Finite Group Databasebeta

← C2×#20291473 #28329531

Subgroups — C2×#20291473 #28329531

Order 13568.

2730 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811692C211yesmaximal, characteristic
2C2×#16811691C211yesmaximal, characteristic, complemented
3#20291473C2116yesmaximal, direct product factor
4C2×#16811663C212yesmaximal, complemented
5C2×#16811662C212yesmaximal, complemented
6C2×Q16×#6157C212yesmaximal, complemented
7C2×SD16×#6157C212yesmaximal, complemented
8C2×#16811634C211yesmaximal, characteristic, complemented
9C2×#16811613C211yesmaximal, characteristic
10C22×#13133280C211yesmaximal, characteristic, complemented
11C2×#16811589C211yesmaximal, characteristic, complemented
12C2×#137×D53C211yesmaximal, characteristic
13C22×D53⋊C8C2211yescharacteristic
14#16811692—24no—
15#16811692C2218yes—
16#16811691—24no—
17#16811691C2218yescomplemented
18C2×Q8×#6157—21no—
19C2×Q8×#6157—21no—
20C2×Q8×#6157C2212yes—
21C2×Q8×#6157C2212yes—
22C2×Q8×#6157C2212yes—
23C2×D4×#6157—22no—
24C2×D4×#6157C2212yes—
25C2×#13133296—21no—
26C2×#13133296—22no—
27C2×#13133296C2211yescharacteristic
28C2×#13133296C2211yescharacteristic
29C22×C4⋊#6157—21no—
30C22×C4⋊#6157C2211yescharacteristic
31#16811663C22116yescomplemented
32#16811662C22116yescomplemented
33Q16×#6157C22116yescomplemented
34SD16×#6157C22116yescomplemented
35#16811634C2218yescomplemented
36C2×#13133286C2212yes—
37C2×#13133285C2212yes—
38#16811613C2218yes—
39C2×#13133280C2212yes—
40C2×#13133280C2212yes—
41C2×#13133280C2211yescharacteristic
42C2×#13133280C2211yescharacteristic
43C2×#13133280C2218yescomplemented
44C2×#13133279C2211yescharacteristic
45C2×#13133279C2211yescharacteristic
46#16811589C2218yescomplemented
47C2×#13133271C2212yes—
48C2×C8×#6157C2212yes—
49C2×#41×D53C2211yescharacteristic
50C22×Q8×D53C2211yescharacteristic
51C2×#13133250C411yescharacteristic, complemented
52C2×#13133249C412yescomplemented
53C2×#13133248C411yescharacteristic, complemented
54C2×#13133247C411yescharacteristic, complemented
55C2×#13133246C412yescomplemented
56#137×D53C418yescomplemented
57#137×D53C2218yes—
58C2×Q16×D53C2212yes—
59C2×SD16×D53C2212yes—
60C2×M16×D53C2211yescharacteristic
61C2×#137×C53C411yescharacteristic, complemented
62C23×#6157—21no—
63C23×#6157—22no—
64C2×D53⋊C8—22no—
65C2×D53⋊C8—21no—
66C2×D53⋊C8C2311yescharacteristic
67C2×D53⋊C8C2311yescharacteristic
68C2×D53⋊C8C2314yes—
69C22×#88324—21no—
70Q8×#6157—28no—
71Q8×#6157—28no—
72Q8×#6157—24no—
73Q8×#6157—24no—
74Q8×#6157—24no—
75Q8×#6157C2318yes—
76Q8×#6157C2318yes—
77Q8×#6157C2318yes—
78D4×#6157—216no—
79D4×#6157—24no—
80D4×#6157C2318yes—
81#13133296—22no—
82#13133296—216no—
83#13133296—28no—
