Finite Group Databasebeta

← C2×#20285597 #28254778

Subgroups — C2×#20285597 #28254778

Order 13568.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic
2#20285597C2116yesmaximal, direct product factor
3C2×#16810956C211yesmaximal, characteristic, complemented
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810951C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810862C211yesmaximal, characteristic, complemented
10C2×#16810854C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810783C211yesmaximal, characteristic, complemented
13C2×#16810779C211yesmaximal, characteristic, complemented
14C2×#16810762C211yesmaximal, characteristic, complemented
15C2×#16810590C211yesmaximal, characteristic, complemented
16C2×C53×#536C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811201—24no—
25#16811201C2218yes—
26C2×#13133196C2211yescharacteristic
27C2×#13133196C2211yescharacteristic
28C2×#13133193—21no—
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133189—21no—
32C2×#13133189—21no—
33C2×#13133188—21no—
34C22×C4⋊Dic53C2211yescharacteristic
35#16810964C2218yescomplemented
36#16810956C2218yescomplemented
37#16810951C2218yescomplemented
38#16810947C2218yescomplemented
39#16810879C2218yescomplemented
40#16810871C2218yescomplemented
41#16810862C2218yescomplemented
42#16810854C2218yescomplemented
43#16810783C2218yescomplemented
44#16810783C2218yescomplemented
45#16810779C2218yescomplemented
46#16810762C2218yescomplemented
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59#16810590C2218yescomplemented
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C22⋊#88322C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C23×Q8×C53C2211yescharacteristic
66C53×#536—24no—
67C53×#536C2218yescomplemented
68C2×C4⋊Q8×C53—21no—
69C2×#124×C53—21no—
70C2×#123×C53—21no—
71C2×#123×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C2×C22⋊Q8×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C2×#11719925—42no—
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C2×#11719925C2314yes—
92C2×#11719924—42no—
93C2×#11719924—42no—
94C2×#11719924C2314yes—
95C2×#11719924C2314yes—
96C2×#11719917—42no—
97C2×#11719917C2314yes—
98C22×#88322—42no—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103C22×#88322C2314yes—
104#13133196—22no—
105#13133196—22no—
106#13133196C2314yes—
107#13133196C2314yes—
108#13133193—28no—
109#13133191—22no—
110#13133191—22no—
111#13133191C2314yes—
112#13133191C2314yes—
113#13133189—28no—
114#13133189—28no—
115#13133188—28no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—22no—
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2314yes—
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×C22⋊Dic53—21no—
124C2×C22⋊Dic53—21no—
125C2×#11719921—21no—
126C2×#11719921—21no—
127#13133150C2314yes—
128#13133150C2314yes—
129#13133148C2314yes—
130#13133148C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133141C2314yes—
134#13133141C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133137C2314yes—
138#13133137C2314yes—
139C22⋊#88322C2314yes—
140C22⋊#88322C2314yes—
141C22⋊#88322C2314yes—
142C22⋊#88322C2314yes—
143C2×#41×C53—42no—
144C2×#41×C53—42no—
145C2×#41×C53D414yes—
146C2×#41×C53C2314yes—
147C22×Q8×C53—21no—
148C22×Q8×C53—22no—
149C22×Q8×C53—42no—
150C22×Q8×C53—42no—
151C22×Q8×C53D411yescharacteristic
152C22×Q8×C53C2311yescharacteristic
153C22×Q8×C53C2311yescharacteristic
154C22×Q8×C53C2314yes—
155C22×D4×C53D411yescharacteristic
156C22×D4×C53D411yescharacteristic
157C22×D4×C53D411yescharacteristic
158C23×C4×C53—21no—
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C4⋊Q8×C53—28no—
163#124×C53—28no—
164#123×C53—28no—
165#123×C53—28no—
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53—22no—
169C22⋊Q8×C53—22no—
170C22⋊Q8×C53C2314yes—
171C22⋊Q8×C53C2314yes—
172C22⋊Q8×C53C2314yes—
173C22⋊Q8×C53C2314yes—
174#117×C53—22no—
175#117×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C22⋊C4×C53—21no—
187C2×C42×C53—21no—
188C24×C53C2×D411yescharacteristic
