Finite Group Databasebeta

← #27400233

Subgroups — #27400233

Order 13568.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277564C212yesmaximal, complemented
2#20275701C212yesmaximal, complemented
3#20275174C212yesmaximal, complemented
4#20275169C212yesmaximal
5#20274792C211yesmaximal, characteristic, complemented
6#20274789C211yesmaximal, characteristic, complemented
7#20274703C211yesmaximal, characteristic, complemented
8C4×#13133132C211yesmaximal, characteristic, complemented
9#20274448C211yesmaximal, characteristic, complemented
10C2×#16810390C211yesmaximal, characteristic, complemented
11C2×C53×#551C211yesmaximal, characteristic
12C2×#13133176C2212yes—
13C22×C22⋊Dic53C2212yes—
14C2×#13133132C2212yes—
15C2×#13133132C2212yes—
16#16810516—22no—
17#16810516—22no—
18#16810498—22no—
19#16810486C2212yes—
20#16810483C2212yes—
21#16810479C2212yes—
22C22⋊C4×Dic53—22no—
23C4×C22⋊Dic53C2212yes—
24#16810390C2211yescharacteristic
25#16810390C2211yescharacteristic
26#16810390C2212yes—
27#16810390C2211yescharacteristic
28#16810390C2212yes—
29#16810390C2211yescharacteristic
30#16810390C2212yes—
31#16810390C2212yes—
32C53×#551—22no—
33C53×#551—22no—
34C53×#551—22no—
35C53×#551—22no—
36C2×#126×C53C411yescharacteristic, complemented
37C2×#126×C53C411yescharacteristic, complemented
38C2×#124×C53C411yescharacteristic, complemented
39C2×#123×C53C411yescharacteristic, complemented
40C2×#123×C53C411yescharacteristic, complemented
41C2×#123×C53C2211yescharacteristic
42C2×C22⋊Q8×C53C411yescharacteristic, complemented
43C2×C22⋊Q8×C53C2211yescharacteristic
44C2×#120×C53C2211yescharacteristic
45C2×C4×D4×C53C411yescharacteristic, complemented
46C2×C4×D4×C53C2211yescharacteristic
47C2×#117×C53C411yescharacteristic, complemented
48C2×#117×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C23×Dic53—22no—
52#13133176—24no—
53#13133176—42no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C22⋊Dic53—22no—
57C2×C22⋊Dic53—22no—
58C2×C22⋊Dic53—22no—
59C2×C22⋊Dic53—24no—
60C2×C22⋊Dic53—42no—
61C2×C22⋊Dic53C2312yes—
62C2×C22⋊Dic53C2312yes—
63C2×C22⋊Dic53C2312yes—
64C2×C22⋊Dic53C2312yes—
65C2×C4×Dic53—22no—
66C2×C4×Dic53—22no—
67#13133132—24no—
68#13133132—42no—
69#13133124—22no—
70#13133124—22no—
71#13133124—22no—
72#13133124—22no—
73C25×C53C2311yescharacteristic
74C22×Q8×C53C2×C411yescharacteristic, complemented
75C22×D4×C53C2×C411yescharacteristic
76C22×D4×C53C2×C411yescharacteristic
77C22×D4×C53C2311yescharacteristic
78C23×C4×C53C2×C411yescharacteristic
79C23×C4×C53C2×C411yescharacteristic
80C23×C4×C53C2×C411yescharacteristic, complemented
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83#126×C53—22no—
84#126×C53—22no—
85#126×C53—22no—
86#126×C53—22no—
87#124×C53—22no—
88#124×C53—22no—
89#123×C53—22no—
90#123×C53—22no—
91#123×C53—22no—
92#123×C53—22no—
93#123×C53—22no—
94#123×C53—22no—
95C22⋊Q8×C53—22no—
96C22⋊Q8×C53—22no—
97C22⋊Q8×C53—22no—
98C22⋊Q8×C53—22no—
99#120×C53—22no—
100#120×C53—22no—
101C4×D4×C53—21no—
102C4×D4×C53—21no—
103C4×D4×C53—21no—
104C4×D4×C53—21no—
105C4×D4×C53—22no—
106C4×D4×C53—22no—
107#117×C53—21no—
108#117×C53—21no—
109#117×C53—21no—
110#117×C53—21no—
111#117×C53—22no—
112#117×C53—22no—
113C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
115C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
116C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
117C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
118C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
