Finite Group Databasebeta

← C2×#20287428 #28263762

Subgroups — C2×#20287428 #28263762

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811342C211yesmaximal, characteristic, complemented
2C2×D4×Dic106C211yesmaximal, characteristic, complemented
3#20287428C2116yesmaximal, direct product factor
4C2×#16810982C211yesmaximal, characteristic, complemented
5C2×#16810981C211yesmaximal, characteristic, complemented
6C2×#16810972C211yesmaximal, characteristic, complemented
7C2×#16810919C211yesmaximal, characteristic, complemented
8C2×#16810916C211yesmaximal, characteristic, complemented
9C2×#16810901C211yesmaximal, characteristic, complemented
10C2×#16810836C211yesmaximal, characteristic
11C2×#16810826C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810724C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×D8×Dic53C211yesmaximal, characteristic
16C2×C53×#463C211yesmaximal, characteristic
17C23×Dic106—21no—
18C22×#11719923C2211yescharacteristic
19#16811342—24no—
20#16811342C2218yescomplemented
21D4×Dic106—24no—
22D4×Dic106C2218yescomplemented
23C2×#13133217C2211yescharacteristic
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133215C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133210—21no—
29C2×#13133204C2211yescharacteristic
30C2×#13133196—21no—
31C2×#13133194—21no—
32C2×#13133194—21no—
33C2×#13133194—21no—
34C2×Q8×Dic53C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133173—21no—
41#16810982C2218yescomplemented
42#16810981C2218yescomplemented
43#16810972C2218yescomplemented
44#16810919C2218yescomplemented
45#16810916C2218yescomplemented
46#16810901C2218yescomplemented
47#16810836C2218yes—
48#16810826C2218yescomplemented
49#16810752C2218yescomplemented
50#16810724C2218yescomplemented
51#16810723C2218yescomplemented
52D8×Dic53C2218yes—
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yes—
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106—28no—
81C22×Dic106—48no—
82C22×Dic106D411yescharacteristic
83C22×Dic106C2311yescharacteristic
84C23×Dic53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C2×#11719923—24no—
88C2×#11719923C2314yes—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133217—22no—
92#13133217C2314yes—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133215—22no—
98#13133215C2314yes—
99#13133210—28no—
100#13133210—28no—
101#13133204—22no—
102#13133204C2314yes—
103#13133196—28no—
104#13133194—28no—
105#13133194—28no—
106#13133194—28no—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109C4×Dic106—22no—
110C4×Dic106D414yes—
111C4×Dic106C2314yes—
112C4×Dic106C2314yes—
113D4×Dic53—22no—
114D4×Dic53—22no—
115D4×Dic53—22no—
116D4×Dic53C2314yes—
117D4×Dic53C2314yes—
118D4×Dic53C2314yes—
119#13133173—28no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141C2×C4×Dic53C2311yescharacteristic
142#13133151C2314yes—
143#13133151C2314yes—
144#13133150C2314yes—
145#13133146C2314yes—
146#13133146C2314yes—
147#13133142C2314yes—
148#13133142C2314yes—
149#13133141C2314yes—
150#13133141C2314yes—
151#13133140C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133128C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53—21no—
162C2×SD16×C53—24no—
163C2×SD16×C53C2314yes—
164C2×D8×C53—24no—
165C2×D8×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168#124×C53—22no—
169#124×C53C2314yes—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C4⋊C8×C53C2314yes—
178#103×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C24×C53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53#4114yes—
192C2×D4×C53C2412yes—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—44no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—24no—
206C22×Dic53—24no—
207C22×Dic53—24no—
208C22×Dic53—44no—
209C22×Dic53—44no—
210C22×Dic53—44no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C2×Dic106—24no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—21no—
219C2×Dic106—24no—
220C2×Dic106—24no—
221C2×Dic106—24no—
222C2×Dic106—432no—
223C2×Dic106—44no—
224C2×Dic106—44no—
225C2×Dic106—44no—
226C2×Dic106C2×D414yes—
227C2×Dic106C2412yes—
228SD16×C53—28no—
229D8×C53—28no—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719923—28no—
