Finite Group Databasebeta

← C2×#20286796 #28260618

Subgroups — C2×#20286796 #28260618

Order 13568.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811330C211yesmaximal, characteristic, complemented
2#20286796C2116yesmaximal, direct product factor
3C2×#16810982C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810934C211yesmaximal, characteristic, complemented
6C2×#16810903C211yesmaximal, characteristic, complemented
7C2×#16810867C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810842C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810774C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C22×#13133138C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic, complemented
18C22×#11719923C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719917C2211yescharacteristic, complemented
21C23×#88322C2211yescharacteristic
22#16811330—24no—
23#16811330C2218yescomplemented
24C2×#13133217C2211yescharacteristic, complemented
25C2×#13133208—21no—
26C2×#13133196C2211yescharacteristic
27C2×#13133196C2211yescharacteristic, complemented
28C2×#13133194—21no—
29C2×#13133194—21no—
30C2×C4×Dic106C2211yescharacteristic, complemented
31C2×D4×Dic53—21no—
32C22×C4⋊Dic53C2211yescharacteristic
33C22×C4⋊Dic53C2211yescharacteristic, complemented
34#16810982C2218yescomplemented
35#16810956C2218yescomplemented
36#16810934C2218yescomplemented
37#16810903C2218yescomplemented
38#16810867C2218yescomplemented
39#16810862C2218yescomplemented
40#16810842C2218yescomplemented
41#16810785C2218yescomplemented
42#16810774C2218yescomplemented
43#16810723C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic, complemented
46C2×#13133150C2211yescharacteristic, complemented
47C2×#13133150C2211yescharacteristic, complemented
48C2×C4⋊#88322C2211yescharacteristic, complemented
49#16810624C2218yescomplemented
50C2×#13133141C2211yescharacteristic, complemented
51C2×#13133141C2211yescharacteristic, complemented
52C2×#13133141C2211yescharacteristic, complemented
53C2×#13133140C2211yescharacteristic, complemented
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2218yescomplemented
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic, complemented
63C2×#13133128C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C23×D4×C53C2211yescharacteristic
66C53×#546—24no—
67C53×#546C2218yes—
68C2×#124×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×#121×C53—21no—
72C2×#121×C53C2211yescharacteristic
73C2×#120×C53—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C22⋊C4×C53—21no—
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C23×Dic53—21no—
80C23×Dic53—21no—
81C2×#11719925—42no—
82C2×#11719925C2314yescomplemented
83C2×#11719923—24no—
84C2×#11719923—42no—
85C2×#11719923C2314yes—
86C2×#11719923C2314yes—
87C2×#11719917—42no—
88C2×#11719917C2314yescomplemented
89C22×#88322—42no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95#13133217—22no—
96#13133217C2314yescomplemented
97#13133208—28no—
98#13133196—22no—
99#13133196—22no—
100#13133196C2314yes—
101#13133196C2314yescomplemented
102#13133194—28no—
103#13133194—28no—
104C4×Dic106—22no—
105C4×Dic106C2314yescomplemented
106D4×Dic53—28no—
107C2×C4⋊Dic53—22no—
108C2×C4⋊Dic53—21no—
109C2×C4⋊Dic53—22no—
110C2×C4⋊Dic53—21no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2311yescharacteristic
113C2×C4⋊Dic53C2314yes—
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2311yescharacteristic
116C2×C4⋊Dic53C2314yescomplemented
117C2×#11719919—21no—
118C2×#11719919—21no—
119C2×#11719919—21no—
120C2×C22⋊Dic53—21no—
121C2×C22⋊Dic53—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yescomplemented
124#13133150C2314yescomplemented
125#13133150C2314yescomplemented
126C4⋊#88322C2314yescomplemented
127#13133141C2314yescomplemented
128#13133141C2314yescomplemented
129#13133141C2314yescomplemented
130#13133140C2314yescomplemented
131#13133138C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yescomplemented
139#13133128C2314yescomplemented
140C25×C53—21no—
141C2×#41×C53—22no—
142C2×#41×C53—24no—
143C2×#41×C53—42no—
144C2×#41×C53C2314yes—
145C22×Q8×C53C2311yescharacteristic
146C22×D4×C53—24no—
147C22×D4×C53—21no—
148C22×D4×C53—21no—
149C22×D4×C53—21no—
150C22×D4×C53—22no—
151C22×D4×C53—42no—
152C22×D4×C53D411yescharacteristic
153C22×D4×C53C2311yescharacteristic
154C22×D4×C53C2314yes—
155C22×D4×C53C2311yescharacteristic
156C23×C4×C53—21no—
