C23—221no—
1009C23—222no—
1010C23—221no—
1011C23—448no—
1012C23—448no—
1013C23—448no—
1014C23—448no—
1015C23—448no—
1016C23—448no—
1017C23C22×C4×D1114yes—
1018C23C2×D4×D1114yes—
1019C23C2×Q8×D1114yes—
1020C23C24×D1111yescharacteristic
1021D4—1132no—
1022D4—1116no—
1023D4C4⋊C4×D11116yescomplemented
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—84no—
1050C2×C4—112no—
1051C2×C4—112no—
1052C2×C4—112no—
1053C2×C4—1116no—
1054C2×C4—112no—
1055C2×C4—114no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—228no—
1059C2×C4—221no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—222no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—222no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—221no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—448no—
1083C2×C4—448no—
1084C2×C4—448no—
1085C2×C4—448no—
1086C2×C4—448no—
1087C2×C4—444no—
1088C2×C4—448no—
1089C2×C4—448no—
1090C2×C4—884no—
1091C2×C4—884no—
1092C2×C4—884no—
1093C2×C4C22×C4×D1114yes—
1094C2×C4C22×C4×D1112yes—
1095C2×C4C22×C4×D1112yes—
1096C2×C4C22×C4×D1112yes—
1097C2×C4C2×D4×D1112yes—
1098C2×C4C2×Q8×D1112yes—
1099C2×C4#6704212yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—114no—
1107C22—118no—
1108C22—222no—
1109C22—224no—
1110C22—222no—
1111C22—224no—
1112C22—222no—
1113C22—224no—
1114C22—222no—
1115C22—224no—
1116C22—224no—
1117C22—222no—
1118C22—224no—
1119C22—222no—
1120C22—4432no—
1121C22C2×C4⋊C4×D1118yes—
1122C22C23×C4×D1111yescharacteristic
1123C22C22×D4×D1111yescharacteristic
1124C22C22×Q8×D1111yescharacteristic
1125C22C2×#6704211yescharacteristic
1126C22#1062345311yescharacteristic
1127C22D11×H(5,𝔽2)11yescharacteristic
1128C22#1062345511yescharacteristic
1129C4—22no—
1130C4—22no—
1131C4—24no—
1132C4—22no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—42no—
1137C4—41no—
1138C4—114no—
1139C4—222no—
1140C4—222no—
1141C4—224no—
1142C4—222no—
1143C4—442no—
1144C4—442no—
1145C4—441no—
1146C4—441no—
1147C4—441no—
1148C4C2×C4⋊C4×D1114yes—
1149C2—28no—
1150C2—224no—
1151C2—228no—
1152C2C22×C4⋊C4×D1111yescharacteristic
1153C2#1308182011yescharacteristic
1154C2C4×#6704211yescharacteristic
1155C2#1308224611yescharacteristic
1156C2#1308225311yescharacteristic
1157C2#1308241311yescharacteristic
1158C2#1308241511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2349C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2349D11
hypocenterC11#34248
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2349

