Finite Group Databasebeta

← C2×#20284932 #28252358

Subgroups — C2×#20284932 #28252358

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811233C211yesmaximal, characteristic, complemented
2C2×#16811104C211yesmaximal, characteristic
3#20284932C2116yesmaximal, direct product factor
4C2×#16810958C211yesmaximal, characteristic, complemented
5C2×#16810933C211yesmaximal, characteristic, complemented
6C2×#16810922C211yesmaximal, characteristic, complemented
7C2×#16810832C211yesmaximal, characteristic, complemented
8C2×#16810827C211yesmaximal, characteristic, complemented
9C2×#16810787C211yesmaximal, characteristic
10C2×#16810783C211yesmaximal, characteristic
11C2×#16810729C211yesmaximal, characteristic, complemented
12C2×#16810726C211yesmaximal, characteristic, complemented
13C2×#16810715C211yesmaximal, characteristic, complemented
14C2×#16810710C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811233—24no—
23#16811233C2218yescomplemented
24C2×#13133215C2211yescharacteristic
25C2×#13133210—21no—
26C2×#13133210—21no—
27C2×#13133208—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133196C2211yescharacteristic
31#16811104—24no—
32#16811104C2218yes—
33C2×Q8×Dic53C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C2×#13133182C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53—21no—
41C2×#13133176C2211yescharacteristic
42C2×#13133175—21no—
43C2×C4⋊C4×D53—21no—
44#16810958C2218yescomplemented
45#16810933C2218yescomplemented
46#16810922C2218yescomplemented
47#16810832C2218yescomplemented
48#16810827C2218yescomplemented
49#16810787C2218yes—
50#16810783C2218yes—
51#16810729C2218yescomplemented
52#16810726C2218yescomplemented
53#16810715C2218yescomplemented
54#16810710C2218yescomplemented
55#16810681C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#483C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×Dic106C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×Dic212—24no—
89C2×Dic212C2314yes—
90C2×#11719925—24no—
91C2×#11719925C2314yes—
92C2×#11719913—24no—
93C2×#11719913C2314yes—
94C2×#11719924—24no—
95C2×#11719924C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98#13133215—22no—
99#13133215C2314yes—
100#13133210—28no—
101#13133210—28no—
102#13133208—28no—
103#13133208—22no—
104#13133208C2314yes—
105#13133207—28no—
106#13133196—22no—
107#13133196C2314yes—
108Q8×Dic53—22no—
109Q8×Dic53C2314yes—
110#13133182—22no—
111#13133182—22no—
112#13133182—22no—
113#13133182C2314yes—
114#13133182C2314yes—
115#13133182C2314yes—
116#13133179—22no—
117#13133179—22no—
118#13133179C2314yes—
119#13133179C2314yes—
120C4×C22⋊D53—28no—
121C4×C22⋊D53—28no—
122#13133176D414yes—
123#13133176C2314yes—
124#13133175—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53D411yescharacteristic
128C2×C4⋊Dic53D411yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C4⋊C4×D53—28no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53D411yescharacteristic
140C2×C22⋊Dic53D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133150C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133139C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160#13133127C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—22no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—24no—
195C22×C4×C53—82no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—28no—
201C2×C22⋊D53—24no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209#11719945—216no—
210#11719945—28no—
211#11719945—28no—
212C2×D212—21no—
213C2×D212—22no—
214C2×D212#4114yes—
215C2×D212C2412yes—
216C2×C4×D53—28no—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—82no—
221C2×C4×D53—82no—
222C2×Dic106—21no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106#4114yes—
228C2×Dic106C2412yes—
229C2×Dic106C2412yes—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C4⋊C4×C53C2412yes—
242C22⋊C4×C53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53C2×D414yes—