157C23×C4×C53—21no—
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160#124×C53—22no—
161#124×C53C2314yes—
162#123×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53C2314yes—
165#121×C53—28no—
166#121×C53—22no—
167#121×C53C2314yes—
168#120×C53—28no—
169C4×D4×C53—22no—
170C4×D4×C53D414yes—
171C4×D4×C53C2314yes—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—28no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—24no—
188C24×C53—44no—
189C24×C53—44no—
190C24×C53—82no—
191C24×C53C2×D411yescharacteristic
192C24×C53C2×D411yescharacteristic
193#41×C53—28no—
194#41×C53—44no—
195#41×C53—48no—
196C2×Q8×C53—21no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53C2412yes—
200C2×D4×C53—24no—
201C2×D4×C53—28no—
202C2×D4×C53—24no—
203C2×D4×C53—24no—
204C2×D4×C53—21no—
205C2×D4×C53—24no—
206C2×D4×C53—21no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—44no—
211C2×D4×C53—48no—
212C2×D4×C53—44no—
213C2×D4×C53—44no—
214C2×D4×C53—82no—
215C2×D4×C53C2×D414yes—
216C2×D4×C53#4114yes—
217C2×D4×C53C2412yes—
218C2×D4×C53C2412yes—
219C22×C4×C53—22no—
220C22×C4×C53—22no—
221C22×C4×C53—22no—
222C22×C4×C53—22no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—24no—
226C22×C4×C53—24no—
227C22×C4×C53—44no—
228C22×C4×C53—82no—
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2412yes—
236C22×C4×C53C2412yes—
237C22×C4×C53C2411yescharacteristic
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—24no—
243C22×Dic53—24no—
244C22×Dic53—82no—
245C22×Dic53—82no—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106—24no—
250C2×Dic106—82no—
251C2×Dic106C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2×D414yes—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C22⋊C4×C53—24no—
261C22⋊C4×C53C2×D414yes—
262C22⋊C4×C53C2×D414yes—
263C42×C53C2×D412yes—
264C42×C53C2412yes—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267#11719925—44no—
268#11719923—28no—
269#11719923—44no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—24no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282C4×Dic53—24no—
283#11719917—44no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322—44no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—24no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—48no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—48no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—84no—
309C23×C53—816no—
310C23×C53#13714yes—
311C23×C53C22×D412yes—
312C23×C53C22×D412yes—
313C23×C53C22×D411yescharacteristic
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—42no—
317D4×C53—28no—
318D4×C53—24no—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—22no—
322D4×C53—48no—
323D4×C53—48no—
324D4×C53—42no—
325D4×C53—84no—
326D4×C53C2×#4114yes—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—24no—
332C2×C4×C53—24no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—48no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—84no—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D412yes—
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53C2×#4112yes—
349C2×C4×C53H(5,𝔽2)12yes—
350C2×C4×C53C2511yescharacteristic
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—42no—
356C2×Dic53—42no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53—84no—
360C2×Dic53—84no—
361Dic106—22no—
362Dic106—22no—
363Dic106—42no—
364Dic106—84no—
365#88322—22no—
366#88322—22no—
367#88322—22no—
368#88322—22no—
369C2×#3314—531nomaximal, Sylow
370C22×C53—22no—
371C22×C53—28no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—24no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—44no—
378C22×C53—48no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53—42no—
383C22×C53—42no—
384C22×C53—816no—
385C22×C53—84no—
386C22×C53#54612yes—
387C22×C53C2×#13714yes—
388C22×C53C2×#13712yes—
389C22×C53#57612yes—
390C22×C53C23×D411yescharacteristic
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—22no—
394C4×C53—22no—
395C4×C53—42no—
396C4×C53—42no—
397C4×C53#54612yes—
398C4×C53C22×#4111yescharacteristic
399C4×C53C2×H(5,𝔽2)11yescharacteristic
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#554—531no—
405C2×#546D5311yescharacteristic
406#3314—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480—531no—
410C2×#474—531no—
411C2×#468—531no—
412C2×#467—531no—
413C2×#464—531no—
414C2×#452—531no—
415C2×#450—531no—
