Finite Group Databasebeta

← #27289955

Subgroups — #27289955

Order 13568.

1338 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810481C211yesmaximal, characteristic
2C2×#16810481C211yesmaximal, characteristic
3C2×C22⋊C4×Dic53C211yesmaximal, characteristic
4C2×#16810390C211yesmaximal, characteristic
5C2×#16810389C211yesmaximal, characteristic
6C2×#16810389C211yesmaximal, characteristic
7C2×C53×#342C211yesmaximal, characteristic
8C24×Dic53C2211yescharacteristic
9C22×#11719919—21no—
10C22×#11719919C412yescomplemented
11C22×C22⋊Dic53C2211yescharacteristic
12C22×C22⋊Dic53C2211yescharacteristic
13C22×C22⋊Dic53C2211yescharacteristic
14C22×C4×Dic53—21no—
15#16810481—22no—
16#16810481—21no—
17#16810481—21no—
18#16810481—21no—
19#16810481—21no—
20#16810481C414yescomplemented
21C22⋊C4×Dic53—22no—
22C22⋊C4×Dic53C414yescomplemented
23C2×#13133124—21no—
24C2×#13133124—21no—
25C2×#13133124C412yescomplemented
26#16810390—22no—
27#16810389—22no—
28#16810389—22no—
29C22×C22⋊C4×C53C2211yescharacteristic
30C22×C22⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C53×#342—22no—
33C23×Dic53—21no—
34C23×Dic53—21no—
35C23×Dic53—44no—
36C23×Dic53C2×C411yescharacteristic
37C23×Dic53C2×C412yes—
38C23×Dic53C2×C411yescharacteristic
39C23×Dic53C2×C412yes—
40C23×Dic53C2×C412yes—
41C23×Dic53D411yescharacteristic
42C23×Dic53D411yescharacteristic
43C23×Dic53D411yescharacteristic
44C23×Dic53D411yescharacteristic
45C23×Dic53D412yes—
46C23×Dic53Q812yes—
47C2×#11719919—24no—
48C2×#11719919—22no—
49C2×#11719919—22no—
50C2×#11719919—44no—
51C2×#11719919—44no—
52C2×C22⋊Dic53—21no—
53C2×C22⋊Dic53—21no—
54C2×C22⋊Dic53—21no—
55C2×C22⋊Dic53—21no—
56C2×C22⋊Dic53—21no—
57C2×C22⋊Dic53—21no—
58C2×C22⋊Dic53—21no—
59C2×C22⋊Dic53—21no—
60C2×C22⋊Dic53—21no—
61C2×C22⋊Dic53—21no—
62C2×C22⋊Dic53—21no—
63C2×C22⋊Dic53—21no—
64C2×C22⋊Dic53—21no—
65C2×C22⋊Dic53—21no—
66C2×C22⋊Dic53C2×C412yes—
67C2×C22⋊Dic53C2×C412yes—
68C2×C22⋊Dic53D412yes—
69C2×C22⋊Dic53Q812yes—
70C2×C4×Dic53—24no—
71C2×C4×Dic53—44no—
72#13133124—24no—
73#13133124—24no—
74#13133124—22no—
75#13133124—22no—
76C25×C53C2311yescharacteristic
77C23×C4×C53—21no—
78C23×C4×C53—21no—
79C23×C4×C53C2×C412yes—
80C2×C22⋊C4×C53—21no—
81C2×C22⋊C4×C53—21no—
82C2×C22⋊C4×C53—21no—
83C2×C22⋊C4×C53—21no—
84C2×C22⋊C4×C53—21no—
85C2×C22⋊C4×C53—21no—
86C2×C22⋊C4×C53—21no—
87C2×C22⋊C4×C53—21no—
88C2×C22⋊C4×C53—21no—
89C2×C22⋊C4×C53—21no—
90C2×C22⋊C4×C53—21no—
91C2×C22⋊C4×C53—21no—
92C2×C22⋊C4×C53—21no—
93C2×C22⋊C4×C53—21no—
94C2×C22⋊C4×C53C2×C412yes—
95C2×C22⋊C4×C53C2×C412yes—
96C2×C22⋊C4×C53D412yes—
97C2×C22⋊C4×C53Q812yes—
98C24×C53—42no—
99C24×C53—42no—
100C24×C53C22×C411yescharacteristic
101C24×C53C22×C411yescharacteristic
102C24×C53C22×C411yescharacteristic
103C24×C53C2×D411yescharacteristic
104C24×C53C2×D411yescharacteristic
105C24×C53C2×D411yescharacteristic
106C24×C53C2×D411yescharacteristic
107C24×C53C2×D411yescharacteristic
108C24×C53C2×Q811yescharacteristic
109C24×C53C2×Q811yescharacteristic
110C24×C53C2×Q811yescharacteristic
111C24×C53#4111yescharacteristic
