Finite Group Databasebeta

← C2×#20285077 #28253337

Subgroups — C2×#20285077 #28253337

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811250C211yesmaximal, characteristic, complemented
2C2×#16811193C211yesmaximal, characteristic
3#20285077C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810990C211yesmaximal, characteristic, complemented
6C2×#16810981C211yesmaximal, characteristic, complemented
7C2×#16810977C211yesmaximal, characteristic, complemented
8C2×#16810976C211yesmaximal, characteristic, complemented
9C2×#16810975C211yesmaximal, characteristic, complemented
10C2×#16810972C211yesmaximal, characteristic, complemented
11C2×#16810621C211yesmaximal, characteristic
12C2×#16810630C211yesmaximal, characteristic, complemented
13C2×#16810616C211yesmaximal, characteristic
14C2×#103×D53C211yesmaximal, characteristic, complemented
15C2×#16810580C211yesmaximal, characteristic, complemented
16C2×C53×#489C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811250—24no—
22#16811250C2218yescomplemented
23#16811193—24no—
24#16811193C2218yes—
25C2×#13133217C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133215—21no—
28C2×#13133215C2211yescharacteristic
29C2×#13133209C2211yescharacteristic
30C2×#13133208C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133204C2211yescharacteristic
33C2×#13133199—21no—
34C2×#13133199—21no—
35C2×#13133195—21no—
36C2×#13133194—21no—
37C2×#13133194—21no—
38C2×#13133193—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810992C2218yescomplemented
43#16810990C2218yescomplemented
44#16810981C2218yescomplemented
45#16810977C2218yescomplemented
46#16810976C2218yescomplemented
47#16810975C2218yescomplemented
48#16810972C2218yescomplemented
49#16810630C2218yescomplemented
50#16810621C2218yes—
51#16810616C2218yes—
52C2×#13133142C2211yescharacteristic
53C2×#13133142C2211yescharacteristic
54C2×#13133142C2211yescharacteristic
55C2×#13133142C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62#103×D53C2218yescomplemented
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65#16810580C2218yescomplemented
66C2×#13133127C2211yescharacteristic
67C2×C4×#88322C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C53×#489C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719947—22no—
78C2×#11719947—24no—
79C2×#11719947—24no—
80C2×#11719947C2314yes—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2311yescharacteristic
85C2×Q8×D53—22no—
86C2×Q8×D53—24no—
87C2×Q8×D53—24no—
88C2×Q8×D53C2314yes—
89C22×C22⋊D53—21no—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C2×#11719912—24no—
95C2×#11719912C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C2×C8×D53—24no—
99C2×C8×D53C2314yes—
100#13133217—22no—
101#13133217C2314yes—
102#13133216—22no—
103#13133216C2314yes—
104#13133215—28no—
105#13133215—22no—
106#13133215C2314yes—
107#13133209—22no—
108#13133209C2314yes—
109#13133208—22no—
110#13133208C2314yes—
111#13133207—28no—
112#13133204—22no—
113#13133204C2314yes—
114#13133199—28no—
115#13133199—28no—
116#13133195—28no—
117#13133194—28no—
118#13133194—28no—
119#13133193—28no—
120#13133175—22no—
121#13133175C2314yes—
122#13133174D414yes—
123#13133174C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×#11719919D411yescharacteristic
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133142C2314yes—
148#13133142C2314yes—
149#13133142C2314yes—
150#13133142C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133140C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133127C2314yes—
160C4×#88322C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53—21no—
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4⋊Q8×C53—22no—
168C4⋊Q8×C53C2314yes—
169#124×C53—22no—
170#124×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#103×C53C2314yes—
178#103×C53C2314yes—
179#102×C53C2314yes—
180#102×C53C2314yes—
181#97×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×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—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—44no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—24no—
207C22×Dic53—44no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211Q8×D53—28no—
212Q8×D53—28no—
213Q8×D53—48no—
214#11719947—28no—
215#11719947—28no—
216#11719947—48no—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—44no—
220C2×C4×D53—82no—
221C2×C4×D53C2×D412yes—
222C2×C4×D53#4114yes—
223C2×C4×D53#4114yes—
224C2×C4×D53C2412yes—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—21no—
230C2×Dic106—21no—
231C2×Dic106—24no—
232C2×Dic106—24no—
233C2×Dic106—44no—
234C2×Dic106—82no—
235C2×Dic106C2412yes—
236C2×Dic106C2412yes—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C2×C8×C53C2412yes—