119C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
120C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53C2×C411yescharacteristic
124C2×C22⋊C4×C53C2×C411yescharacteristic
125C2×C22⋊C4×C53C2×C411yescharacteristic
126C2×C22⋊C4×C53C2×C411yescharacteristic
127C2×C22⋊C4×C53C2×C411yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C22⋊C4×C53C2×C411yescharacteristic
131C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
133C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
134C2×C22⋊C4×C53D412yes—
135C2×C22⋊C4×C53D412yes—
136C2×C22⋊C4×C53D412yes—
137C2×C22⋊C4×C53D412yes—
138C2×C22⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53C2311yescharacteristic
141C2×C42×C53C2×C411yescharacteristic, complemented
142C2×C42×C53C2×C411yescharacteristic, complemented
143C2×C42×C53C2×C411yescharacteristic, complemented
144C24×C53—22no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—42no—
148C24×C53—81no—
149C24×C53C22×C411yescharacteristic
150C24×C53C22×C411yescharacteristic
151C24×C53C22×C411yescharacteristic
152C24×C53C2×D412yes—
153C24×C53C2×D412yes—
154C24×C53C2411yescharacteristic
155C2×Q8×C53—22no—
156C2×Q8×C53—81no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—22no—
164C2×D4×C53—42no—
165C2×D4×C53—81no—
166C22×C4×C53—22no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—42no—
176C22×C4×C53—81no—
177C22×C4×C53—81no—
178C22×C4×C53—81no—
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C22×C411yescharacteristic
183C22×C4×C53C22×C411yescharacteristic
184C22×C4×C53C22×C411yescharacteristic
185C22×C4×C53C22×C411yescharacteristic
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C22×C411yescharacteristic
188C22×C4×C53C22×C411yescharacteristic
189C22×C4×C53C22×C411yescharacteristic
190C22×C4×C53C2×D412yes—
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D412yes—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—44no—
199C22×Dic53—44no—
200C22×Dic53—82no—
201C4⋊C4×C53—22no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—22no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—21no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—22no—
211C4⋊C4×C53—22no—
212C22⋊C4×C53—22no—
213C22⋊C4×C53—22no—
214C22⋊C4×C53—21no—
215C22⋊C4×C53—21no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—21no—
221C22⋊C4×C53—21no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—22no—
224C22⋊C4×C53C22⋊C411yescharacteristic
225C22⋊C4×C53C22⋊C411yescharacteristic
226C22⋊C4×C53C22⋊C411yescharacteristic
227C22⋊C4×C53C22⋊C411yescharacteristic
228C22⋊C4×C53C22⋊C412yes—
229C22⋊C4×C53C22⋊C412yes—
230C22⋊C4×C53C22⋊C412yes—
231C22⋊C4×C53C22⋊C412yes—
232C22⋊C4×C53C22⋊C412yes—
233C22⋊C4×C53C22⋊C412yes—
234C42×C53—21no—
235C42×C53—21no—
236C42×C53—21no—
237C42×C53—21no—
238C42×C53—21no—
239C42×C53—21no—
240C22⋊Dic53—22no—
241C22⋊Dic53—22no—
242C22⋊Dic53—22no—
243C22⋊Dic53—22no—
244C22⋊Dic53—22no—
245C22⋊Dic53—22no—
246C22⋊Dic53—22no—
247C22⋊Dic53—44no—
248C22⋊Dic53—44no—
249C22⋊Dic53—82no—
250C22⋊Dic53#4114yes—
251C4⋊Dic53—44no—
252C4⋊Dic53—82no—
253C4×Dic53—44no—
254C4×Dic53—82no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—24no—
260C23×C53—22no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—42no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—84no—
279C23×C53—82no—
280C23×C53—82no—
281C23×C53C2×C22⋊C411yescharacteristic
282C23×C53C2×C22⋊C412yes—
283C23×C53C2×C22⋊C411yescharacteristic
284C23×C53C23×C411yescharacteristic
285C23×C53C22×D412yes—
