Finite Group Databasebeta

← C2×#20279802 #27554182

Subgroups — C2×#20279802 #27554182

Order 13568.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133208C211yesmaximal, characteristic, complemented
2C22×#13133193C211yesmaximal, characteristic
3#20279802C2116yesmaximal, direct product factor
4C2×#16810560C211yesmaximal, characteristic
5C2×#16810555C211yesmaximal, characteristic, complemented
6C2×#16810545C211yesmaximal, characteristic
7C2×#16810530C211yesmaximal, characteristic, complemented
8C2×#16810522C211yesmaximal, characteristic, complemented
9C2×#16810519C211yesmaximal, characteristic, complemented
10C2×#16810515C211yesmaximal, characteristic
11C2×#16810513C211yesmaximal, characteristic
12C2×#16810506C211yesmaximal, characteristic, complemented
13C2×#16810494C211yesmaximal, characteristic
14C2×#16810474C211yesmaximal, characteristic, complemented
15C2×#16810470C211yesmaximal, characteristic
16C2×C53×#395C211yesmaximal, characteristic, complemented
17C23×C4×D53C2211yescharacteristic
18C2×#13133208—28no—
19C2×#13133208C2218yescomplemented
20C2×#13133193—28no—
21C2×#13133193C2218yes—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4⋊Dic53C2211yescharacteristic
26C22×C4⋊Dic53C2211yescharacteristic
27C22×C4⋊Dic53C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42#16810560C2218yes—
43#16810555C2218yescomplemented
44#16810545C2218yes—
45#16810530C2218yescomplemented
46#16810522C2218yescomplemented
47#16810519C2218yescomplemented
48#16810515C2218yes—
49#16810513C2218yes—
50#16810506C2218yescomplemented
51#16810494C2218yes—
52#16810474C2218yescomplemented
53#16810470C2218yes—
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C23×Q8×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C53×#395C2218yescomplemented
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C22×C4×D53—24no—
78C22×C4×D53—24no—
79C22×C4×D53—42no—
80C22×C4×D53C2314yes—
81#13133208—232no—
82#13133193—232no—
83C2×C4⋊Dic53—24no—
84C2×C4⋊Dic53—24no—
85C2×C4⋊Dic53—24no—
86C2×C4⋊Dic53—24no—
87C2×C4⋊Dic53—24no—
88C2×C4⋊Dic53—24no—
89C2×C4⋊Dic53C2314yes—
90C2×C4⋊Dic53C2314yes—
91C2×C4⋊Dic53C2314yes—
92C2×C4⋊Dic53C2314yes—
93C2×C4⋊Dic53C2314yes—
94C2×C4⋊Dic53C2314yes—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—24no—
98C2×#11719919D418yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719921—24no—
104C2×#11719921—24no—
105C2×#11719921—24no—
106C2×#11719921—24no—
107C2×#11719921—42no—
108C2×#11719921Q818yescomplemented
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113C2×#11719921C2314yes—
114C2×#11719921C2314yes—
115C2×C4×Dic53—24no—
116C2×C4×Dic53—24no—
117C2×C4×Dic53—42no—
118C2×C4×Dic53—42no—
119C2×C4×Dic53C2314yes—
120C2×C4×Dic53C2314yes—
121C2×C4×Dic53C2314yes—
122C2×C4×Dic53C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130C22×Q8×C53—24no—
131C22×Q8×C53—24no—
132C22×Q8×C53—42no—
133C22×Q8×C53C2314yes—
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53—24no—
142C2×C4⋊C4×C53—24no—
143C2×C4⋊C4×C53—42no—
144C2×C4⋊C4×C53C2314yes—
145C2×C4⋊C4×C53C2314yes—
146C2×C4⋊C4×C53C2314yes—
147#95×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150C24×C53C2411yescharacteristic
151C23×D53—22no—
152C23×D53—22no—
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53C2×Q814yes—
158C23×D53C2412yes—
