Finite Group Databasebeta

← C2×#20274822 #27383946

Subgroups — C2×#20274822 #27383946

Order 13568.

1554 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811096C211yesmaximal, characteristic
2C22×#13133131C211yesmaximal, characteristic
3C22×#13133131C211yesmaximal, characteristic
4#20274822C218yesmaximal, direct product factor
5C2×#16810390C211yesmaximal, characteristic, complemented
6C2×#16810389C211yesmaximal, characteristic, complemented
7C2×#16810389C211yesmaximal, characteristic, complemented
8C2×C53×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D53C2211yescharacteristic
10#16811096—22no—
11#16811096—22no—
12#16811096C414yescomplemented
13#16811096C2214yes—
14C2×C4×C22⋊D53—22no—
15C2×#13133177—22no—
16C2×#13133173C412yescomplemented
17C22×C22⋊Dic53C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C2×C22⋊C4×D53C412yescomplemented
21C2×#13133131—22no—
22C2×#13133131—22no—
23C2×#13133131—22no—
24C2×#13133131—22no—
25C2×#13133131C2214yes—
26C2×#13133131C2214yes—
27#16810390C2214yescomplemented
28#16810389C2214yescomplemented
29#16810389C2214yescomplemented
30C22×C22⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2211yescharacteristic
33C53×#342C2214yescomplemented
34C24×D53C2×C411yescharacteristic
35C22×C22⋊D53—21no—
36C22×C22⋊D53—21no—
37C22×C22⋊D53—21no—
38C22×C22⋊D53—21no—
39C22×C22⋊D53—21no—
40C22×C22⋊D53—21no—
41C22×C22⋊D53—21no—
42C22×C22⋊D53—21no—
43C22×C22⋊D53C2×C412yes—
44C22×C22⋊D53D412yes—
45C22×C22⋊D53D412yes—
46C22×C22⋊D53D412yes—
47C22×C22⋊D53D412yes—
48C22×C22⋊D53C2312yes—
49C23×Dic53—21no—
50C23×Dic53—21no—
51C23×Dic53—21no—
52C23×Dic53C2×C411yescharacteristic
53C22×C4×D53—22no—
54C4×C22⋊D53—28no—
55C4×C22⋊D53—28no—
56#13133177—28no—
57#13133177—28no—
58#13133173—24no—
59#13133173C2×C418yescomplemented
60C2×#11719919—22no—
61C2×C22⋊Dic53—21no—
62C2×C22⋊Dic53—21no—
63C2×C22⋊Dic53—21no—
64C2×C22⋊Dic53—21no—
65C2×C22⋊Dic53—21no—
66C2×C22⋊Dic53—21no—
67C2×C22⋊Dic53—21no—
68C2×C22⋊Dic53—21no—
69C2×C22⋊Dic53—21no—
70C2×C22⋊Dic53—21no—
71C2×C22⋊Dic53—21no—
72C2×C22⋊Dic53—21no—
73C2×C22⋊Dic53—21no—
74C2×C22⋊Dic53C2×C412yes—
75C2×C22⋊Dic53C2×C412yes—
76C2×C22⋊Dic53C2312yes—
77C2×C22⋊Dic53C2312yes—
78C2×C22⋊Dic53C2312yes—
79C2×#11719921—22no—
80C22⋊C4×D53—24no—
81C22⋊C4×D53C2×C418yescomplemented
82C2×C4×Dic53—22no—
83#13133131—28no—
84#13133131—28no—
85C25×C53C2311yescharacteristic
86C23×C4×C53—21no—
87C23×C4×C53—21no—
88C23×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×C53—21no—
95C2×C22⋊C4×C53—21no—
96C2×C22⋊C4×C53—21no—
97C2×C22⋊C4×C53—21no—
98C2×C22⋊C4×C53—21no—
99C2×C22⋊C4×C53—21no—
100C2×C22⋊C4×C53—21no—
101C2×C22⋊C4×C53—21no—
102C2×C22⋊C4×C53C2×C412yes—
103C2×C22⋊C4×C53C2×C412yes—
104C2×C22⋊C4×C53C2312yes—
105C2×C22⋊C4×C53C2312yes—
106C2×C22⋊C4×C53C2312yes—
107C24×C53—82no—
108C24×C53C22×C411yescharacteristic
109C24×C53C22×C411yescharacteristic
110C24×C53C2×D411yescharacteristic
111C24×C53C2×D411yescharacteristic
112C24×C53C2×D411yescharacteristic
113C24×C53C2×D411yescharacteristic
114C24×C53#4111yescharacteristic
115C24×C53#4111yescharacteristic
116C24×C53#4111yescharacteristic
117C24×C53#4111yescharacteristic
118C24×C53#4111yescharacteristic
