Finite Group Databasebeta

← #28312926

Subgroups — #28312926

Order 13568.

2366 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
1C2×#16811574C212yesmaximal, complemented
2C2×#16811565C212yesmaximal
3C2×#16811565C211yesmaximal, characteristic
4C2×C4×C22⋊#6157C211yesmaximal, characteristic
5#20289900C214yesmaximal, complemented
6#20289892C212yesmaximal, complemented
7#20289889C212yesmaximal
8C22×C4⋊C4×D53C211yesmaximal, characteristic
9C22×C4⋊#6157C2212yes—
10C22×C4⋊#6157C2214yes—
11C22×C22⋊#6157C2212yes—
12C22×C22⋊#6157C2211yescharacteristic
13C22×C22⋊#6157C2211yescharacteristic
14C22×C4×#6157C2212yes—
15#16811574—28no—
16#16811565—28no—
17#16811565—24no—
18C4×C22⋊#6157—24no—
19C2×(C2×#6157)⋊C4C2212yes—
20C2×(C2×#6157)⋊C4C2214yes—
21C2×(C2×#6157)⋊C4C2212yes—
22C2×(C2×#6157)⋊C4C2214yes—
23C2×(C2×#6157)⋊C4C2214yes—
24C23×C4×D53C2212yes—
25C23×C4×D53C2211yescharacteristic
26C22×C4⋊Dic53C411yescharacteristic, complemented
27C22×#11719919C412yescomplemented
28C2×C4⋊C4×D53—28no—
29C2×C4⋊C4×D53C411yescharacteristic, complemented
30C2×C4⋊C4×D53C412yescomplemented
31C2×C4⋊C4×D53C411yescharacteristic, complemented
32C2×C4⋊C4×D53C2211yescharacteristic
33C2×C4⋊C4×D53C2212yes—
34C2×C4⋊C4×D53C2211yescharacteristic
35C22×C4⋊C4×C53C411yescharacteristic, complemented
36C23×#6157C2314yes—
37C23×#6157C2312yes—
38C23×#6157C2312yes—
39C2×C4⋊#6157—28no—
40C2×C4⋊#6157—24no—
41C2×C4⋊#6157—28no—
42C2×C4⋊#6157—24no—
43C2×C4⋊#6157—24no—
44C2×C4⋊#6157—44no—
45C2×C22⋊#6157—22no—
46C2×C22⋊#6157—22no—
47C2×C22⋊#6157—22no—
48C2×C22⋊#6157—22no—
49C2×C22⋊#6157—24no—
50C2×C22⋊#6157—24no—
51C2×C22⋊#6157—24no—
52C2×C22⋊#6157D414yes—
53C2×C22⋊#6157Q814yes—
54C2×C4×#6157—24no—
55C2×C4×#6157—24no—
56C2×C4×#6157—24no—
57(C2×#6157)⋊C4—28no—
58(C2×#6157)⋊C4—24no—
59(C2×#6157)⋊C4—24no—
60(C2×#6157)⋊C4—28no—
61(C2×#6157)⋊C4—44no—
62C24×D53C2311yescharacteristic
63C23×Dic53C2×C412yes—
64C23×Dic53C2×C411yescharacteristic
65C22×C4×D53—24no—
66C22×C4×D53—24no—
67C22×C4×D53—24no—
68C22×C4×D53—24no—
69C22×C4×D53—28no—
70C22×C4×D53—44no—
71C22×C4×D53C2×C412yes—
72C22×C4×D53C2×C412yes—
73C22×C4×D53C2×C411yescharacteristic
74C22×C4×D53C2×C411yescharacteristic
75C22×C4×D53D414yes—
76C22×C4×D53Q814yes—
77C22×C4×D53C2312yes—
78C22×C4×D53C2312yes—
79C22×C4×D53C2311yescharacteristic
80C22×C4×D53C2311yescharacteristic
81C2×C4⋊Dic53—24no—
82C2×C4⋊Dic53C2×C411yescharacteristic
83C2×C4⋊Dic53C2×C412yes—
84C2×C4⋊Dic53C2×C411yescharacteristic
85C2×#11719919—28no—
86C2×#11719919C2×C412yes—
87C2×#11719919C2×C412yes—
88C2×#11719919C2×C412yes—
89C2×#11719919C2×C412yes—
90C4⋊C4×D53—24no—
91C4⋊C4×D53—24no—
92C4⋊C4×D53—28no—
93C4⋊C4×D53—28no—
94C4⋊C4×D53—24no—
95C4⋊C4×D53D418yes—
96C23×C4×C53C2×C412yes—
