Finite Group Databasebeta

← C4×D53⋊#99 #28318130

Subgroups — C4×D53⋊#99 #28318130

Order 13568.

2242 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D53⋊#99C212yesmaximal
2C2×C4×C22⋊#6157C212yesmaximal, complemented
3#20290462C212yesmaximal, complemented
4C4×#13133276C212yesmaximal, complemented
5#20290460C212yesmaximal, complemented
6C4×#13133275C212yesmaximal, complemented
7#20290412C212yesmaximal, complemented
8C2×C4×D4×D53C211yesmaximal, characteristic
9C22×C22⋊#6157C2214yes—
10C22×C4×#6157—22no—
11C2×#13133276C2214yes—
12D53⋊#99C4116yesdirect product factor
13C2×#13133275C2214yes—
14C4×C22⋊#6157—22no—
15C4×C22⋊#6157—22no—
16C4×C22⋊#6157C2214yescomplemented
17C4×C22⋊#6157C2214yescomplemented
18C2×(C2×#6157)⋊C4—22no—
19#16811501C2214yescomplemented
20#16811501C2214yescomplemented
21C22×D4×D53C2211yescharacteristic
22C23×C4×D53C411yescharacteristic, complemented
23C23×C4×D53C2211yescharacteristic
24C2×C4×D212C2211yescharacteristic
25C2×D4×Dic53C411yescharacteristic, complemented
26C2×#13133179C2211yescharacteristic
27C2×C4×C22⋊D53C411yescharacteristic, complemented
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×#13133177C411yescharacteristic, complemented
30C2×#13133177C2211yescharacteristic
31C4×D4×D53—22no—
32C4×D4×D53—22no—
33C4×D4×D53—22no—
34C4×D4×D53—22no—
35C2×C4⋊C4×D53C411yescharacteristic, complemented
36C2×C22⋊C4×D53C411yescharacteristic, complemented
37C2×C22⋊C4×D53C2211yescharacteristic
38C2×C42×D53C411yescharacteristic, complemented
39C2×C4×D4×C53C411yescharacteristic, complemented
40C23×#6157—24no—
41C2×C22⋊#6157—24no—
42C2×C22⋊#6157—28no—
43C2×C22⋊#6157C2×C4116yescomplemented
44C2×C22⋊#6157C2318yes—
45C2×C4×#6157—24no—
46C2×C4×#6157—24no—
47C2×C4×#6157—48no—
48#13133276C2×C4116yescomplemented
49#13133275C2×C4116yescomplemented
50(C2×#6157)⋊C4—24no—
51(C2×#6157)⋊C4—24no—
52C24×D53C2×C411yescharacteristic
53C24×D53C2311yescharacteristic
54C22×D212C2311yescharacteristic
55C22×C22⋊D53C2×C411yescharacteristic
56C22×C22⋊D53C2311yescharacteristic
57C2×D4×D53—22no—
58C2×D4×D53—22no—
59C2×D4×D53—24no—
60C2×D4×D53C2×C418yes—
61C23×Dic53C2×C411yescharacteristic
62C23×Dic53C2×C411yescharacteristic, complemented
63C22×C4×D53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C22×C4×D53—21no—
67C22×C4×D53—44no—
68C22×C4×D53—44no—
69C22×C4×D53C2×C411yescharacteristic
70C22×C4×D53C2×C411yescharacteristic
71C22×C4×D53C2×C411yescharacteristic
72C22×C4×D53C2×C411yescharacteristic
73C22×C4×D53C2×C411yescharacteristic
74C22×C4×D53C2×C411yescharacteristic, complemented
75C22×C4×D53C2×C411yescharacteristic, complemented
76C22×C4×D53D412yes—
77C22×C4×D53D412yes—
78C22×C4×D53D412yes—
79C22×C4×D53D412yes—
80C22×C4×D53C2311yescharacteristic
81C22×C4×D53C2311yescharacteristic
82C4×D212—22no—
83C4×D212—22no—
84D4×Dic53—22no—
85D4×Dic53—22no—
86#13133179—22no—
87#13133179—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90C4×C22⋊D53—22no—
91C4×C22⋊D53—22no—
92#13133177—22no—
93#13133177—22no—
94#13133177—22no—
95#13133177—22no—
96C2×C4⋊Dic53C2×C411yescharacteristic, complemented
97C2×#11719919C2×C411yescharacteristic, complemented
98C2×#11719919C2×C411yescharacteristic, complemented