119C24×C53#4111yescharacteristic
120C24×C53#4111yescharacteristic
121C24×C53#4111yescharacteristic
122C24×C53C2411yescharacteristic
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—82no—
128C23×D53C22⋊C412yes—
129C23×D53C22⋊C412yes—
130C23×D53C22×C412yes—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—41no—
137C22×C4×C53—41no—
138C22×C4×C53—41no—
139C22×C4×C53—41no—
140C22×C4×C53—82no—
141C22×C4×C53—82no—
142C22×C4×C53—82no—
143C2×C22⋊D53—22no—
144C2×C22⋊D53—22no—
145C2×C22⋊D53—22no—
146C2×C22⋊D53—22no—
147C2×C22⋊D53—22no—
148C2×C22⋊D53—22no—
149C2×C22⋊D53—22no—
150C2×C22⋊D53—22no—
151C2×C22⋊D53—22no—
152C2×C22⋊D53—22no—
153C2×C22⋊D53—22no—
154C2×C22⋊D53—22no—
155C2×C22⋊D53—22no—
156C2×C22⋊D53—22no—
157C2×C22⋊D53—22no—
158C2×C22⋊D53—22no—
159C2×C22⋊D53—22no—
160C2×C22⋊D53—22no—
161C2×C22⋊D53—22no—
162C2×C22⋊D53—22no—
163C2×C22⋊D53—22no—
164C2×C22⋊D53—22no—
165C2×C22⋊D53—22no—
166C2×C22⋊D53—22no—
167C2×C22⋊D53C22⋊C414yes—
168C2×C22⋊D53C22⋊C414yes—
169C2×C22⋊D53C2×D414yes—
170C2×C22⋊D53C2×D414yes—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—41no—
181C22×Dic53—41no—
182C22×Dic53—41no—
183C22×Dic53—41no—
184C22×Dic53—82no—
185C22×Dic53—82no—
186C22×Dic53—82no—
187C22×Dic53C22⋊C412yes—
188C22×Dic53C22⋊C412yes—
189C22×Dic53C22×C412yes—
190C2×C4×D53—28no—
191C2×C4×D53—84no—
192C22⋊C4×C53—22no—
193C22⋊C4×C53—22no—
194C22⋊C4×C53—22no—
195C22⋊C4×C53—22no—
196C22⋊C4×C53—22no—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—22no—
199C22⋊C4×C53—41no—
200C22⋊C4×C53—41no—
201C22⋊C4×C53—41no—
202C22⋊C4×C53—41no—
203C22⋊C4×C53C22×C414yes—
204C22⋊Dic53—22no—
205C22⋊Dic53—22no—
206C22⋊Dic53—22no—
207C22⋊Dic53—22no—
208C22⋊Dic53—22no—
209C22⋊Dic53—22no—
210C22⋊Dic53—22no—
211C22⋊Dic53—41no—
212C22⋊Dic53—41no—
213C22⋊Dic53—41no—
214C22⋊Dic53—41no—
215C22⋊Dic53C22×C414yes—
216#11719921—28no—
217#11719919—28no—
218C4×Dic53—28no—
219C23×C53—42no—
220C23×C53—42no—
221C23×C53—42no—
222C23×C53—42no—
223C23×C53—42no—
224C23×C53—42no—
225C23×C53—42no—
226C23×C53—81no—
227C23×C53—81no—
228C23×C53—81no—
229C23×C53—81no—
230C23×C53—81no—
231C23×C53—81no—
232C23×C53—81no—
233C23×C53—81no—
234C23×C53C2×C22⋊C411yescharacteristic
235C23×C53C2×C22⋊C411yescharacteristic
236C23×C53C2×C22⋊C411yescharacteristic
237C23×C53C2×C22⋊C411yescharacteristic
238C23×C53#11711yescharacteristic
239C23×C53#11711yescharacteristic
240C23×C53#11711yescharacteristic
241C23×C53#11711yescharacteristic
242C23×C53#11711yescharacteristic
243C23×C53#11711yescharacteristic
244C23×C53#11711yescharacteristic
245C23×C53#11711yescharacteristic
246C23×C53#12311yescharacteristic
247C23×C53#12311yescharacteristic
248C23×C53#12311yescharacteristic
249C23×C53#12311yescharacteristic
250C23×C53#12311yescharacteristic
251C23×C53#12311yescharacteristic
252C23×C53#12311yescharacteristic
253C23×C53#12311yescharacteristic
254C23×C53#12311yescharacteristic
255C23×C53#12311yescharacteristic
256C23×C53#12311yescharacteristic
257C23×C53#12311yescharacteristic
258C23×C53#12311yescharacteristic
259C23×C53#12311yescharacteristic
260C23×C53#12311yescharacteristic
261C23×C53#12311yescharacteristic
262C23×C53C23×C411yescharacteristic
263C23×C53C22×D411yescharacteristic