416C2×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#102—531no—
420C2×C53—24no—
421C2×C53—42no—
422C2×C53—44no—
423C2×C53—82no—
424C2×C53#331414yescomplemented
425C2×C53C2×#54611yescharacteristic
426C2×C53C22×#13711yescharacteristic
427C2×C53C2×#57611yescharacteristic
428C22×#41C2×D5311yescharacteristic
429C23×D4C2×D5311yescharacteristic
430C22×Q16—531no—
431C22×SD16—531no—
432C22×SD16—531no—
433C22×M16—531no—
434C23×C8—531no—
435#554—538no—
436#554—1064no—
437#546—24no—
438#546C2×D5318yes—
439C2×C4⋊Q8—531no—
440C2×#125—1061no—
441C2×#124C2×D5311yescharacteristic
442C2×#123—21no—
443C2×C22⋊Q8—531no—
444C2×C22⋊Q8—531no—
445C2×C22⋊Q8—1061no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8C2×D5311yescharacteristic
448C2×#121—21no—
449C2×#121C2×D5311yescharacteristic
450C2×#120—21no—
451C2×C4×Q8—531no—
452C2×C4×D4—1061no—
453C2×C4×D4C2×D5311yescharacteristic
454C2×C4×D4C2×D5311yescharacteristic
455C22×C4⋊C4—531no—
456C22×C4⋊C4—531no—
457C22×C22⋊C4—21no—
458#489—538no—
459#484—538no—
460#480—538no—
461#474—538no—
462#468—538no—
463#467—538no—
464#464—538no—
465#452—538no—
466#450—538no—
467#440—538no—
468#435—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107—531no—
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—538no—
484C2×#102—531no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×#97—531no—
488C53C2×#331411yescharacteristic, complemented, Sylow
489C25—21no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D5314yes—
494C22×Q8—531no—
495C22×Q8—1061no—
496C22×Q8C22×D5311yescharacteristic
497C22×D4—24no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—42no—
503C22×D4C22⋊D5311yescharacteristic
504C22×D4C22×D5311yescharacteristic
505C22×D4C22×D5314yes—
506C22×D4C22×D5311yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—1061no—
510C23×C4—1061no—
511C23×C4C22×D5311yescharacteristic
512C23×C4C22×D5311yescharacteristic
513C2×Q16—534no—
514C2×Q16—2122no—
515C2×SD16—534no—
516C2×SD16—534no—
517C2×SD16—1064no—
518C2×SD16—2122no—
519C2×M16—534no—
520C2×M16—2122no—
521C22×C8—531no—
522C22×C8—531no—
523C22×C8—531no—
524C22×C8—531no—
525C22×C8—534no—
526C22×C8—2122no—
527C4⋊Q8—534no—
528C4⋊Q8—1062no—
529#125—1068no—
530#124—22no—
531#124C22×D5314yes—
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—534no—
535C22⋊Q8—534no—
536C22⋊Q8—1062no—
537C22⋊Q8—1062no—
538C22⋊Q8—1068no—
539C22⋊Q8—1068no—
540C22⋊Q8C22×D5314yes—
541#121—22no—
542#121—28no—
543#121C22×D5314yes—
544#120—28no—
545C4×Q8—534no—
546C4×Q8—1062no—
547C4×D4—22no—
548C4×D4—1068no—
549C4×D4C22⋊D5314yes—
550C4×D4C22×D5314yes—
551C4×D4C22×D5314yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—534no—
557C2×C4⋊C4—534no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1062no—
561C2×C4⋊C4—1062no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4C22⋊D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—28no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4C22⋊D5311yescharacteristic
577C2×C22⋊C4C22⋊D5311yescharacteristic
578C2×C42—1061no—
579C2×C42C22×D5311yescharacteristic
580#107—534no—
581#107—534no—
582#107—534no—
583C4⋊C8—534no—
584#103—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#102—534no—
589#102—534no—
590#102—534no—
591#102—534no—
592#102—534no—
593#102—534no—
594C22⋊C8—534no—
595C22⋊C8—534no—
596#97—534no—
597C24—21no—
598C24—21no—
599C24—24no—
600C24—44no—
601C24—44no—
602C24—82no—
603C24C2×C22⋊D5311yescharacteristic
604C24C2×C22⋊D5311yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—532no—
612C2×Q8—1064no—
613C2×Q8—1061no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—4242no—
617C2×Q8C23×D5312yes—
618C2×D4—24no—
619C2×D4—28no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—48no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—82no—
633C2×D4#1171994714yes—
634C2×D4C2×C22⋊D5314yes—
635C2×D4C23×D5312yes—
636C2×D4C23×D5312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—44no—
646C22×C4—82no—
647C22×C4—1064no—
648C22×C4—1064no—
649C22×C4—1061no—
650C22×C4—1061no—
651C22×C4—1061no—
652C22×C4—1061no—
653C22×C4—4242no—
654C22×C4—4242no—
655C22×C4C2×C22⋊D5312yes—
656C22×C4C2×C22⋊D5312yes—
657C22×C4C2×C22⋊D5311yescharacteristic
658C22×C4C2×C22⋊D5311yescharacteristic
659C22×C4C2×C22⋊D5311yescharacteristic
660C22×C4C2×C22⋊D5311yescharacteristic
661C22×C4C23×D5312yes—
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—2124no—
665SD16—1068no—
666SD16—2124no—