240C2×C8×C53C2412yes—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53C2412yes—
245C4⋊C4×C53C2412yes—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C42×C53C2×D412yes—
249C42×C53C2412yes—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252#11719921—24no—
253#11719921C2×D414yes—
254#11719921C2×D414yes—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—21no—
259C4⋊Dic53—24no—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919C2×D414yes—
270#11719919C2×D414yes—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278#11719912—28no—
279C8×D53—28no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—22no—
287C22×D53#12414yes—
288C22×D53C22×D412yes—
289Q8×C53—22no—
290Q8×C53—22no—
291Q8×C53—42no—
292Q8×C53—84no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—42no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C2×#4112yes—
308C2×C4×C53C2×#4112yes—
309C2×C4×C53C2511yescharacteristic
310C22⋊D53—48no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—48no—
322C2×Dic53#12414yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C4×D53—48no—
327C4×D53—84no—
328C4×D53#12418yes—
329C4×D53C2×#4114yes—
330C4×D53C2×#4114yes—
331Dic106—22no—
332Dic106—22no—
333Dic106—22no—
334Dic106—22no—
335Dic106—42no—
336Dic106—42no—
337Dic106—48no—
338Dic106—84no—
339C8×C53—22no—
340C8×C53—22no—
341#88322—22no—
342#88322—22no—
343C2×#3137—531nomaximal, Sylow
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—84no—
348C22×C53C2×#12412yes—
349C22×C53#57712yes—
350C22×C53#57812yes—
351C22×C53C23×D411yescharacteristic
352C2×D53—28no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53C2×#12414yes—
356C4×C53—22no—
357C4×C53—22no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53C2×#12412yes—
362C4×C53C22×#4111yescharacteristic
363C4×C53C22×#4111yescharacteristic
364Dic53—22no—
365Dic53—22no—
366Dic53—42no—
367Dic53—42no—
368Dic53—42no—
369Dic53—42no—
370Dic53C2×#12414yes—
371C2×#544—531no—
372C2×#536—531no—
373#3137—5316no—
374C2×#491—531no—
375C2×#491—531no—
376C2×#489—531no—
377C2×#489D5311yescharacteristic, complemented
378C2×#488—531no—
379C2×#488—531no—
380C2×#487—531no—
381C2×#487—531no—
382C2×#417—531no—
383C2×#419—531no—
384C2×#416—531no—
385C22×#103—531no—
386C2×#405—531no—
387C2×C53—82no—
388C2×C53#313714yescomplemented
389C2×C53C22×#12411yescharacteristic
390C2×C53C2×#57711yescharacteristic
391C2×C53C2×#57811yescharacteristic
392D53—24no—
393C22×#41—531no—
394C23×Q8—531no—
395C22×M16—531no—
396C23×C8—531no—
397#544—538no—
398#544—1064no—
399#536—538no—
400#536—1064no—
401C2×C4⋊Q8—531no—
402C2×C4⋊Q8—531no—
403C2×C4⋊Q8—531no—
404C2×C4⋊Q8—1061no—
405C2×C4⋊Q8C2×D5311yescharacteristic
406C2×#125—531no—
407C2×#125—531no—
408C2×#125—1061no—
409C2×#124—531no—
410C2×#124C2×D5311yescharacteristic
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—1061no—
414C2×C22⋊Q8—1061no—
415C2×C22⋊Q8—1061no—
416C2×C22⋊Q8—1061no—
417C2×#117—531no—
418C2×#117—531no—
419C22×C4⋊C4—531no—
420#491—538no—
421#491—538no—
422#489—538no—
423#489C2×D5318yescomplemented
424#488—538no—
425#488—538no—
426#487—538no—
427#487—538no—
428#419—538no—
429#417—538no—
430#416—538no—
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—538no—
442C2×#103C2×D5311yescharacteristic
443C2×#103C2×D5311yescharacteristic
444C2×#102—531no—
445C2×#102—531no—
446C2×#102C2×D5311yescharacteristic
447C2×#102C2×D5311yescharacteristic
448#405—538no—
449C2×#97—531no—
450C2×#97C2×D5311yescharacteristic
451C2×C4×C8—531no—
452C2×C4×C8—531no—
453C53C2×#313711yescharacteristic, complemented, Sylow
454C2×#41—534no—
455C2×#41—1062no—
456C2×#41—1064no—
457C2×#41—1064no—
458C22×Q8—21no—
459C22×Q8—534no—
460C22×Q8—531no—
461C22×Q8—531no—
462C22×Q8—1061no—
463C22×Q8—1061no—
464C22×Q8—1062no—
465C22×Q8—1064no—
466C22×Q8—1064no—
467C22×Q8C22×D5311yescharacteristic
468C22×D4—1061no—
469C22×D4C22×D5311yescharacteristic
470C23×C4—531no—
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C2×M16—534no—
475C2×M16—1064no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—534no—
479C22×C8—1064no—
480C22×C8C22×D5311yescharacteristic
481C22×C8C22×D5311yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—534no—
484C4⋊Q8—534no—
485C4⋊Q8—534no—
486C4⋊Q8—1062no—
487C4⋊Q8—1062no—
488C4⋊Q8—1068no—
489C4⋊Q8—1062no—
490C4⋊Q8C22×D5314yes—
491#125—534no—
492#125—534no—
493#125—1062no—
494#125—1068no—
495#125—1062no—
496#124—22no—
497#124—534no—
498#124—1062no—
499#124C22×D5314yes—
500#123—1068no—
501#123—1068no—
502C22⋊Q8—1068no—
503C22⋊Q8—1068no—
504C22⋊Q8—1068no—
505C22⋊Q8—1068no—
506#117—534no—
507#117—534no—
508#117—534no—