159C2×Q8×C53—28no—
160C2×Q8×C53—28no—
161C2×Q8×C53—44no—
162C2×Q8×C53—416no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53C2×D414yes—
180C22×C4×C53C2×Q814yes—
181C22×C4×C53#4114yes—
182C22×C4×C53#4114yes—
183C22×C4×C53#4114yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53C2×D414yes—
210C22×Dic53C2×D414yes—
211C22×Dic53C2×Q814yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C2×C4×D53—28no—
220C2×C4×D53—28no—
221C2×C4×D53—44no—
222C2×C4×D53—416no—
223C4⋊C4×C53—28no—
224C4⋊C4×C53—28no—
225C4⋊C4×C53—44no—
226#11719921—28no—
227#11719921—28no—
228#11719921—28no—
229#11719921—28no—
230#11719921—44no—
231#11719921C2×Q8116yescomplemented
232C4⋊Dic53—28no—
233C4⋊Dic53—28no—
234C4⋊Dic53—28no—
235C4⋊Dic53—28no—
236C4⋊Dic53—28no—
237C4⋊Dic53—28no—
238#11719919—28no—
239#11719919—28no—
240#11719919—28no—
241#11719919C2×D4116yes—
242C4×Dic53—28no—
243C4×Dic53—28no—
244C4×Dic53—44no—
245C4×Dic53—44no—
246C23×C53C22×D412yes—
247C23×C53C22×Q812yes—
248C23×C53C2×#4112yes—
249C23×C53C2×#4112yes—
250C23×C53C2×#4112yes—
251C23×C53H(5,𝔽2)12yes—
252C23×C532−1+412yes—
253C23×C53C2511yescharacteristic
254C22×D53—28no—
255C22×D53—28no—
256C22×D53—28no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—44no—
264C22×D53—44no—
265C22×D53—44no—
266C22×D53—44no—
267C22×D53C22×Q814yes—
268Q8×C53—416no—
269C2×C4×C53—28no—
270C2×C4×C53—28no—
271C2×C4×C53—28no—
272C2×C4×C53—28no—
273C2×C4×C53—28no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—44no—
291C2×C4×C53—44no—
292C2×C4×C53C22×D414yes—
293C2×C4×C53C22×Q814yes—
294C2×C4×C53C2×#4114yes—
295C2×C4×C53C2×#4114yes—
296C2×C4×C53C2×#4114yes—
297C2×Dic53—28no—
298C2×Dic53—28no—
299C2×Dic53—28no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—44no—
319C2×Dic53—44no—
320C2×Dic53—44no—
321C2×Dic53—44no—
322C2×Dic53C22×D414yes—
323C2×Dic53C22×D414yes—
324C2×Dic53C22×Q814yes—
325C4×D53—416no—
326C2×#2556—531nomaximal, Sylow
327C22×C53#53214yes—
328C22×C53#53314yes—
329C22×C53#53914yes—
330C22×C53#54614yes—
331C22×C53D4×Q814yes—
332C22×C53#55214yes—
333C22×C53#55414yes—
334C22×C53C23×D411yescharacteristic
335C22×C53C23×Q811yescharacteristic
336C22×C53C22×#4111yescharacteristic
337C22×C53C22×#4111yescharacteristic
338C22×C53C22×#4111yescharacteristic
339C22×C53C2×H(5,𝔽2)11yescharacteristic
340C22×C53C2×2−1+411yescharacteristic
341C2×D53—24no—
342C2×D53—24no—
343C2×D53—24no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—416no—
349C4×C53—24no—
350C4×C53—24no—
351C4×C53—24no—
352C4×C53—24no—
353C4×C53—24no—
354C4×C53—42no—
355C4×C53—42no—
356Dic53—24no—
357Dic53—24no—
358Dic53—24no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363C22×#125—531no—
364C22×C22⋊Q8—531no—
365#2556—5316no—
366C2×#399—531no—
367C2×#398—531no—
368C2×#396—531no—
369C2×#395D5311yescharacteristic, complemented
370C2×#391—531no—
371C2×#389—531no—
372C2×#389—531no—
373C2×#388—531no—
374C2×#388—531no—
375C2×#387—531no—
376C2×#385—531no—
377C2×C4×C4⋊C4—531no—
378C2×C4×C22⋊C4—531no—
379C2×C53#255618yescomplemented
380C2×C53C2×#53211yescharacteristic
381C2×C53C2×#53311yescharacteristic
382C2×C53C2×#53911yescharacteristic
383C2×C53C2×#54611yescharacteristic
384C2×C53C2×D4×Q811yescharacteristic
385C2×C53C2×#55211yescharacteristic
386C2×C53C2×#55411yescharacteristic
387D53—44no—
