Finite Group Databasebeta

← C2×#20285818 #28255481

Subgroups — C2×#20285818 #28255481

Order 13568.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811199C211yesmaximal, characteristic, complemented
2#20285818C2116yesmaximal, direct product factor
3C2×#16811018C211yesmaximal, characteristic, complemented
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810985C211yesmaximal, characteristic, complemented
6C2×#16810975C211yesmaximal, characteristic, complemented
7C2×#16810845C211yesmaximal, characteristic, complemented
8C2×#16810833C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810828C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic
13C2×#16810778C211yesmaximal, characteristic, complemented
14C2×#16810761C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#542C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719923C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719923C2211yescharacteristic
25C22×#11719924C2211yescharacteristic
26C22×#11719922C2211yescharacteristic
27#16811199—24no—
28#16811199C2218yescomplemented
29C2×#13133217C2211yescharacteristic
30C2×#13133217C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133205C2211yescharacteristic
33C2×#13133201—21no—
34C2×#13133201—21no—
35C2×#13133197—21no—
36C2×#13133197—21no—
37#16811018C2218yescomplemented
38#16811005C2218yescomplemented
39#16810985C2218yescomplemented
40#16810975C2218yescomplemented
41#16810845C2218yescomplemented
42#16810838C2218yescomplemented
43#16810833C2218yescomplemented
44#16810828C2218yescomplemented
45#16810783C2218yescomplemented
46#16810778C2218yescomplemented
47#16810766C2218yes—
48#16810761C2218yescomplemented
49#16810684C2218yescomplemented
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#542—24no—
65C53×#542C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#123×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106—22no—
83C22×Dic106—42no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2314yes—
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C2×#11719925—42no—
94C2×#11719925—42no—
95C2×#11719925—42no—
96C2×#11719925C2314yes—
97C2×#11719925C2314yes—
98C2×#11719925C2314yes—
99C2×#11719923—42no—
100C2×#11719923—42no—
101C2×#11719923—42no—
102C2×#11719923C2314yes—
103C2×#11719923C2314yes—
104C2×#11719923C2314yes—
105C2×#11719924—42no—
106C2×#11719924C2314yes—
107C2×#11719922—42no—
108C2×#11719922C2314yes—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111C22×#88322C2311yescharacteristic
112C22×#88322C2311yescharacteristic
113#13133217—22no—
114#13133217—22no—
115#13133217C2314yes—
116#13133217C2314yes—
117#13133205—22no—
118#13133205—22no—
119#13133205C2314yes—
120#13133205C2314yes—
121#13133201—28no—
122#13133201—28no—
123#13133197—28no—
124#13133197—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×#11719921—21no—
130C2×#11719921—21no—
131C2×#11719921—21no—
132C2×#11719921—21no—
133C4⋊#88322C2314yes—
134C4⋊#88322C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133140C2314yes—
138#13133140C2314yes—
139#13133140C2314yes—
140#13133140C2314yes—
141#13133137C2314yes—
142#13133137C2314yes—
143C22⋊#88322C2314yes—
144C22⋊#88322C2314yes—
145#13133128C2314yes—
146C4×#88322C2314yes—
147C22×Q8×C53—21no—
148C22×Q8×C53C2311yescharacteristic
149C22×D4×C53—21no—
150C22×D4×C53C2311yescharacteristic
151C23×C4×C53—21no—
152C23×C4×C53C2311yescharacteristic
153C4⋊Q8×C53—22no—
154C4⋊Q8×C53C2314yes—
155#126×C53—28no—
156#124×C53—28no—
157#124×C53—22no—
158#124×C53C2314yes—
159#123×C53—28no—
160C22⋊Q8×C53—28no—
161C22⋊Q8×C53—22no—
162C22⋊Q8×C53C2314yes—
163#121×C53—22no—
164#121×C53C2314yes—
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yes—
