Finite Group Databasebeta

← #15617561

Subgroups — #15617561

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic
2#13077283C212yesmaximal, complemented
3#13077279C212yesmaximal, complemented
4#13077279C212yesmaximal, complemented
5#13077277C212yesmaximal, complemented
6#13077276C211yesmaximal, characteristic, complemented
7#13077274C211yesmaximal, characteristic, complemented
8#13077273C211yesmaximal, characteristic, complemented
9#13077273C211yesmaximal, characteristic, complemented
10#13077271C211yesmaximal, characteristic, complemented
11#13077271C211yesmaximal, characteristic, complemented
12#13077270C211yesmaximal, characteristic, complemented
13#13077264C212yesmaximal, complemented
14#13077262C212yesmaximal, complemented
15#13077257C212yesmaximal, complemented
16#13077255C212yesmaximal, complemented
17#13077177C211yesmaximal, characteristic, complemented
18D11×#424C211yesmaximal, characteristic, complemented
19#13077059C211yesmaximal, characteristic
20C2×#10622340C211yesmaximal, characteristic
21#13077032C211yesmaximal, characteristic, complemented
22D11×#405C211yesmaximal, characteristic, complemented
23C11×#2924C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×M16×D11C2211yescharacteristic
28C2×M16×D11C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623054C411yescharacteristic
32#10623054C411yescharacteristic
33#10623054C411yescharacteristic
34#10623054C411yescharacteristic
35#10623053C2212yes—
36#10623053C2212yes—
37#10623052C412yes—
38D11×#117C2211yescharacteristic
39D11×#117C2211yescharacteristic
40D11×#117C2211yescharacteristic
41D11×#117C2211yescharacteristic
42#10623047C412yes—
43#10623035C411yescharacteristic
44#10623035C411yescharacteristic
45#10623035C411yescharacteristic
46#10623035C411yescharacteristic
47#10623017C412yes—
48#10623017C412yes—
49C4×#4339C2212yes—
50C4×#4339C2212yes—
51C11×#433C2212yescomplemented
52C11×#433C2212yescomplemented
53C11×#432C2212yescomplemented
54C11×#431C2212yescomplemented
55C11×#424C2211yescharacteristic
56C11×#424C2211yescharacteristic
57C11×#407C2211yescharacteristic
58C2×C11×C22⋊C8C2211yescharacteristic
59C11×#405C2211yescharacteristic
60C11×#405C2211yescharacteristic
61#10622820C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63#10622739C2211yescharacteristic
64#10622739C2211yescharacteristic
65#10622735C2211yescharacteristic
66#10622735C2211yescharacteristic
67#10622732C2211yescharacteristic
68#10622732C2211yescharacteristic
69C2×(C2×D11)⋊C8C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71#10622715C2211yescharacteristic
72#10622715C2211yescharacteristic
73#10622714C2211yescharacteristic
74#10622714C2211yescharacteristic
75#10622613C2212yescomplemented
76#10622613C2212yescomplemented
77#10622612C2211yescharacteristic
78#10622612C2211yescharacteristic
79#10622610C2211yescharacteristic
80#10622610C2211yescharacteristic
81#10622539C2212yescomplemented
82#10622538C2212yescomplemented
83#10622453C2212yescomplemented
84#10622453C2212yescomplemented
85#10622453C2212yescomplemented
86#10622453C2212yescomplemented
87#10622452C2212yescomplemented
88#10622452C2212yescomplemented
89#10622452C2212yescomplemented
90#10622452C2212yescomplemented
91#10622450C2212yescomplemented
92#10622450C2212yescomplemented
93#10622448C2212yescomplemented
94#10622448C2212yescomplemented
95#10622446C2212yescomplemented
96#10622446C2212yescomplemented
97D11×C4⋊C8C2212yescomplemented
98D11×C4⋊C8C2212yescomplemented
99#10622340C2211yescharacteristic
100#10622340C2212yes—
101#10622340C2211yescharacteristic
102#10622340C2212yes—
103#10622340C2211yescharacteristic
104#10622340C2211yescharacteristic
105#10622340C2211yescharacteristic
106#10622340C2212yes—
107#10622340C2211yescharacteristic