286C23×C53C2×#4112yes—
287C23×C53H(5,𝔽2)11yescharacteristic
288C23×C532−1+411yescharacteristic
289Q8×C53—82no—
290D4×C53—42no—
291D4×C53—42no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—82no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—81no—
325C2×C4×C53—81no—
326C2×C4×C53—81no—
327C2×C4×C53—81no—
328C2×C4×C53C2×C22⋊C411yescharacteristic
329C2×C4×C53C2×C22⋊C411yescharacteristic
330C2×C4×C53C2×C22⋊C412yes—
331C2×C4×C53C2×C22⋊C411yescharacteristic
332C2×C4×C53C2×C22⋊C411yescharacteristic
333C2×C4×C53C2×C22⋊C412yes—
334C2×Dic53—24no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—88no—
347#22477—531nomaximal, Sylow
348C22×C53—21no—
349C22×C53—22no—
350C22×C53—21no—
351C22×C53—22no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—22no—
356C22×C53—21no—
357C22×C53—22no—
358C22×C53—21no—
359C22×C53—22no—
360C22×C53—42no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—41no—
370C22×C53—82no—
371C22×C53—82no—
372C22×C53—81no—
373C22×C53—81no—
374C22×C53—81no—
375C22×C53—81no—
376C22×C53#41012yes—
377C22×C53C22×C22⋊C411yescharacteristic
378C22×C53C4×#4111yescharacteristic
379C22×C53#52011yescharacteristic
380C22×C53#54612yes—
381C22×C53#54712yes—
382C4×C53—21no—
383C4×C53—22no—
384C4×C53—21no—
385C4×C53—21no—
386C4×C53—21no—
387C4×C53—22no—
388C4×C53—41no—
389C4×C53—41no—
390C4×C53—41no—
391C4×C53—41no—
392C4×C53—41no—
393C4×C53—41no—
394C4×C53—41no—
395Dic53—44no—
396Dic53—82no—
397Dic53—82no—
398Dic53—82no—
399C2×#551D5311yescharacteristic
400#2342—532no—
401#1996—532no—
402#1899—532no—
403#1898—532no—
404#1820—531no—
405#1819—531no—
406#1799—531no—
407C4×#99—531no—
408#1740—531no—
409C2×#342—531no—
410C2×C53—22no—
411C2×C53—22no—
412C2×C53—22no—
413C2×C53—21no—
414C2×C53—21no—
415C2×C53—41no—
416C2×C53—42no—
417C2×C53—81no—
418C2×C53#233911yescharacteristic
419C2×C53C2×#41011yescharacteristic
420C2×C53#288311yescharacteristic
421#551—22no—
422#551—22no—
423#551—22no—
424#551—22no—
425C2×#126Dic5311yescharacteristic, complemented
426C2×#126Dic5311yescharacteristic, complemented
427C2×#124Dic5311yescharacteristic, complemented
428C2×#123Dic5311yescharacteristic, complemented
429C2×#123Dic5311yescharacteristic, complemented
430C2×#123C2×D5311yescharacteristic
431C2×C22⋊Q8Dic5311yescharacteristic, complemented
432C2×C22⋊Q8C2×D5311yescharacteristic
433C2×#120C2×D5311yescharacteristic
434C2×C4×D4Dic5311yescharacteristic, complemented
435C2×C4×D4C2×D5311yescharacteristic
436C2×#117—532no—
437C2×#117Dic5311yescharacteristic, complemented
438C2×#117C2×D5311yescharacteristic
439C22×C22⋊C4—532no—
440C22×C22⋊C4C2×D5311yescharacteristic
441C22×C22⋊C4C2×D5311yescharacteristic
442C2×#99—532no—
443C2×#99—532no—
444#388—1062no—
445#388—1062no—
446#385—1062no—
447#381—532no—
448#380—532no—
449#379—532no—
450C4×C22⋊C4—532no—
451C4×C22⋊C4—1062no—
452#342—531no—
453#342—531no—
454#342—531no—
455#342—532no—
456#342—532no—
457#342—532no—
458#342—532no—
459#342—531no—
460C53#2247711yescharacteristic, complemented, Sylow
461C25C22×D5311yescharacteristic
462C22×Q8C2×Dic5311yescharacteristic, complemented
463C22×D4C2×Dic5311yescharacteristic
464C22×D4C2×Dic5311yescharacteristic
465C22×D4C22×D5311yescharacteristic
466C23×C4—1062no—
467C23×C4C2×Dic5311yescharacteristic
468C23×C4C2×Dic5311yescharacteristic
469C23×C4C2×Dic5311yescharacteristic, complemented
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472#126—22no—
473#126—22no—
474#126—22no—
475#126—22no—