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169#117×C53D414yes—
170#117×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53D411yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C22⋊C4×C53D411yescharacteristic
185C2×C42×C53—21no—
186C2×C42×C53C2311yescharacteristic
187C2×C42×C53C2311yescharacteristic
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191C2×Q8×C53—21no—
192C2×Q8×C53—24no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—82no—
196C2×Q8×C53C2412yes—
197C2×D4×C53—24no—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—82no—
202C2×D4×C53C2412yes—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—24no—
209C22×C4×C53—82no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—24no—
224C22×Dic53—44no—
225#11719945—44no—
226#11719945—44no—
227#11719945—48no—
228C2×D212—22no—
229C2×D212—22no—
230C2×D212—21no—
231C2×D212C2412yes—
232C2×C4×D53—24no—
233C2×C4×D53—44no—
234C2×Dic106—22no—
235C2×Dic106—22no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—24no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106—21no—
244C2×Dic106—44no—
245C2×Dic106—44no—
246C2×Dic106—44no—
247C2×Dic106—48no—
248C2×Dic106C2412yes—
249C2×Dic106C2412yes—
250C2×Dic106C2412yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2×D414yes—
257C4⋊C4×C53C2×D414yes—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—24no—
265C22⋊C4×C53C2×D414yes—
266C22⋊C4×C53C2×D414yes—
267C42×C53—24no—
268C42×C53C2×D412yes—
269C42×C53C2×D412yes—
270C42×C53C2412yes—
271C42×C53C2412yes—
272#11719925—44no—
273#11719925—44no—
274#11719925—44no—
275#11719924—44no—
276#11719923—44no—
277#11719923—44no—
278#11719923—44no—
279#11719922—44no—
280#11719921—24no—
281#11719921—24no—
282#11719921—24no—
283#11719921—24no—
284C4⋊Dic53—24no—
285C4⋊Dic53—24no—
286C4⋊Dic53—24no—
287C4⋊Dic53—24no—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322—22no—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53C22×D412yes—
304C23×C53C22×D411yescharacteristic
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—42no—
312Q8×C53—84no—
313D4×C53—22no—
314D4×C53—22no—
315D4×C53—42no—
316D4×C53—84no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—24no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—84no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D412yes—
337C2×C4×C53C22×D411yescharacteristic
338C2×C4×C53H(5,𝔽2)12yes—
339C2×C4×C53H(5,𝔽2)12yes—
340C2×C4×C53C2511yescharacteristic
341C22⋊D53—48no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—48no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349D212—22no—
350D212—22no—
351D212—42no—
352C4×D53—48no—
353Dic106—22no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—42no—
361Dic106—42no—
362Dic106—42no—
363#88322—22no—
364#88322—22no—
365#88322—22no—
366#88322—22no—
367C2×#3225—531nomaximal, Sylow
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—84no—
376C22×C53#53512yes—
377C22×C53#57712yes—
378C22×C53#57812yes—
379C22×C53C23×D411yescharacteristic
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#53512yes—
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#542D5311yescharacteristic, complemented
399C2×#536—531no—
400#3225—5316no—
401C2×#497—531no—
402C2×#495—531no—
403C2×#489—531no—
404C2×#487—531no—
405C2×#464—531no—
406C2×#462—531no—
407C2×#463—531no—
408C2×#461—531no—
409C2×#452—531no—
410C2×#449—531no—
411C2×#451—531no—
412C2×#448—531no—
413C2×#433—531no—
414C2×C53—42no—
415C2×C53—82no—
416C2×C53#322514yescomplemented
417C2×C53C2×#53511yescharacteristic
418C2×C53C2×#57711yescharacteristic
419C2×C53C2×#57811yescharacteristic
420D53—82no—
421C22×#41—531no—
422C23×Q8—531no—
