Finite Group Databasebeta

← C2×#20286285 #28259137

Subgroups — C2×#20286285 #28259137

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
3C2×#16811284C211yesmaximal, characteristic
4#20286285C2116yesmaximal, direct product factor
5C2×#16811016C211yesmaximal, characteristic, complemented
6C2×#16810878C211yesmaximal, characteristic, complemented
7C2×#16810852C211yesmaximal, characteristic, complemented
8C2×#16810847C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810784C211yesmaximal, characteristic, complemented
11C2×#16810779C211yesmaximal, characteristic, complemented
12C2×#16810777C211yesmaximal, characteristic, complemented
13C2×#16810762C211yesmaximal, characteristic, complemented
14C2×#16810730C211yesmaximal, characteristic, complemented
15C2×#16810694C211yesmaximal, characteristic, complemented
16C23×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C2×#13133249—28no—
20C2×#13133249C2218yescomplemented
21C22×#11719925C2211yescharacteristic
22C22×#11719925C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25C22×#11719924C2211yescharacteristic
26C22×#11719912C2211yescharacteristic
27Q8×C22⋊D53—24no—
28Q8×C22⋊D53C2218yescomplemented
29#16811284—24no—
30#16811284C2218yes—
31C2×#13133215—21no—
32C2×#13133215C2211yescharacteristic
33C2×#13133206—21no—
34C2×#13133206C2211yescharacteristic
35C2×#13133196—21no—
36C2×#13133196C2211yescharacteristic
37C2×#13133193—21no—
38C2×#13133193—21no—
39C2×#13133193C2211yescharacteristic
40C2×#13133193C2211yescharacteristic
41C2×#13133191—21no—
42C2×#13133191C2211yescharacteristic
43C2×Q8×Dic53C2211yescharacteristic
44C2×Q8×Dic53C2211yescharacteristic
45C2×C4×C22⋊D53—21no—
46C2×C4×C22⋊D53—21no—
47C2×C4×C22⋊D53C2211yescharacteristic
48#16811016C2218yescomplemented
49#16810878C2218yescomplemented
50#16810852C2218yescomplemented
51#16810847C2218yescomplemented
52#16810831C2218yescomplemented
53#16810784C2218yescomplemented
54#16810779C2218yescomplemented
55#16810777C2218yescomplemented
56#16810762C2218yescomplemented
57#16810730C2218yescomplemented
58#16810694C2218yescomplemented
59C2×#13133149C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×C22⋊#88322C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#13133127C2211yescharacteristic
70C23×Q8×C53C2211yescharacteristic
71C23×Q8×C53C2211yescharacteristic
72C22×Q16×C53—28no—
73C22×Q16×C53C2211yescharacteristic
74C22×Q16×C53C2211yescharacteristic
75C22×Q16×C53C2211yescharacteristic
76C22×Q16×C53C2211yescharacteristic
77C22×Q16×C53C2218yescomplemented
78C23×C8×C53C2211yescharacteristic
79C2×#11719949—22no—
80C2×#11719949—24no—
81C2×#11719949—42no—
82C2×#11719949C2314yes—
83C22×Dic106—21no—
84C22×Dic106C2311yescharacteristic
85C2×Q8×D53—22no—
86C2×Q8×D53—24no—
87C2×Q8×D53—42no—
88C2×Q8×D53C2314yes—
89C22×D212—21no—
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53D411yescharacteristic
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96#13133249—232no—
97C2×#11719925—24no—
98C2×#11719925—42no—
99C2×#11719925C2314yes—
100C2×#11719925C2314yes—
101C2×#11719913—24no—
102C2×#11719913C2314yes—
103C2×#11719924—24no—
104C2×#11719924—42no—
105C2×#11719924C2314yes—
106C2×#11719924C2314yes—
107C2×#11719912—24no—
108C2×#11719912C2314yes—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111#13133215—28no—
112#13133215—22no—