Complements

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

NH ≅ G/Ntype
4. #13071525C2semidirect
5. #13071524C2semidirect
6. #13071523C2semidirect
7. #13071522C2semidirect
8. #13071521C2semidirect
9. C4⋊C4×D44C2semidirect
10. D4×C4⋊Dic11C2semidirect
11. #13071517C2semidirect
12. #13071514C2semidirect
13. D4×Dic11⋊C4C2semidirect
14. #13071512C2semidirect
15. #13071241C2semidirect
16. #13071238C2semidirect
17. #13071229C2semidirect
18. #13071227C2semidirect
19. #13071097C2semidirect
20. #13071096C2semidirect
21. C2×#10622281C2semidirect
22. D11×#385C2semidirect
23. C11×#2349C2semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×Dic11⋊C4C22semidirect
40. #10623076C4semidirect
48. C2×C4⋊C4×D11C22semidirect
49. C2×C4⋊C4×D11C22semidirect
62. C11×#389C22semidirect
63. C11×#389C22semidirect
64. C11×#385C22semidirect
65. C11×#385C22semidirect
66. C11×#382C22semidirect
67. C11×#380C22semidirect
68. C4×C11×C4⋊C4C22semidirect
69. C2×C11×#95C22semidirect
70. #10622825C22semidirect
71. #10622823C22semidirect
72. #10622823C22semidirect
73. C2×C11⋊#95C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622600C22semidirect
81. #10622600C22semidirect
82. #10622598C22semidirect
83. #10622598C22semidirect
84. #10622590C22semidirect
85. #10622589C22semidirect
86. #10622589C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. #10622586C22semidirect
89. #10622586C22semidirect
90. #10622585C22semidirect
91. #10622585C22semidirect
92. #10622563C22semidirect
93. #10622563C22semidirect
94. #10622559C22semidirect
95. #10622559C22semidirect
96. #10622555C22semidirect
97. #10622555C22semidirect
98. #10622548C22semidirect
99. C4×C4⋊Dic11C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. #10622541C22semidirect
103. #10622541C22semidirect
110. #10622281C22semidirect
111. #10622281C22semidirect
112. #10622281C22semidirect
113. #10622281C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
116. #10622280C22semidirect
117. #10622280C22semidirect
118. D11×#95C22semidirect
119. D11×#95C22semidirect
120. #10622263C22semidirect
121. #10622262C22semidirect
122. #10622260C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
154. C4×D4×C11C2×C4semidirect
173. D4×Dic11C2×C4semidirect
176. C4×C22⋊D11C2×C4semidirect
178. C2×(C2×D11)⋊C4C2×C4semidirect
226. #66946C2×C4semidirect
228. #66945C2×C4semidirect
234. (C22⋊D11)⋊C4C2×C4semidirect
237. C22⋊C4×D11C2×C4semidirect
240. C4×D44C2×C4semidirect
242. #66925C2×C4semidirect
286. C22×C4×C11C22×C4semidirect
308. C22×Dic11C22×C4semidirect
319. D4×D11C4⋊C4semidirect
350. C2×C4×D11C22×C4semidirect
351. C2×C4×D11C22×C4semidirect
360. C11×C4⋊C4C22×C4semidirect
363. C11×C22⋊C4C22×C4semidirect
366. C42×C11C22×C4semidirect
369. C22⋊Dic11C22×C4semidirect
380. (C2×D11)⋊C4C22×C4semidirect
381. (C2×D11)⋊C4C22×C4semidirect
390. C4⋊Dic11C22×C4semidirect
404. Dic11⋊C4C22×C4semidirect
405. Dic11⋊C4C22×C4semidirect
411. C4×Dic11C22×C4semidirect
412. C4×Dic11C22×C4semidirect
421. #2349D11semidirect
458. C22×D11C2×C4⋊C4semidirect
465. D4×C11C2×C4⋊C4semidirect
499. C22⋊D11C2×C4⋊C4semidirect
533. D44C2×C4⋊C4semidirect
543. C4×D11C2×C4⋊C4semidirect
594. #389C2×D11semidirect
595. #389C2×D11semidirect
620. #385C2×D11semidirect
621. #385C2×D11semidirect
627. #382C2×D11semidirect
635. #380C2×D11semidirect
641. C4×C4⋊C4C2×D11semidirect
645. C2×#95C2×D11semidirect
738. C4×D4C4×D11semidirect
921. C22×C4C2×C4×D11semidirect
962. C4⋊C4C2×C4×D11semidirect
980. C22⋊C4C2×C4×D11semidirect
990. C42C2×C4×D11semidirect
991. C11#34248semidirect
1023. D4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
C2×C4×D4×D112
#130715252
#130715242
#130715232
#130715222
#130715212
C4⋊C4×D442
D4×C4⋊Dic112
#130715172
#130715142
D4×Dic11⋊C42
#130715122
#130712412
#130712382
#130712292
#130712272
#130710972
#130710962
C2×#106222812
D11×#3852
C11×#23492
#3424811