99C4⋊C4×D53—22no—
100C4⋊C4×D53—22no—
101C2×C22⋊Dic53C2×C411yescharacteristic
102C2×C22⋊Dic53C2×C411yescharacteristic, complemented
103C2×#11719921C2×C411yescharacteristic, complemented
104C2×#11719921C2×C411yescharacteristic, complemented
105C2×#11719921C2311yescharacteristic
106C2×#11719921C2311yescharacteristic
107C22⋊C4×D53—22no—
108C22⋊C4×D53—22no—
109C22⋊C4×D53—22no—
110C22⋊C4×D53—22no—
111C2×C4×Dic53C2×C411yescharacteristic, complemented
112C2×C4×Dic53C2×C411yescharacteristic, complemented
113C2×C4×Dic53C2×C411yescharacteristic, complemented
114C42×D53—21no—
115C42×D53—21no—
116C42×D53—21no—
117C42×D53—21no—
118C22×D4×C53C2×C411yescharacteristic
119C23×C4×C53C2×C411yescharacteristic
120C23×C4×C53C2×C411yescharacteristic, complemented
121C4×D4×C53—22no—
122C4×D4×C53—22no—
123C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
124C2×C22⋊C4×C53C2×C411yescharacteristic
125C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
126C2×C42×C53C2×C411yescharacteristic, complemented
127C24×C53C22×C411yescharacteristic
128C24×C53C22×C411yescharacteristic
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—22no—
132C23×D53—42no—
133C23×D53—42no—
134C23×D53—42no—
135C23×D53—42no—
136C23×D53C4214yescomplemented
137C23×D53C22×C411yescharacteristic
138C23×D53C22×C411yescharacteristic
139C23×D53C22×C414yes—
140C23×D53C2×D412yes—
141C23×D53C2×D412yes—
142C23×D53#4114yes—
143C23×D53C2411yescharacteristic
144C22×#6157—216no—
145C22×#6157—28no—
146C22×#6157—48no—
147C22×#6157—48no—
148C2×D4×C53—22no—
149C2×D4×C53—22no—
150C2×D4×C53C4214yescomplemented
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53C22⋊C412yes—
156C22×C4×C53C22⋊C412yes—
157C22×C4×C53C22×C411yescharacteristic
158C22×C4×C53C22×C411yescharacteristic
159C22×C4×C53C22×C411yescharacteristic
160C22×C4×C53C22×C411yescharacteristic
161C22×C4×C53C22×C411yescharacteristic
162C2×C22⋊D53—22no—
163C2×C22⋊D53—22no—
164C2×C22⋊D53—22no—
165C2×C22⋊D53—22no—
166C2×C22⋊D53C4214yescomplemented
167C2×C22⋊D53C22×C414yes—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53C22⋊C412yes—
173C22×Dic53C22⋊C412yes—
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C22×Dic53C22×C411yescharacteristic
178C22×Dic53C22×C411yescharacteristic
179D4×D53—216no—
180D4×D53—216no—
181C2×D212—22no—
182C2×D212—22no—
183C2×D212C22×C414yes—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—22no—
187C2×C4×D53—24no—
188C2×C4×D53—28no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—21no—
196C2×C4×D53—21no—
197C2×C4×D53—44no—
198C2×C4×D53—42no—
199C2×C4×D53—44no—
200C2×C4×D53—42no—
201C2×C4×D53—42no—
202C2×C4×D53—44no—
203C2×C4×D53—44no—
204C2×C4×D53—44no—
205C2×C4×D53—44no—
206C2×C4×D53—44no—
207C2×C4×D53—42no—
208C2×C4×D53—42no—
209C2×C4×D53—42no—
210C2×C4×D53—42no—
211C2×C4×D53C4214yescomplemented
212C2×C4×D53C22⋊C411yescharacteristic
213C2×C4×D53C22⋊C411yescharacteristic
214C2×C4×D53C22⋊C411yescharacteristic
215C2×C4×D53C22⋊C412yes—
216C2×C4×D53C22⋊C412yes—
217C2×C4×D53C22⋊C411yescharacteristic
218C2×C4×D53C2×D412yes—
219C2×C4×D53C2×D412yes—
220C2×C4×D53C2×D412yes—
221C2×C4×D53C2×D412yes—
222C22⋊#6157—216no—