97C23×C4×C53C2×C411yescharacteristic
98C2×C4⋊C4×C53—24no—
99C2×C4⋊C4×C53C2×C411yescharacteristic
100C2×C4⋊C4×C53C2×C412yes—
101C2×C4⋊C4×C53C2×C411yescharacteristic
102C24×C53C22×C411yescharacteristic
103C23×D53—22no—
104C23×D53—22no—
105C23×D53—22no—
106C23×D53—22no—
107C23×D53C22×C411yescharacteristic
108C23×D53C2×D412yes—
109C23×D53C2×D412yes—
110C23×D53C2×Q812yes—
111C23×D53C2×Q812yes—
112C23×D53#4112yes—
113C23×D53#4112yes—
114C23×D53C2411yescharacteristic
115C22×#6157—22no—
116C22×#6157—22no—
117C22×#6157—22no—
118C22×#6157—22no—
119C22×#6157—22no—
120C22×#6157—22no—
121C22×#6157—22no—
122C22×#6157—22no—
123C22×#6157—22no—
124C22×#6157—22no—
125C22×#6157—22no—
126C22×#6157—22no—
127C22×#6157—24no—
128C22×#6157—24no—
129C22×#6157—24no—
130C22×#6157—24no—
131C22×#6157—24no—
132C22×#6157—24no—
133C22×#6157—24no—
134C22×#6157C2×D414yes—
135C22×#6157C2×Q814yes—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—24no—
139C22×C4×C53—24no—
140C22×C4×C53—42no—
141C22×C4×C53C4⋊C414yescomplemented
142C22×C4×C53C22×C412yes—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C22×C411yescharacteristic
145C22×C4×C53C22×C411yescharacteristic
146C22×Dic53—22no—
147C22×Dic53—22no—
148C22×Dic53—24no—
149C22×Dic53—24no—
150C22×Dic53—42no—
151C22×Dic53C4⋊C414yescomplemented
152C22×Dic53C22×C412yes—
153C22×Dic53C22×C412yes—
154C22×Dic53C22×C411yescharacteristic
155C22×Dic53C22×C411yescharacteristic
156C2×C4×D53—22no—
157C2×C4×D53—22no—
158C2×C4×D53—22no—
159C2×C4×D53—22no—
160C2×C4×D53—24no—
161C2×C4×D53—22no—
162C2×C4×D53—22no—
163C2×C4×D53—22no—
164C2×C4×D53—22no—
165C2×C4×D53—216no—
166C2×C4×D53—216no—
167C2×C4×D53—24no—
168C2×C4×D53—24no—
169C2×C4×D53—24no—
170C2×C4×D53—22no—
171C2×C4×D53—22no—
172C2×C4×D53—24no—
173C2×C4×D53—24no—
174C2×C4×D53—24no—
175C2×C4×D53—416no—
176C2×C4×D53—416no—
177C2×C4×D53—42no—
178C2×C4×D53—42no—
179C2×C4×D53C4⋊C414yescomplemented
180C2×C4×D53C4⋊C414yescomplemented
181C2×C4×D53C2×D418yes—
182C2×C4×D53C2×D412yes—
183C2×C4×D53C2×D412yes—
184C2×C4×D53C2×D414yes—
185C2×C4×D53C2×Q812yes—
186C2×C4×D53C2×Q812yes—
187C2×C4×D53#4114yes—
188C22⋊#6157—28no—
189C22⋊#6157—28no—
190C22⋊#6157—48no—
191C4⋊#6157—416no—
192C4⋊#6157—48no—
193C4×#6157—48no—
194C4⋊C4×C53—24no—
195C4⋊C4×C53—22no—
196C4⋊C4×C53C22⋊C414yescomplemented
197C4⋊Dic53—22no—
198C4⋊Dic53—24no—
199C4⋊Dic53C22⋊C414yescomplemented
200#11719919—24no—
201#11719919—24no—
202#11719919—24no—
203#11719919C22⋊C418yescomplemented
204C23×C53—21no—
205C23×C53—21no—
206C23×C53—21no—
207C23×C53—21no—
208C23×C53C2×C4⋊C412yes—
209C23×C53C4×D412yes—
210C23×C53C4×Q812yes—
211C23×C53C23×C411yescharacteristic
212C22×D53—21no—
213C22×D53—21no—
214C22×D53—21no—
215C22×D53—21no—