264C23×C53C22×D411yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C23×C53C2×#4111yescharacteristic
267C23×C53C2×#4111yescharacteristic
268C23×C53C2×#4111yescharacteristic
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—44no—
276C22×D53—82no—
277C22×D53—82no—
278C22×D53—82no—
279C22×D53—82no—
280C22×D53—82no—
281C22×D53—82no—
282C22×D53C2×C22⋊C414yes—
283C2×C4×C53—24no—
284C2×C4×C53—44no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—82no—
288C2×C4×C53—82no—
289C2×C4×C53—82no—
290C2×C4×C53—82no—
291C2×C4×C53—82no—
292C2×C4×C53—82no—
293C2×C4×C53—82no—
294C2×C4×C53—82no—
295C22⋊D53—24no—
296C22⋊D53—24no—
297C22⋊D53—24no—
298C22⋊D53—24no—
299C22⋊D53—24no—
300C22⋊D53—24no—
301C22⋊D53—24no—
302C22⋊D53—24no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—24no—
310C2×Dic53—44no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—82no—
314C2×Dic53—82no—
315C2×Dic53—82no—
316C2×Dic53—82no—
317C2×Dic53—82no—
318C2×Dic53—82no—
319C2×Dic53—82no—
320C2×Dic53—82no—
321C2×Dic53C2×C22⋊C414yes—
322C4×D53—88no—
323C2×#1828—531nomaximal, Sylow
324C22×C53—22no—
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×C53—41no—
348C22×C53—41no—
349C22×C53—41no—
350C22×C53—41no—
351C22×C53—41no—
352C22×C53—41no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53#38111yescharacteristic
360C22×C53#38111yescharacteristic
361C22×C53#38111yescharacteristic
362C22×C53#38111yescharacteristic
363C22×C53#38111yescharacteristic
364C22×C53#38111yescharacteristic
365C22×C53#38111yescharacteristic
366C22×C53#38111yescharacteristic
367C22×C53C22×C22⋊C411yescharacteristic
368C22×C53C2×#11711yescharacteristic
369C22×C53C2×#11711yescharacteristic
370C22×C53C2×#12311yescharacteristic
371C22×C53C2×#12311yescharacteristic
372C22×C53C2×#12311yescharacteristic
373C22×C53C2×#12311yescharacteristic
374C2×D53—24no—
375C2×D53—44no—
376C2×D53—44no—
377C2×D53—44no—
378C2×D53—82no—
379C2×D53—82no—
380C2×D53—82no—
381C2×D53—82no—
382C4×C53—44no—
383C4×C53—82no—
384C4×C53—82no—
385Dic53—24no—
386Dic53—44no—
387Dic53—82no—
388Dic53—82no—
389C2×#518—531no—
390C22×#99—531no—
391C22×#99—531no—
392#1828—538no—
393C2×#342—531no—
394C2×#342—531no—
395C2×#342—531no—
396C2×#342D5311yescharacteristic, complemented
397C2×C53—21no—
398C2×C53—21no—
399C2×C53—21no—
400C2×C53—21no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—21no—
404C2×C53—21no—
405C2×C53—21no—
406C2×C53—21no—
407C2×C53—21no—
408C2×C53—21no—
409C2×C53—21no—
410C2×C53—21no—
411C2×C53#182812yescomplemented
412C2×C53C2×#38111yescharacteristic
413D53—44no—
414C23×D4—531no—
415#518—534no—
416#518—534no—
417#518—1062no—
418#518—1062no—
419C2×C4×D4—1062no—
420C2×C4×D4—1062no—
421C2×#117—532no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4—532no—
424C22×C22⋊C4—531no—
425C22×C22⋊C4—531no—
426C22×C22⋊C4C2×D5311yescharacteristic
427C22×C22⋊C4C2×D5311yescharacteristic
428C22×C22⋊C4C2×D5311yescharacteristic
429C2×#99—534no—
430C2×#99—534no—
431C2×#99—1062no—
432C2×#99—1062no—
433C2×#99—1062no—
434C2×#99—1062no—
435#342—534no—
436#342—534no—
437#342—534no—
438#342C2×D5314yescomplemented
439C53C2×#182811yescharacteristic, complemented, Sylow
440C25—531no—
441C25C22×D5311yescharacteristic