113#13133215C2314yes—
114#13133206—28no—
115#13133206—22no—
116#13133206C2314yes—
117#13133196—28no—
118#13133196—22no—
119#13133196C2314yes—
120#13133193—28no—
121#13133193—28no—
122#13133193—22no—
123#13133193—22no—
124#13133193C2314yes—
125#13133193C2314yes—
126#13133191—22no—
127#13133191—28no—
128#13133191C2314yes—
129Q8×Dic53—22no—
130Q8×Dic53—22no—
131Q8×Dic53C2314yes—
132Q8×Dic53C2314yes—
133C4×C22⋊D53—28no—
134C4×C22⋊D53—28no—
135C4×C22⋊D53D414yes—
136C4×C22⋊D53C2314yes—
137C2×C4⋊Dic53—21no—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919—21no—
145C2×#11719919—21no—
146C2×#11719919D411yescharacteristic
147C2×C22⋊Dic53—21no—
148C2×C22⋊Dic53D411yescharacteristic
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921D411yescharacteristic
155C2×C4×Dic53—21no—
156C2×C4×Dic53—21no—
157C2×C4×Dic53C2311yescharacteristic
158#13133149C2314yes—
159#13133146C2314yes—
160#13133142C2314yes—
161#13133141C2314yes—
162#13133141C2314yes—
163#13133141C2314yes—
164#13133141C2314yes—
165#13133139C2314yes—
166C22⋊#88322C2314yes—
167#13133129C2314yes—
168#13133127C2314yes—
169C22×Q8×C53—22no—
170C22×Q8×C53—22no—
171C22×Q8×C53—21no—
172C22×Q8×C53—21no—
173C22×Q8×C53—24no—
174C22×Q8×C53—24no—
175C22×Q8×C53—42no—
176C22×Q8×C53—42no—
177C22×Q8×C53C2311yescharacteristic
178C22×Q8×C53C2311yescharacteristic
179C22×Q8×C53C2314yes—
180C22×Q8×C53C2314yes—
181C22×Q8×C53C2311yescharacteristic
182C22×Q8×C53C2311yescharacteristic
183C23×C4×C53—21no—
184C23×C4×C53—21no—
185C23×C4×C53C2311yescharacteristic
186C2×Q16×C53—232no—
187C2×Q16×C53—24no—
188C2×Q16×C53—24no—
189C2×Q16×C53—24no—
190C2×Q16×C53D418yescomplemented
191C2×Q16×C53C2314yes—
192C2×Q16×C53C2314yes—
193C2×Q16×C53C2314yes—
194C2×Q16×C53C2314yes—
195C22×C8×C53—24no—
196C22×C8×C53C2311yescharacteristic
197C22×C8×C53C2314yes—
198C22×C8×C53C2311yescharacteristic
199C24×C53C2×D411yescharacteristic
200C23×D53—21no—
201C23×D53C2×D411yescharacteristic
202C2×Q8×C53—21no—
203C2×Q8×C53—21no—
204C2×Q8×C53—24no—
205C2×Q8×C53—21no—
206C2×Q8×C53—24no—
207C2×Q8×C53—21no—
208C2×Q8×C53—22no—
209C2×Q8×C53—22no—
210C2×Q8×C53—28no—
211C2×Q8×C53—28no—
212C2×Q8×C53—22no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53—22no—
216C2×Q8×C53—44no—
217C2×Q8×C53—44no—
218C2×Q8×C53—44no—
219C2×Q8×C53—44no—
220C2×Q8×C53—48no—
221C2×Q8×C53—48no—
222C2×Q8×C53C2×D414yes—
223C2×Q8×C53C2×D414yes—
224C2×Q8×C53C2412yes—
225C2×Q8×C53C2412yes—
226C2×Q8×C53C2412yes—
227C2×Q8×C53C2412yes—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—22no—
231C22×C4×C53—22no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—24no—
235C22×C4×C53—24no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D412yes—
240C22×C4×C53C2412yes—
241C22×C4×C53C2411yescharacteristic
242C2×C22⋊D53—24no—
243C2×C22⋊D53—24no—
244C2×C22⋊D53—44no—
245C2×C22⋊D53C2×D414yes—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53C2×D411yescharacteristic
250C22×Dic53C2×D411yescharacteristic
251C22×Dic53C2×D411yescharacteristic
252#11719949—28no—
253#11719949—44no—
254#11719949—48no—
255Q8×D53—28no—
256Q8×D53—44no—
257Q8×D53—48no—
258C2×D212—22no—
259C2×D212—22no—
260C2×D212—24no—
261C2×D212—21no—
262C2×D212—44no—
263C2×D212C2412yes—
264C2×C4×D53—22no—
265C2×C4×D53—22no—
266C2×C4×D53—24no—
267C2×C4×D53—24no—
268C2×C4×D53—44no—
269C2×C4×D53—44no—
270C2×C4×D53C2×D412yes—