476#124—22no—
477#124—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#120—22no—
489#120—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117—1064no—
503#117—2122no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
507C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
508C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
509C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
510C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
511C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
512C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
513C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—532no—
517C2×C22⋊C4—532no—
518C2×C22⋊C4—532no—
519C2×C22⋊C4—532no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1062no—
522C2×C22⋊C4—1062no—
523C2×C22⋊C4—1062no—
524C2×C22⋊C4—2122no—
525C2×C22⋊C4C2×Dic5311yescharacteristic
526C2×C22⋊C4C2×Dic5311yescharacteristic
527C2×C22⋊C4C2×Dic5311yescharacteristic
528C2×C22⋊C4C2×Dic5311yescharacteristic
529C2×C22⋊C4C2×Dic5311yescharacteristic
530C2×C22⋊C4C2×Dic5311yescharacteristic
531C2×C22⋊C4C2×Dic5311yescharacteristic
532C2×C22⋊C4C2×Dic5311yescharacteristic
533C2×C22⋊C4C2×Dic5311yescharacteristic, complemented
534C2×C22⋊C4C2×Dic5311yescharacteristic, complemented
535C2×C22⋊C4C2×Dic5311yescharacteristic, complemented
536C2×C22⋊C4C22⋊D5312yes—
537C2×C22⋊C4C22⋊D5312yes—
538C2×C22⋊C4C22⋊D5312yes—
539C2×C22⋊C4C22⋊D5312yes—
540C2×C22⋊C4C22×D5311yescharacteristic
541C2×C22⋊C4C22×D5311yescharacteristic
542C2×C22⋊C4C22×D5311yescharacteristic
543C2×C42—1062no—
544C2×C42—1062no—
545C2×C42C2×Dic5311yescharacteristic, complemented
546C2×C42C2×Dic5311yescharacteristic, complemented
547C2×C42C2×Dic5311yescharacteristic, complemented
548#99—1064no—
549#99—2122no—
550#95—1062no—
551#95—1062no—
552#95—1062no—
553#95—1062no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24C22×Dic5311yescharacteristic
560C24C22×Dic5311yescharacteristic
561C24C22×Dic5311yescharacteristic
562C24C2×C22⋊D5312yes—
563C24C2×C22⋊D5312yes—
564C24C23×D5311yescharacteristic
565C2×Q8—22no—
566C2×Q8—81no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—81no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—4242no—
594C22×C4—2124no—
595C22×C4—2124no—
596C22×C4C22×Dic5311yescharacteristic
597C22×C4C22×Dic5311yescharacteristic
598C22×C4C22×Dic5311yescharacteristic
599C22×C4C22×Dic5311yescharacteristic
600C22×C4C22×Dic5311yescharacteristic
601C22×C4C22×Dic5311yescharacteristic
602C22×C4C22×Dic5311yescharacteristic
603C22×C4C22×Dic5311yescharacteristic
604C22×C4C22×Dic5311yescharacteristic
605C22×C4C22×Dic5311yescharacteristic
606C22×C4C22×Dic5311yescharacteristic
607C22×C4C2×C22⋊D5312yes—
608C22×C4C2×C22⋊D5312yes—
609C22×C4C2×C22⋊D5312yes—
610C22×C4C2×C22⋊D5312yes—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—4242no—
623C4⋊C4—2124no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—534no—
637C22⋊C4—1062no—
638C22⋊C4—1062no—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—4242no—
645C22⋊C4—2124no—
646C22⋊C4—2124no—
647C22⋊C4C22⋊Dic5311yescharacteristic
648C22⋊C4C22⋊Dic5311yescharacteristic
649C22⋊C4C22⋊Dic5311yescharacteristic
650C22⋊C4C22⋊Dic5311yescharacteristic
651C22⋊C4C22⋊Dic5312yes—
652C22⋊C4C22⋊Dic5312yes—
653C22⋊C4C22⋊Dic5312yes—
654C22⋊C4C22⋊Dic5312yes—
655C22⋊C4C22⋊Dic5312yes—
656C22⋊C4C22⋊Dic5312yes—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—4242no—
664C42—2124no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—82no—