423C22×Q16—531no—
424C22×Q16—531no—
425C22×Q16—531no—
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×SD16—531no—
430C22×D8—531no—
431#542—24no—
432#542C2×D5318yescomplemented
433#536—538no—
434#536—1064no—
435C2×C4⋊Q8—531no—
436C2×C4⋊Q8—531no—
437C2×C4⋊Q8C2×D5311yescharacteristic
438C2×#126—21no—
439C2×#124—21no—
440C2×#124—531no—
441C2×#124—531no—
442C2×#124C2×D5311yescharacteristic
443C2×#123—21no—
444C2×#123—1061no—
445C2×#123—1061no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—1061no—
448C2×C22⋊Q8—1061no—
449C2×C22⋊Q8C2×D5311yescharacteristic
450C2×#121C2×D5311yescharacteristic
451C2×C4×Q8C2×D5311yescharacteristic
452C2×C4×D4C2×D5311yescharacteristic
453C2×#117C2×D5311yescharacteristic
454#497—538no—
455#495—538no—
456#489—538no—
457#487—538no—
458#464—538no—
459#463—538no—
460#462—538no—
461#461—538no—
462#452—538no—
463#451—538no—
464#449—538no—
465#448—538no—
466#433—538no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×C22⋊C8—531no—
478C2×C22⋊C8—531no—
479C2×#97—531no—
480C2×C4×C8—531no—
481C53C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—534no—
483C2×#41—1062no—
484C2×#41—2122no—
485C2×#41—2122no—
486C22×Q8—21no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8—531no—
490C22×Q8—534no—
491C22×Q8—1061no—
492C22×Q8—1062no—
493C22×Q8—2122no—
494C22×Q8—2122no—
495C22×Q8C22×D5311yescharacteristic
496C22×D4—21no—
497C22×D4—531no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C23×C4—21no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4C22×D5311yescharacteristic
504C2×Q16—534no—
505C2×Q16—534no—
506C2×Q16—534no—
507C2×Q16—2122no—
508C2×Q16—2122no—
509C2×Q16—2122no—
510C2×SD16—534no—
511C2×SD16—534no—
512C2×SD16—534no—
513C2×SD16—534no—
514C2×SD16—2122no—
515C2×SD16—2122no—
516C2×SD16—2122no—
517C2×SD16—2122no—
518C2×D8—534no—
519C2×D8—2122no—
520C22×C8—531no—
521C22×C8—531no—
522C22×C8—531no—
523C22×C8—531no—
524C4⋊Q8—22no—
525C4⋊Q8—534no—
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528C4⋊Q8—1062no—
529C4⋊Q8C22×D5314yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—534no—
534#124—534no—
535#124—1062no—
536#124—1062no—
537#124C22×D5314yes—
538#123—28no—
539#123—1068no—
540#123—1068no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1068no—
544C22⋊Q8—1068no—
545C22⋊Q8C22×D5314yes—
546#121—22no—
547#121C22×D5314yes—
548C4×Q8—22no—
549C4×Q8C22×D5314yes—
550C4×D4—22no—
551C4×D4C22×D5314yes—
552#117C22⋊D5314yes—
553#117C22×D5314yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4C22⋊D5311yescharacteristic
562C2×C4⋊C4C22⋊D5311yescharacteristic
563C2×C4⋊C4C22×D5311yescharacteristic
564C2×C4⋊C4C22×D5311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4C22⋊D5311yescharacteristic
575C2×C22⋊C4C22⋊D5311yescharacteristic
576C2×C42—21no—
577C2×C42C22×D5311yescharacteristic
578C2×C42C22×D5311yescharacteristic
579C4⋊C8—534no—
580C4⋊C8—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#103—534no—
585#103—534no—
586#103—534no—
587#102—534no—
588#102—534no—
589C22⋊C8—534no—
590C22⋊C8—534no—
591#97—534no—
592C4×C8—534no—
593C24—21no—
594C24—1061no—
595C24C2×C22⋊D5311yescharacteristic
596#41—2124no—
597#41—2124no—
598#41—2128no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—532no—
605C2×Q8—532no—
606C2×Q8—532no—
607C2×Q8—1064no—
608C2×Q8—1061no—
609C2×Q8—1061no—
610C2×Q8—1061no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8—1062no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—2124no—
618C2×Q8—2124no—
619C2×Q8—2124no—
620C2×Q8—2128no—
621C2×Q8C23×D5312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—532no—
628C2×D4—1064no—
629C2×D4—1061no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—2124no—