108#10622340C2211yescharacteristic
109#10622340C2212yes—
110#10622340C2211yescharacteristic
111#10622333C2212yescomplemented
112#10622333C2212yescomplemented
113#10622333C2212yescomplemented
114#10622333C2212yescomplemented
115#10622332C2212yescomplemented
116#10622332C2212yescomplemented
117#10622331C2212yescomplemented
118#10622331C2212yescomplemented
119#10622322C2212yescomplemented
120#10622322C2212yescomplemented
121#10622321C2212yescomplemented
122#10622321C2212yescomplemented
123#10622320C2212yescomplemented
124#10622318C2212yescomplemented
125#10622318C2212yescomplemented
126D11×#97C2212yescomplemented
127#10622303C2212yescomplemented
128#10622303C2212yescomplemented
129#10622302C2212yescomplemented
130#10622302C2212yescomplemented
131C4×#4313C2212yescomplemented
132#10622298C2212yescomplemented
133#10622298C2212yescomplemented
134C4×C8×D11C2212yescomplemented
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11C2×C411yescharacteristic
137C22×C22⋊D11C2×C411yescharacteristic
138C2×#4339—24no—
139C2×#4339—24no—
140C2×#4339C2×C411yescharacteristic
141C2×#4339C2×C411yescharacteristic
142C2×#4339C2×C411yescharacteristic
143C2×#4339C2×C411yescharacteristic
144C2×#4339C2311yescharacteristic
145C2×#4339C2311yescharacteristic
146C2×#4339C2311yescharacteristic
147C2×#4339C2311yescharacteristic
148C22×D44C2×C411yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×Dic22C2×C411yescharacteristic
152C2×C11×M16C2311yescharacteristic
153C2×C11×M16C2311yescharacteristic
154C22×C8×C11C2311yescharacteristic
155C22×C8×C11C2311yescharacteristic
156C11×#117C2×C412yes—
157C11×#117C2×C411yescharacteristic
158C11×#117C2×C411yescharacteristic
159C11×#117C2311yescharacteristic
160C11×#117C2311yescharacteristic
161C11×#117C2312yes—
162C2×C11×C4⋊C4C2×C411yescharacteristic
163C2×C11×C4⋊C4C2×C411yescharacteristic
164C2×C11×C22⋊C4C2×C412yes—
165C2×C42×C11C2312yes—
166C2×C22⋊Dic11C2×C412yes—
167C4×C22⋊D11C2×C412yes—
168C4×C22⋊D11C2×C412yes—
169C4×C22⋊D11C2×C412yes—
170C4×C22⋊D11C2×C412yes—
171C4×C22⋊D11C2×C412yes—
172C4×C22⋊D11C2×C412yes—
173C4×C22⋊D11C2×C412yes—
174C4×C22⋊D11C2×C412yes—
175#66979C2×C411yescharacteristic
176#66979C2×C411yescharacteristic
177#66979C2×C412yes—
178#66979C2311yescharacteristic
179#66979C2311yescharacteristic
180#66979C2312yes—
181C2×C4⋊Dic11C2×C411yescharacteristic
182C2×C4⋊Dic11C2×C411yescharacteristic
183C2×C4×Dic11C2312yes—
184C2×#4318C2311yescharacteristic
185C2×#4318C2311yescharacteristic
186C22×C11⋊C8C2311yescharacteristic
187C22×C11⋊C8C2311yescharacteristic
188M16×D11—24no—
189M16×D11—24no—
190C2×#4313—24no—
191C2×#4313C2311yescharacteristic
192C2×#4313C2311yescharacteristic
193C2×#4313C2311yescharacteristic
194C2×#4313C2311yescharacteristic
195C2×#4313C2312yes—
196C2×#4313C2312yes—
197C2×C8×D11—24no—
198C2×C8×D11C2311yescharacteristic
199C2×C8×D11C2311yescharacteristic
200C2×C8×D11C2311yescharacteristic
201C2×C8×D11C2311yescharacteristic
202C2×C8×D11C2312yes—
203C2×C8×D11C2312yes—
204#66946C2×C412yes—
205#66946C2×C412yes—
206#66946C2×C412yes—
207#66946C2×C412yes—
208#66945C2×C411yescharacteristic
209#66945C2×C411yescharacteristic
210#66945C2×C411yescharacteristic
211#66945C2×C411yescharacteristic
212#66945C2×C411yescharacteristic
213#66945C2×C411yescharacteristic
214#66945C2×C411yescharacteristic
215#66945C2×C411yescharacteristic
216C4⋊C4×D11C2×C411yescharacteristic
217C4⋊C4×D11C2×C411yescharacteristic
218C4⋊C4×D11C2×C411yescharacteristic
219C4⋊C4×D11C2×C411yescharacteristic
220C4⋊C4×D11C2×C411yescharacteristic
221C4⋊C4×D11C2×C411yescharacteristic
222C4⋊C4×D11C2×C411yescharacteristic
223C4⋊C4×D11C2×C411yescharacteristic
224#66940C2×C412yes—
225#66940C2×C412yes—
226#66940C2×C412yes—