245C22⋊Dic53C2×D414yes—
246#11719925—28no—
247#11719924—28no—
248#11719921—24no—
249#11719921—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2×D414yes—
254C4⋊Dic53C2×D414yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C4×Dic53C2412yes—
271C2×#88322—22no—
272C2×#88322—22no—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275Dic212—28no—
276#11719913—28no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—24no—
283C22×D53—22no—
284C22×D53—42no—
285C22×D53—42no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—42no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—84no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4112yes—
305C2×C4×C53C2×#4112yes—
306C2×C4×C53C2511yescharacteristic
307C22⋊D53—216no—
308C2×Dic53—24no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322D212—24no—
323D212—22no—
324D212C2×#4114yes—
325C4×D53—216no—
326C4×D53—84no—
327C4×D53—84no—
328Dic106—24no—
329Dic106—22no—
330Dic106—22no—
331Dic106—22no—
332Dic106—42no—
333Dic106C2×#4114yes—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3120—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—44no—
343C22×C53#52512yes—
344C22×C53#57712yes—
345C22×C53#57812yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—24no—
348C2×D53—48no—
349C2×D53—42no—
350C2×D53—42no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53#52512yes—
357C4×C53C22×#4111yescharacteristic
358C4×C53C22×#4111yescharacteristic
359Dic53—24no—
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—22no—
364Dic53—42no—
365Dic53—42no—
366C2×#541—531no—
367C2×#520—531no—
368#3120—5316no—
369C2×#484—531no—
370C2×#483D5311yescharacteristic, complemented
371C2×#479—531no—
372C2×#478—531no—
373C2×#462—531no—
374C2×#461—531no—
375C2×#452—531no—
376C2×#452—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—42no—
383C2×C53#312014yescomplemented
384C2×C53C2×#52511yescharacteristic
385C2×C53C2×#57711yescharacteristic
386C2×C53C2×#57811yescharacteristic
387D53—44no—
388C22×#41—531no—
389C22×Q16—531no—
390C22×Q16—531no—
391C22×SD16—531no—
392C22×SD16—531no—
393#541—538no—
394#541—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8C2×D5311yescharacteristic
403#520—538no—
404#520—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×D4—531no—
410C2×C4×D4—531no—
411C2×C4×D4—1061no—
412C2×C4×D4—1061no—
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—1061no—
416C22×C4⋊C4C2×D5311yescharacteristic
417#484—538no—
418#483C2×D5318yescomplemented
419#479—538no—
420#478—538no—
421#462—538no—
422#461—538no—
423#452—538no—
424#452—538no—
425#441—538no—
426#440—538no—
427C4×Q16—538no—
428C4×SD16—538no—
429#433—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#106C2×D5311yescharacteristic
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8C2×D5311yescharacteristic
446C2×#97—531no—
447C2×C4×C8—531no—
448C53C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—534no—
450C2×#41—1064no—
451C2×#41—1064no—
452C2×#41—1062no—
453C22×Q8—531no—
454C22×Q8—531no—
455C22×Q8C22×D5311yescharacteristic
456C22×D4—531no—
457C22×D4—1061no—
458C23×C4—21no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×Q16—534no—
464C2×Q16—534no—
465C2×Q16—1064no—
466C2×Q16—1064no—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—1064no—
470C2×SD16—1064no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#126—1068no—
479#125—534no—
480#125—1062no—
481#125—1068no—
482#125—1068no—
483C22⋊Q8—22no—
484C22⋊Q8—534no—
485C22⋊Q8—1062no—
486C22⋊Q8C22×D5314yes—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×Q8—1062no—
494C4×Q8—1062no—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1068no—
500C4×D4—1068no—
501#117—534no—
502#117—534no—
503#117—1068no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—1068no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5314yes—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42—1061no—