84#13133296D414yes—
85#13133296C2314yes—
86#13133296C2314yes—
87C2×C4⋊#6157—22no—
88C2×C4⋊#6157—22no—
89C2×C4⋊#6157—22no—
90C2×C4⋊#6157—21no—
91C2×C4⋊#6157—22no—
92C2×C4⋊#6157—28no—
93C2×C4⋊#6157D411yescharacteristic
94C2×C4⋊#6157D411yescharacteristic
95C2×C4⋊#6157C2311yescharacteristic
96C2×C4⋊#6157C2311yescharacteristic
97C2×C4⋊#6157C2312yes—
98C2×C4⋊#6157C2314yes—
99C2×C22⋊#6157—21no—
100C2×C22⋊#6157—22no—
101C2×C22⋊#6157D412yes—
102C2×C4×#6157—22no—
103C2×C4×#6157—22no—
104C2×C4×#6157—22no—
105C2×C4×#6157—21no—
106C2×C4×#6157C2312yes—
107#13133286C2318yes—
108#13133285C2318yes—
109#13133280C2318yes—
110#13133280C2318yes—
111#13133280C2314yes—
112#13133280C2314yes—
113#13133279C2314yes—
114#13133279C2314yes—
115#13133271C2318yes—
116C8×#6157C2318yes—
117C2×#11719949C2×C411yescharacteristic
118C2×#11719945—21no—
119C2×#11719945C2×C411yescharacteristic
120C2×#11719947—21no—
121C2×#11719947C2×C411yescharacteristic
122#41×D53—22no—
123#41×D53—22no—
124#41×D53C2×C414yes—
125#41×D53C2314yes—
126C22×Dic106—21no—
127C22×Dic106C2×C411yescharacteristic, complemented
128C2×Q8×D53—21no—
129C2×Q8×D53—22no—
130C2×Q8×D53—22no—
131C2×Q8×D53—21no—
132C2×Q8×D53C2×C412yescomplemented
133C2×Q8×D53C2×C414yescomplemented
134C2×Q8×D53C2312yes—
135C2×Q8×D53C2311yescharacteristic
136C2×Q8×D53C2314yes—
137C2×D4×D53—21no—
138C2×D4×D53C2311yescharacteristic
139C22×C4×D53—21no—
140C22×C4×D53—21no—
141C22×C4×D53C2311yescharacteristic
142#13133250C2×C418yescomplemented
143#13133249C2×C4116yescomplemented
144#13133248C2×C418yescomplemented
145#13133247C2×C418yescomplemented
146#13133246C2×C4116yescomplemented
147C2×Dic212C2×C412yescomplemented
148C2×#11719925C2×C412yescomplemented
149C2×#11719925C2×C412yescomplemented
150Q16×D53C2×C418yescomplemented
151Q16×D53C2318yes—
152C2×#11719913C2×C412yescomplemented
153C2×#11719923C2×C412yescomplemented
154C2×#11719924C2×C412yescomplemented
155SD16×D53C2×C418yescomplemented
156SD16×D53C2318yes—
157C2×#11719917C2×C411yescharacteristic, complemented
158C2×#11719912C2×C412yescomplemented
159M16×D53C2×C414yescomplemented
160M16×D53C2314yes—
161C2×C8×D53C2312yes—
162C2×#41×C53C2×C411yescharacteristic
163C22×Q8×C53C2×C411yescharacteristic, complemented
164#137×C53C2×C418yescomplemented
165C2×Q16×C53C2×C412yescomplemented
166C2×SD16×C53C2×C412yescomplemented
167C2×M16×C53C2×C411yescharacteristic, complemented
168C23×D53—21no—
169C23×D53C2×D411yescharacteristic
170C22×#6157—21no—
171C22×#6157—21no—
172C22×#6157—22no—
173C22×#6157—24no—
174C22×#6157—28no—
175C22×#6157—84no—
176C22×#6157—82no—
177C22×#6157C2×D412yes—
178C22×#6157C2×D412yes—
179#41×C53—22no—
180#41×C53C22×C414yes—