667M16—2124no—
668C2×C8—532no—
669C2×C8—532no—
670C2×C8—532no—
671C2×C8—532no—
672C2×C8—1062no—
673C2×C8—1062no—
674C2×C8—1062no—
675C2×C8—1062no—
676C2×C8—2124no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—532no—
680C4⋊C4—532no—
681C4⋊C4—532no—
682C4⋊C4—1061no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1061no—
686C4⋊C4—1061no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4C2×C22⋊D5314yes—
692C4⋊C4C23×D5312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4C2×C22⋊D5314yes—
701C22⋊C4C2×C22⋊D5314yes—
702C42—1064no—
703C42C2×C22⋊D5312yes—
704C42C23×D5312yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—48no—
718C23—42no—
719C23—42no—
720C23—84no—
721C23—816no—
722C23#1313324714yes—
723C23C22×C22⋊D5312yes—
724C23C22×C22⋊D5312yes—
725C23C22×C22⋊D5311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1062no—
730Q8—1062no—
731Q8—4244no—
732Q8—2122no—
733D4—28no—
734D4—24no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—48no—
740D4—42no—
741D4—84no—
742D4C2×#1171994714yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—84no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—4244no—
764C2×C4—4244no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4C22×C22⋊D5312yes—
770C2×C4C22×C22⋊D5312yes—
771C2×C4C22×C22⋊D5312yes—
772C2×C4C22×C22⋊D5312yes—
773C2×C4C22×C22⋊D5311yescharacteristic
774C2×C4C2×#1171994712yes—
775C2×C4#1313326212yes—
776C2×C4C24×D5311yescharacteristic
777C8—1062no—
778C8—1062no—
779C8—1062no—
780C8—1062no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—24no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—48no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—816no—
796C22—84no—
797C22#1681126712yes—
798C22C2×#1313324714yes—
799C22C2×#1313324712yes—
800C22#1681142612yes—
801C22C23×C22⋊D5311yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—2122no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126712yes—
813C4C22×#1171994711yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—24no—
816C2—42no—
817C2—44no—
818C2—82no—
819C2#2028679614yesdirect product factor
820C2C2×#1681126711yescharacteristic
821C2C22×#1313324711yescharacteristic
822C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3314
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16811330C2semidirect
2. #20286796C2direct (N × H)
3. C2×#16810982C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810934C2semidirect
6. C2×#16810903C2semidirect
7. C2×#16810867C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810842C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810774C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810624C2semidirect
15. C22×#13133138C2semidirect
17. C22×#11719925C22semidirect
20. C22×#11719917C22semidirect
23. #16811330C22semidirect
24. C2×#13133217C22semidirect
27. C2×#13133196C22semidirect
30. C2×C4×Dic106C22semidirect
33. C22×C4⋊Dic53C22semidirect
34. #16810982C22semidirect
35. #16810956C22semidirect
36. #16810934C22semidirect
37. #16810903C22semidirect
38. #16810867C22semidirect
39. #16810862C22semidirect
40. #16810842C22semidirect
41. #16810785C22semidirect
42. #16810774C22semidirect
43. #16810723C22semidirect
44. #16810695C22semidirect
45. C2×#13133150C22semidirect
46. C2×#13133150C22semidirect
47. C2×#13133150C22semidirect
48. C2×C4⋊#88322C22semidirect
49. #16810624C22semidirect
50. C2×#13133141C22semidirect
51. C2×#13133141C22semidirect
52. C2×#13133141C22semidirect
53. C2×#13133140C22semidirect
60. C2×#13133138C22semidirect
62. C2×C22⋊#88322C22semidirect
63. C2×#13133128C22semidirect
82. C2×#11719925C23semidirect
88. C2×#11719917C23semidirect
96. #13133217C23semidirect
101. #13133196C23semidirect
105. C4×Dic106C23semidirect
116. C2×C4⋊Dic53C23semidirect
123. #13133150C23semidirect
124. #13133150C23semidirect
125. #13133150C23semidirect
126. C4⋊#88322C23semidirect
127. #13133141C23semidirect
128. #13133141C23semidirect
129. #13133141C23semidirect
130. #13133140C23semidirect
138. C22⋊#88322C23semidirect
139. #13133128C23semidirect
424. C2×C53#3314semidirect
488. C53C2×#3314semidirect
819. C2#20286796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113302
#202867962
C2×#168109822
C2×#168109562
C2×#168109342
C2×#168109032
C2×#168108672
C2×#168108622
C2×#168108422
C2×#168107852
C2×#168107742
C2×#168107232
C2×#168106952
C2×#168106242
C22×#131331382
C2×C53×#5462
C2×#331453