227#66940C2×C412yes—
228(C22⋊D11)⋊C4C2×C412yes—
229(C22⋊D11)⋊C4C2×C412yes—
230(C22⋊D11)⋊C4C2×C412yes—
231(C22⋊D11)⋊C4C2×C412yes—
232(C22⋊D11)⋊C4C2×C412yes—
233(C22⋊D11)⋊C4C2×C412yes—
234(C22⋊D11)⋊C4C2×C412yes—
235(C22⋊D11)⋊C4C2×C412yes—
236C22⋊C4×D11C2×C412yes—
237C22⋊C4×D11C2×C412yes—
238C22⋊C4×D11C2×C412yes—
239C22⋊C4×D11C2×C412yes—
240#66930C2×C412yes—
241#66930C2×C412yes—
242#66930C2×C412yes—
243#66930C2×C412yes—
244C4×D44C2×C412yes—
245C4×D44C2×C412yes—
246C4×D44C2×C412yes—
247C4×D44C2×C412yes—
248#66925C2312yes—
249#66925C2312yes—
250#66925C2312yes—
251#66925C2312yes—
252C42×D11C2312yes—
253C42×D11C2312yes—
254C42×D11C2312yes—
255C42×D11C2312yes—
256C4×Dic22C2×C412yes—
257C4×Dic22C2×C412yes—
258C4×Dic22C2×C412yes—
259C4×Dic22C2×C412yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2312yes—
262C11×C4⋊C8C2312yes—
263C11×C4⋊C8C2312yes—
264C11×C22⋊C8C2311yescharacteristic
265C11×C22⋊C8C2312yes—
266C11×C22⋊C8C2311yescharacteristic
267C11×C22⋊C8C2311yescharacteristic
268C11×C22⋊C8C2311yescharacteristic
269C11×C22⋊C8C2312yes—
270C11×#97C2312yes—
271C11×#97C2312yes—
272C4×C8×C11C2312yes—
273C4×C8×C11C2312yes—
274C22⋊(C11⋊C8)C2311yescharacteristic
275C22⋊(C11⋊C8)C2312yes—
276C22⋊(C11⋊C8)C2311yescharacteristic
277C22⋊(C11⋊C8)C2311yescharacteristic
278C22⋊(C11⋊C8)C2311yescharacteristic
279C22⋊(C11⋊C8)C2312yes—
280(C2×D11)⋊C8C2311yescharacteristic
281(C2×D11)⋊C8C2311yescharacteristic
282(C2×D11)⋊C8C2311yescharacteristic
283(C2×D11)⋊C8C2311yescharacteristic
284(C2×D11)⋊C8C2311yescharacteristic
285(C2×D11)⋊C8C2311yescharacteristic
286(C2×D11)⋊C8C2311yescharacteristic
287(C2×D11)⋊C8C2311yescharacteristic
288(C2×D11)⋊C8C2312yes—
289(C2×D11)⋊C8C2312yes—
290(C2×D11)⋊C8C2312yes—
291(C2×D11)⋊C8C2312yes—
292#66879C2312yes—
293#66879C2312yes—
294#66879C2312yes—
295#66879C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302Dic11⋊C8C2312yes—
303Dic11⋊C8C2312yes—
304C8×Dic11C2312yes—
305C8×Dic11C2312yes—
306C8×Dic11C2312yes—
307C8×Dic11C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309C4⋊(C11⋊C8)C2312yes—
310C4⋊(C11⋊C8)C2312yes—
311C4⋊(C11⋊C8)C2312yes—
312#66867C2312yes—
313#66867C2312yes—
314C4×C11⋊C8C2312yes—
315C4×C11⋊C8C2312yes—
316#60126—111nomaximal, Sylow
317C24×C11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C23×D11C22×C411yescharacteristic
320C22×C4×C11—22no—
321C22×C4×C11—22no—
322C22×C4×C11C22×C411yescharacteristic
323C22×C4×C11C22×C411yescharacteristic
324C22×C4×C11C22×C411yescharacteristic
325C22×C4×C11C22×C412yes—
326C22×C4×C11C22×C412yes—
327C22×C4×C11C2411yescharacteristic
328C22×C4×C11C2411yescharacteristic
329C22×C4×C11C2411yescharacteristic
330C2×C22⋊D11—24no—
331C2×C22⋊D11—24no—
332C2×C22⋊D11C22×C411yescharacteristic
333C2×C22⋊D11C22×C411yescharacteristic
334C2×C22⋊D11C22×C411yescharacteristic
335C2×C22⋊D11C22×C411yescharacteristic
336C2×C22⋊D11C22×C411yescharacteristic
337C2×C22⋊D11C22×C411yescharacteristic
338C2×C22⋊D11C22×C411yescharacteristic
339C2×C22⋊D11C22×C411yescharacteristic
340C22×Dic11C22×C411yescharacteristic
341C22×Dic11C22×C412yes—
342C22×Dic11C22×C412yes—
343C22×Dic11C22×C411yescharacteristic
344#4339—24no—
345#4339—24no—
346#4339—24no—
347#4339—24no—
348#4339—22no—
349#4339—22no—
350#4339—22no—
351#4339—22no—
352#4339—22no—
353#4339—22no—
354#4339—22no—
355#4339—22no—
356C2×D44—24no—
357C2×D44C22×C411yescharacteristic
358C2×D44C22×C411yescharacteristic
359C2×D44C22×C411yescharacteristic
360C2×D44C22×C411yescharacteristic
361C2×C4×D11—22no—
362C2×C4×D11—22no—
363C2×C4×D11C22×C411yescharacteristic
364C2×C4×D11C22×C411yescharacteristic
365C2×C4×D11C22×C412yes—
366C2×C4×D11C22×C412yes—
367C2×C4×D11C22×C412yes—
368C2×C4×D11C22×C412yes—
369C2×C4×D11C22×C412yes—
370C2×C4×D11C22×C412yes—