271C2×C4×D53C2412yes—
272C2×Dic106—22no—
273C2×Dic106—22no—
274C2×Dic106—21no—
275C2×Dic106—24no—
276C2×Dic106—44no—
277C2×Dic106C2412yes—
278Q16×C53—28no—
279Q16×C53—28no—
280Q16×C53—28no—
281Q16×C53C2×D4116yescomplemented
282C2×C8×C53—22no—
283C2×C8×C53—28no—
284C2×C8×C53C2×D414yes—
285C2×C8×C53C2412yes—
286C2×C8×C53C2412yes—
287C22⋊Dic53—24no—
288C22⋊Dic53C2×D414yes—
289#11719925—28no—
290#11719925—44no—
291#11719924—28no—
292#11719924—44no—
293#11719921—24no—
294#11719921—24no—
295#11719921—24no—
296#11719921—24no—
297#11719921—24no—
298#11719921C2×D414yes—
299C4⋊Dic53—21no—
300C4⋊Dic53—21no—
301C4⋊Dic53—24no—
302C4⋊Dic53—24no—
303C4⋊Dic53C2412yes—
304C4⋊Dic53C2412yes—
305#11719919—24no—
306#11719919—24no—
307#11719919—24no—
308#11719919—24no—
309#11719919—24no—
310#11719919C2×D414yes—
311C4×Dic53—24no—
312C4×Dic53—24no—
313C4×Dic53C2×D412yes—
314C4×Dic53C2412yes—
315C2×#88322—22no—
316C2×#88322—22no—
317C2×#88322C2412yes—
318C2×#88322C2412yes—
319#11719913—28no—
320#11719912—28no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53#13714yescomplemented
324C23×C53C22×D412yes—
325C23×C53C22×D411yescharacteristic
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—22no—
329C22×D53—22no—
330C22×D53—42no—
331C22×D53—42no—
332C22×D53—42no—
333C22×D53C22×D412yes—
334Q8×C53—24no—
335Q8×C53—24no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—22no—
339Q8×C53—22no—
340Q8×C53—22no—
341Q8×C53—22no—
342Q8×C53—48no—
343Q8×C53—48no—
344Q8×C53—42no—
345Q8×C53—42no—
346Q8×C53C22×D414yes—
347Q8×C53C22×D414yes—
348C2×C4×C53—24no—
349C2×C4×C53—24no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—48no—
359C2×C4×C53—48no—
360C2×C4×C53—42no—
361C2×C4×C53—42no—
362C2×C4×C53C22×D412yes—
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C22×D412yes—
365C2×C4×C53H(5,𝔽2)12yes—
366C2×C4×C53C2511yescharacteristic
367C22⋊D53—28no—
368C22⋊D53—48no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—42no—
376C2×Dic53—42no—
377C2×Dic53—42no—
378C2×Dic53C22×D412yes—
379C2×Dic53C22×D412yes—
380C2×Dic53C22×D412yes—
381D212—22no—
382D212—22no—
383D212—48no—
384D212—42no—
385C4×D53—24no—
386C4×D53—22no—
387C4×D53—22no—
388C4×D53—48no—
389C4×D53—48no—
390Dic106—22no—
391Dic106—22no—
392Dic106—48no—
393Dic106—42no—
394C8×C53—22no—
395C8×C53C22×D414yes—
396#88322—22no—
397#88322—22no—
398C2×#3270—531nomaximal, Sylow
399C22×C53—22no—
400C22×C53—28no—
401C22×C53—22no—
402C22×C53D4212yes—
403C22×C53C2×#13712yes—
404C22×C53C2×#13714yescomplemented
405C22×C53#57812yes—
406C22×C53C23×D411yescharacteristic
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—22no—
410C2×D53—44no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—84no—
415C4×C53—24no—
416C4×C53—24no—
417C4×C53—22no—
418C4×C53—42no—
419C4×C53—42no—
420C4×C53D4212yes—
421C4×C53C23×D411yescharacteristic
422C4×C53C2×H(5,𝔽2)11yescharacteristic
423Dic53—22no—
424Dic53—22no—
425Dic53—22no—
426Dic53—42no—
427Dic53—42no—
428Dic53—42no—
429C22×#137—531no—
430C23×Q16D5311yescharacteristic, complemented
431C2×D4×Q8—531no—
432C2×#548—531no—
433#3270—5316no—
434C2×#497—531no—
435C2×#470—531no—
436C2×#465—531no—
437C2×#464—531no—
438C2×#462—531no—
439C2×#452—531no—
440C2×#451—531no—
441C2×#451—531no—
442C2×#448—531no—
443C2×#441—531no—
444C2×#435—531no—
445C2×C53—24no—
446C2×C53#327014yescomplemented