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53C22×C412yes—
184C2×Q8×C53C22×C411yescharacteristic
185C2×Q8×C53C22×C414yescomplemented
186C2×D4×C53—21no—
187C2×D4×C53C22×C411yescharacteristic
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C22×C411yescharacteristic
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53#4111yescharacteristic
197#11719949—22no—
198#11719949C22×C414yes—
199Q8×D53—24no—
200Q8×D53—24no—
201Q8×D53—24no—
202Q8×D53—22no—
203Q8×D53—24no—
204Q8×D53—21no—
205Q8×D53—22no—
206Q8×D53—24no—
207Q8×D53—21no—
208Q8×D53C22×C414yes—
209Q8×D53C22×C412yes—
210Q8×D53C22×C418yescomplemented
211Q8×D53C2414yes—
212Q8×D53C2412yes—
213#11719947—24no—
214#11719947—24no—
215#11719947—22no—
216#11719947C22×C414yes—
217D4×D53—24no—
218D4×D53—24no—
219D4×D53—21no—
220D4×D53—21no—
221D4×D53C22×C412yes—
222D4×D53C2412yes—
223#11719945—22no—
224#11719945—24no—
225#11719945—24no—
226#11719945C22×C414yes—
227C2×D212—21no—
228C2×D212C22×C411yescharacteristic
229C2×C4×D53—24no—
230C2×C4×D53—22no—
231C2×C4×D53—21no—
232C2×C4×D53—22no—
233C2×C4×D53—24no—
234C2×C4×D53—21no—
235C2×C4×D53—21no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53C22×C412yes—
239C2×C4×D53C22×C411yescharacteristic
240C2×C4×D53C2×D411yescharacteristic
241C2×C4×D53C2×D412yes—
242C2×C4×D53#4112yes—
243C2×C4×D53#4111yescharacteristic
244C2×C4×D53C2411yescharacteristic
245C2×C4×D53C2412yes—
246C2×Dic106—22no—
247C2×Dic106—21no—
248C2×Dic106—24no—
249C2×Dic106—22no—
250C2×Dic106—22no—
251C2×Dic106—24no—
252C2×Dic106—21no—
253C2×Dic106C22×C412yes—
254C2×Dic106C22×C411yescharacteristic
255C2×Dic106C22×C414yescomplemented
256C22⋊#6157—24no—
257C22⋊#6157—28no—
258C22⋊#6157C2×D418yes—
259C2×#88324—21no—
260C2×#88324—21no—
261C2×#88324—24no—
262C4⋊#6157—28no—
263C4⋊#6157—28no—
264C4⋊#6157—28no—
265C4⋊#6157—24no—
266C4⋊#6157—22no—
267C4⋊#6157—21no—
268C4⋊#6157—21no—
269C4⋊#6157C2×D414yes—
270C4⋊#6157C2×D414yes—
271C4⋊#6157C2412yes—
272C4⋊#6157C2412yes—
273C4⋊#6157C2414yes—
274C4×#6157—28no—
275C4×#6157—28no—
276C4×#6157—28no—
277C4×#6157—24no—
278C4×#6157C2×D414yes—
279C4×#6157C2414yes—
280D53⋊C8—24no—
281D53⋊C8—21no—
282D53⋊C8—21no—
283D53⋊C8C2412yes—
284D53⋊C8C2412yes—
285Q16×C53C22×C418yescomplemented
286SD16×C53C22×C418yescomplemented
287M16×C53C22×C414yescomplemented
288C2×C8×C53C22×C412yes—
289#11719925C22×C418yescomplemented
290#11719925C22×C418yescomplemented
291#11719924C22×C418yescomplemented
292#11719923C22×C418yescomplemented
293#11719917C22×C414yescomplemented
294C2×#88322C22×C412yes—
295Dic212C22×C418yescomplemented
296#11719913C22×C418yescomplemented
297#11719912C22×C418yescomplemented