112C24×C53#4111yescharacteristic
113C24×C53#4111yescharacteristic
114C24×C53#4111yescharacteristic
115C22×C4×C53—22no—
116C22×C4×C53—22no—
117C22×C4×C53—22no—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—22no—
121C22×C4×C53—22no—
122C22×C4×C53—42no—
123C22×C4×C53—42no—
124C22×C4×C53—42no—
125C22×C4×C53—42no—
126C22×C4×C53—41no—
127C22×C4×C53—41no—
128C22×C4×C53—42no—
129C22×C4×C53—42no—
130C22×Dic53—24no—
131C22×Dic53—24no—
132C22×Dic53—24no—
133C22×Dic53—22no—
134C22×Dic53—22no—
135C22×Dic53—22no—
136C22×Dic53—22no—
137C22×Dic53—22no—
138C22×Dic53—22no—
139C22×Dic53—22no—
140C22×Dic53—44no—
141C22×Dic53—44no—
142C22×Dic53—44no—
143C22×Dic53—44no—
144C22×Dic53—42no—
145C22×Dic53—42no—
146C22×Dic53—42no—
147C22×Dic53—42no—
148C22×Dic53—42no—
149C22×Dic53—42no—
150C22×Dic53—42no—
151C22×Dic53—41no—
152C22×Dic53—41no—
153C22×Dic53—42no—
154C22×Dic53—42no—
155C22×Dic53C4212yes—
156C22×Dic53C4212yes—
157C22×Dic53C22⋊C411yescharacteristic
158C22×Dic53C22⋊C411yescharacteristic
159C22×Dic53C22⋊C412yes—
160C22×Dic53C22⋊C411yescharacteristic
161C22×Dic53C22⋊C412yes—
162C22×Dic53C22⋊C412yes—
163C22×Dic53C22⋊C412yes—
164C22×Dic53C22⋊C411yescharacteristic
165C22×Dic53C4⋊C412yes—
166C22×Dic53C4⋊C412yes—
167C22×Dic53C4⋊C412yes—
168C22×Dic53C4⋊C412yes—
169C22×Dic53C4⋊C412yes—
170C22×Dic53C4⋊C412yes—
171C22⋊C4×C53—22no—
172C22⋊C4×C53—22no—
173C22⋊C4×C53—22no—
174C22⋊C4×C53—22no—
175C22⋊C4×C53—22no—
176C22⋊C4×C53—41no—
177C22⋊C4×C53—41no—
178C22⋊C4×C53—41no—
179C22⋊C4×C53—41no—
180C22⋊C4×C53—41no—
181C22⋊C4×C53—41no—
182C22⋊C4×C53C4⋊C414yescomplemented
183C22⋊Dic53—22no—
184C22⋊Dic53—22no—
185C22⋊Dic53—22no—
186C22⋊Dic53—22no—
187C22⋊Dic53—22no—
188C22⋊Dic53—41no—
189C22⋊Dic53—41no—
190C22⋊Dic53—41no—
191C22⋊Dic53—41no—
192C22⋊Dic53—41no—
193C22⋊Dic53—41no—
194C22⋊Dic53C4⋊C414yescomplemented
195#11719919—44no—
196#11719919—48no—
197#11719919—44no—
198C4×Dic53—48no—
199C23×C53—22no—
200C23×C53—22no—
201C23×C53—22no—
202C23×C53—22no—
203C23×C53—22no—
204C23×C53—22no—
205C23×C53—41no—
206C23×C53—41no—
207C23×C53—41no—
208C23×C53—41no—
209C23×C53—41no—
210C23×C53—41no—
211C23×C53—42no—
212C23×C53—41no—
213C23×C53—42no—
214C23×C53—42no—
215C23×C53—41no—
216C23×C53—42no—
217C23×C53—42no—
218C23×C53—42no—
219C23×C53—42no—
220C23×C53—42no—
221C23×C53C2×C4211yescharacteristic
222C23×C53C2×C22⋊C411yescharacteristic
223C23×C53C2×C22⋊C411yescharacteristic
224C23×C53C2×C22⋊C411yescharacteristic
225C23×C53C2×C4⋊C411yescharacteristic
226C23×C53C2×C4⋊C411yescharacteristic
227C23×C53C2×C4⋊C411yescharacteristic
228C23×C53C2×C4⋊C411yescharacteristic
229C23×C53C2×C4⋊C411yescharacteristic
230C23×C53#11711yescharacteristic
231C23×C53#11711yescharacteristic
232C23×C53C4×D411yescharacteristic
233C23×C53C4×D411yescharacteristic
234C23×C53C4×D411yescharacteristic
235C23×C53C4×D411yescharacteristic
236C23×C53C4×Q811yescharacteristic
237C23×C53C4×Q811yescharacteristic
238C23×C53C4×Q811yescharacteristic
239C23×C53C4×Q811yescharacteristic
240C23×C53#12111yescharacteristic