371C2×C4×D11C22×C412yes—
372C2×C4×D11C22×C412yes—
373C2×C4×D11C22×C411yescharacteristic
374C2×C4×D11C22×C411yescharacteristic
375C2×C4×D11#4114yes—
376C2×C4×D11#4114yes—
377C2×C4×D11C2411yescharacteristic
378C2×C4×D11C2411yescharacteristic
379C2×C4×D11C2411yescharacteristic
380C2×C4×D11C2411yescharacteristic
381C2×Dic22—24no—
382C2×Dic22C22×C411yescharacteristic
383C2×Dic22C22×C411yescharacteristic
384C2×Dic22C22×C411yescharacteristic
385C2×Dic22C22×C411yescharacteristic
386C11×M16—22no—
387C11×M16—22no—
388C2×C8×C11—22no—
389C2×C8×C11—22no—
390C2×C8×C11C2411yescharacteristic
391C2×C8×C11C2411yescharacteristic
392C2×C8×C11C2412yes—
393C2×C8×C11C2412yes—
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2411yescharacteristic
396C11×C4⋊C4C22×C412yes—
397C11×C4⋊C4C22×C412yes—
398C11×C4⋊C4C22×C411yescharacteristic
399C11×C4⋊C4C22×C411yescharacteristic
400C11×C4⋊C4C22×C411yescharacteristic
401C11×C4⋊C4C22×C411yescharacteristic
402C11×C22⋊C4C22×C412yes—
403C11×C22⋊C4C22×C412yes—
404C11×C22⋊C4C22×C412yes—
405C11×C22⋊C4C22×C412yes—
406C42×C11C22×C412yes—
407C42×C11C22×C412yes—
408C42×C11C2412yes—
409C42×C11C2412yes—
410C22⋊Dic11C22×C412yes—
411C22⋊Dic11C22×C412yes—
412C22⋊Dic11C22×C412yes—
413C22⋊Dic11C22×C412yes—
414(C2×D11)⋊C4C22×C412yes—
415(C2×D11)⋊C4C22×C412yes—
416(C2×D11)⋊C4C22×C412yes—
417(C2×D11)⋊C4C22×C412yes—
418(C2×D11)⋊C4C22×C412yes—
419(C2×D11)⋊C4C22×C412yes—
420(C2×D11)⋊C4C22×C412yes—
421(C2×D11)⋊C4C22×C412yes—
422C4⋊Dic11C22×C412yes—
423C4⋊Dic11C22×C412yes—
424C4⋊Dic11C22×C411yescharacteristic
425C4⋊Dic11C22×C411yescharacteristic
426C4⋊Dic11C22×C411yescharacteristic
427C4⋊Dic11C22×C411yescharacteristic
428Dic11⋊C4C22×C412yes—
429Dic11⋊C4C22×C412yes—
430Dic11⋊C4C22×C412yes—
431Dic11⋊C4C22×C412yes—
432Dic11⋊C4C22×C412yes—
433Dic11⋊C4C22×C412yes—
434Dic11⋊C4C22×C412yes—
435Dic11⋊C4C22×C412yes—
436C4×Dic11C22×C412yes—
437C4×Dic11C22×C412yes—
438C4×Dic11C22×C412yes—
439C4×Dic11C22×C412yes—
440C4×Dic11C22×C412yes—
441C4×Dic11C22×C412yes—
442C4×Dic11C22×C412yes—
443C4×Dic11C22×C412yes—
444C4×Dic11C22×C412yes—
445C4×Dic11C22×C412yes—
446C4×Dic11C2412yes—
447C4×Dic11C2412yes—
448#4318—22no—
449#4318—22no—
450C2×C11⋊C8—22no—
451C2×C11⋊C8—22no—
452C2×C11⋊C8C2411yescharacteristic
453C2×C11⋊C8C2411yescharacteristic
454C2×C11⋊C8C2412yes—
455C2×C11⋊C8C2412yes—
456C2×C11⋊C8C2411yescharacteristic
457C2×C11⋊C8C2411yescharacteristic
458#4313—22no—
459#4313—22no—
460#4313—22no—
461#4313—22no—
462#4313—24no—
463#4313—24no—
464C8×D11—22no—
465C8×D11—22no—
466C8×D11—22no—
467C8×D11—22no—
468C8×D11—24no—
469C8×D11—24no—
470#3428—111no—
471#2925—112no—
472#2925—112no—
473#2925—112no—
474#2925—112no—
475#2924—111no—
476#2924—111no—
477#2924—111no—
478#2924—111no—
479#2924—111no—
480#2924—111no—
481#2924—111no—
482#2924D1111yescharacteristic, complemented
483#2923—112no—
484#2923—112no—
485#2922—112no—
486#2922—112no—
487#2905—111no—
488C2×#424—111no—
489#2879—111no—
490C2×#408—111no—
491#2873—111no—
492C2×#405—111no—
493C23×C11—22no—
494C23×C11—41no—
495C23×C11—41no—
496C23×C11C23×C411yescharacteristic
497C23×C11C23×C411yescharacteristic
498C23×C11C23×C411yescharacteristic
499C22×D11—22no—
500C22×D11—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11#11714yes—
505C22×D11C23×C411yescharacteristic
506C22×D11C23×C411yescharacteristic
507C22×D11C23×C411yescharacteristic
508C22×D11C23×C411yescharacteristic
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—42no—
517C2×C4×C11—42no—
518C2×C4×C11C23×C411yescharacteristic
519C2×C4×C11C23×C412yes—
520C2×C4×C11C23×C412yes—
521C2×C4×C11C23×C412yes—
522C2×C4×C11C23×C412yes—
523C2×C4×C11C23×C411yescharacteristic
524C2×C4×C11C23×C411yescharacteristic
525C2×C4×C11C2×#4112yes—
526C2×C4×C11C2×#4112yes—