690C23—82no—
691C23C2×C22⋊Dic5312yes—
692C23C2×C22⋊Dic5311yescharacteristic
693C23C2×C22⋊Dic5311yescharacteristic
694C23C23×Dic5311yescharacteristic
695C23C22×C22⋊D5312yes—
696C23#41×D5312yes—
697C23#1313326311yescharacteristic
698C23#1313326411yescharacteristic
699Q8—82no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—1064no—
739C2×C4—4248no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4C2×C22⋊Dic5311yescharacteristic
752C2×C4C2×C22⋊Dic5311yescharacteristic
753C2×C4C2×C22⋊Dic5311yescharacteristic
754C2×C4C2×C22⋊Dic5311yescharacteristic
755C2×C4C2×C22⋊Dic5312yes—
756C2×C4C2×C22⋊Dic5312yes—
757C22—21no—
758C22—22no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—22no—
768C22—21no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—82no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#1681059712yes—
786C22C22×C22⋊Dic5311yescharacteristic
787C22#41×Dic5311yescharacteristic
788C22#1681110611yescharacteristic
789C22#1681126112yes—
790C22#1681127212yes—
791C4—21no—
792C4—21no—
793C4—22no—
794C4—21no—
795C4—22no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—4242no—
805C4—4242no—
806C4—4242no—
807C4—2124no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2#2027754511yescharacteristic
817C2C2×#1681059711yescharacteristic
818C2#2028317611yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC2×C53×#551C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#120×C53C22
cosocleC24×C53C24
hypercenterC2×#551D53
hypocenterC53#22477
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #20277564C2semidirect
2. #20275701C2semidirect
3. #20275174C2semidirect
5. #20274792C2semidirect
6. #20274789C2semidirect
7. #20274703C2semidirect
8. C4×#13133132C2semidirect
9. #20274448C2semidirect
10. C2×#16810390C2semidirect
36. C2×#126×C53C4semidirect
37. C2×#126×C53C4semidirect
38. C2×#124×C53C4semidirect
39. C2×#123×C53C4semidirect
40. C2×#123×C53C4semidirect
42. C2×C22⋊Q8×C53C4semidirect
45. C2×C4×D4×C53C4semidirect
47. C2×#117×C53C4semidirect
74. C22×Q8×C53C2×C4semidirect
80. C23×C4×C53C2×C4semidirect
113. C2×C4⋊C4×C53C2×C4semidirect
114. C2×C4⋊C4×C53C2×C4semidirect
115. C2×C4⋊C4×C53C2×C4semidirect
116. C2×C4⋊C4×C53C2×C4semidirect
117. C2×C4⋊C4×C53C2×C4semidirect
118. C2×C4⋊C4×C53C2×C4semidirect
119. C2×C4⋊C4×C53C2×C4semidirect
120. C2×C4⋊C4×C53C2×C4semidirect
131. C2×C22⋊C4×C53C2×C4semidirect
132. C2×C22⋊C4×C53C2×C4semidirect
133. C2×C22⋊C4×C53C2×C4semidirect
141. C2×C42×C53C2×C4semidirect
142. C2×C42×C53C2×C4semidirect
143. C2×C42×C53C2×C4semidirect
425. C2×#126Dic53semidirect
426. C2×#126Dic53semidirect
427. C2×#124Dic53semidirect
428. C2×#123Dic53semidirect
429. C2×#123Dic53semidirect
431. C2×C22⋊Q8Dic53semidirect
434. C2×C4×D4Dic53semidirect
437. C2×#117Dic53semidirect
460. C53#22477semidirect
462. C22×Q8C2×Dic53semidirect
469. C23×C4C2×Dic53semidirect
506. C2×C4⋊C4C2×Dic53semidirect
507. C2×C4⋊C4C2×Dic53semidirect
508. C2×C4⋊C4C2×Dic53semidirect
509. C2×C4⋊C4C2×Dic53semidirect
510. C2×C4⋊C4C2×Dic53semidirect
511. C2×C4⋊C4C2×Dic53semidirect
512. C2×C4⋊C4C2×Dic53semidirect
513. C2×C4⋊C4C2×Dic53semidirect
533. C2×C22⋊C4C2×Dic53semidirect
534. C2×C22⋊C4C2×Dic53semidirect
535. C2×C22⋊C4C2×Dic53semidirect
545. C2×C42C2×Dic53semidirect
546. C2×C42C2×Dic53semidirect
547. C2×C42C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202775642
#202757012
#202751742
#202751692
#202747922
#202747892
#202747032
C4×#131331322
#202744482
C2×#168103902
C2×C53×#5512
#2247753