Finite Group Databasebeta

← C2×#20287769 #28265085

Subgroups — C2×#20287769 #28265085

Order 13568.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811356C211yesmaximal, characteristic
2C2×#16811351C211yesmaximal, characteristic, complemented
3#20287769C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic, complemented
5C2×#16811014C211yesmaximal, characteristic, complemented
6C2×#16810994C211yesmaximal, characteristic
7C2×#16810845C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810822C211yesmaximal, characteristic
11C2×#16810828C211yesmaximal, characteristic, complemented
12C2×#16810827C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×#16810717C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719923C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25#16811356—24no—
26#16811356C2218yes—
27#16811351—24no—
28#16811351C2218yescomplemented
29C2×#13133217C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133215C2211yescharacteristic
32C2×#13133213C2211yescharacteristic
33C2×#13133209—21no—
34C2×#13133207—21no—
35C2×#13133207—21no—
36C2×#13133205C2211yescharacteristic
37C2×#13133204C2211yescharacteristic
38C2×#13133203—21no—
39C2×#13133200—21no—
40C2×#13133199—21no—
41C2×C4×Dic106—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133182C2211yescharacteristic
46C2×#13133179C2211yescharacteristic
47C2×C4×C22⋊D53—21no—
48#16811017C2218yescomplemented
49#16811014C2218yescomplemented
50#16810994C2218yes—
51#16810845C2218yescomplemented
52#16810844C2218yescomplemented
53#16810832C2218yescomplemented
54#16810828C2218yescomplemented
55#16810827C2218yescomplemented
56#16810822C2218yes—
57#16810751C2218yescomplemented
58#16810722C2218yescomplemented
59#16810717C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C2×Dic212—24no—
86C2×Dic212—42no—
87C2×Dic212C2314yes—
88C2×Dic212C2314yes—
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C2×#11719913—24no—
92C2×#11719913—42no—
93C2×#11719913C2314yes—
94C2×#11719913C2314yes—
95C2×#11719923—42no—
96C2×#11719923—42no—
97C2×#11719923C2314yes—
98C2×#11719923C2314yes—
99C2×#11719924—42no—
100C2×#11719924C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133217—22no—
104#13133217C2314yes—
105#13133215—22no—
106#13133215—22no—
107#13133215C2314yes—
108#13133215C2314yes—
109#13133213—22no—
110#13133213C2314yes—
111#13133209—28no—
112#13133207—28no—
113#13133207—28no—
114#13133205—22no—
115#13133205C2314yes—
116#13133204—22no—
117#13133204C2314yes—
118#13133203—28no—
119#13133200—28no—
120#13133199—28no—
121C4×Dic106—28no—
122C4×Dic106D414yes—
123C4×Dic106C2314yes—
124#13133182—22no—
125#13133182—22no—
126#13133182—22no—
127#13133182C2314yes—
128#13133182C2314yes—
129#13133182C2314yes—
130#13133179—22no—
131#13133179C2314yes—
132C4×C22⋊D53—28no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919D411yescharacteristic
144C2×#11719919D411yescharacteristic
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yes—
156#13133146C2314yes—
157#13133146C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133137C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C23×D53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—82no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53—82no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212C2412yes—
218C2×C4×D53—24no—
219C2×C4×D53—82no—
220C2×Dic106—24no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106—21no—
229C2×Dic106—21no—
230C2×Dic106C2×D414yes—
231C2×Dic106C2412yes—
232C2×Dic106C2412yes—
233C2×Dic106C2412yes—
234SD16×C53—28no—
235C2×C8×C53—22no—
236C2×C8×C53#4114yes—
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C42×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2412yes—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250#11719925—44no—
251#11719924—44no—
252#11719923—44no—
253#11719923—44no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2×D414yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919C2×D414yes—
268#11719919C2×D414yes—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280Dic212—28no—
281Dic212—44no—
282#11719913—28no—
283#11719913—44no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293Q8×C53—22no—
294Q8×C53—22no—
295Q8×C53—42no—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—42no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—84no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53H(5,𝔽2)12yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—48no—