536#107—534no—
537#107—534no—
538#106C22×D5314yes—
539#106C22×D5314yes—
540C4⋊C8—534no—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103C22×D5314yes—
547#103C22×D5314yes—
548#102—534no—
549#102—534no—
550C22⋊C8—534no—
551C22⋊C8C22×D5314yes—
552#97—534no—
553C4×C8—534no—
554C24—1061no—
555C24D4×D5311yescharacteristic
556#41—1068no—
557#41—1068no—
558#41—10616no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—534no—
563C2×Q8—532no—
564C2×Q8—532no—
565C2×Q8—1061no—
566C2×Q8—1061no—
567C2×Q8—1062no—
568C2×Q8—1062no—
569C2×Q8—1062no—
570C2×Q8C23×D5312yes—
571C2×D4—534no—
572C2×D4—532no—
573C2×D4—1068no—
574C2×D4—1064no—
575C2×D4—1061no—
576C2×D4—1062no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—1068no—
592C22×C4—1061no—
593C22×C4—1064no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—4242no—
597C22×C4—4242no—
598C22×C4D4×D5312yes—
599C22×C4D4×D5311yescharacteristic
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602Q16—1068no—
603Q16—1068no—
604SD16—1068no—
605SD16—1068no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8C23×D5312yes—
613C2×C8C23×D5312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—534no—
620C4⋊C4—534no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1061no—
631C4⋊C4—1064no—
632C4⋊C4C23×D5312yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—534no—
637C22⋊C4—534no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C42—532no—
642C42—532no—
643C42—532no—
644C42—532no—
645C42—1064no—
646C42—1064no—
647C42—1064no—
648C42—1064no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1064no—
653C23—1062no—
654C23—2122no—
655C23—2122no—
656C23C2×D4×D5312yes—
657C23C2×D4×D5311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—534no—
662Q8—1064no—
663Q8—1062no—
664Q8—1062no—
665Q8—1062no—
666Q8—2122no—
667D4—534no—
668D4—10616no—
669D4—1064no—
670D4—1062no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—10616no—
689C2×C4—1064no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—4244no—
698C2×C4—4244no—
699C2×C4—2122no—
700C2×C4—2122no—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#41×D5312yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1064no—
715C22—2128no—
716C22—2122no—
717C22—2122no—
718C22#1681113112yes—
719C22#1681142912yes—
720C22#1681143912yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—1062no—
731C4—1064no—
732C4—2122no—
733C4—2122no—
734C4#1681113112yes—
735C4C2×#41×D5311yescharacteristic
736C4C2×#41×D5311yescharacteristic
737C2—42no—
738C2—2124no—
739C2#2028493214yesdirect product factor
740C2C2×#1681113111yescharacteristic
741C2C2×#1681142911yescharacteristic
742C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#483D53
hypocenterC53C2×#3120
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#16811233C2semidirect
3. #20284932C2direct (N × H)
4. C2×#16810958C2semidirect
5. C2×#16810933C2semidirect
6. C2×#16810922C2semidirect
7. C2×#16810832C2semidirect
8. C2×#16810827C2semidirect
11. C2×#16810729C2semidirect
12. C2×#16810726C2semidirect
13. C2×#16810715C2semidirect
14. C2×#16810710C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#483C2semidirect
23. #16811233C22semidirect
44. #16810958C22semidirect
45. #16810933C22semidirect
46. #16810922C22semidirect
47. #16810832C22semidirect
48. #16810827C22semidirect
51. #16810729C22semidirect
52. #16810726C22semidirect
53. #16810715C22semidirect
54. #16810710C22semidirect
55. #16810681C22semidirect
71. C53×#483C22semidirect
370. C2×#483D53semidirect
383. C2×C53#3120semidirect
418. #483C2×D53semidirect
448. C53C2×#3120semidirect
739. C2#20284932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168111042
#202849322
C2×#168109582
C2×#168109332
C2×#168109222
C2×#168108322
C2×#168108272
C2×#168107872
C2×#168107832
C2×#168107292
C2×#168107262
C2×#168107152
C2×#168107102
C2×#168106812
C2×C53×#4832
C2×#312053