442C22×D4—532no—
443C22×D4—532no—
444C22×D4—532no—
445C22×D4—532no—
446C22×D4—532no—
447C22×D4—532no—
448C22×D4—1061no—
449C22×D4—1061no—
450C22×D4—1061no—
451C22×D4—1061no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4—1061no—
455C22×D4—1061no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—531no—
460C23×C4—1062no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C4×D4—1068no—
465C4×D4—1068no—
466C4×D4—1068no—
467C4×D4—1068no—
468#117—538no—
469#117—1064no—
470C2×C4⋊C4—1062no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—532no—
485C2×C22⋊C4—532no—
486C2×C22⋊C4—532no—
487C2×C22⋊C4—538no—
488C2×C22⋊C4—532no—
489C2×C22⋊C4—532no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—1062no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4C4×D5312yes—
506C2×C22⋊C4C4×D5312yes—
507C2×C22⋊C4C22×D5312yes—
508C2×C22⋊C4C22×D5312yes—
509C2×C22⋊C4C22×D5312yes—
510C2×C42—1062no—
511#99—1068no—
512#99—1068no—
513C24—82no—
514C24—532no—
515C24—532no—
516C24—532no—
517C24—1061no—
518C24—1061no—
519C24—1061no—
520C24—1061no—
521C24—4242no—
522C24C2×C4×D5311yescharacteristic
523C24C2×C4×D5311yescharacteristic
524C24#1171994511yescharacteristic
525C24#1171994511yescharacteristic
526C24#1171994511yescharacteristic
527C24#1171994511yescharacteristic
528C24D4×D5311yescharacteristic
529C24D4×D5311yescharacteristic
530C24D4×D5311yescharacteristic
531C24D4×D5311yescharacteristic
532C24#1171994711yescharacteristic
533C24#1171994711yescharacteristic
534C24#1171994911yescharacteristic
535C24#1171994911yescharacteristic
536C24C23×D5311yescharacteristic
537C2×D4—534no—
538C2×D4—534no—
539C2×D4—534no—
540C2×D4—534no—
541C2×D4—1062no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—1062no—
545C2×D4—1062no—
546C2×D4—1062no—
547C2×D4—1062no—
548C2×D4—1062no—
549C2×D4—1062no—
550C2×D4—1062no—
551C2×D4—1062no—
552C2×D4—1062no—
553C2×D4—1062no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—1062no—
564C2×D4—1062no—
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—82no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—1068no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—4244no—
591C22×C4—4242no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4—2121no—
595C22×C4—2121no—
596C22×C4—2121no—
597C22×C4—2121no—
598C4⋊C4—1068no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—534no—
611C22⋊C4—1068no—
612C22⋊C4—1062no—
613C22⋊C4—1062no—
614C22⋊C4—1062no—
615C22⋊C4—1062no—
616C22⋊C4—1062no—
617C22⋊C4—1062no—
618C22⋊C4—1062no—
619C22⋊C4—2121no—
620C22⋊C4—2121no—
621C22⋊C4—2121no—
622C22⋊C4—2121no—
623C22⋊C4C2×C4×D5314yes—
624C42—1068no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—534no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—4242no—
648C23—4242no—
649C23—4242no—
650C23—4242no—
651C23—4242no—
652C23—4242no—
653C23—2124no—
654C23C22⋊C4×D5311yescharacteristic
655C23C22⋊C4×D5311yescharacteristic
656C23C22⋊C4×D5311yescharacteristic
657C23C22⋊C4×D5311yescharacteristic
658C23#1313317411yescharacteristic
659C23#1313317411yescharacteristic
660C23#1313317411yescharacteristic
661C23#1313317411yescharacteristic
662C23#1313317511yescharacteristic
663C23#1313317511yescharacteristic
664C23#1313317511yescharacteristic