527C2×C4×C11C2511yescharacteristic
528C22⋊D11—22no—
529C22⋊D11—22no—
530C22⋊D11—22no—
531C22⋊D11—22no—
532C22⋊D11—22no—
533C22⋊D11—22no—
534C22⋊D11—22no—
535C22⋊D11—22no—
536C2×Dic11—22no—
537C2×Dic11—42no—
538C2×Dic11—42no—
539C2×Dic11#11714yes—
540C2×Dic11C23×C411yescharacteristic
541C2×Dic11C23×C411yescharacteristic
542C2×Dic11C23×C412yes—
543C2×Dic11C23×C412yes—
544C2×Dic11C23×C412yes—
545C2×Dic11C23×C412yes—
546C2×Dic11C23×C411yescharacteristic
547C2×Dic11C23×C411yescharacteristic
548D44—22no—
549D44—22no—
550D44—22no—
551D44—22no—
552C4×D11—22no—
553C4×D11—22no—
554C4×D11—21no—
555C4×D11—21no—
556C4×D11—21no—
557C4×D11—21no—
558C4×D11—42no—
559C4×D11—42no—
560C4×D11—42no—
561C4×D11—42no—
562C4×D11—42no—
563C4×D11—42no—
564C4×D11—42no—
565C4×D11—42no—
566C4×D11#11714yes—
567C4×D11#11714yes—
568C4×D11C2×#4112yes—
569C4×D11C2×#4112yes—
570C4×D11C2×#4112yes—
571C4×D11C2×#4112yes—
572Dic22—22no—
573Dic22—22no—
574Dic22—22no—
575Dic22—22no—
576C8×C11—21no—
577C8×C11—21no—
578C8×C11—22no—
579C8×C11—22no—
580C8×C11—21no—
581C8×C11—21no—
582C11⋊C8—21no—
583C11⋊C8—21no—
584C11⋊C8—22no—
585C11⋊C8—22no—
586C11⋊C8—21no—
587C11⋊C8—21no—
588C22×#41—111no—
589C22×M16—111no—
590C22×M16—111no—
591C22×M16—111no—
592C23×C8—111no—
593#520—111no—
594#520—111no—
595#520—111no—
596#520—111no—
597#520—111no—
598#520—111no—
599#520—111no—
600#520—111no—
601#519—112no—
602#518—112no—
603#518—112no—
604#518—112no—
605C4×#41—112no—
606C4×#41—112no—
607C4×#41—112no—
608C4×#41—112no—
609C2×#117—111no—
610C2×#117—111no—
611C2×#117—111no—
612C2×#117—111no—
613C2×#117—111no—
614C2×#117C2×D1111yescharacteristic
615#433—112no—
616#433—112no—
617#433—112no—
618#433—112no—
619#433—112no—
620#433—112no—
621#433—112no—
622#433—112no—
623#433—112no—
624#433—112no—
625#433—112no—
626#433—112no—
627#433—112no—
628#433—112no—
629#433C2×D1112yescomplemented
630#433C2×D1112yescomplemented
631#432—112no—
632#432—112no—
633#432—112no—
634#432—112no—
635#432—112no—
636#432—112no—
637#432—112no—
638#432C2×D1112yescomplemented
639#431—112no—
640#431—112no—
641#431—112no—
642#431—112no—
643#431—112no—
644#431—112no—
645#431—112no—
646#431C2×D1112yescomplemented
647#424—111no—
648#424—111no—
649#424—111no—
650#424—111no—
651#424—111no—
652#424—111no—
653#424—112no—
654#424—112no—
655#424—112no—
656#424—112no—
657#424C2×D1111yescharacteristic
658#424C2×D1111yescharacteristic
659#423—112no—
660#423—112no—
661C2×C4⋊C8—112no—
662C2×C4⋊C8—112no—
663#408—111no—
664#408—111no—
665#408—111no—
666#408—111no—
667#408—111no—
668#408—111no—
669#408—111no—
670#408—111no—
671#408—112no—
672#408—112no—
673#408—112no—
674#408—112no—
675#407—111no—
676#407—111no—
677#407—111no—
678#407C2×D1111yescharacteristic
679C2×C22⋊C8—111no—
680C2×C22⋊C8—111no—
681C2×C22⋊C8—111no—
682C2×C22⋊C8C2×D1111yescharacteristic
683#405—111no—
684#405—111no—
685#405—111no—
686#405—111no—
687#405—111no—
688#405—111no—
689#405—112no—
690#405—112no—
691#405—112no—
692#405—112no—
693#405C2×D1111yescharacteristic
694#405C2×D1111yescharacteristic
695C4×M16—112no—
696C4×M16—112no—
697C2×#97—112no—
698C2×C4×C8—112no—
699C22×C11—21no—
700C22×C11—21no—
701C22×C11—21no—
702C22×C11—21no—
703C22×C11—21no—
704C22×C11—21no—
705C22×C11—21no—
706C22×C11—21no—
707C22×C11—82no—
708C22×C11C2×#11712yes—
709C22×C11C24×C411yescharacteristic
710C2×D11—21no—
711C2×D11—21no—
712C2×D11—21no—
713C2×D11—21no—
714C2×D11—21no—
715C2×D11—21no—
716C2×D11—21no—
717C2×D11—21no—
718C2×D11—21no—
719C2×D11—21no—
720C2×D11—44no—
721C2×D11—82no—
722C2×D11C2×#11712yes—
723C2×D11C2×#11712yes—
724C4×C11—21no—
725C4×C11—21no—
726C4×C11—22no—
727C4×C11—22no—
728C4×C11—22no—
729C4×C11—22no—
730C4×C11C2×#11712yes—
731C4×C11C22×#4111yescharacteristic