447C2×C53C2×D4211yescharacteristic
448C2×C53C22×#13711yescharacteristic
449C2×C53C2×#57811yescharacteristic
450D53—42no—
451D53—82no—
452C22×#41—531no—
453C23×Q8—531no—
454C23×Q8C2×D5311yescharacteristic
455C23×Q8C2×D5311yescharacteristic
456C2×#137—538no—
457C2×#137—1068no—
458C22×Q16—28no—
459C22×Q16—531no—
460C22×Q16—531no—
461C22×Q16C2×D5311yescharacteristic
462C22×Q16C2×D5311yescharacteristic
463C22×Q16C2×D5311yescharacteristic
464C22×Q16C2×D5311yescharacteristic
465C22×Q16C2×D5318yescomplemented
466C22×SD16—531no—
467C22×SD16—531no—
468C22×SD16—531no—
469C22×M16—531no—
470C23×C8C2×D5311yescharacteristic
471D4×Q8—538no—
472D4×Q8—1064no—
473#548—538no—
474#548—1064no—
475C2×C4⋊Q8—531no—
476C2×C4⋊Q8—1061no—
477C2×#124—531no—
478C2×#124—1061no—
479C2×C22⋊Q8—531no—
480C2×C22⋊Q8—531no—
481C2×C22⋊Q8—531no—
482C2×C22⋊Q8—1061no—
483C2×C22⋊Q8—1061no—
484C2×C22⋊Q8—1061no—
485C2×#121—531no—
486C2×#121—1061no—
487C2×C4×Q8—531no—
488C2×C4×Q8—531no—
489C2×C4×D4—531no—
490C2×C4×D4—1061no—
491C2×C4×D4—1061no—
492#497—538no—
493#470—538no—
494#465—538no—
495#464—538no—
496#462—538no—
497#452—538no—
498#451—538no—
499#451—538no—
500#448—538no—
501#441—538no—
502#435—538no—
503C2×#106—531no—
504C2×C4⋊C8—531no—
505C2×#103—531no—
506C2×#103—531no—
507C2×#103—531no—
508C2×#103—531no—
509C2×#103—531no—
510C2×#102—531no—
511C2×C22⋊C8—531no—
512C2×C22⋊C8—531no—
513C2×#97—531no—
514C53C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—534no—
516C2×#41—1062no—
517C2×#41—1064no—
518C2×#41—2122no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—42no—
527C22×Q8—534no—
528C22×Q8—531no—
529C22×Q8—1061no—
530C22×Q8—1062no—
531C22×Q8—1064no—
532C22×Q8—2122no—
533C22×Q8C22×D5311yescharacteristic
534C22×Q8C22×D5311yescharacteristic
535C22×Q8C22×D5314yes—
536C22×Q8C22×D5314yes—
537C22×Q8C22×D5311yescharacteristic
538C22×Q8C22×D5311yescharacteristic
539C22×D4—531no—
540C22×D4—531no—
541C22×D4—1061no—
542C22×D4—1061no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—531no—
546C23×C4—1061no—
547C23×C4—1061no—
548C23×C4C22×D5311yescharacteristic
549#137—10632no—
550C2×Q16—24no—
551C2×Q16—24no—
552C2×Q16—232no—
553C2×Q16—24no—
554C2×Q16—534no—
555C2×Q16—534no—
556C2×Q16—1064no—
557C2×Q16—2122no—
558C2×Q16C22⋊D5318yescomplemented
559C2×Q16C22×D5314yes—
560C2×Q16C22×D5314yes—
561C2×Q16C22×D5314yes—
562C2×Q16C22×D5314yes—
563C2×SD16—534no—
564C2×SD16—534no—
565C2×SD16—534no—
566C2×SD16—1064no—
567C2×SD16—1064no—
568C2×SD16—2122no—
569C2×M16—534no—
570C2×M16—1064no—
571C22×C8—24no—
572C22×C8—531no—
573C22×C8—531no—
574C22×C8C22×D5311yescharacteristic
575C22×C8C22×D5314yes—
576C22×C8C22×D5311yescharacteristic
577C4⋊Q8—534no—
578C4⋊Q8—1062no—
579C4⋊Q8—1068no—
580#124—534no—
581#124—1062no—
582#124—1068no—
583C22⋊Q8—534no—
584C22⋊Q8—534no—
585C22⋊Q8—534no—
586C22⋊Q8—1068no—
587C22⋊Q8—1068no—
588C22⋊Q8—1068no—
589C22⋊Q8—1062no—
590C22⋊Q8—1062no—
591C22⋊Q8—1062no—
592#121—534no—
593#121—1068no—
594#121—1062no—
595C4×Q8—534no—
596C4×Q8—534no—
597C4×Q8—1062no—
598C4×Q8—1062no—
599C4×D4—534no—
600C4×D4—534no—
601C4×D4—1068no—
602C4×D4—1068no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—531no—
605C2×C4⋊C4—531no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4—1061no—
610C2×C4⋊C4—1061no—
611C2×C4⋊C4—1061no—
612C2×C4⋊C4—1061no—
613C2×C22⋊C4—531no—