216C22×D53—24no—
217C22×D53—24no—
218C22×D53—24no—
219C22×D53—24no—
220C22×D53—24no—
221C22×D53—24no—
222C22×D53—24no—
223C22×D53—24no—
224C22×D53—24no—
225C22×D53—24no—
226C22×D53—24no—
227C22×D53—24no—
228C22×D53C2×C4⋊C412yes—
229C22×D53C4×D412yes—
230C22×D53C4×Q812yes—
231C22×D53#12114yes—
232C22×D53C22⋊Q814yes—
233C22×D53#12514yes—
234C22×D53C4⋊Q814yes—
235C22×D53C22×D411yescharacteristic
236C22×D53C22×D412yes—
237C22×D53C22×D411yescharacteristic
238C22×D53C22×Q811yescharacteristic
239C22×D53C22×Q811yescharacteristic
240C22×D53C2×#4112yes—
241C22×D53C2×#4111yescharacteristic
242C22×D53C2×#4111yescharacteristic
243C22×D53H(5,𝔽2)12yes—
244C22×D532−1+412yes—
245C2×#6157—24no—
246C2×#6157—24no—
247C2×#6157—24no—
248C2×#6157—24no—
249C2×#6157—24no—
250C2×#6157—24no—
251C2×#6157—42no—
252C2×#6157—42no—
253C2×#6157—42no—
254C2×#6157—42no—
255C2×#6157—42no—
256C2×#6157—42no—
257C2×#6157—42no—
258C2×#6157—42no—
259C2×#6157—44no—
260C2×#6157—44no—
261C2×#6157—44no—
262C2×#6157—44no—
263C2×#6157—44no—
264C2×#6157—44no—
265C2×#6157—44no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—28no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—48no—
275C2×C4×C53C2×C22⋊C414yes—
276C2×C4×C53C2×C22⋊C412yes—
277C2×C4×C53C2×C4⋊C412yes—
278C2×C4×C53C2×C4⋊C412yes—
279C2×C4×C53#11712yes—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—28no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—48no—
289C2×Dic53C2×C22⋊C414yes—
290C2×Dic53C2×C22⋊C412yes—
291C2×Dic53C2×C4⋊C412yes—
292C2×Dic53C2×C4⋊C412yes—
293C2×Dic53#11712yes—
294C4×D53—24no—
295C4×D53—24no—
296C4×D53—28no—
297C4×D53—28no—
298C4×D53—28no—
299C4×D53—28no—
300C4×D53—48no—
301C4×D53—48no—
302C4×D53—44no—
303C4×D53—44no—
304C4×D53#12118yes—
305C4×D53C22⋊Q818yes—
306#13907—531nomaximal, Sylow
307C22×C53—22no—
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53#38914yescomplemented
314C22×C53C22×C22⋊C411yescharacteristic
315C22×C53C22×C4⋊C411yescharacteristic
316C22×C53C2×#11711yescharacteristic
317C22×C53C2×C4×D411yescharacteristic
318C22×C53C2×C4×Q811yescharacteristic
319C22×C53#51811yescharacteristic
320C22×C53#51911yescharacteristic
321C2×D53—22no—
322C2×D53—22no—
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—28no—
328C2×D53—28no—
329C2×D53—28no—
330C2×D53—28no—
331C2×D53#38914yescomplemented
332C2×D53C2×#12111yescharacteristic
333C2×D53C2×#12112yes—
334C2×D53C2×C22⋊Q811yescharacteristic
335C2×D53C2×C22⋊Q812yes—
336C2×D53C2×#12511yescharacteristic
337C2×D53C2×C4⋊Q811yescharacteristic
338C2×D53#53712yes—
339C2×D53#54412yes—
340C2×D53D4212yes—
341C2×D53#54612yes—
342C2×D53#54712yes—
343C2×D53#54812yes—
344C2×D53D4×Q812yes—
345C2×D53#55212yes—
346C2×D53#55312yes—
347C2×D53#55412yes—