315C22⋊D53—84no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53#13714yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330D212—22no—
331D212—22no—
332D212—42no—
333C4×D53—84no—
334Dic106—28no—
335Dic106—22no—
336Dic106—22no—
337Dic106—22no—
338Dic106—22no—
339Dic106—22no—
340Dic106—22no—
341Dic106—42no—
342Dic106—42no—
343Dic106—42no—
344C8×C53—22no—
345C8×C53C2×#4114yes—
346#88322—22no—
347#88322—22no—
348C2×#3400—531nomaximal, Sylow
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—84no—
353C22×C53#55012yes—
354C22×C53C2×#13712yes—
355C22×C53#57712yes—
356C22×C53C23×D411yescharacteristic
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—84no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53#55012yes—
367C4×C53C22×#4111yescharacteristic
368C4×C53C2×H(5,𝔽2)11yescharacteristic
369Dic53—22no—
370Dic53—22no—
371Dic53—22no—
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53C2×#13714yes—
376C2×#559—531no—
377C2×#557—531no—
378#3400—5316no—
379C2×#497—531no—
380C2×#497—531no—
381C2×#492—531no—
382C2×#464—531no—
383C2×#464—531no—
384C2×#462—531no—
385C2×#460—531no—
386C2×#461—531no—
387C2×#461—531no—
388C2×#446—531no—
389C2×#440—531no—
390C2×#440D5311yescharacteristic, complemented
391C2×C4×Q16—531no—
392C2×C53—82no—
393C2×C53#340014yescomplemented
394C2×C53C2×#55011yescharacteristic
395C2×C53C22×#13711yescharacteristic
396C2×C53C2×#57711yescharacteristic
397D53—82no—
398C22×Q16—531no—
399C22×Q16—531no—
400C22×Q16—531no—
401C22×SD16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
404C22×SD16—531no—
405C22×SD16—531no—
406C22×SD16C2×D5311yescharacteristic
407#559—538no—
408#559—1064no—
409#557—538no—
410#557—1064no—
411C2×C4⋊Q8—531no—
412C2×C4⋊Q8—531no—
413C2×C4⋊Q8—531no—
414C2×#127—531no—
415C2×#125—1061no—
416C2×#125—1061no—
417C2×#125—1061no—
418C2×#124—531no—
419C2×#124—531no—
420C2×#124—1061no—
421C2×#123—1061no—
422C2×#123—1061no—
423C2×C4×Q8—531no—
424C2×C4×Q8—531no—
425C2×C4×Q8—531no—
426C2×C4×Q8—531no—
427C2×C4×Q8—1061no—
428C2×C4×Q8C2×D5311yescharacteristic
429C2×C4×D4—531no—
430C2×C4×D4—1061no—
431C2×C4×D4C2×D5311yescharacteristic
432#497—538no—
433#497—538no—
434#492—538no—
435#464—538no—
436#464—538no—
437#462—538no—
438#461—538no—
439#461—538no—
440#460—538no—
441#446—538no—
442#440—538no—
443#440C2×D5318yescomplemented
444C4×Q16—538no—
445C2×#107C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×C4⋊C8—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103C2×D5311yescharacteristic
453C2×#102—531no—
454C2×#102C2×D5311yescharacteristic
455C2×#97—531no—
456C2×#97C2×D5311yescharacteristic
457C2×C4×C8—531no—
458C53C2×#340011yescharacteristic, complemented, Sylow
459C22×Q8—531no—
460C22×Q8—531no—
461C22×Q8—531no—
462C22×Q8—531no—
463C22×Q8C22×D5311yescharacteristic
464C22×D4—531no—
465C22×D4—1061no—
466C22×D4—1061no—
467C22×D4C22×D5311yescharacteristic
468C23×C4—21no—
469C23×C4—1061no—
470C2×Q16—534no—
471C2×Q16—534no—
472C2×Q16—534no—
473C2×Q16—1064no—
474C2×Q16—2122no—
475C2×Q16—2122no—
476C2×SD16—24no—
477C2×SD16—534no—
478C2×SD16—534no—
479C2×SD16—534no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—2122no—
484C2×SD16—2122no—
485C2×SD16—2122no—
486C2×SD16—2122no—
487C2×SD16C22×D5314yes—
488C22×C8—531no—
489C22×C8—531no—
490C22×C8C22×D5311yescharacteristic
491C22×C8C22×D5311yescharacteristic
492C4⋊Q8—534no—
493C4⋊Q8—534no—
494C4⋊Q8—534no—
495C4⋊Q8—1062no—
496C4⋊Q8—1062no—
497C4⋊Q8—1062no—
498#127—534no—
499#127—1062no—
500#125—1068no—
501#125—1068no—
502#125—1068no—
503#124—534no—
504#124—534no—
505#124—1062no—
506#124—1068no—
507#124—1062no—
508#123—1068no—
509#123—1068no—
510C4×Q8—22no—
511C4×Q8—534no—
512C4×Q8—534no—
513C4×Q8—534no—
514C4×Q8—534no—
515C4×Q8—534no—
516C4×Q8—1068no—
517C4×Q8—1062no—
518C4×Q8—1062no—
519C4×Q8—1062no—
520C4×Q8C22×D5314yes—
521C4×D4—22no—
522C4×D4—534no—
523C4×D4—1062no—
524C4×D4—1068no—
525C4×D4C22×D5314yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—531no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4C22×D5311yescharacteristic
540C2×C4⋊C4C22×D5311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C42—21no—
548C2×C42—531no—
549C2×C42—531no—
550C2×C42—1061no—
551C2×C42—1061no—
552C2×C42—1061no—
553C2×C42C22×D5311yescharacteristic
554#107C22×D5314yes—