241C23×C53#12111yescharacteristic
242C23×C53#12111yescharacteristic
243C23×C53#12111yescharacteristic
244C23×C53C22⋊Q811yescharacteristic
245C23×C53C22⋊Q811yescharacteristic
246C23×C53C22⋊Q811yescharacteristic
247C23×C53C22⋊Q811yescharacteristic
248C23×C53#12411yescharacteristic
249C23×C53#12411yescharacteristic
250C23×C53#12511yescharacteristic
251C23×C53#12511yescharacteristic
252C23×C53#12711yescharacteristic
253C23×C53C4⋊Q811yescharacteristic
254C23×C53C4⋊Q811yescharacteristic
255C23×C53C4⋊Q811yescharacteristic
256C2×C4×C53—24no—
257C2×C4×C53—44no—
258C2×C4×C53—42no—
259C2×C4×C53—44no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53—42no—
264C2×C4×C53—42no—
265C2×C4×C53—42no—
266C2×C4×C53—42no—
267C2×C4×C53—82no—
268C2×C4×C53—82no—
269C2×C4×C53—82no—
270C2×C4×C53—82no—
271C2×Dic53—22no—
272C2×Dic53—22no—
273C2×Dic53—22no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—24no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—44no—
288C2×Dic53—42no—
289C2×Dic53—44no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—82no—
298C2×Dic53—82no—
299C2×Dic53—82no—
300C2×Dic53—82no—
301C2×Dic53#9512yes—
302C2×Dic53#9512yes—
303C2×Dic53#9512yes—
304C2×Dic53#9512yes—
305C2×Dic53#9914yes—
306#10854—531nomaximal, Sylow
307C22×C53—22no—
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—21no—
314C22×C53—21no—
315C22×C53—21no—
316C22×C53—21no—
317C22×C53—21no—
318C22×C53—21no—
319C22×C53—21no—
320C22×C53—21no—
321C22×C53—21no—
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—21no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53—41no—
347C22×C53C2×#9511yescharacteristic
348C22×C53C4×C4⋊C411yescharacteristic
349C22×C53C4×C4⋊C411yescharacteristic
350C22×C53#38011yescharacteristic
351C22×C53#38011yescharacteristic
352C22×C53#38211yescharacteristic
353C22×C53#38411yescharacteristic
354C22×C53#38911yescharacteristic
355C22×C53#38911yescharacteristic
356C22×C53#38911yescharacteristic
357C22×C53#38911yescharacteristic
358C22×C53#39011yescharacteristic
359C22×C53#39011yescharacteristic
360C22×C53#39111yescharacteristic
361C22×C53#39111yescharacteristic
362C22×C53C2×#9912yes—
363C22×C53#41012yes—
364C4×C53—44no—
365C4×C53—82no—
366C4×C53—82no—
367Dic53—22no—
368Dic53—22no—
369Dic53—22no—
370Dic53—44no—
371Dic53—82no—
372Dic53—82no—
373Dic53#34214yescomplemented
374C2×#380—531no—
375C2×#380—531no—
376C2×C4×C22⋊C4—531no—
377C2×#342—531no—
378C2×#342—531no—
379C2×#342—531no—
380C2×#342D5311yescharacteristic
381C2×C53—21no—
382C2×C53—21no—
383C2×C53—21no—
384C2×C53—21no—
385C2×C53—21no—
386C2×C53—21no—
387C2×C53—21no—
388C2×C53—21no—
389C2×C53—21no—
390C2×C53—21no—
391C2×C53—21no—
392C2×C53—21no—
393C2×C53C4⋊#9511yescharacteristic
394C2×C53C2×#34211yescharacteristic
395C2×C53#174011yescharacteristic
396C2×C53#196412yes—
397C2×C53#199612yes—
398C24×C4—531no—
399C22×C4⋊C4—532no—
400C22×C4⋊C4—1061no—
401C22×C22⋊C4—531no—
402C22×C22⋊C4—531no—
403C22×C22⋊C4—531no—
404C22×C22⋊C4C2×D5311yescharacteristic
405C22×C22⋊C4C2×D5311yescharacteristic
406C22×C22⋊C4C2×D5311yescharacteristic