509#117—1062no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—531no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C42—531no—
537C2×C42—1061no—
538C2×C42C22×D5311yescharacteristic
539#103—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103C22×D5314yes—
550#103C22×D5314yes—
551#102—534no—
552#102—534no—
553#102C22×D5314yes—
554#102C22×D5314yes—
555#97—534no—
556#97C22×D5314yes—
557C4×C8—534no—
558C4×C8—534no—
559C24—21no—
560C24—531no—
561#41—1068no—
562#41—1068no—
563#41—2128no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—532no—
570C2×Q8—532no—
571C2×Q8—1064no—
572C2×Q8—1064no—
573C2×Q8—1068no—
574C2×Q8—1068no—
575C2×Q8—1061no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×Q8—1062no—
581C2×Q8—4242no—
582C2×Q8—2124no—
583C2×Q8—2128no—
584C2×Q8C23×D5312yes—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—1064no—
589C2×D4—2124no—
590C2×D4C23×D5312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—531no—
595C22×C4—532no—
596C22×C4—534no—
597C22×C4—534no—
598C22×C4—532no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—1064no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—4242no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4D4×D5311yescharacteristic
612C22×C4D4×D5311yescharacteristic
613C22×C4C23×D5311yescharacteristic
614M16—1068no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—532no—
618C2×C8—532no—
619C2×C8—1068no—
620C2×C8—1062no—
621C2×C8—1062no—
622C2×C8C23×D5312yes—
623C2×C8C23×D5312yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—532no—
630C4⋊C4—532no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1061no—
638C4⋊C4—1061no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4C23×D5312yes—
644C4⋊C4C23×D5312yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—534no—
648C22⋊C4—534no—
649C22⋊C4—1064no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C42—532no—
653C42—532no—
654C42—1064no—
655C42D4×D5312yes—
656C42C23×D5312yes—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—534no—
662C23—532no—
663C23—1062no—
664C23—1062no—
665C23C2×D4×D5311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—1062no—
671Q8—1062no—
672Q8—1062no—
673Q8—1062no—
674Q8—4244no—
675Q8—2128no—
676Q8—2122no—
677Q8—2122no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—2128no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—534no—
691C2×C4—532no—
692C2×C4—538no—
693C2×C4—534no—
694C2×C4—534no—
695C2×C4—532no—
696C2×C4—532no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—4244no—
704C2×C4—2128no—
705C2×C4—2128no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4C2×D4×D5312yes—
711C2×C4C2×D4×D5312yes—
712C2×C4C2×D4×D5311yescharacteristic
713C2×C4#41×D5312yes—
714C2×C4#41×D5312yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1062no—
719C8—1062no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—534no—
725C22—1068no—
726C22—1062no—
727C22—1062no—
728C22#124×D5312yes—
729C22#1681143312yes—
730C22#1681143912yes—
731C22C22×D4×D5311yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—534no—
738C4—1062no—
739C4—1062no—
740C4—2122no—
741C4—2122no—
742C4—2122no—
743C4—2122no—
744C4#124×D5312yes—
745C4C2×#41×D5311yescharacteristic
746C4C2×#41×D5311yescharacteristic
747C2—82no—
748C2—1064no—
749C2#2028507714yesdirect product factor
750C2C2×#124×D5311yescharacteristic
751C2C2×#1681143311yescharacteristic
752C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#489C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
hypercenterC2×#489D53
hypocenterC53C2×#3137
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16811250C2semidirect
3. #20285077C2direct (N × H)
4. C2×#16810992C2semidirect
5. C2×#16810990C2semidirect
6. C2×#16810981C2semidirect
7. C2×#16810977C2semidirect
8. C2×#16810976C2semidirect
9. C2×#16810975C2semidirect
10. C2×#16810972C2semidirect
12. C2×#16810630C2semidirect
14. C2×#103×D53C2semidirect
15. C2×#16810580C2semidirect
16. C2×C53×#489C2semidirect
22. #16811250C22semidirect
42. #16810992C22semidirect
43. #16810990C22semidirect
44. #16810981C22semidirect
45. #16810977C22semidirect
46. #16810976C22semidirect
47. #16810975C22semidirect
48. #16810972C22semidirect
49. #16810630C22semidirect
62. #103×D53C22semidirect
65. #16810580C22semidirect
71. C53×#489C22semidirect
377. C2×#489D53semidirect
388. C2×C53#3137semidirect
423. #489C2×D53semidirect
453. C53C2×#3137semidirect
749. C2#20285077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112502
C2×#168111932
#202850772
C2×#168109922
C2×#168109902
C2×#168109812
C2×#168109772
C2×#168109762
C2×#168109752
C2×#168109722
C2×#168106212
C2×#168106302
C2×#168106162
C2×#103×D532
C2×#168105802
C2×C53×#4892
C2×#313753