223C22⋊#6157—28no—
224C22⋊#6157C22×C4116yescomplemented
225C4×#6157—48no—
226C4×#6157—48no—
227C4⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C42×C53—21no—
231C42×C53—21no—
232C22⋊Dic53—22no—
233C22⋊Dic53—22no—
234#11719921—22no—
235#11719921—22no—
236#11719921—22no—
237#11719921—22no—
238C4⋊Dic53—22no—
239#11719919—22no—
240#11719919—22no—
241C4×Dic53—21no—
242C4×Dic53—21no—
243C4×Dic53—21no—
244C4×Dic53—21no—
245C4×Dic53—21no—
246C4×Dic53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53C2×C4212yes—
254C23×C53C2×C4212yescomplemented
255C23×C53C2×C22⋊C412yes—
256C23×C53#11712yes—
257C23×C53C23×C411yescharacteristic
258C22×D53—22no—
259C22×D53—24no—
260C22×D53—22no—
261C22×D53—24no—
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—24no—
265C22×D53—24no—
266C22×D53—48no—
267C22×D53—48no—
268C22×D53—42no—
269C22×D53—41no—
270C22×D53—42no—
271C22×D53—41no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—48no—
275C22×D53—48no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53C2×C4212yes—
281C22×D53C2×C4212yescomplemented
282C22×D53C2×C22⋊C411yescharacteristic
283C22×D53C2×C22⋊C411yescharacteristic
284C22×D53#11712yes—
285C22×D53C4×D418yes—
286C22×D53C4×D418yes—
287C22×D53C23×C412yes—
288C22×D53C22×D412yes—
289C22×D53C2×#4112yes—
290C2×#6157—216no—
291C2×#6157—48no—
292C2×#6157—48no—
293C2×#6157—432no—
294D4×C53—28no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—22no—
298C2×C4×C53—24no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—42no—
302C2×C4×C53—41no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53C2×C4212yescomplemented
308C2×C4×C53C2×C22⋊C411yescharacteristic
309C2×C4×C53C2×C22⋊C412yes—
310C2×C4×C53C2×C22⋊C411yescharacteristic
311C22⋊D53—28no—
312C22⋊D53—28no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—22no—
316C2×Dic53—24no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53C2×C4212yescomplemented
326C2×Dic53C2×C22⋊C411yescharacteristic
327C2×Dic53C2×C22⋊C412yes—
328C2×Dic53C2×C22⋊C411yescharacteristic
329D212—28no—
330C4×D53—24no—
331C4×D53—24no—
332C4×D53—22no—
333C4×D53—24no—
334C4×D53—24no—
335C4×D53—22no—
336C4×D53—24no—
337C4×D53—22no—
338C4×D53—42no—
339C4×D53—42no—
340C4×D53—42no—
341C4×D53—42no—
342C4×D53—42no—
343C4×D53—42no—
344C4×D53—42no—
345C4×D53—42no—
346C4×D53—42no—
347C4×D53—42no—
348C4×D53—42no—
349C4×D53#9914yescomplemented
350C2×C4×#99—531nomaximal, Sylow
351C22×C53—21no—
352C22×C53—22no—
353C22×C53—21no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53C4×C22⋊C414yes—
363C22×C53C22×C4211yescharacteristic
364C22×C53C22×C22⋊C411yescharacteristic
365C22×C53C2×#11711yescharacteristic
366C2×D53—21no—
367C2×D53—22no—
368C2×D53—21no—
369C2×D53—22no—
370C2×D53—216no—
371C2×D53—24no—
372C2×D53—24no—
373C2×D53—22no—
374C2×D53—48no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—48no—
378C2×D53—42no—
379C2×D53—41no—
380C2×D53—41no—
381C2×D53—48no—
382C2×D53—42no—
383C2×D53C4×C22⋊C412yes—
384C2×D53C4×C22⋊C412yes—
385C2×D53C2×#9912yes—
386C2×D53#41012yes—
387C2×D53C2×C4×D414yes—
388#6157—416no—
389C4×C53—21no—
390C4×C53—22no—
391C4×C53—22no—
392C4×C53—41no—
393C4×C53—41no—
394C4×C53C2×#9912yescomplemented