732C4×C11C22×#4111yescharacteristic
733Dic11—21no—
734Dic11—21no—
735Dic11—22no—
736Dic11—22no—
737Dic11—22no—
738Dic11—22no—
739Dic11C2×#11712yes—
740Dic11C2×#11712yes—
741C2×#41—111no—
742C2×#41—111no—
743C2×#41—111no—
744C2×#41—111no—
745C2×#41—111no—
746C2×#41—111no—
747C2×#41—111no—
748C2×#41—111no—
749C2×#41—224no—
750C2×#41—224no—
751C22×Q8—111no—
752C22×D4—111no—
753C22×D4—111no—
754C22×D4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4C22×D1111yescharacteristic
758C2×M16—111no—
759C2×M16—111no—
760C2×M16—111no—
761C2×M16—112no—
762C2×M16—111no—
763C2×M16—111no—
764C2×M16—112no—
765C2×M16—111no—
766C2×M16—224no—
767C2×M16—224no—
768C2×M16—224no—
769C2×M16C22×D1111yescharacteristic
770C2×M16C22×D1111yescharacteristic
771C22×C8—111no—
772C22×C8—111no—
773C22×C8—111no—
774C22×C8—111no—
775C22×C8—111no—
776C22×C8—111no—
777C22×C8—112no—
778C22×C8—112no—
779C22×C8—224no—
780C22×C8C22×D1111yescharacteristic
781C22×C8C22×D1111yescharacteristic
782C4×Q8—112no—
783C4×Q8—112no—
784C4×Q8—112no—
785C4×Q8—112no—
786C4×Q8—112no—
787C4×Q8—112no—
788C4×Q8—112no—
789C4×Q8—112no—
790C4×D4—112no—
791C4×D4—112no—
792C4×D4—112no—
793C4×D4—112no—
794C4×D4—112no—
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—112no—
802C4×D4—112no—
803C4×D4—112no—
804C4×D4—112no—
805C4×D4—112no—
806C4×D4—112no—
807C4×D4—112no—
808C4×D4—112no—
809C4×D4—112no—
810C4×D4—112no—
811C4×D4—112no—
812C4×D4—112no—
813C4×D4—112no—
814#117—112no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—112no—
820#117—111no—
821#117—111no—
822#117—111no—
823#117—111no—
824#117—111no—
825#117—111no—
826#117—111no—
827#117—111no—
828#117—112no—
829#117—112no—
830#117—112no—
831#117—112no—
832#117—112no—
833#117—112no—
834#117—112no—
835#117—112no—
836#117C4×D1112yes—
837#117C4×D1111yescharacteristic
838#117C4×D1111yescharacteristic
839#117C22×D1111yescharacteristic
840#117C22×D1111yescharacteristic
841#117C22×D1112yes—
842C2×C4⋊C4—111no—
843C2×C4⋊C4—111no—
844C2×C4⋊C4—111no—
845C2×C4⋊C4—111no—
846C2×C4⋊C4—111no—
847C2×C4⋊C4—111no—
848C2×C4⋊C4—111no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—111no—
851C2×C4⋊C4—111no—
852C2×C4⋊C4C4×D1111yescharacteristic
853C2×C4⋊C4C4×D1111yescharacteristic
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4C4×D1112yes—
860C2×C42—112no—
861C2×C42—112no—
862C2×C42—112no—
863C2×C42—112no—
864C2×C42—112no—
865C2×C42C22×D1112yes—
866C4⋊C8—112no—
867C4⋊C8—112no—
868C4⋊C8—112no—
869C4⋊C8—112no—
870C4⋊C8—112no—
871C4⋊C8—112no—
872C4⋊C8—112no—
873C4⋊C8—112no—
874C4⋊C8—112no—
875C4⋊C8—112no—
876C4⋊C8—112no—
877C4⋊C8—112no—
878C4⋊C8C22×D1112yes—
879C4⋊C8C22×D1112yes—
880C4⋊C8C22×D1112yes—
881C4⋊C8C22×D1112yes—
882C22⋊C8—111no—
883C22⋊C8—111no—
884C22⋊C8—111no—
885C22⋊C8—111no—
886C22⋊C8—112no—
887C22⋊C8—112no—
888C22⋊C8—111no—
889C22⋊C8—111no—
890C22⋊C8—111no—
891C22⋊C8—111no—
892C22⋊C8—111no—
893C22⋊C8—111no—
894C22⋊C8—111no—
895C22⋊C8—111no—
896C22⋊C8—112no—
897C22⋊C8—112no—
898C22⋊C8—112no—
899C22⋊C8—112no—
900C22⋊C8C22×D1111yescharacteristic
901C22⋊C8C22×D1111yescharacteristic
902C22⋊C8C22×D1111yescharacteristic
903C22⋊C8C22×D1111yescharacteristic
904C22⋊C8C22×D1112yes—
905C22⋊C8C22×D1112yes—
906#97—112no—
907#97—112no—
908#97—112no—
909#97—112no—
910#97—112no—
911#97—112no—
912#97C22×D1112yes—
913#97C22×D1112yes—
914C4×C8—112no—
915C4×C8—112no—
916C4×C8—112no—
917C4×C8—112no—
918C4×C8—112no—
919C4×C8—112no—
920C4×C8C22×D1112yes—
921C4×C8C22×D1112yes—
922C2×C11—22no—
923C2×C11—41no—
924C2×C11—41no—
925C2×C11C22×#11711yescharacteristic
926C2×C11#357311yescharacteristic
927C2×C11#357311yescharacteristic
928D11—22no—
929D11—22no—
930D11—41no—
931D11—41no—
932C24—111no—
933C24—111no—
934C24C2×C4×D1111yescharacteristic