189C24×C53C2×D411yescharacteristic
190C24×C53C2×D411yescharacteristic
191C23×D53—21no—
192#41×C53—48no—
193#41×C53—44no—
194#41×C53—44no—
195C2×Q8×C53—21no—
196C2×Q8×C53—21no—
197C2×Q8×C53—24no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53—42no—
203C2×Q8×C53—44no—
204C2×Q8×C53—44no—
205C2×Q8×C53—44no—
206C2×Q8×C53—48no—
207C2×Q8×C53C2×D414yes—
208C2×Q8×C53C2412yes—
209C2×Q8×C53C2412yes—
210C2×D4×C53—42no—
211C2×D4×C53—42no—
212C2×D4×C53—42no—
213C2×D4×C53C2×D414yes—
214C2×D4×C53C2×D414yes—
215C2×D4×C53C2×D414yes—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—22no—
220C22×C4×C53—22no—
221C22×C4×C53—22no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—24no—
227C22×C4×C53—44no—
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2412yes—
235C22×C4×C53C2412yes—
236C22×C4×C53C2412yes—
237C22×C4×C53C2411yescharacteristic
238C2×C22⋊D53—24no—
239C2×C22⋊D53—24no—
240C2×C22⋊D53—24no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53—82no—
243C2×C22⋊D53—82no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—24no—
248C22×Dic53—82no—
249#11719945—44no—
250#11719945—44no—
251#11719945—48no—
252C2×D212—22no—
253C2×D212—22no—
254C2×D212—21no—
255C2×D212C2412yes—
256C2×C4×D53—24no—
257C2×C4×D53—44no—
258C2×Dic106—22no—
259C2×Dic106—22no—
260C2×Dic106—21no—
261C2×Dic106C2412yes—
262C4⋊C4×C53—24no—
263C4⋊C4×C53—24no—
264C4⋊C4×C53—24no—
265C4⋊C4×C53—24no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53C2412yes—
269C4⋊C4×C53C2412yes—
270C22⋊C4×C53—24no—
271C22⋊C4×C53—24no—
272C22⋊C4×C53—24no—
273C22⋊C4×C53—24no—
274C22⋊C4×C53—24no—
275C42×C53—24no—
276C22⋊Dic53—24no—
277C22⋊Dic53—24no—
278#11719925—44no—
279#11719925—44no—
280#11719924—44no—
281#11719924—44no—
282#11719921—24no—
283#11719921—24no—
284C4⋊Dic53—24no—
285C4⋊Dic53—21no—
286C4⋊Dic53—21no—
287C4⋊Dic53C2412yes—
288C4⋊Dic53C2412yes—
289#11719919—24no—
290#11719919—24no—
291#11719917—44no—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322—22no—
295C2×#88322—22no—
296C2×#88322—44no—
297C2×#88322C2412yes—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300C2×#88322C2412yes—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53C22×D412yes—
311C23×C53C22×D412yes—
312C23×C53C22×D412yes—
313C23×C53C22×D411yescharacteristic
314C22×D53—22no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318Q8×C53—22no—
319Q8×C53—22no—
320Q8×C53—22no—
321Q8×C53—22no—
322Q8×C53—44no—
323Q8×C53—48no—
324Q8×C53—42no—
325Q8×C53—42no—
326D4×C53—44no—
327D4×C53—44no—
328D4×C53—44no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—24no—
333C2×C4×C53—24no—
334C2×C4×C53—24no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—48no—
346C2×C4×C53—42no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D411yescharacteristic
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53H(5,𝔽2)12yes—
356C2×C4×C53C2511yescharacteristic
357C22⋊D53—48no—
358C22⋊D53—84no—
359C22⋊D53—84no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—42no—
364C2×Dic53—42no—
365C2×Dic53—42no—
366C2×Dic53—84no—
367D212—22no—
368D212—22no—
369D212—42no—
370C4×D53—48no—
371Dic106—22no—
372Dic106—22no—
373Dic106—42no—
374#88322—22no—
375#88322—22no—
376#88322—22no—
377#88322—22no—
378C2×#3201—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—44no—
389C22×C53—44no—
390C22×C53—44no—
391C22×C53#53412yes—
392C22×C53#57712yes—
393C22×C53#57812yes—
394C22×C53C23×D411yescharacteristic
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—84no—
399C4×C53—22no—
400C4×C53—22no—
401C4×C53—22no—
402C4×C53—42no—
403C4×C53—42no—
404C4×C53—42no—
405C4×C53—42no—
406C4×C53#53412yes—
407C4×C53C2×H(5,𝔽2)11yescharacteristic
408C4×C53C2×H(5,𝔽2)11yescharacteristic
409Dic53—42no—
410Dic53—42no—
411Dic53—42no—
412C2×#537—531no—
413C2×#536D5311yescharacteristic, complemented
414#3201—5316no—
415C2×#484—531no—
416C2×#485—531no—
417C2×#482—531no—
418C2×#483—531no—
419C2×#470—531no—
420C2×#468—531no—
421C2×#467—531no—
422C2×#465—531no—
423C2×#452—531no—