298C8×D53C22×C414yes—
299C8×D53C2414yes—
300C23×C53—21no—
301C23×C53C4×D411yescharacteristic
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—21no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53C4×D411yescharacteristic
310C22×D53C4×D412yes—
311C22×D53C22×D412yes—
312C22×D53C22×D411yescharacteristic
313C2×#6157—24no—
314C2×#6157—24no—
315C2×#6157—22no—
316C2×#6157—22no—
317C2×#6157—24no—
318C2×#6157—42no—
319C2×#6157—44no—
320C2×#6157—42no—
321C2×#6157—88no—
322C2×#6157—84no—
323C2×#6157C22×D414yes—
324C2×#6157C22×D414yes—
325Q8×C53—22no—
326Q8×C53—24no—
327Q8×C53—21no—
328Q8×C53C23×C414yes—
329Q8×C53C23×C412yes—
330D4×C53—24no—
331D4×C53—21no—
332D4×C53C23×C412yes—
333C2×C4×C53—22no—
334C2×C4×C53—24no—
335C2×C4×C53—21no—
336C2×C4×C53—24no—
337C2×C4×C53C4×D411yescharacteristic
338C2×C4×C53C4×D412yes—
339C2×C4×C53C23×C411yescharacteristic
340C2×C4×C53C23×C412yes—
341C22⋊D53—24no—
342C22⋊D53—24no—
343C22⋊D53—22no—
344C22⋊D53—22no—
345C2×Dic53—22no—
346C2×Dic53—24no—
347C2×Dic53—21no—
348C2×Dic53—24no—
349C2×Dic53C4×D411yescharacteristic
350C2×Dic53C4×D412yes—
351C2×Dic53C2×#4111yescharacteristic
352C2×Dic53C2×#4112yes—
353D212—24no—
354D212—21no—
355D212C23×C412yes—
356C4×D53—22no—
357C4×D53—24no—
358C4×D53—28no—
359C4×D53—22no—
360C4×D53—24no—
361C4×D53—24no—
362C4×D53—24no—
363C4×D53C4×D412yes—
364C4×D53C4×D412yes—
365C4×D53C4×D412yes—
366C4×D53C23×C411yescharacteristic
367C4×D53C23×C412yes—
368C4×D53C22×D412yes—
369C4×D53C22×D411yescharacteristic
370C4×D53C2×#4112yes—
371C4×D53C2×#4111yescharacteristic
372C4×D53C2511yescharacteristic
373Dic106—22no—
374Dic106—24no—
375Dic106—21no—
376Dic106—24no—
377Dic106—28no—
378Dic106—22no—
379Dic106—24no—
380Dic106—22no—
381Dic106C23×C414yes—
382Dic106C23×C412yes—
383#88324—22no—
384#88324—22no—
385C8×C53C23×C414yes—
386#88322C23×C414yes—
387C2×#2947—531nomaximal, Sylow
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—42no—
391C22×C53C2×C4×D412yes—
392C22×C53C2×C4×D411yescharacteristic
393C2×D53—22no—
394C2×D53—24no—
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—22no—
398C2×D53—42no—
399C2×D53—44no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53C2×C4×D412yes—
403C2×D53C2×C4×D411yescharacteristic
404C2×D53#57712yes—
405C2×D53#57812yes—
406C2×D53C23×D411yescharacteristic
407#6157—24no—
408#6157—24no—
409#6157—42no—
410#6157—44no—
411#6157—42no—
412C4×C53—24no—
413C4×C53—22no—
414C4×C53C2×C4×D411yescharacteristic
415C4×C53C2×C4×D412yes—
416C4×C53C24×C411yescharacteristic
417Dic53—24no—
418Dic53—22no—
419Dic53C2×C4×D411yescharacteristic
420Dic53C2×C4×D412yes—
421Dic53C22×#4111yescharacteristic
422C22×#137—531no—