388C23×Q8C2×D5311yescharacteristic
389C24×C4—531no—
390C2×#125—538no—
391C2×#125—1068no—
392C2×C22⋊Q8—538no—
393C2×C22⋊Q8—1068no—
394C22×C4⋊C4—531no—
395C22×C4⋊C4—531no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4C2×D5311yescharacteristic
405C22×C4⋊C4C2×D5311yescharacteristic
406C22×C4⋊C4C2×D5311yescharacteristic
407C22×C22⋊C4—531no—
408C22×C22⋊C4—531no—
409C22×C22⋊C4—531no—
410C22×C22⋊C4—531no—
411C22×C22⋊C4—531no—
412C22×C22⋊C4—531no—
413C22×C42—531no—
414C22×C42—531no—
415C22×C42—531no—
416C22×C42—531no—
417#399—538no—
418#398—538no—
419#396—538no—
420#395C2×D5318yescomplemented
421#391—538no—
422#389—538no—
423#389—538no—
424#388—538no—
425#388—538no—
426#387—538no—
427#385—538no—
428C4×C4⋊C4—538no—
429C4×C22⋊C4—538no—
430C2×#95—531no—
431C2×#95—531no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—531no—
435C2×#95—531no—
436C2×#95—531no—
437C2×#95C2×D5311yescharacteristic
438C2×#95C2×D5311yescharacteristic
439C2×#95C2×D5311yescharacteristic
440C53C2×#255611yescharacteristic, complemented, Sylow
441C25—531no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—42no—
445C22×Q8C22×D5314yes—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—534no—
454C23×C4—1064no—
455C23×C4—1064no—
456C23×C4—2122no—
457C23×C4C22×D5311yescharacteristic
458C23×C4C22×D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C23×C4C22×D5311yescharacteristic
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5311yescharacteristic
464#125—10632no—
465C22⋊Q8—10632no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—538no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—534no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—1064no—
481C2×C4⋊C4—1064no—
482C2×C4⋊C4—1064no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1064no—
486C2×C4⋊C4—1064no—
487C2×C4⋊C4—1064no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4C22×D5314yes—
490C2×C4⋊C4C22×D5314yes—
491C2×C4⋊C4C22×D5314yes—
492C2×C22⋊C4—538no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—534no—
497C2×C22⋊C4—534no—
498C2×C22⋊C4—534no—
499C2×C22⋊C4—1064no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—1064no—
503C2×C22⋊C4—2122no—
504C2×C42—534no—
505C2×C42—534no—
506C2×C42—534no—
507C2×C42—534no—
508C2×C42—1064no—
509C2×C42—1064no—
510C2×C42—2122no—
511C2×C42—2122no—
512#95—534no—
513#95—534no—
514#95—534no—
515#95—534no—
516#95—534no—
517#95—534no—
518#95—534no—
519#95C22×D5314yes—
520#95C22×D5314yes—
521#95C22×D5314yes—
522C24—534no—
523C24—532no—
524C24—1062no—
525C24—1062no—
526C24—1062no—
527C24—1062no—
528C24—1062no—
529C24—1062no—
530C24C23×D5311yescharacteristic
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—44no—
534C2×Q8—416no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—534no—
552C22×C4—534no—
553C22×C4—534no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—1068no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1068no—
581C22×C4—2124no—
582C22×C4—21216no—
583C22×C4D4×D5314yes—
584C22×C4#1171994714yes—
585C22×C4Q8×D5314yes—
586C22×C4#1171994914yes—
587C22×C4#1171994914yes—
588C22×C4C23×D5312yes—
589C22×C4C23×D5312yes—
590C22×C4C23×D5312yes—
591C22×C4C23×D5312yes—
592C22×C4C23×D5312yes—
593C22×C4C23×D5312yes—
594C22×C4C23×D5312yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—44no—
598C4⋊C4—5316no—