407C22×C42—1061no—
408#380—534no—
409#380—1061no—
410#380—1061no—
411#380—1061no—
412#380—1061no—
413#380—1062no—
414C4×C22⋊C4—534no—
415C4×C22⋊C4—1062no—
416C2×#95—532no—
417C2×#95—1061no—
418C2×#95—1061no—
419#342—22no—
420#342—1062no—
421#342—1062no—
422#342—1062no—
423C53#1085411yescharacteristic, complemented, Sylow
424C25C22×D5311yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—531no—
428C23×C4—531no—
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—532no—
432C23×C4—532no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—532no—
436C23×C4—532no—
437C23×C4—532no—
438C23×C4—1061no—
439C23×C4—1061no—
440C23×C4—2124no—
441C23×C4C4×D5312yes—
442C2×C4⋊C4—1062no—
443C2×C4⋊C4—1062no—
444C2×C4⋊C4—1064no—
445C2×C4⋊C4—2124no—
446C2×C4⋊C4—2124no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—532no—
462C2×C22⋊C4—532no—
463C2×C22⋊C4—532no—
464C2×C22⋊C4—532no—
465C2×C22⋊C4—1061no—
466C2×C22⋊C4—1061no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4Dic10612yes—
480C2×C22⋊C4C4×D5312yes—
481C2×C22⋊C4C4×D5312yes—
482C2×C22⋊C4C22⋊D5312yes—
483C2×C42—1064no—
484C2×C42—2124no—
485#95—1062no—
486#95—1062no—
487#95—1064no—
488#95—1064no—
489C24—42no—
490C24—42no—
491C24C2×Dic10611yescharacteristic
492C24C2×C4×D5311yescharacteristic
493C24C2×C4×D5311yescharacteristic
494C24C2×C4×D5311yescharacteristic
495C24#1171994511yescharacteristic
496C24#1171994511yescharacteristic
497C24D4×D5311yescharacteristic
498C24D4×D5311yescharacteristic
499C24D4×D5311yescharacteristic
500C24D4×D5311yescharacteristic
501C24#1171994711yescharacteristic
502C24#1171994711yescharacteristic
503C24Q8×D5311yescharacteristic
504C24Q8×D5311yescharacteristic
505C24C2×C22⋊D5311yescharacteristic
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—531no—
522C22×C4—532no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—531no—
526C22×C4—531no—
527C22×C4—531no—
528C22×C4—532no—
529C22×C4—532no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—532no—
533C22×C4—532no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—1064no—
538C22×C4—1064no—
539C22×C4—1064no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—2124no—
548C22×C4—2124no—
549C22×C4—2124no—
550C22×C4—2124no—
551C22×C4—2122no—
552C22×C4—2122no—
553C22×C4—2122no—
554C22×C4—2122no—
555C22×C4—2122no—
556C22×C4—2121no—
557C22×C4—2121no—
558C22×C4—2122no—
559C22×C4—2122no—
560C22×C4—2122no—
561C22×C4—2122no—
562C4⋊C4—2124no—
563C4⋊C4—2128no—
564C4⋊C4—2124no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—534no—
577C22⋊C4—1062no—
578C22⋊C4—1062no—
579C22⋊C4—1062no—
580C22⋊C4—1062no—
581C22⋊C4—1062no—
582C22⋊C4—2121no—
583C22⋊C4—2121no—
584C22⋊C4—2121no—
585C22⋊C4—2121no—
586C22⋊C4—2121no—
587C22⋊C4—2121no—
588C22⋊C4#1171991914yescomplemented
589C42—2128no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23C42×D5311yescharacteristic
613C23C22⋊C4×D5311yescharacteristic
614C23C22⋊C4×D5311yescharacteristic
615C23C22⋊C4×D5311yescharacteristic
616C23C4⋊C4×D5311yescharacteristic
617C23C4⋊C4×D5311yescharacteristic