423C2×#520—531no—
424C2×#519—531no—
425#2947—5316no—
426C2×#441—532no—
427C2×#440—532no—
428C2×C4×Q16—532no—
429C2×C4×SD16—532no—
430C2×#428—531no—
431C2×#416—531no—
432C22×#103—531no—
433C2×#405—531no—
434C2×C53—22no—
435C2×C53—42no—
436C2×C53#294712yescomplemented
437C2×C53C22×C4×D411yescharacteristic
438D53—22no—
439D53—42no—
440D53#294712yescomplemented
441D53C2×#57711yescharacteristic
442D53C2×#57811yescharacteristic
443C22×#41—531no—
444C23×Q8—531no—
445C2×#137—531no—
446C2×#137—531no—
447C2×#137—538no—
448C2×#137—538no—
449C2×#137—532no—
450C2×#137—532no—
451C2×#137—531no—
452C2×#137#615711yescharacteristic, complemented
453C22×Q16—532no—
454C22×SD16—532no—
455C22×M16—531no—
456C23×C8—531no—
457#520—538no—
458#520—1064no—
459#519—538no—
460#519—1064no—
461C2×C4×Q8—532no—
462C2×C4×Q8—532no—
463C2×C4×Q8—532no—
464C2×C4×Q8—1061no—
465C2×C4×Q8—1061no—
466C2×C4×D4—532no—
467C2×C4×D4—1062no—
468C2×#117—531no—
469C2×#117—531no—
470C2×#117—1062no—
471C2×#117—1061no—
472C22×C4⋊C4—531no—
473C22×C4⋊C4—1061no—
474#441—5316no—
475#440—5316no—
476C4×Q16—5316no—
477C4×SD16—5316no—
478#428—538no—
479C2×#107—532no—
480C2×#106—532no—
481#416—538no—
482C2×#103—532no—
483C2×#103—532no—
484C2×#103—538no—
485C2×#103—531no—
486C2×#103—531no—
487C2×#102—531no—
488C2×#102—531no—
489#405—538no—
490C2×#97—532no—
491C2×C4×C8—532no—
492C53C2×#294711yescharacteristic, complemented, Sylow
493C2×#41—534no—
494C2×#41—534no—
495C2×#41—531no—
496C2×#41—531no—
497C2×#41—531no—
498C2×#41—1061no—
499C2×#41—1061no—
500C2×#41—1062no—
501C2×#41—1062no—
502C2×#41C2×#615711yescharacteristic
503C22×Q8—532no—
504C22×Q8—531no—
505C22×Q8—532no—
506C22×Q8—534no—
507C22×Q8—534no—
508C22×Q8—531no—
509C22×Q8—1061no—
510C22×Q8—1061no—
511C22×Q8—1062no—
512C22×Q8—1062no—
513C22×Q8—1061no—
514C22×Q8C2×#615711yescharacteristic, complemented
515C22×D4—531no—
516C22×D4—1061no—
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4—1062no—
521C23×C4—1061no—
522#137—538no—
523#137—538no—
524#137—5316no—
525#137—5316no—
526#137—538no—
527#137C2×#615718yescomplemented
528C2×Q16—532no—
529C2×Q16—532no—
530C2×Q16—538no—
531C2×Q16—538no—
532C2×Q16—532no—
533C2×Q16C2×#615712yescomplemented
534C2×SD16—532no—
535C2×SD16—532no—
536C2×SD16—538no—
537C2×SD16—538no—
538C2×SD16—532no—
539C2×SD16C2×#615712yescomplemented
540C2×M16—531no—
541C2×M16—534no—
542C2×M16—534no—
543C2×M16—532no—
544C2×M16C2×#615711yescharacteristic, complemented
545C22×C8—532no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—534no—
549C22×C8—1061no—
550C22×C8—1062no—
551C22×C8—1061no—
552C4×Q8—538no—
553C4×Q8—538no—
554C4×Q8—538no—
555C4×Q8—1064no—
556C4×Q8—1064no—