935#41—224no—
936#41—224no—
937#41—224no—
938#41—224no—
939#41—222no—
940#41—222no—
941#41—222no—
942#41—222no—
943#41—222no—
944#41—222no—
945#41—222no—
946#41—222no—
947C2×Q8—111no—
948C2×Q8—111no—
949C2×Q8—111no—
950C2×Q8—111no—
951C2×Q8—224no—
952C2×D4—111no—
953C2×D4—111no—
954C2×D4—111no—
955C2×D4—111no—
956C2×D4—111no—
957C2×D4—111no—
958C2×D4—111no—
959C2×D4—111no—
960C2×D4—111no—
961C2×D4—111no—
962C2×D4—111no—
963C2×D4—111no—
964C2×D4—224no—
965C2×D4—224no—
966C2×D4—224no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—111no—
972C22×C4—114no—
973C22×C4—114no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—112no—
978C22×C4—112no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4C2×C4×D1111yescharacteristic
994C22×C4C2×C4×D1111yescharacteristic
995C22×C4C2×C4×D1111yescharacteristic
996C22×C4C2×C4×D1112yes—
997C22×C4C2×C4×D1112yes—
998C22×C4C23×D1111yescharacteristic
999C22×C4C23×D1111yescharacteristic
1000C22×C4C23×D1111yescharacteristic
1001M16—22no—
1002M16—22no—
1003M16—222no—
1004M16—222no—
1005M16—222no—
1006M16—222no—
1007M16—224no—
1008M16—224no—
1009M16—222no—
1010M16—222no—
1011C2×C8—22no—
1012C2×C8—22no—
1013C2×C8—111no—
1014C2×C8—112no—
1015C2×C8—111no—
1016C2×C8—112no—
1017C2×C8—111no—
1018C2×C8—111no—
1019C2×C8—222no—
1020C2×C8—222no—
1021C2×C8—222no—
1022C2×C8—222no—
1023C2×C8—224no—
1024C2×C8—224no—
1025C2×C8—222no—
1026C2×C8—222no—
1027C2×C8C23×D1111yescharacteristic
1028C2×C8C23×D1111yescharacteristic
1029C2×C8C23×D1112yes—
1030C2×C8C23×D1112yes—
1031C2×C8C23×D1111yescharacteristic
1032C2×C8C23×D1111yescharacteristic
1033C4⋊C4—111no—
1034C4⋊C4—111no—
1035C4⋊C4—111no—
1036C4⋊C4—111no—
1037C4⋊C4—112no—
1038C4⋊C4—112no—
1039C4⋊C4—112no—
1040C4⋊C4—112no—
1041C4⋊C4—112no—
1042C4⋊C4—112no—
1043C4⋊C4—112no—
1044C4⋊C4—112no—
1045C4⋊C4—112no—
1046C4⋊C4—112no—
1047C4⋊C4C2×C4×D1111yescharacteristic
1048C4⋊C4C2×C4×D1111yescharacteristic
1049C4⋊C4C2×C4×D1111yescharacteristic
1050C4⋊C4C2×C4×D1111yescharacteristic
1051C4⋊C4C2×C4×D1112yes—
1052C4⋊C4C2×C4×D1112yes—
1053C22⋊C4—112no—
1054C22⋊C4—112no—
1055C22⋊C4—112no—
1056C22⋊C4—112no—
1057C22⋊C4—112no—
1058C22⋊C4—112no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—112no—
1063C22⋊C4—112no—
1064C22⋊C4—112no—
1065C22⋊C4C2×C4×D1112yes—
1066C22⋊C4C2×C4×D1112yes—
1067C22⋊C4C2×C4×D1112yes—
1068C22⋊C4C2×C4×D1112yes—
1069C42—112no—
1070C42—112no—
1071C42—112no—
1072C42—112no—
1073C42—112no—
1074C42—112no—
1075C42—112no—
1076C42—112no—
1077C42—112no—
1078C42—112no—
1079C42—112no—
1080C42—112no—
1081C42C2×C4×D1112yes—
1082C42C2×C4×D1112yes—
1083C42C23×D1112yes—
1084C42C23×D1112yes—
1085C11#6012611yescharacteristic, complemented, Sylow
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—111no—
1090C23—111no—
1091C23—114no—
1092C23—111no—
1093C23—111no—
1094C23—222no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23C22×C4×D1111yescharacteristic
1100C23C22×C4×D1111yescharacteristic
1101C23C22×C4×D1111yescharacteristic
1102Q8—222no—
1103Q8—222no—
1104Q8—222no—
1105Q8—222no—
1106D4—222no—
1107D4—222no—
1108D4—222no—
1109D4—222no—
1110D4—222no—
1111D4—222no—
1112D4—222no—
1113D4—222no—
1114D4—222no—
1115D4—222no—
1116D4—222no—
1117D4—222no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—114no—
1128C2×C4—111no—
1129C2×C4—111no—
1130C2×C4—114no—
1131C2×C4—114no—
1132C2×C4—112no—
1133C2×C4—112no—
1134C2×C4—112no—
1135C2×C4—112no—
1136C2×C4—112no—
1137C2×C4—112no—
1138C2×C4—112no—
1139C2×C4—112no—
1140C2×C4—111no—
1141C2×C4—111no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—221no—
1148C2×C4—221no—
1149C2×C4—442no—
1150C2×C4—442no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—442no—
1154C2×C4—442no—
1155C2×C4—442no—
1156C2×C4—442no—