247C4⋊Dic53—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53C2×D414yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919C2×D414yes—
262#11719919C2×D414yes—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53C2×D412yes—
266C4×Dic53C2×D412yes—
267C4×Dic53C2412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273C23×C53—24no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D411yescharacteristic
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—42no—
285D4×C53—24no—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—22no—
289D4×C53—42no—
290D4×C53C2×#4114yes—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—48no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C2×#4112yes—
302C2×C4×C532−1+412yes—
303C2×C4×C53C2511yescharacteristic
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—48no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—48no—
317C2×Dic53—48no—
318C2×Dic53AGL(1,ℤ/8)14yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323Dic106—28no—
324Dic106—22no—
325Dic106—22no—
326Dic106—48no—
327Dic106—48no—
328Dic106—42no—
329Dic106—48no—
330C8×C53—22no—
331C8×C53—22no—
332#88322—22no—
333#88322—22no—
334C2×#3367—531nomaximal, Sylow
335C22×C53—24no—
336C22×C53—48no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—84no—
343C22×C53#54812yes—
344C22×C53C2×AGL(1,ℤ/8)12yes—
345C22×C53#57812yes—
346C22×C53C23×D411yescharacteristic
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53#54812yes—
352C4×C53C22×#4111yescharacteristic
353C4×C53C2×2−1+411yescharacteristic
354Dic53—22no—
355Dic53—22no—
356Dic53—22no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361Dic53C2×AGL(1,ℤ/8)14yes—
362C2×#556—531no—
363C2×D4×Q8—531no—
364#3367—5316no—
365C2×#489—531no—
366C2×#489—531no—
367C2×#487—531no—
368C2×#477—531no—
369C2×#477—531no—
370C2×#474—531no—
371C2×#463—531no—
372C2×#463D5311yescharacteristic
373C2×#461—531no—
374C2×#446—531no—
375C2×#440—531no—
376C2×#440—531no—
377C2×C4×D8—531no—
378C2×C53—44no—
379C2×C53—82no—
380C2×C53#336714yescomplemented
381C2×C53C2×#54811yescharacteristic
382C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C53C2×#57811yescharacteristic
384C23×Q8—1061no—
385C22×SD16—531no—
386C22×SD16C2×D5311yescharacteristic
387C22×D8C2×D5311yescharacteristic
388#556—538no—
389#556—1064no—
390D4×Q8—538no—
391D4×Q8—1064no—
392C2×C4⋊Q8—531no—
393C2×C4⋊Q8—531no—
394C2×C4⋊Q8—531no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#124—531no—
399C2×#124C2×D5311yescharacteristic
400C2×C22⋊Q8—1061no—
401C2×C22⋊Q8—1061no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8—1061no—
404C2×C4×Q8—531no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4C2×D5311yescharacteristic
411C2×#117—1061no—
412#489—538no—
413#489—538no—
414#487—538no—
415#477—538no—
416#477—538no—
417#474—538no—
418#463—538no—
419#463C2×D5318yes—
420#461—538no—
421#446—538no—
422#440—538no—
423#440—538no—
424C4×D8—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×C4⋊C8—531no—
429C2×C4⋊C8—531no—
430C2×C4⋊C8C2×D5311yescharacteristic
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103C2×D5311yescharacteristic
437C2×#102—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102C2×D5311yescharacteristic
441C2×#97—531no—
442C2×#97—531no—
443C2×C4×C8—531no—
444C53C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—531no—
446C22×Q8—531no—
447C22×Q8—1061no—
448C22×Q8—1061no—
449C22×Q8—1068no—
450C22×Q8—1061no—
451C22×Q8—2128no—
452C22×Q8C22×D5311yescharacteristic
453C22×D4C22×D5311yescharacteristic
454C22×D4C22×D5311yescharacteristic
455C23×C4—21no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C2×SD16—24no—
460C2×SD16—534no—
461C2×SD16—1064no—
462C2×SD16C22×D5314yes—
463C2×D8—24no—
464C2×D8C22×D5314yes—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C4⋊Q8—534no—
470C4⋊Q8—534no—
471C4⋊Q8—534no—
472C4⋊Q8—534no—
473C4⋊Q8—1062no—
474C4⋊Q8—1062no—
475C4⋊Q8—1062no—
476C4⋊Q8—1062no—
477#126—1068no—
478#126—1068no—
479#124—22no—
480#124—534no—
481#124—1062no—
482#124C22×D5314yes—
483C22⋊Q8—1068no—
484C22⋊Q8—1068no—
485C22⋊Q8—1068no—
486C22⋊Q8—1068no—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×D4—22no—
494C4×D4—534no—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4C22×D5314yes—