557C4×Q8—1064no—
558C4×Q8—1068no—
559C4×Q8—1068no—
560C4×D4—538no—
561C4×D4—1064no—
562C4×D4—10616no—
563#117—534no—
564#117—534no—
565#117—534no—
566#117—10616no—
567#117—1068no—
568#117—1062no—
569C2×C4⋊C4—531no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—532no—
572C2×C4⋊C4—534no—
573C2×C4⋊C4—531no—
574C2×C4⋊C4—531no—
575C2×C4⋊C4—1068no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1062no—
578C2×C4⋊C4—1062no—
579C2×C4⋊C4—1062no—
580C2×C4⋊C4—1062no—
581C2×C22⋊C4—532no—
582C2×C22⋊C4—1062no—
583C2×C22⋊C4—1061no—
584C2×C42—532no—
585C2×C42—1061no—
586C2×C42—1062no—
587C2×C42—1062no—
588C2×C42—1062no—
589#107—538no—
590#106—538no—
591#103—538no—
592#103—538no—
593#103—534no—
594#103—534no—
595#102—534no—
596#102—534no—
597#97—538no—
598C4×C8—538no—
599C24—531no—
600C24—1061no—
601#41—22no—
602#41—534no—
603#41—534no—
604#41—534no—
605#41—1064no—
606#41—1064no—
607#41—1064no—
608#41—1064no—
609#41—1062no—
610#41—1062no—
611#41—1062no—
612#41C22×#615714yes—
613C2×Q8—22no—
614C2×Q8—21no—
615C2×Q8—534no—
616C2×Q8—532no—
617C2×Q8—538no—
618C2×Q8—534no—
619C2×Q8—532no—
620C2×Q8—532no—
621C2×Q8—531no—
622C2×Q8—534no—
623C2×Q8—1064no—
624C2×Q8—1064no—
625C2×Q8—1062no—
626C2×Q8—1062no—
627C2×Q8—1061no—
628C2×Q8—1062no—
629C2×Q8—1064no—
630C2×Q8—1061no—
631C2×Q8—1064no—
632C2×Q8—1064no—
633C2×Q8—1064no—
634C2×Q8—1062no—
635C2×Q8—1064no—
636C2×Q8—1061no—
637C2×Q8—1062no—
638C2×Q8—1061no—
639C2×Q8C22×#615712yes—
640C2×Q8C22×#615711yescharacteristic
641C2×Q8C22×#615714yescomplemented
642C2×D4—21no—
643C2×D4—532no—
644C2×D4—532no—
645C2×D4—531no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—1061no—
649C2×D4—1061no—
650C2×D4—1064no—
651C2×D4—1064no—
652C2×D4—1061no—
653C2×D4—1061no—
654C2×D4C22×#615711yescharacteristic
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—532no—
660C22×C4—532no—
661C22×C4—531no—
662C22×C4—532no—
663C22×C4—531no—
664C22×C4—531no—
665C22×C4—532no—
666C22×C4—532no—
667C22×C4—532no—
668C22×C4—1064no—
669C22×C4—1061no—
670C22×C4—1064no—
671C22×C4—1061no—
672C22×C4—1062no—
673C22×C4—1064no—
674C22×C4—1064no—
675C22×C4—1062no—
676C22×C4—1061no—
677C22×C4—1068no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—1064no—
681C22×C4—1061no—
682C22×C4—1061no—
683C22×C4—1062no—
684C22×C4—4244no—
685C22×C4—4242no—
686C22×C4C22×#615711yescharacteristic
687Q16—538no—
688Q16—538no—
689Q16—538no—
690Q16C22×#615718yescomplemented
691SD16—538no—
692SD16—538no—
693SD16—538no—
694SD16C22×#615718yescomplemented
695M16—534no—
696M16—538no—
697M16C22×#615714yescomplemented
698C2×C8—532no—
699C2×C8—534no—
700C2×C8—534no—
701C2×C8—532no—
702C2×C8—532no—