599C4⋊C4—1068no—
600C4⋊C4—1068no—
601C4⋊C4—1068no—
602C4⋊C4—1068no—
603C4⋊C4—1068no—
604C4⋊C4—1068no—
605C4⋊C4—1068no—
606C4⋊C4—1068no—
607C4⋊C4—1068no—
608C22⋊C4—5316no—
609C22⋊C4—1068no—
610C22⋊C4—1068no—
611C22⋊C4—1068no—
612C22⋊C4—1068no—
613C22⋊C4—2124no—
614C42—1068no—
615C42—1068no—
616C42—2124no—
617C42—2124no—
618C23—534no—
619C23—1068no—
620C23—1068no—
621C23—1068no—
622C23—1062no—
623C23—1062no—
624C23—1062no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23—2124no—
629C23—2124no—
630C23—2124no—
631C23—2124no—
632C23C2×D4×D5312yes—
633C23C2×Q8×D5312yes—
634C23C2×#1171994712yes—
635C23C2×#1171994912yes—
636C23C2×#1171994912yes—
637C23#1313326212yes—
638C23#1313326412yes—
639C23C24×D5311yescharacteristic
640Q8—416no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—534no—
665C2×C4—534no—
666C2×C4—534no—
667C2×C4—1068no—
668C2×C4—1068no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1068no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—21216no—
689C2×C4—2124no—
690C2×C4—2124no—
691C2×C4—2124no—
692C2×C4—2124no—
693C2×C4C2×D4×D5314yes—
694C2×C4C2×Q8×D5314yes—
695C2×C4C2×#1171994714yes—
696C2×C4C2×#1171994914yes—
697C2×C4C2×#1171994914yes—
698C22—1064no—
699C22—1064no—
700C22—1064no—
701C22—2122no—
702C22—2122no—
703C22—2122no—
704C22—21216no—
705C22—2122no—
706C22#1681117414yes—
707C22#1681117814yes—
708C22#1681122214yes—
709C22#1681126014yes—
710C22#1681128614yes—
711C22#1681131514yes—
712C22#1681133414yes—
713C22C22×D4×D5311yescharacteristic
714C22C22×Q8×D5311yescharacteristic
715C22C22×#1171994711yescharacteristic
716C22C22×#1171994911yescharacteristic
717C22C22×#1171994911yescharacteristic
718C22C2×#1313326211yescharacteristic
719C22C2×#1313326411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—1064no—
728C4—1064no—
729C4—1064no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C2—2124no—
735C2#2027980218yesdirect product factor
736C2C2×#1681117411yescharacteristic
737C2C2×#1681117811yescharacteristic
738C2C2×#1681122211yescharacteristic
739C2C2×#1681126011yescharacteristic
740C2C2×#1681128611yescharacteristic
741C2C2×#1681131511yescharacteristic
742C2C2×#1681133411yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#395C2
socleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#395D53
hypocenterC53C2×#2556
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#13133208C2semidirect
3. #20279802C2direct (N × H)
5. C2×#16810555C2semidirect
7. C2×#16810530C2semidirect
8. C2×#16810522C2semidirect
9. C2×#16810519C2semidirect
12. C2×#16810506C2semidirect
14. C2×#16810474C2semidirect
16. C2×C53×#395C2semidirect
19. C2×#13133208C22semidirect
43. #16810555C22semidirect
45. #16810530C22semidirect
46. #16810522C22semidirect
47. #16810519C22semidirect
50. #16810506C22semidirect
52. #16810474C22semidirect
65. C53×#395C22semidirect
108. C2×#11719921Q8semidirect
231. #11719921C2×Q8semidirect
369. C2×#395D53semidirect
379. C2×C53#2556semidirect
420. #395C2×D53semidirect
440. C53C2×#2556semidirect
735. C2#20279802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332082
C22×#131331932
#202798022
C2×#168105602
C2×#168105552
C2×#168105452
C2×#168105302
C2×#168105222
C2×#168105192
C2×#168105152
C2×#168105132
C2×#168105062
C2×#168104942
C2×#168104742
C2×#168104702
C2×C53×#3952
C2×#255653