618C23C4⋊C4×D5311yescharacteristic
619C23C4⋊C4×D5311yescharacteristic
620C23C2×#1171991911yescharacteristic
621C23#1313317311yescharacteristic
622C23#1313317411yescharacteristic
623C23#1313317711yescharacteristic
624C23#1313317711yescharacteristic
625C23C4×C22⋊D5311yescharacteristic
626C23C4×C22⋊D5311yescharacteristic
627C23#1313318211yescharacteristic
628C23#1313318211yescharacteristic
629C23C4×Dic10611yescharacteristic
630C23C4×Dic10611yescharacteristic
631C23#1313318911yescharacteristic
632C23#1313318911yescharacteristic
633C23#1313319011yescharacteristic
634C23#1313319011yescharacteristic
635C23#1313319411yescharacteristic
636C23#1313319411yescharacteristic
637C23#1313319511yescharacteristic
638C23#1313319511yescharacteristic
639C23#1313320311yescharacteristic
640C23#1313320311yescharacteristic
641C23#1313320711yescharacteristic
642C23#1313320711yescharacteristic
643C23#1313321311yescharacteristic
644C23#1313321511yescharacteristic
645C23#1313321611yescharacteristic
646C23#1313321611yescharacteristic
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—534no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—532no—
666C2×C4—532no—
667C2×C4—1064no—
668C2×C4—1064no—
669C2×C4—1064no—
670C2×C4—1064no—
671C2×C4—1064no—
672C2×C4—1064no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1064no—
677C2×C4—4242no—
678C2×C4—4242no—
679C2×C4—4242no—
680C2×C4—4242no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2124no—
696C2×C4—2124no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#95×D5311yescharacteristic
738C22#1681047411yescharacteristic
739C22C4×#1171991911yescharacteristic
740C22#1681048111yescharacteristic
741C22#1681048211yescharacteristic
742C22#1681048711yescharacteristic
743C22#1681049211yescharacteristic
744C22#1681051811yescharacteristic
745C22#1681051811yescharacteristic
746C22#1681052011yescharacteristic
747C22#1681052011yescharacteristic
748C22#1681052311yescharacteristic
749C22#1681052311yescharacteristic
750C22#1681052711yescharacteristic
751C22#1681052711yescharacteristic
752C22#99×D5312yes—
753C22#1681059512yes—
754C4—44no—
755C4—82no—
756C4—82no—
757C4—534no—
758C4—1062no—
759C4—1062no—
760C4—1062no—
761C4—4242no—
762C4—4242no—
763C4—2124no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2#2027294311yescharacteristic
777C2#342×D5311yescharacteristic
778C2#2027444611yescharacteristic
779C2#2027554912yes—
780C2#2027569812yes—
subgroupG/H
centerC23C22⋊C4×D53
commutatorC23×C53C2×C42
FrattiniC25C22×D53
FittingC2×C53×#342C2
socleC23×C53C2×C22⋊C4
prime radical, cosocleC25×C53C23
hypercenterC2×#342D53
hypocenterC53#10854
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
10. C22×#11719919C4semidirect
20. #16810481C4semidirect
22. C22⋊C4×Dic53C4semidirect
25. C2×#13133124C4semidirect
182. C22⋊C4×C53C4⋊C4semidirect
194. C22⋊Dic53C4⋊C4semidirect
373. Dic53#342semidirect
423. C53#10854semidirect
588. C22⋊C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168104812
C2×C22⋊C4×Dic532
C2×#168103902
C2×#168103892
C2×C53×#3422
#1085453