703C2×C8—1064no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1064no—
709C2×C8C22×#615712yes—
710C4⋊C4—534no—
711C4⋊C4—534no—
712C4⋊C4—532no—
713C4⋊C4—532no—
714C4⋊C4—534no—
715C4⋊C4—1064no—
716C4⋊C4—1062no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1068no—
720C4⋊C4—1068no—
721C4⋊C4—1068no—
722C22⋊C4—538no—
723C22⋊C4—1068no—
724C22⋊C4—1064no—
725C42—534no—
726C42—534no—
727C42—1064no—
728C42—1068no—
729C42—1068no—
730C42—1068no—
731C23—21no—
732C23—531no—
733C23—532no—
734C23—532no—
735C23—531no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—1061no—
741C23—2122no—
742C23—2122no—
743C23D4×#615711yescharacteristic
744Q8—22no—
745Q8—24no—
746Q8—21no—
747Q8—534no—
748Q8—532no—
749Q8—1064no—
750Q8—1068no—
751Q8—1064no—
752Q8—1062no—
753Q8—1062no—
754Q8—1064no—
755Q8—1062no—
756Q8—1061no—
757Q8C23×#615714yes—
758Q8C23×#615712yes—
759D4—24no—
760D4—21no—
761D4—532no—
762D4—1064no—
763D4—1062no—
764D4—1062no—
765D4—1064no—
766D4—1064no—
767D4—1061no—
768D4C23×#615712yes—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—532no—
774C2×C4—532no—
775C2×C4—531no—
776C2×C4—531no—
777C2×C4—532no—
778C2×C4—532no—
779C2×C4—532no—
780C2×C4—531no—
781C2×C4—532no—
782C2×C4—531no—
783C2×C4—532no—
784C2×C4—531no—
785C2×C4—532no—
786C2×C4—531no—
787C2×C4—534no—
788C2×C4—534no—
789C2×C4—1064no—
790C2×C4—1062no—
791C2×C4—1064no—
792C2×C4—1062no—
793C2×C4—1064no—
794C2×C4—1068no—
795C2×C4—1064no—
796C2×C4—1064no—
797C2×C4—1064no—
798C2×C4—1064no—
799C2×C4—1061no—
800C2×C4—1062no—
801C2×C4—1064no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—1064no—
805C2×C4—4248no—
806C2×C4—4244no—
807C2×C4—2122no—
808C2×C4—2122no—
809C2×C4—2124no—
810C2×C4D4×#615712yes—
811C2×C4D4×#615711yescharacteristic
812C2×C4C23×#615712yes—
813C2×C4C23×#615711yescharacteristic
814C8—534no—
815C8—1062no—
816C8—1062no—
817C8C23×#615714yes—
818C22—22no—
819C22—22no—
820C22—42no—
821C22—531no—
822C22—531no—
823C22—532no—
824C22—532no—
825C22—532no—
826C22—1062no—
827C22—1062no—
828C22—1064no—
829C22—1062no—
830C22—1062no—
831C22—2122no—
832C22—2122no—
833C22—2124no—
834C22—2122no—
835C22C2×D4×#615712yes—
836C22C2×D4×#615711yescharacteristic
837C4—22no—
838C4—24no—
839C4—531no—
840C4—532no—
841C4—531no—
842C4—1064no—
843C4—1064no—
844C4—1062no—
845C4—1064no—
846C4—2124no—
847C4—2122no—
848C4—2122no—
849C4C2×D4×#615712yes—
850C4C2×D4×#615711yescharacteristic
851C4C24×#615711yescharacteristic
852C2—22no—
853C2—42no—
854C2—531no—
855C2—531no—
856C2—532no—
857C2—1062no—
858C2—2122no—
859C2#2029147312yesdirect product factor
860C2C22×D4×#615711yescharacteristic
subgroupG/H
centerC22C2×D4×#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC2×#137×C53C4