348#6157—44no—
349#6157—44no—
350#6157—84no—
351C4×C53—24no—
352C4×C53—22no—
353C4×C53—42no—
354C4×C53#38014yescomplemented
355Dic53—24no—
356Dic53—22no—
357Dic53—42no—
358Dic53#38014yescomplemented
359C23×C4⋊C4—531no—
360C2×#389—532no—
361C2×#380—532no—
362C2×#380—531no—
363C2×C4×C22⋊C4—531no—
364#1441—534no—
365C4⋊#95—532no—
366C22⋊#95—532no—
367C2×C53—24no—
368C2×C53C2×#38011yescharacteristic
369C2×C53C2×#38911yescharacteristic
370C2×C53#231611yescharacteristic
371C2×C53D4×C22⋊C411yescharacteristic
372C2×C53Q8×C22⋊C411yescharacteristic
373C2×C53#234411yescharacteristic
374C2×C53#234511yescharacteristic
375D53—24no—
376D53#241612yes—
377D53#241712yes—
378D53#244012yes—
379D53#244212yes—
380C24×C4—531no—
381C24×C4—532no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—532no—
384C22×C4⋊C4—531no—
385C22×C4⋊C4—532no—
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4—532no—
390C22×C4⋊C4—532no—
391C22×C4⋊C4—534no—
392C22×C4⋊C4—1068no—
393C22×C4⋊C4#615711yescharacteristic, complemented
394C22×C22⋊C4—531no—
395C22×C22⋊C4—531no—
396C22×C22⋊C4—532no—
397C22×C42—532no—
398#389—1068no—
399#380—1068no—
400#380—1064no—
401C4×C22⋊C4—1064no—
402C2×#95—534no—
403C2×#95—534no—
404C2×#95—532no—
405C2×#95—532no—
406C2×#95—534no—
407C53#1390711yescharacteristic, complemented, Sylow
408C25—531no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—534no—
412C23×C4—534no—
413C23×C4—532no—
414C23×C4—531no—
415C23×C4—531no—
416C23×C4—531no—
417C23×C4—532no—
418C23×C4—532no—
419C23×C4—532no—
420C23×C4—532no—
421C23×C4—532no—
422C23×C4—532no—
423C23×C4—534no—
424C23×C4—1064no—
425C23×C4—1064no—
426C23×C4—1068no—
427C23×C4—1064no—
428C23×C4—1064no—
429C23×C4—2124no—
430C23×C4C2×#615712yes—
431C23×C4C2×#615711yescharacteristic
432C2×C4⋊C4—24no—
433C2×C4⋊C4—532no—
434C2×C4⋊C4—531no—
435C2×C4⋊C4—538no—
436C2×C4⋊C4—532no—
437C2×C4⋊C4—532no—
438C2×C4⋊C4—532no—
439C2×C4⋊C4—532no—
440C2×C4⋊C4—531no—
441C2×C4⋊C4—1068no—
442C2×C4⋊C4—1064no—
443C2×C4⋊C4—1064no—
444C2×C4⋊C4—1068no—
445C2×C4⋊C4—1068no—
446C2×C4⋊C4—1064no—
447C2×C4⋊C4—1064no—
448C2×C4⋊C4—1064no—
449C2×C4⋊C4—1068no—
450C2×C4⋊C4—1064no—
451C2×C4⋊C4—1068no—
452C2×C4⋊C4—1064no—
453C2×C4⋊C4—2124no—
454C2×C4⋊C4C2×#615711yescharacteristic
455C2×C4⋊C4C2×#615712yes—
456C2×C4⋊C4C2×#615711yescharacteristic
457C2×C22⋊C4—534no—
458C2×C22⋊C4—534no—
459C2×C22⋊C4—1062no—
460C2×C22⋊C4—1062no—
461C2×C22⋊C4—1062no—
462C2×C22⋊C4—1062no—
463C2×C22⋊C4—1064no—
464C2×C22⋊C4—1064no—
465C2×C22⋊C4—1064no—
466C2×C42—1064no—
467C2×C42—1064no—
468C2×C42—1064no—
469#95—1064no—
470#95—1064no—
471#95—1068no—
472#95—1068no—
473#95—2124no—
474C24—531no—
475C24—532no—
476C24—532no—
477C24—532no—
478C24—532no—
479C24—532no—
