Finite Group Databasebeta

← C2×#20286141 #28257018

Subgroups — C2×#20286141 #28257018

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811235C211yesmaximal, characteristic, complemented
2#20286141C2116yesmaximal, direct product factor
3C2×#16810930C211yesmaximal, characteristic, complemented
4C2×#16810915C211yesmaximal, characteristic, complemented
5C2×#16810905C211yesmaximal, characteristic, complemented
6C2×#16810923C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810867C211yesmaximal, characteristic
9C2×#16810862C211yesmaximal, characteristic, complemented
10C2×#16810850C211yesmaximal, characteristic
11C2×#16810842C211yesmaximal, characteristic, complemented
12C2×#16810842C211yesmaximal, characteristic, complemented
13C2×#16810833C211yesmaximal, characteristic, complemented
14C2×#16810828C211yesmaximal, characteristic, complemented
15C2×#16810650C211yesmaximal, characteristic, complemented
16C2×C53×#542C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719917C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23#16811235—24no—
24#16811235C2218yescomplemented
25C2×#13133217C2211yescharacteristic
26C2×#13133210—21no—
27C2×#13133210—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133207—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133196C2211yescharacteristic
33C2×C4×Dic106C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35#16810930C2218yescomplemented
36#16810923C2218yescomplemented
37#16810915C2218yescomplemented
38#16810905C2218yescomplemented
39#16810879C2218yescomplemented
40#16810867C2218yes—
41#16810862C2218yescomplemented
42#16810850C2218yes—
43#16810842C2218yescomplemented
44#16810842C2218yescomplemented
45#16810833C2218yescomplemented
46#16810828C2218yescomplemented
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51#16810650C2218yescomplemented
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×C4⋊#88322C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C53×#542—24no—
65C53×#542C2218yes—
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
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C2×#11719925—42no—
80C2×#11719925—42no—
81C2×#11719925C2314yes—
82C2×#11719925C2314yes—
83C2×#11719923—42no—
84C2×#11719923—42no—
85C2×#11719923C2314yes—
86C2×#11719923C2314yes—
87C2×#11719917—42no—
88C2×#11719917C2314yes—
89C22×#88322—42no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95#13133217—22no—
96#13133217C2314yes—
97#13133210—28no—
98#13133210—28no—
99#13133209—22no—
100#13133209C2314yes—
101#13133207—28no—
102#13133207—28no—
103#13133196—22no—
104#13133196—22no—
105#13133196C2314yes—
106#13133196C2314yes—
107C4×Dic106—22no—
108C4×Dic106—22no—
109C4×Dic106C2314yes—
110C4×Dic106C2314yes—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53—21no—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×#11719919—21no—
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×#11719919—21no—
119C2×#11719919—21no—
120C2×#11719919—21no—
121C2×C22⋊Dic53—21no—
122C2×C22⋊Dic53—21no—
123C2×C4×Dic53—21no—
124C2×C4×Dic53—21no—
125#13133150C2314yes—
126#13133150C2314yes—
127#13133148C2314yes—
128#13133148C2314yes—
129C4⋊#88322C2314yes—
130C4⋊#88322C2314yes—
131C4⋊#88322C2314yes—
132C4⋊#88322C2314yes—
133#13133141C2314yes—
134#13133141C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133140C2314yes—
138#13133140C2314yes—
139#13133138C2314yes—
140#13133138C2314yes—
141C22×Q8×C53—21no—
142C22×Q8×C53C2311yescharacteristic
143C22×D4×C53—21no—
144C22×D4×C53C2311yescharacteristic
145C23×C4×C53—21no—
146C23×C4×C53C2311yescharacteristic
147C4⋊Q8×C53—22no—
148C4⋊Q8×C53C2314yes—
149#126×C53—28no—
150#124×C53—28no—
151#124×C53—22no—
152#124×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—28no—
155C22⋊Q8×C53—22no—
156C22⋊Q8×C53C2314yes—
157#121×C53—22no—
158#121×C53C2314yes—
159C4×Q8×C53—22no—
160C4×Q8×C53C2314yes—
161C4×D4×C53—22no—
162C4×D4×C53C2314yes—
163#117×C53D414yes—
164#117×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—24no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—82no—
189C2×Q8×C53C2412yes—
190C2×D4×C53—24no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—82no—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—82no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2411yescharacteristic