socleC22×C53C2×C4×D4
prime radicalC2×#41×D53C22
cosocleC4×D53C25
hypercenterC2×#137#6157
hypocenterC53C2×#2947
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#16811691C2semidirect
3. #20291473C2direct (N × H)
4. C2×#16811663C2semidirect
5. C2×#16811662C2semidirect
6. C2×Q16×#6157C2semidirect
7. C2×SD16×#6157C2semidirect
8. C2×#16811634C2semidirect
10. C22×#13133280C2semidirect
11. C2×#16811589C2semidirect
17. #16811691C22semidirect
31. #16811663C22semidirect
32. #16811662C22semidirect
33. Q16×#6157C22semidirect
34. SD16×#6157C22semidirect
35. #16811634C22semidirect
43. C2×#13133280C22semidirect
46. #16811589C22semidirect
51. C2×#13133250C4semidirect
52. C2×#13133249C4semidirect
53. C2×#13133248C4semidirect
54. C2×#13133247C4semidirect
55. C2×#13133246C4semidirect
56. #137×D53C4semidirect
61. C2×#137×C53C4semidirect
127. C22×Dic106C2×C4semidirect
132. C2×Q8×D53C2×C4semidirect
133. C2×Q8×D53C2×C4semidirect
142. #13133250C2×C4semidirect
143. #13133249C2×C4semidirect
144. #13133248C2×C4semidirect
145. #13133247C2×C4semidirect
146. #13133246C2×C4semidirect
147. C2×Dic212C2×C4semidirect
148. C2×#11719925C2×C4semidirect
149. C2×#11719925C2×C4semidirect
150. Q16×D53C2×C4semidirect
152. C2×#11719913C2×C4semidirect
153. C2×#11719923C2×C4semidirect
154. C2×#11719924C2×C4semidirect
155. SD16×D53C2×C4semidirect
157. C2×#11719917C2×C4semidirect
158. C2×#11719912C2×C4semidirect
159. M16×D53C2×C4semidirect
163. C22×Q8×C53C2×C4semidirect
164. #137×C53C2×C4semidirect
165. C2×Q16×C53C2×C4semidirect
166. C2×SD16×C53C2×C4semidirect
167. C2×M16×C53C2×C4semidirect
185. C2×Q8×C53C22×C4semidirect
210. Q8×D53C22×C4semidirect
255. C2×Dic106C22×C4semidirect
285. Q16×C53C22×C4semidirect
286. SD16×C53C22×C4semidirect
287. M16×C53C22×C4semidirect
289. #11719925C22×C4semidirect
290. #11719925C22×C4semidirect
291. #11719924C22×C4semidirect
292. #11719923C22×C4semidirect
293. #11719917C22×C4semidirect
295. Dic212C22×C4semidirect
296. #11719913C22×C4semidirect
297. #11719912C22×C4semidirect
436. C2×C53#2947semidirect
440. D53#2947semidirect
452. C2×#137#6157semidirect
492. C53C2×#2947semidirect
514. C22×Q8C2×#6157semidirect
527. #137C2×#6157semidirect
533. C2×Q16C2×#6157semidirect
539. C2×SD16C2×#6157semidirect
544. C2×M16C2×#6157semidirect
641. C2×Q8C22×#6157semidirect
690. Q16C22×#6157semidirect
694. SD16C22×#6157semidirect
697. M16C22×#6157semidirect
859. C2#20291473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168116922
C2×#168116912
#202914732
C2×#168116632
C2×#168116622
C2×Q16×#61572
C2×SD16×#61572
C2×#168116342
C2×#168116132
C22×#131332802
C2×#168115892
C2×#137×D532
C2×#294753