480C24—532no—
481C24—531no—
482C24—1062no—
483C24—1062no—
484C24—1062no—
485C24—1062no—
486C24C22×#615711yescharacteristic
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—42no—
492C22×C4—531no—
493C22×C4—534no—
494C22×C4—532no—
495C22×C4—532no—
496C22×C4—534no—
497C22×C4—534no—
498C22×C4—532no—
499C22×C4—531no—
500C22×C4—538no—
501C22×C4—534no—
502C22×C4—534no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—534no—
506C22×C4—534no—
507C22×C4—532no—
508C22×C4—1062no—
509C22×C4—1062no—
510C22×C4—10616no—
511C22×C4—10616no—
512C22×C4—1064no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1064no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1064no—
520C22×C4—1064no—
521C22×C4—1064no—
522C22×C4—1064no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1064no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1064no—
542C22×C4—1064no—
543C22×C4—1064no—
544C22×C4—1064no—
545C22×C4—1064no—
546C22×C4—1064no—
547C22×C4—1064no—
548C22×C4—1064no—
549C22×C4—1064no—
550C22×C4—2122no—
551C22×C4—2122no—
552C22×C4—21216no—
553C22×C4—21216no—
554C22×C4—2122no—
555C22×C4C4⋊#615714yescomplemented
556C22×C4C22×#615712yes—
557C22×C4C22×#615712yes—
558C22×C4C22×#615711yescharacteristic
559C22×C4C22×#615711yescharacteristic
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—538no—
563C4⋊C4—534no—
564C4⋊C4—1064no—
565C4⋊C4—1064no—
566C4⋊C4—1064no—
567C4⋊C4—1064no—
568C4⋊C4—1062no—
569C4⋊C4—2128no—
570C4⋊C4—21216no—
571C4⋊C4C22⋊#615714yescomplemented
572C22⋊C4—1068no—
573C22⋊C4—1068no—
574C22⋊C4—2128no—
575C42—2128no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—532no—
581C23—531no—
582C23—531no—
583C23—532no—
584C23—531no—
585C23—531no—
586C23—531no—
587C23—531no—
588C23—532no—
589C23—532no—
590C23—534no—
591C23—534no—
592C23—534no—
593C23—534no—
594C23—532no—
595C23—532no—
596C23—532no—
597C23—1064no—
598C23—1064no—
599C23—1064no—
600C23—1064no—
601C23—1064no—
602C23—1064no—
603C23—1064no—
604C23—1064no—
605C23—1064no—
606C23—1064no—
607C23—1064no—
608C23—1064no—
609C23—1061no—
610C23—1061no—
611C23—1061no—
612C23—1061no—
613C23C2×C4⋊#615712yes—
614C23D4×#615712yes—
615C23Q8×#615712yes—
616C23C23×#615711yescharacteristic
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—48no—
626C2×C4—532no—
627C2×C4—532no—
628C2×C4—532no—
629C2×C4—538no—
630C2×C4—538no—
631C2×C4—534no—
632C2×C4—532no—
633C2×C4—1068no—
634C2×C4—1068no—
635C2×C4—1064no—
636C2×C4—1064no—
637C2×C4—1068no—
638C2×C4—1068no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1068no—
644C2×C4—1064no—
645C2×C4—1064no—
646C2×C4—1064no—
647C2×C4—1064no—
648C2×C4—1064no—
649C2×C4—1064no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—2128no—
654C2×C4—2128no—