424C2×#452—531no—
425C2×#451—531no—
426C2×#448—531no—
427C2×#408—531no—
428C2×C53—42no—
429C2×C53—42no—
430C2×C53—42no—
431C2×C53#320114yescomplemented
432C2×C53C2×#53411yescharacteristic
433C2×C53C2×#57711yescharacteristic
434C2×C53C2×#57811yescharacteristic
435D53—82no—
436C22×#41—531no—
437C22×#41C2×D5311yescharacteristic
438C23×Q8C2×D5311yescharacteristic
439C22×Q16—531no—
440C22×Q16—531no—
441C22×SD16—531no—
442C22×SD16—531no—
443C22×M16—531no—
444C23×C8—531no—
445#537—538no—
446#537—1064no—
447#536—24no—
448#536C2×D5318yescomplemented
449C2×C4⋊Q8—21no—
450C2×#124—21no—
451C2×#123—21no—
452C2×#123—21no—
453C2×C22⋊Q8—531no—
454C2×C22⋊Q8—531no—
455C2×C22⋊Q8—1061no—
456C2×C22⋊Q8C2×D5311yescharacteristic
457C2×C22⋊Q8C2×D5311yescharacteristic
458C2×C22⋊Q8C2×D5311yescharacteristic
459C2×C22⋊Q8C2×D5311yescharacteristic
460C2×#121—531no—
461C2×#121—531no—
462C2×#121—1061no—
463C2×#121—1061no—
464C2×#121—1061no—
465C2×#117C2×D5311yescharacteristic
466C22×C4⋊C4—531no—
467#485—538no—
468#484—538no—
469#483—538no—
470#482—538no—
471#470—538no—
472#468—538no—
473#467—538no—
474#465—538no—
475#452—538no—
476#452—538no—
477#451—538no—
478#448—538no—
479C2×#107—531no—
480C2×#107—531no—
481C2×#106—531no—
482C2×#106—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#103—531no—
487C2×#103—531no—
488C2×#103—531no—
489C2×#102—531no—
490C2×#102—531no—
491#408—538no—
492C2×C22⋊C8—531no—
493C2×C22⋊C8—531no—
494C2×C22⋊C8—531no—
495C2×C22⋊C8—531no—
496C53C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—534no—
500C2×#41—1062no—
501C2×#41—2122no—
502C2×#41—2122no—
503C2×#41C22⋊D5314yes—
504C2×#41C22×D5314yes—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—42no—
508C22×Q8—42no—
509C22×Q8—531no—
510C22×Q8C22⋊D5311yescharacteristic
511C22×Q8C22×D5311yescharacteristic
512C22×Q8C22×D5311yescharacteristic
513C22×Q8C22×D5314yes—
514C22×D4—531no—
515C22×D4—1061no—
516C22×D4—1061no—
517C22×D4—1061no—
518C22×D4C22⋊D5311yescharacteristic
519C22×D4C22⋊D5311yescharacteristic
520C22×D4C22⋊D5311yescharacteristic
521C23×C4—21no—
522C23×C4—1061no—
523C23×C4—1061no—
524C23×C4C22×D5311yescharacteristic
525C23×C4C22×D5311yescharacteristic
526C23×C4C22×D5311yescharacteristic
527C2×Q16—534no—
528C2×Q16—534no—
529C2×Q16—2122no—
530C2×Q16—2122no—
531C2×SD16—534no—
532C2×SD16—534no—
533C2×SD16—2122no—
534C2×SD16—2122no—
535C2×M16—534no—
536C2×M16—2122no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—531no—
540C22×C8—531no—
541C22×C8—534no—
542C22×C8—2122no—
543C4⋊Q8—28no—
544#124—28no—
545#123—28no—
546#123—28no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—534no—
552C22⋊Q8—534no—
553C22⋊Q8—1068no—
554C22⋊Q8—1062no—
555C22⋊Q8—1062no—
556C22⋊Q8C22×D5314yes—
557C22⋊Q8C22×D5314yes—
558C22⋊Q8C22×D5314yes—
559C22⋊Q8C22×D5314yes—
560#121—534no—
561#121—534no—
562#121—1068no—
563#121—1068no—
564#121—1068no—
565#121—1062no—
566#121—1062no—
567#117—22no—
568#117C22×D5314yes—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—531no—
574C2×C4⋊C4—531no—
575C2×C4⋊C4—534no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1062no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4C22×D5311yescharacteristic
581C2×C4⋊C4C22×D5311yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C42—21no—
592#107—534no—
593#107—534no—
594#106—534no—
595#106—534no—
596#103—534no—
597#103—534no—
598#103—534no—
599#103—534no—
600#103—534no—
601#103—534no—
602#102—534no—
603#102—534no—
604C22⋊C8—534no—
605C22⋊C8—534no—
606C22⋊C8—534no—
607C22⋊C8—534no—
608C24—1061no—
609C24C2×C22⋊D5311yescharacteristic
610C24C2×C22⋊D5311yescharacteristic
611C24C2×C22⋊D5311yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—2124no—
616#41—2124no—
617#41—2128no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—48no—
630C2×Q8—532no—
631C2×Q8—1061no—
632C2×Q8—1062no—
633C2×Q8—1062no—
634C2×Q8C2×C22⋊D5314yes—
635C2×Q8C23×D5312yes—
636C2×Q8C23×D5312yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—532no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1061no—