633C2×D4C23×D5312yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—1064no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—1064no—
646C22×C4—2124no—
647C22×C4—2124no—
648C22×C4C2×C22⋊D5312yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C2×C22⋊D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657Q16—2124no—
658Q16—2124no—
659SD16—2124no—
660SD16—2124no—
661SD16—2124no—
662SD16—2124no—
663D8—2124no—
664C2×C8—532no—
665C2×C8—532no—
666C2×C8—532no—
667C2×C8—532no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8—1062no—
671C2×C8—1062no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4C2×C22⋊D5314yes—
682C4⋊C4C2×C22⋊D5314yes—
683C4⋊C4C23×D5312yes—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4C2×C22⋊D5314yes—
695C22⋊C4C2×C22⋊D5314yes—
696C42—24no—
697C42C2×C22⋊D5312yes—
698C42C2×C22⋊D5312yes—
699C42C23×D5312yes—
700C42C23×D5312yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—1062no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C22×C22⋊D5312yes—
713C23C22×C22⋊D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—1062no—
719Q8—1062no—
720Q8—1062no—
721Q8—1062no—
722Q8—1062no—
723Q8—1062no—
724Q8—2128no—
725Q8—2122no—
726Q8—2122no—
727Q8—2122no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—1062no—
733D4—1062no—
734D4—2128no—
735D4—2122no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—2128no—
755C2×C4—2128no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4C22×C22⋊D5312yes—
760C2×C4C22×C22⋊D5312yes—
761C2×C4C22×C22⋊D5312yes—
762C2×C4C22×C22⋊D5312yes—
763C2×C4C22×C22⋊D5312yes—
764C2×C4C22×C22⋊D5311yescharacteristic
765C2×C4#1313326312yes—
766C2×C4#1313326312yes—
767C2×C4C24×D5311yescharacteristic
768C8—1062no—
769C8—1062no—
770C8—1062no—
771C8—1062no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—4244no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22#1681118712yes—
785C22#1681143412yes—
786C22#1681143812yes—
787C22C23×C22⋊D5311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2122no—
797C4—2122no—
798C4—2122no—
799C4#1681118712yes—
800C4C2×#1313326311yescharacteristic
801C4C2×#1313326311yescharacteristic
802C2—42no—
803C2—82no—
804C2—4242no—
805C2#2028581814yesdirect product factor
806C2C2×#1681118711yescharacteristic
807C2C2×#1681143411yescharacteristic
808C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
hypercenterC2×#542D53
hypocenterC53C2×#3225
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16811199C2semidirect
2. #20285818C2direct (N × H)
3. C2×#16811018C2semidirect
4. C2×#16811005C2semidirect
5. C2×#16810985C2semidirect
6. C2×#16810975C2semidirect
7. C2×#16810845C2semidirect
8. C2×#16810833C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810828C2semidirect
11. C2×#16810783C2semidirect
13. C2×#16810778C2semidirect
14. C2×#16810761C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#542C2semidirect
28. #16811199C22semidirect
37. #16811018C22semidirect
38. #16811005C22semidirect
39. #16810985C22semidirect
40. #16810975C22semidirect
41. #16810845C22semidirect
42. #16810838C22semidirect
43. #16810833C22semidirect
44. #16810828C22semidirect
45. #16810783C22semidirect
46. #16810778C22semidirect
48. #16810761C22semidirect
49. #16810684C22semidirect
65. C53×#542C22semidirect
398. C2×#542D53semidirect
416. C2×C53#3225semidirect
432. #542C2×D53semidirect
481. C53C2×#3225semidirect
805. C2#20285818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111992
#202858182
C2×#168110182
C2×#168110052
C2×#168109852
C2×#168109752
C2×#168108452
C2×#168108332
C2×#168108382
C2×#168108282
C2×#168107832
C2×#168107662
C2×#168107782
C2×#168107612
C2×#168106842
C2×C53×#5422
C2×#322553