1157C2×C4—442no—
1158C2×C4—442no—
1159C2×C4C22×C4×D1111yescharacteristic
1160C2×C4C22×C4×D1112yes—
1161C2×C4C22×C4×D1112yes—
1162C2×C4C22×C4×D1112yes—
1163C2×C4C22×C4×D1112yes—
1164C2×C4C22×C4×D1111yescharacteristic
1165C2×C4C22×C4×D1111yescharacteristic
1166C2×C4#41×D1112yes—
1167C2×C4#41×D1112yes—
1168C2×C4C24×D1111yescharacteristic
1169C8—21no—
1170C8—21no—
1171C8—21no—
1172C8—21no—
1173C8—22no—
1174C8—22no—
1175C8—221no—
1176C8—221no—
1177C8—222no—
1178C8—222no—
1179C8—221no—
1180C8—221no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—82no—
1190C22—112no—
1191C22—112no—
1192C22—221no—
1193C22—221no—
1194C22—221no—
1195C22—221no—
1196C22—221no—
1197C22—221no—
1198C22—221no—
1199C22—221no—
1200C22—221no—
1201C22—221no—
1202C22—444no—
1203C22—882no—
1204C22D11×#11712yes—
1205C22C23×C4×D1111yescharacteristic
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—112no—
1213C4—112no—
1214C4—221no—
1215C4—221no—
1216C4—222no—
1217C4—222no—
1218C4—222no—
1219C4—222no—
1220C4D11×#11712yes—
1221C4C2×#41×D1111yescharacteristic
1222C4C2×#41×D1111yescharacteristic
1223C2—22no—
1224C2—41no—
1225C2—41no—
1226C2—222no—
1227C2—222no—
1228C2—441no—
1229C2—441no—
1230C2C2×D11×#11711yescharacteristic
1231C2#1308332711yescharacteristic
1232C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2924C2
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenter#2924D11
hypocenterC11#60126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13077283C2semidirect
3. #13077279C2semidirect
4. #13077279C2semidirect
5. #13077277C2semidirect
6. #13077276C2semidirect
7. #13077274C2semidirect
8. #13077273C2semidirect
9. #13077273C2semidirect
10. #13077271C2semidirect
11. #13077271C2semidirect
12. #13077270C2semidirect
13. #13077264C2semidirect
14. #13077262C2semidirect
15. #13077257C2semidirect
16. #13077255C2semidirect
17. #13077177C2semidirect
18. D11×#424C2semidirect
21. #13077032C2semidirect
22. D11×#405C2semidirect
23. C11×#2924C2semidirect
51. C11×#433C22semidirect
52. C11×#433C22semidirect
53. C11×#432C22semidirect
54. C11×#431C22semidirect
75. #10622613C22semidirect
76. #10622613C22semidirect
81. #10622539C22semidirect
82. #10622538C22semidirect
83. #10622453C22semidirect
84. #10622453C22semidirect
85. #10622453C22semidirect
86. #10622453C22semidirect
87. #10622452C22semidirect
88. #10622452C22semidirect
89. #10622452C22semidirect
90. #10622452C22semidirect
91. #10622450C22semidirect
92. #10622450C22semidirect
93. #10622448C22semidirect
94. #10622448C22semidirect
95. #10622446C22semidirect
96. #10622446C22semidirect
97. D11×C4⋊C8C22semidirect
98. D11×C4⋊C8C22semidirect
111. #10622333C22semidirect
112. #10622333C22semidirect
113. #10622333C22semidirect
114. #10622333C22semidirect
115. #10622332C22semidirect
116. #10622332C22semidirect
117. #10622331C22semidirect
118. #10622331C22semidirect
119. #10622322C22semidirect
120. #10622322C22semidirect
121. #10622321C22semidirect
122. #10622321C22semidirect
123. #10622320C22semidirect
124. #10622318C22semidirect
125. #10622318C22semidirect
126. D11×#97C22semidirect
127. #10622303C22semidirect
128. #10622303C22semidirect
129. #10622302C22semidirect
130. #10622302C22semidirect
131. C4×#4313C22semidirect
132. #10622298C22semidirect
133. #10622298C22semidirect
134. C4×C8×D11C22semidirect
482. #2924D11semidirect
629. #433C2×D11semidirect
630. #433C2×D11semidirect
638. #432C2×D11semidirect
646. #431C2×D11semidirect
1085. C11#60126semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130772832
#130772792
#130772772
#130772762
#130772742
#130772732
#130772712
#130772702
#130772642
#130772622
#130772572
#130772552
#130771772
D11×#4242
#130770592
C2×#106223402
#130770322
D11×#4052
C11×#29242
#6012611