645C2×D4—1062no—
646C2×D4—1062no—
647C2×D4—4242no—
648C2×D4—4242no—
649C2×D4—2124no—
650C2×D4C2×C22⋊D5314yes—
651C2×D4C2×C22⋊D5314yes—
652C2×D4C2×C22⋊D5314yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—44no—
665C22×C4—1064no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—1061no—
669C22×C4—1064no—
670C22×C4—4242no—
671C22×C4—2124no—
672C22×C4C2×C22⋊D5312yes—
673C22×C4C2×C22⋊D5312yes—
674C22×C4C2×C22⋊D5312yes—
675C22×C4C2×C22⋊D5311yescharacteristic
676C22×C4C2×C22⋊D5311yescharacteristic
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C23×D5312yes—
679C22×C4C23×D5312yes—
680C22×C4C23×D5312yes—
681C22×C4C23×D5311yescharacteristic
682Q16—2124no—
683Q16—2124no—
684SD16—2124no—
685SD16—2124no—
686M16—2124no—
687C2×C8—532no—
688C2×C8—532no—
689C2×C8—532no—
690C2×C8—532no—
691C2×C8—1062no—
692C2×C8—1062no—
693C2×C8—1062no—
694C2×C8—1062no—
695C2×C8—2124no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—532no—
703C4⋊C4—532no—
704C4⋊C4—1064no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1064no—
708C4⋊C4—1064no—
709C4⋊C4C23×D5312yes—
710C4⋊C4C23×D5312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4—1064no—
720C42—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—1062no—
731C23—2122no—
732C23—2122no—
733C23—2122no—
734C23C22×C22⋊D5312yes—
735C23C22×C22⋊D5312yes—
736C23C22×C22⋊D5312yes—
737C23C22×C22⋊D5311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—1062no—
747Q8—1062no—
748Q8—2122no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—1062no—
753D4—1062no—
754D4—4244no—
755D4—4244no—
756D4—2128no—
757D4—2122no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—4244no—
783C2×C4—2128no—
784C2×C4—2122no—
785C2×C4—2122no—
786C2×C4—2122no—
787C2×C4C22×C22⋊D5312yes—
788C2×C4C22×C22⋊D5312yes—
789C2×C4C22×C22⋊D5312yes—
790C2×C4C22×C22⋊D5311yescharacteristic
791C2×C4#1313326212yes—
792C2×C4#1313326212yes—
793C2×C4C24×D5311yescharacteristic
794C8—1062no—
795C8—1062no—
796C8—1062no—
797C8—1062no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—4244no—
811C22—2122no—
812C22—2122no—
813C22—2122no—
814C22#1681118212yes—
815C22#1681143112yes—
816C22#1681143812yes—
817C22C23×C22⋊D5311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—2122no—
826C4—2122no—
827C4—2122no—
828C4#1681118212yes—
829C4C2×#1313326211yescharacteristic
830C4C2×#1313326211yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—4242no—
835C2#2028559714yesdirect product factor
836C2C2×#1681118211yescharacteristic
837C2C2×#1681143111yescharacteristic
838C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#536C2
socleC23×C53C22×D4
prime radicalC2×#16811201C2
hypercenterC2×#536D53
hypocenterC53C2×#3201
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #20285597C2direct (N × H)
3. C2×#16810956C2semidirect
4. C2×#16810964C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810951C2semidirect
7. C2×#16810879C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810862C2semidirect
10. C2×#16810854C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810783C2semidirect
13. C2×#16810779C2semidirect
14. C2×#16810762C2semidirect
15. C2×#16810590C2semidirect
16. C2×C53×#536C2semidirect
35. #16810964C22semidirect
36. #16810956C22semidirect
37. #16810951C22semidirect
38. #16810947C22semidirect
39. #16810879C22semidirect
40. #16810871C22semidirect
41. #16810862C22semidirect
42. #16810854C22semidirect
43. #16810783C22semidirect
44. #16810783C22semidirect
45. #16810779C22semidirect
46. #16810762C22semidirect
59. #16810590C22semidirect
67. C53×#536C22semidirect
413. C2×#536D53semidirect
431. C2×C53#3201semidirect
448. #536C2×D53semidirect
496. C53C2×#3201semidirect
835. C2#20285597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112012
#202855972
C2×#168109562
C2×#168109642
C2×#168109472
C2×#168109512
C2×#168108792
C2×#168108712
C2×#168108622
C2×#168108542
C2×#168107832
C2×#168107792
C2×#168107622
C2×#168105902
C2×C53×#5362
C2×#320153