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—21no—
220C2×Dic106—21no—
221C2×Dic106C2412yes—
222C2×Dic106C2412yes—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53C2×D414yes—
229C4⋊C4×C53C2×D414yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—24no—
236C22⋊C4×C53—24no—
237C22⋊C4×C53C2×D414yes—
238C22⋊C4×C53C2×D414yes—
239C42×C53—24no—
240C42×C53C2×D412yes—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719925—44no—
247#11719925—44no—
248#11719923—44no—
249#11719923—44no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264#11719917—44no—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322—44no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D412yes—
282C23×C53C22×D411yescharacteristic
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—42no—
286Q8×C53—84no—
287D4×C53—22no—
288D4×C53—22no—
289D4×C53—42no—
290D4×C53—84no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—24no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—84no—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53H(5,𝔽2)12yes—
313C2×C4×C532−1+412yes—
314C2×C4×C53C2511yescharacteristic
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323Dic106—22no—
324Dic106—22no—
325Dic106—22no—
326Dic106—22no—
327Dic106—42no—
328Dic106—42no—
329#88322—22no—
330#88322—22no—
331#88322—22no—
332#88322—22no—
333C2×#3258—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—44no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—84no—
342C22×C53#53712yes—
343C22×C53#57712yes—
344C22×C53#57812yes—
345C22×C53C23×D411yescharacteristic
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53#53712yes—
355C4×C53C2×H(5,𝔽2)11yescharacteristic
356C4×C53C2×2−1+411yescharacteristic
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#542D5311yescharacteristic
362C2×#541—531no—
363#3258—5316no—
364C2×#479—531no—
365C2×#477—531no—
366C2×#475—531no—
367C2×#478—531no—
368C2×#470—531no—
369C2×#468—531no—
370C2×#467—531no—
371C2×#465—531no—
372C2×#464—531no—
373C2×#464—531no—
374C2×#462—531no—
375C2×#461—531no—
376C2×#424—531no—
377C2×C53—42no—
378C2×C53—82no—
379C2×C53#325814yescomplemented
380C2×C53C2×#53711yescharacteristic
381C2×C53C2×#57711yescharacteristic
382C2×C53C2×#57811yescharacteristic
383C22×Q16—531no—
384C22×Q16—531no—
385C22×SD16—531no—
386C22×SD16—531no—
387C22×M16—531no—
388C23×C8—531no—
389#542—24no—
390#542C2×D5318yes—
391#541—538no—
392#541—1064no—
393C2×C4⋊Q8—531no—
394C2×C4⋊Q8C2×D5311yescharacteristic
395C2×#126—21no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×#124—21no—
402C2×#124C2×D5311yescharacteristic
403C2×#123—21no—
404C2×C22⋊Q8—21no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8C2×D5311yescharacteristic
408C2×#121C2×D5311yescharacteristic
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8C2×D5311yescharacteristic
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117C2×D5311yescharacteristic
414#479—538no—
415#478—538no—
416#477—538no—
417#475—538no—
418#470—538no—
419#468—538no—
420#467—538no—
421#465—538no—
422#464—538no—
423#464—538no—
424#462—538no—
425#461—538no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#106—531no—
429C2×#106—531no—
430#424—538no—
431C2×C4⋊C8—531no—
432C2×C4⋊C8—531no—
433C2×C4⋊C8—531no—
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#102—531no—
442C2×#102—531no—
443C53C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—21no—
445C22×Q8—531no—
446C22×Q8—531no—
447C22×Q8C22×D5311yescharacteristic
448C22×D4—21no—
449C22×D4C22×D5311yescharacteristic
450C23×C4—21no—
451C23×C4C22×D5311yescharacteristic
452C2×Q16—534no—
453C2×Q16—534no—
454C2×Q16—2122no—
455C2×Q16—2122no—
456C2×SD16—534no—
457C2×SD16—534no—
458C2×SD16—2122no—
459C2×SD16—2122no—
460C2×M16—534no—
461C2×M16—2122no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22×C8—531no—
466C22×C8—534no—
467C22×C8—2122no—
468C4⋊Q8—22no—
469C4⋊Q8—534no—
470C4⋊Q8—1062no—
471C4⋊Q8C22×D5314yes—
472#126—28no—
473#126—1068no—
474#126—1068no—
475#125—534no—
476#125—1068no—
477#125—1068no—
478#125—1062no—
479#124—28no—
480#124—22no—
481#124C22×D5314yes—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—28no—