395Dic53—21no—
396Dic53—22no—
397Dic53—22no—
398Dic53—41no—
399Dic53—41no—
400Dic53C2×#9912yescomplemented
401C22×C4×D4—531no—
402C22×#99—532no—
403C2×C4×C22⋊C4—532no—
404C4×#99—532no—
405C4×#99—532no—
406C4×#99—532no—
407C4×#99—532no—
408C2×#342—532no—
409C2×C53—21no—
410C2×C53—21no—
411C2×C53—24no—
412C2×C53—42no—
413C2×C53C2×C4×C22⋊C411yescharacteristic
414C2×C53C22×#9911yescharacteristic
415C2×C53C2×#41011yescharacteristic
416D53—24no—
417D53—22no—
418D53—42no—
419D53C4×#9914yescomplemented
420C23×D4—531no—
421C24×C4—531no—
422C24×C4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×C4×D4—531no—
426C2×C4×D4—531no—
427C2×C4×D4—531no—
428C2×C4×D4—531no—
429C2×C4×D4—531no—
430C2×C4×D4—1062no—
431C2×C4×D4—1062no—
432C2×C4×D4—1062no—
433C2×C4×D4—1062no—
434C2×C4×D4#615711yescharacteristic, complemented
435C22×C4⋊C4—531no—
436C22×C22⋊C4—534no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4—531no—
439C22×C42—531no—
440C22×C42—1062no—
441C2×#99—534no—
442C2×#99—5316no—
443C2×#99—534no—
444C4×C22⋊C4—534no—
445C4×C22⋊C4—534no—
446C4×C22⋊C4—1062no—
447C4×C22⋊C4—1062no—
448C2×#95—1062no—
449#342—534no—
450#342—534no—
451C53C2×C4×#9911yescharacteristic, complemented, Sylow
452C25—531no—
453C25—531no—
454C22×D4—531no—
455C22×D4—531no—
456C22×D4—538no—
457C22×D4—531no—
458C22×D4—1062no—
459C22×D4—1062no—
460C22×D4—1064no—
461C22×D4C2×#615711yescharacteristic
462C23×C4—531no—
463C23×C4—532no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—532no—
467C23×C4—532no—
468C23×C4—532no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4—1064no—
482C23×C4—2124no—
483C23×C4—2124no—
484C23×C4C2×#615711yescharacteristic
485C23×C4C2×#615711yescharacteristic, complemented
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494C4×D4—1062no—
495C4×D4—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1062no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1062no—
507C2×C4⋊C4C2×#615711yescharacteristic, complemented
508C2×C22⋊C4—538no—
509C2×C22⋊C4—5316no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—531no—
513C2×C22⋊C4—531no—
514C2×C22⋊C4—531no—
515C2×C22⋊C4—531no—
516C2×C22⋊C4—1062no—
517C2×C22⋊C4—1062no—
518C2×C22⋊C4—1062no—
519C2×C22⋊C4—1062no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1068no—
522C2×C22⋊C4C2×#615711yescharacteristic
523C2×C22⋊C4C2×#615711yescharacteristic, complemented
524C2×C42—531no—
525C2×C42—531no—
526C2×C42—531no—
527C2×C42—1061no—
528C2×C42—1061no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42—1064no—
532C2×C42—1064no—
533C2×C42—2128no—
534C2×C42C2×#615711yescharacteristic, complemented
535#99—5316no—
536#99—5316no—
537#95—1064no—
538#95—1064no—
539C24—532no—
540C24—531no—
541C24—534no—
542C24—532no—
543C24—534no—
544C24—531no—
545C24—534no—
546C24—531no—
547C24—1061no—
548C24—1061no—
549C24—1062no—
550C24—2122no—
551C24—2122no—
552C24—2122no—
553C24—2122no—
554C24C22×#615711yescharacteristic
555C24C22×#615711yescharacteristic
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—534no—
559C2×D4—534no—
560C2×D4—534no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—10616no—
564C2×D4—10616no—