555C4⋊C8—534no—
556C4⋊C8—534no—
557C4⋊C8—534no—
558#103—534no—
559#103—534no—
560#103—534no—
561#103C22×D5314yes—
562#102—534no—
563#102C22×D5314yes—
564#97—534no—
565#97C22×D5314yes—
566C4×C8—534no—
567C24—21no—
568C24—1061no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—534no—
573C2×Q8—532no—
574C2×Q8—532no—
575C2×Q8—532no—
576C2×Q8—1064no—
577C2×Q8—1061no—
578C2×Q8—1061no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8—1062no—
583C2×Q8—1062no—
584C2×Q8—1062no—
585C2×Q8—1062no—
586C2×Q8C23×D5312yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—532no—
591C2×D4—1064no—
592C2×D4—1064no—
593C2×D4—1061no—
594C2×D4—1062no—
595C2×D4—1062no—
596C2×D4—4242no—
597C2×D4—2124no—
598C2×D4C23×D5312yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—531no—
605C22×C4—531no—
606C22×C4—531no—
607C22×C4—531no—
608C22×C4—1064no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—4242no—
613C22×C4D4×D5311yescharacteristic
614C22×C4D4×D5311yescharacteristic
615C22×C4C23×D5311yescharacteristic
616Q16—1068no—
617Q16—2124no—
618Q16—2124no—
619SD16—28no—
620SD16—1068no—
621SD16—2124no—
622SD16—2124no—
623SD16—2124no—
624SD16—2124no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8#1171994514yes—
631C2×C8C23×D5312yes—
632C2×C8C23×D5312yes—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—534no—
637C4⋊C4—534no—
638C4⋊C4—534no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1064no—
646C4⋊C4—1064no—
647C4⋊C4—1064no—
648C4⋊C4C23×D5312yes—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C42—24no—
657C42—532no—
658C42—532no—
659C42—532no—
660C42—532no—
661C42—1064no—
662C42—1064no—
663C42—1064no—
664C42D4×D5312yes—
665C42C23×D5312yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—1062no—
671C23—2122no—
672C23—2122no—
673C23—2122no—
674C23C2×D4×D5311yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—42no—
678Q8—1068no—
679Q8—1062no—
680Q8—1062no—
681Q8—1062no—
682Q8—1062no—
683Q8—1062no—
684Q8—1062no—
685Q8—2122no—
686Q8—2122no—
687Q8—2122no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—1062no—
692D4—1062no—
693D4—4244no—
694D4—2128no—
695D4—2122no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—534no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—532no—
709C2×C4—532no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—4244no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4C2×#1171994512yes—
724C2×C4#1313326312yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—1062no—
728C8—1062no—
729C8C2×#1171994514yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—4244no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22#1681129412yes—
739C22#137×D5312yes—
740C22#1681143312yes—
741C22C22×D4×D5311yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—534no—
748C4—1062no—
749C4—1062no—
750C4—1062no—
751C4—2122no—
752C4—2122no—
753C4—2122no—
754C4#1681129412yes—
755C4C22×#1171994511yescharacteristic
756C4C2×#1313326311yescharacteristic
757C2—82no—
758C2—4242no—
759C2#2028776914yesdirect product factor
760C2C2×#1681129411yescharacteristic
761C2C2×#137×D5311yescharacteristic
762C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#13133213C22
hypercenterC2×#440D53
hypocenterC53C2×#3400
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16811351C2semidirect
3. #20287769C2direct (N × H)
4. C2×#16811017C2semidirect
5. C2×#16811014C2semidirect
7. C2×#16810845C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810832C2semidirect
11. C2×#16810828C2semidirect
12. C2×#16810827C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810722C2semidirect
15. C2×#16810717C2semidirect
16. C2×C53×#440C2semidirect
28. #16811351C22semidirect
48. #16811017C22semidirect
49. #16811014C22semidirect
51. #16810845C22semidirect
52. #16810844C22semidirect
53. #16810832C22semidirect
54. #16810828C22semidirect
55. #16810827C22semidirect
57. #16810751C22semidirect
58. #16810722C22semidirect
59. #16810717C22semidirect
72. C53×#440C22semidirect
390. C2×#440D53semidirect
393. C2×C53#3400semidirect
443. #440C2×D53semidirect
458. C53C2×#3400semidirect
759. C2#20287769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×#168113512
#202877692
C2×#168110172
C2×#168110142
C2×#168109942
C2×#168108452
C2×#168108442
C2×#168108322
C2×#168108222
C2×#168108282
C2×#168108272
C2×#168107512
C2×#168107222
C2×#168107172
C2×C53×#4402
C2×#340053