501#117—1068no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
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×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C42—531no—
525C2×C42—531no—
526C2×C42—1061no—
527C2×C42—1061no—
528C2×C42C22×D5311yescharacteristic
529#107—534no—
530#107—534no—
531#107—534no—
532C4⋊C8—534no—
533C4⋊C8—534no—
534C4⋊C8C22×D5314yes—
535#103—534no—
536#103—534no—
537#103—534no—
538#103—534no—
539#103—534no—
540#103C22×D5314yes—
541#102—534no—
542#102—534no—
543#102—534no—
544#102C22×D5314yes—
545#97—534no—
546#97—534no—
547C4×C8—534no—
548C24—21no—
549C24—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—534no—
554C2×Q8—532no—
555C2×Q8—1064no—
556C2×Q8—1064no—
557C2×Q8—1064no—
558C2×Q8—1061no—
559C2×Q8—1064no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—2124no—
563C2×Q8—2124no—
564C2×Q8—2124no—
565C2×Q8—21232no—
566C2×Q8C23×D5312yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4#1171994714yes—
573C2×D4C23×D5312yes—
574C2×D4C23×D5312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—1064no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4D4×D5311yescharacteristic
594C22×C4D4×D5311yescharacteristic
595C22×C4C23×D5311yescharacteristic
596SD16—28no—
597SD16—1068no—
598D8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—532no—
602C2×C8—532no—
603C2×C8—1062no—
604C2×C8—1062no—
605C2×C8C23×D5312yes—
606C2×C8C23×D5312yes—
607C4⋊C4—21no—
608C4⋊C4—534no—
609C4⋊C4—534no—
610C4⋊C4—534no—
611C4⋊C4—532no—
612C4⋊C4—532no—
613C4⋊C4—532no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4C23×D5312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C42—532no—
634C42—532no—
635C42—532no—
636C42—532no—
637C42—1064no—
638C42—1064no—
639C42D4×D5312yes—
640C42C23×D5312yes—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1068no—
654Q8—1062no—
655Q8—1062no—
656Q8—2128no—
657Q8—2128no—
658Q8—2128no—
659Q8—2122no—
660D4—24no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—42no—
665D4C2×#1171994714yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—534no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—2128no—
686C2×C4—2128no—
687C2×C4—2128no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4C2×D4×D5312yes—
693C2×C4C2×D4×D5312yes—
694C2×C4C2×D4×D5311yescharacteristic
695C2×C4C2×#1171994712yes—
696C2×C4#1313326412yes—
697C2×C4C24×D5311yescharacteristic
698C8—22no—
699C8—22no—
700C8—1062no—
701C8—1062no—
702C22—24no—
703C22—42no—
704C22—48no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1681127912yes—
711C22AGL(1,ℤ/8)×D5312yes—
712C22#1681143712yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—534no—
719C4—1062no—
720C4—1062no—
721C4—1062no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4—2122no—
726C4#1681127912yes—
727C4C22×#1171994711yescharacteristic
728C4C2×#1313326411yescharacteristic
729C2—44no—
730C2—82no—
731C2#2028742814yesdirect product factor
732C2C2×#1681127911yescharacteristic
733C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
734C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC22×D8×C53C22
hypercenterC2×#463D53
hypocenterC53C2×#3367
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811342C2semidirect
2. C2×D4×Dic106C2semidirect
3. #20287428C2direct (N × H)
4. C2×#16810982C2semidirect
5. C2×#16810981C2semidirect
6. C2×#16810972C2semidirect
7. C2×#16810919C2semidirect
8. C2×#16810916C2semidirect
9. C2×#16810901C2semidirect
11. C2×#16810826C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810724C2semidirect
14. C2×#16810723C2semidirect
20. #16811342C22semidirect
22. D4×Dic106C22semidirect
41. #16810982C22semidirect
42. #16810981C22semidirect
43. #16810972C22semidirect
44. #16810919C22semidirect
45. #16810916C22semidirect
46. #16810901C22semidirect
48. #16810826C22semidirect
49. #16810752C22semidirect
50. #16810724C22semidirect
51. #16810723C22semidirect
380. C2×C53#3367semidirect
444. C53C2×#3367semidirect
731. C2#20287428direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113422
C2×D4×Dic1062
#202874282
C2×#168109822
C2×#168109812
C2×#168109722
C2×#168109192
C2×#168109162
C2×#168109012
C2×#168108362
C2×#168108262
C2×#168107522
C2×#168107242
C2×#168107232
C2×D8×Dic532
C2×C53×#4632
C2×#336753