565C2×D4—1062no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—1062no—
569C2×D4C4×#615714yescomplemented
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—531no—
575C22×C4—532no—
576C22×C4—531no—
577C22×C4—531no—
578C22×C4—532no—
579C22×C4—531no—
580C22×C4—534no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—531no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—531no—
591C22×C4—531no—
592C22×C4—1068no—
593C22×C4—1064no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1062no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1068no—
606C22×C4—10616no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—2122no—
610C22×C4—2124no—
611C22×C4—2122no—
612C22×C4—2124no—
613C22×C4—2124no—
614C22×C4—2122no—
615C22×C4—2124no—
616C22×C4—2122no—
617C22×C4—2124no—
618C22×C4—2124no—
619C22×C4—2124no—
620C22×C4—2122no—
621C22×C4—2122no—
622C22×C4—2122no—
623C22×C4—2122no—
624C22×C4—2122no—
625C22×C4—2128no—
626C22×C4—2128no—
627C22×C4C22⋊#615712yes—
628C22×C4C22⋊#615712yes—
629C22×C4C22×#615711yescharacteristic
630C22×C4C22×#615711yescharacteristic
631C22×C4C22×#615711yescharacteristic
632C22×C4C22×#615711yescharacteristic
633C22×C4C22×#615711yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—1062no—
636C4⋊C4—1062no—
637C4⋊C4—1062no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—5316no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—10616no—
646C22⋊C4—1068no—
647C22⋊C4—1062no—
648C22⋊C4—1062no—
649C42—21no—
650C42—21no—
651C42—1061no—
652C42—1061no—
653C42—1061no—
654C42—1061no—
655C42—1061no—
656C42—1061no—
657C42—2128no—
658C42—2128no—
659C23—21no—
660C23—21no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—531no—
666C23—538no—
667C23—532no—
668C23—531no—
669C23—532no—
670C23—532no—
671C23—538no—
672C23—532no—
673C23—532no—
674C23—532no—
675C23—1064no—
676C23—1062no—
677C23—1064no—
678C23—1062no—
679C23—1064no—
680C23—1064no—
681C23—1061no—
682C23—1061no—
683C23—2121no—
684C23—2122no—
685C23—2121no—
686C23—2122no—
687C23—2121no—
688C23—2121no—
689C23—2122no—
690C23—2122no—
691C23—2128no—
692C23—2128no—
693C23—2128no—
694C23—2122no—
695C23—2128no—
696C23—2122no—
697C23C2×C4×#615712yes—
698C23C2×C4×#615712yescomplemented
699C23C2×C22⋊#615712yes—
700C23#1313329612yes—
701C23C23×#615711yescharacteristic
702D4—28no—
703D4—1068no—
704D4—1068no—
705D4—1068no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—531no—
719C2×C4—534no—
720C2×C4—532no—
721C2×C4—531no—
722C2×C4—532no—
723C2×C4—1064no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1064no—
728C2×C4—1064no—
729C2×C4—1064no—
730C2×C4—1062no—
731C2×C4—1061no—
732C2×C4—1061no—
733C2×C4—1064no—
734C2×C4—1062no—
735C2×C4—10616no—
736C2×C4—1061no—
737C2×C4—1061no—
738C2×C4—2122no—
739C2×C4—2122no—
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—2121no—
751C2×C4—2122no—
752C2×C4—2128no—
753C2×C4—21232no—
754C2×C4—2128no—
755C2×C4—2122no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4C2×C4×#615712yescomplemented
759C2×C4C2×C22⋊#615711yescharacteristic
760C2×C4C2×C22⋊#615712yes—
761C2×C4C2×C22⋊#615711yescharacteristic
762C22—21no—
763C22—22no—
764C22—21no—
765C22—22no—