655C2×C4—2124no—
656C2×C4—2124no—
657C2×C4—2128no—
658C2×C4—2124no—
659C2×C4—2124no—
660C2×C4—2124no—
661C2×C4—2124no—
662C2×C4—2124no—
663C2×C4—2124no—
664C2×C4—2124no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4C2×C22⋊#615714yes—
674C2×C4C2×C22⋊#615712yes—
675C2×C4C2×C4⋊#615712yes—
676C2×C4C2×C4⋊#615712yes—
677C2×C4#1313329612yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—532no—
685C22—532no—
686C22—531no—
687C22—531no—
688C22—531no—
689C22—531no—
690C22—532no—
691C22—532no—
692C22—532no—
693C22—532no—
694C22—532no—
695C22—532no—
696C22—532no—
697C22—532no—
698C22—532no—
699C22—532no—
700C22—534no—
701C22—1068no—
702C22—1068no—
703C22—1068no—
704C22—1068no—
705C22—1062no—
706C22—1062no—
707C22—1062no—
708C22—1062no—
709C22—1062no—
710C22—1062no—
711C22#1681157414yescomplemented
712C22C22×C22⋊#615711yescharacteristic
713C22C22×C4⋊#615711yescharacteristic
714C22C2×#1313329611yescharacteristic
715C22C2×D4×#615711yescharacteristic
716C22C2×Q8×#615711yescharacteristic
717C22#1681169011yescharacteristic
718C22#1681169111yescharacteristic
719C4—22no—
720C4—24no—
721C4—42no—
722C4—534no—
723C4—1062no—
724C4—1064no—
725C4—4244no—
726C4—2124no—
727C4—2124no—
728C4—2122no—
729C4#1681156514yescomplemented
730C2—24no—
731C2—532no—
732C2—532no—
733C2—532no—
734C2—532no—
735C2—1064no—
736C2C2×#1681156511yescharacteristic
737C2C2×#1681157411yescharacteristic
738C2#2029119511yescharacteristic
739C2D4×C22⋊#615711yescharacteristic
740C2Q8×C22⋊#615711yescharacteristic
741C2#2029122311yescharacteristic
742C2#2029122411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
FittingC22×C4⋊C4×C53C4
prime radicalC24×D53C23
cosocleC23×D53C24
hypercenterC22×C4⋊C4#6157
hypocenterC53#13907
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16811574C2semidirect
5. #20289900C2semidirect
6. #20289892C2semidirect
26. C22×C4⋊Dic53C4semidirect
27. C22×#11719919C4semidirect
29. C2×C4⋊C4×D53C4semidirect
30. C2×C4⋊C4×D53C4semidirect
31. C2×C4⋊C4×D53C4semidirect
35. C22×C4⋊C4×C53C4semidirect
141. C22×C4×C53C4⋊C4semidirect
151. C22×Dic53C4⋊C4semidirect
179. C2×C4×D53C4⋊C4semidirect
180. C2×C4×D53C4⋊C4semidirect
196. C4⋊C4×C53C22⋊C4semidirect
199. C4⋊Dic53C22⋊C4semidirect
203. #11719919C22⋊C4semidirect
313. C22×C53#389semidirect
331. C2×D53#389semidirect
354. C4×C53#380semidirect
358. Dic53#380semidirect
393. C22×C4⋊C4#6157semidirect
407. C53#13907semidirect
555. C22×C4C4⋊#6157semidirect
571. C4⋊C4C22⋊#6157semidirect
711. C22#16811574semidirect
729. C4#16811565semidirect

Maximal subgroups

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

subgroupindex
C2×#168115742
C2×#168115652
C2×C4×C22⋊#61572
#202899002
#202898922
#202898892
C22×C4⋊C4×D532
#1390753