665C23#1313317511yescharacteristic
666C23#1313319911yescharacteristic
667C23#1313319911yescharacteristic
668C23#1313319911yescharacteristic
669C23#1313319911yescharacteristic
670C23#1313319911yescharacteristic
671C23#1313319911yescharacteristic
672C23#1313319911yescharacteristic
673C23#1313319911yescharacteristic
674C23#1313320211yescharacteristic
675C23#1313320211yescharacteristic
676C23#1313320211yescharacteristic
677C23#1313320211yescharacteristic
678C23#1313320211yescharacteristic
679C23#1313320211yescharacteristic
680C23#1313320211yescharacteristic
681C23#1313320211yescharacteristic
682C23C22×C4×D5311yescharacteristic
683C23C2×D4×D5311yescharacteristic
684C23C2×D4×D5311yescharacteristic
685C23C2×#1171994711yescharacteristic
686C23C2×#1171994511yescharacteristic
687C23C2×#1171994511yescharacteristic
688C23C2×#1171994911yescharacteristic
689D4—1064no—
690D4—1064no—
691D4—1064no—
692D4—1064no—
693D4—1064no—
694D4—1064no—
695D4—1064no—
696D4—1064no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—534no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1064no—
717C2×C4—4248no—
718C2×C4—4242no—
719C2×C4—4242no—
720C2×C4—4242no—
721C2×C4—4242no—
722C2×C4—4242no—
723C2×C4—4242no—
724C2×C4—4242no—
725C2×C4—4242no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2124no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—1064no—
765C22—4242no—
766C22—4242no—
767C22—4242no—
768C22—4242no—
769C22—2124no—
770C22—2124no—
771C22—2124no—
772C22#1681048511yescharacteristic
773C22#1681048511yescharacteristic
774C22#1681048511yescharacteristic
775C22#1681048511yescharacteristic
776C22#1681048511yescharacteristic
777C22#1681048511yescharacteristic
778C22#1681048511yescharacteristic
779C22#1681048511yescharacteristic
780C22C2×C22⋊C4×D5311yescharacteristic
781C22C2×#1313317411yescharacteristic
782C22C2×#1313317511yescharacteristic
783C22C2×#1313319911yescharacteristic
784C22C2×#1313319911yescharacteristic
785C22C2×#1313320211yescharacteristic
786C22C2×#1313320211yescharacteristic
787C4—44no—
788C4—82no—
789C4—82no—
790C4—1064no—
791C4—4242no—
792C4—4242no—
793C4—2124no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—2124no—
809C2#2027482212yesdirect product factor
810C2C2×#1681048511yescharacteristic
subgroupG/H
centerC22#16810485
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC2×C53×#342C2
socleC22×C53#381
prime radicalC23×C22⋊D53C22
cosocleC24×C53C24
hypercenterC2×#342D53
hypocenterC53C2×#1828
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #20274822C2direct (N × H)
5. C2×#16810390C2semidirect
6. C2×#16810389C2semidirect
7. C2×#16810389C2semidirect
8. C2×C53×#342C2semidirect
12. #16811096C4semidirect
16. C2×#13133173C4semidirect
20. C2×C22⋊C4×D53C4semidirect
27. #16810390C22semidirect
28. #16810389C22semidirect
29. #16810389C22semidirect
33. C53×#342C22semidirect
59. #13133173C2×C4semidirect
81. C22⋊C4×D53C2×C4semidirect
396. C2×#342D53semidirect
411. C2×C53#1828semidirect
438. #342C2×D53semidirect
439. C53C2×#1828semidirect
809. C2#20274822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168110962
C22×#131331312
#202748222
C2×#168103902
C2×#168103892
C2×C53×#3422
C2×#182853