766C22—22no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—532no—
774C22—532no—
775C22—532no—
776C22—534no—
777C22—532no—
778C22—10616no—
779C22—1064no—
780C22—1064no—
781C22—1062no—
782C22—1061no—
783C22—1062no—
784C22—1061no—
785C22—1062no—
786C22—2122no—
787C22—2122no—
788C22—2128no—
789C22—2122no—
790C22—2122no—
791C22—2128no—
792C22—2128no—
793C22—2121no—
794C22—2121no—
795C22C4×C22⋊#615714yes—
796C22C22×C4×#615711yescharacteristic
797C22C22×C22⋊#615711yescharacteristic
798C22C2×#1313329611yescharacteristic
799C4—22no—
800C4—21no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—532no—
805C4—1062no—
806C4—1061no—
807C4—1062no—
808C4—21216no—
809C4—2121no—
810C4—2121no—
811C4D53⋊#9912yesdirect product factor
812C2—21no—
813C2—21no—
814C2—24no—
815C2—42no—
816C2—534no—
817C2—1064no—
818C2—1062no—
819C2—2122no—
820C2C2×C4×C22⋊#615711yescharacteristic
821C2C2×D53⋊#9911yescharacteristic
822C2D53⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC22×C53C22×C42
FrattiniC23C23×#6157
FittingC2×C4×D4×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC22×D4×D53C22
cosocleC23×D53C24
hypercenterC2×C4×D4#6157
hypocenterC53C2×C4×#99
LCSG ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊#6157C2semidirect
3. #20290462C2semidirect
4. C4×#13133276C2semidirect
5. #20290460C2semidirect
6. C4×#13133275C2semidirect
7. #20290412C2semidirect
12. D53⋊#99C4direct (N × H)
16. C4×C22⋊#6157C22semidirect
17. C4×C22⋊#6157C22semidirect
19. #16811501C22semidirect
20. #16811501C22semidirect
22. C23×C4×D53C4semidirect
25. C2×D4×Dic53C4semidirect
27. C2×C4×C22⋊D53C4semidirect
29. C2×#13133177C4semidirect
35. C2×C4⋊C4×D53C4semidirect
36. C2×C22⋊C4×D53C4semidirect
38. C2×C42×D53C4semidirect
39. C2×C4×D4×C53C4semidirect
43. C2×C22⋊#6157C2×C4semidirect
48. #13133276C2×C4semidirect
49. #13133275C2×C4semidirect
62. C23×Dic53C2×C4semidirect
74. C22×C4×D53C2×C4semidirect
75. C22×C4×D53C2×C4semidirect
96. C2×C4⋊Dic53C2×C4semidirect
97. C2×#11719919C2×C4semidirect
98. C2×#11719919C2×C4semidirect
102. C2×C22⋊Dic53C2×C4semidirect
103. C2×#11719921C2×C4semidirect
104. C2×#11719921C2×C4semidirect
111. C2×C4×Dic53C2×C4semidirect
112. C2×C4×Dic53C2×C4semidirect
113. C2×C4×Dic53C2×C4semidirect
120. C23×C4×C53C2×C4semidirect
123. C2×C4⋊C4×C53C2×C4semidirect
125. C2×C22⋊C4×C53C2×C4semidirect
126. C2×C42×C53C2×C4semidirect
136. C23×D53C42semidirect
150. C2×D4×C53C42semidirect
166. C2×C22⋊D53C42semidirect
211. C2×C4×D53C42semidirect
224. C22⋊#6157C22×C4semidirect
254. C23×C53C2×C42semidirect
281. C22×D53C2×C42semidirect
307. C2×C4×C53C2×C42semidirect
325. C2×Dic53C2×C42semidirect
349. C4×D53#99semidirect
394. C4×C53C2×#99semidirect
400. Dic53C2×#99semidirect
419. D53C4×#99semidirect
434. C2×C4×D4#6157semidirect
451. C53C2×C4×#99semidirect
485. C23×C4C2×#6157semidirect
507. C2×C4⋊C4C2×#6157semidirect
523. C2×C22⋊C4C2×#6157semidirect
534. C2×C42C2×#6157semidirect
569. C2×D4C4×#6157semidirect
698. C23C2×C4×#6157semidirect
758. C2×C4C2×C4×#6157semidirect
811. C4D53⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D53⋊#992
C2×C4×C22⋊#61572
#202904622
C4×#131332762
#202904602
C4×#131332752
#202904122
C2×C4×D4×D532
C2×C4×#9953