485C22⋊Q8—534no—
486C22⋊Q8—534no—
487C22⋊Q8—1062no—
488C22⋊Q8—1062no—
489C22⋊Q8C22×D5314yes—
490#121—22no—
491#121C22×D5314yes—
492C4×Q8—22no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×Q8—1062no—
497C4×Q8C22×D5314yes—
498C4×D4—22no—
499C4×D4C22×D5314yes—
500#117C22⋊D5314yes—
501#117C22×D5314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4C22⋊D5311yescharacteristic
516C2×C4⋊C4C22⋊D5311yescharacteristic
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4C22⋊D5311yescharacteristic
527C2×C22⋊C4C22⋊D5311yescharacteristic
528C2×C42—21no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533#107—534no—
534#107—534no—
535#106—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8—534no—
540C4⋊C8—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103—534no—
547#102—534no—
548#102—534no—
549C24—21no—
550C24C2×C22⋊D5311yescharacteristic
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—82no—
556C2×Q8—532no—
557C2×Q8—532no—
558C2×Q8—1061no—
559C2×Q8—1061no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—1062no—
564C2×Q8C23×D5312yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D5312yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4C2×C22⋊D5312yes—
583C22×C4C2×C22⋊D5311yescharacteristic
584C22×C4C2×C22⋊D5311yescharacteristic
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590Q16—2124no—
591Q16—2124no—
592SD16—2124no—
593SD16—2124no—
594M16—2124no—
595C2×C8—532no—
596C2×C8—532no—
597C2×C8—532no—
598C2×C8—532no—
599C2×C8—1062no—
600C2×C8—1062no—
601C2×C8—1062no—
602C2×C8—1062no—
603C2×C8—2124no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4C2×C22⋊D5314yes—
622C4⋊C4C2×C22⋊D5314yes—
623C4⋊C4C23×D5312yes—
624C4⋊C4C23×D5312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4C2×C22⋊D5314yes—
633C22⋊C4C2×C22⋊D5314yes—
634C42—24no—
635C42—1064no—
636C42—1064no—
637C42C2×C22⋊D5312yes—
638C42C2×C22⋊D5312yes—
639C42C23×D5312yes—
640C42C23×D5312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D5312yes—
649C23C22×C22⋊D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—1062no—
655Q8—1062no—
656Q8—1062no—
657Q8—1062no—
658Q8—2122no—
659Q8—2122no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4C22×C22⋊D5312yes—
688C2×C4C22×C22⋊D5312yes—
689C2×C4C22×C22⋊D5312yes—
690C2×C4C22×C22⋊D5312yes—
691C2×C4C22×C22⋊D5312yes—
692C2×C4C22×C22⋊D5311yescharacteristic
693C2×C4#1313326312yes—
694C2×C4#1313326412yes—
695C2×C4C24×D5311yescharacteristic
696C8—1062no—
697C8—1062no—
698C8—1062no—
699C8—1062no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1681120112yes—
709C22#1681143412yes—
710C22#1681143812yes—
711C22C23×C22⋊D5311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2122no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4#1681120112yes—
725C4C2×#1313326311yescharacteristic
726C4C2×#1313326411yescharacteristic
727C2—42no—
728C2—82no—
729C2#2028614114yesdirect product factor
730C2C2×#1681120111yescharacteristic
731C2C2×#1681143411yescharacteristic
732C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
hypercenterC2×#542D53
hypocenterC53C2×#3258
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×#16811235C2semidirect
2. #20286141C2direct (N × H)
3. C2×#16810930C2semidirect
4. C2×#16810915C2semidirect
5. C2×#16810905C2semidirect
6. C2×#16810923C2semidirect
7. C2×#16810879C2semidirect
9. C2×#16810862C2semidirect
11. C2×#16810842C2semidirect
12. C2×#16810842C2semidirect
13. C2×#16810833C2semidirect
14. C2×#16810828C2semidirect
15. C2×#16810650C2semidirect
24. #16811235C22semidirect
35. #16810930C22semidirect
36. #16810923C22semidirect
37. #16810915C22semidirect
38. #16810905C22semidirect
39. #16810879C22semidirect
41. #16810862C22semidirect
43. #16810842C22semidirect
44. #16810842C22semidirect
45. #16810833C22semidirect
46. #16810828C22semidirect
51. #16810650C22semidirect
379. C2×C53#3258semidirect
443. C53C2×#3258semidirect
729. C2#20286141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112352
#202861412
C2×#168109302
C2×#168109152
C2×#168109052
C2×#168109232
C2×#168108792
C2×#168108672
C2×#168108622
C2×#168108502
C2×#168108422
C2×#168108332
C2×#168108282
C2×#168106502
C2×C53×#5422
C2×#325853