614C2×C22⋊C4—531no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C22⋊C4—1061no—
618C2×C22⋊C4—1061no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C42—531no—
622C2×C42—1061no—
623C2×C42—1061no—
624#106—534no—
625C4⋊C8—534no—
626#103—534no—
627#103—534no—
628#103—534no—
629#103—534no—
630#103—534no—
631#102—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634#97—534no—
635C24—531no—
636C24—1061no—
637C24D4×D5311yescharacteristic
638#41—1068no—
639#41—2124no—
640#41—2128no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—24no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—28no—
650C2×Q8—28no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—44no—
658C2×Q8—44no—
659C2×Q8—48no—
660C2×Q8—48no—
661C2×Q8—532no—
662C2×Q8—1064no—
663C2×Q8—1061no—
664C2×Q8—1068no—
665C2×Q8—1062no—
666C2×Q8—1062no—
667C2×Q8—2124no—
668C2×Q8—2124no—
669C2×Q8—2128no—
670C2×Q8C2×C22⋊D5314yes—
671C2×Q8C2×C22⋊D5314yes—
672C2×Q8C23×D5312yes—
673C2×Q8C23×D5312yes—
674C2×Q8C23×D5312yes—
675C2×Q8C23×D5312yes—
676C2×D4—534no—
677C2×D4—532no—
678C2×D4—1064no—
679C2×D4—1064no—
680C2×D4—1064no—
681C2×D4—1061no—
682C2×D4—1062no—
683C2×D4—1062no—
684C2×D4—2124no—
685C2×D4—2124no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—531no—
697C22×C4—531no—
698C22×C4—531no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—1064no—
702C22×C4—1064no—
703C22×C4—1062no—
704C22×C4—1062no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—2124no—
709C22×C4—2124no—
710C22×C4D4×D5312yes—
711C22×C4D4×D5311yescharacteristic
712C22×C4C23×D5312yes—
713C22×C4C23×D5311yescharacteristic
714Q16—28no—
715Q16—28no—
716Q16—28no—
717Q16—1068no—
718Q16—2124no—
719Q16C2×C22⋊D53116yescomplemented
720SD16—1068no—
721SD16—1068no—
722SD16—2124no—
723M16—1068no—
724C2×C8—22no—
725C2×C8—28no—
726C2×C8—532no—
727C2×C8—532no—
728C2×C8—1062no—
729C2×C8—1062no—
730C2×C8C2×C22⋊D5314yes—
731C2×C8C23×D5312yes—
732C2×C8C23×D5312yes—
733C4⋊C4—534no—
734C4⋊C4—532no—
735C4⋊C4—532no—
736C4⋊C4—1064no—
737C4⋊C4—1064no—
738C4⋊C4—1064no—
739C4⋊C4—1064no—
740C4⋊C4—1064no—
741C4⋊C4—1064no—
742C4⋊C4—1061no—
743C4⋊C4—1061no—
744C4⋊C4—1064no—
745C22⋊C4—534no—
746C22⋊C4—534no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C22⋊C4—1064no—
753C42—532no—
754C42—532no—
755C42—1064no—
756C42—1064no—
757C23—22no—
758C23—22no—
759C23—532no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—2122no—
765C23—2122no—
766C23—2122no—
767C23#1313324914yescomplemented
768C23C2×D4×D5312yes—
769C23C2×D4×D5311yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—24no—
773Q8—24no—
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—48no—
779Q8—48no—
780Q8—42no—
781Q8—42no—
782Q8—1062no—
783Q8—1062no—
784Q8—2128no—
785Q8—2122no—
786Q8C22×C22⋊D5314yes—
787Q8C22×C22⋊D5314yes—
788D4—1068no—
789D4—1062no—
790D4—1062no—
791D4—2128no—
792D4—2128no—
793D4—2122no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—48no—
805C2×C4—48no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—532no—
809C2×C4—532no—
810C2×C4—532no—
811C2×C4—1062no—
812C2×C4—1062no—
813C2×C4—1062no—
814C2×C4—1062no—
815C2×C4—1062no—
816C2×C4—1064no—
817C2×C4—1062no—
818C2×C4—1062no—
819C2×C4—1062no—
820C2×C4—2128no—
821C2×C4—2128no—
822C2×C4—2122no—
823C2×C4—2122no—
824C2×C4—2122no—
825C2×C4C2×D4×D5312yes—
826C2×C4C2×D4×D5311yescharacteristic
827C2×C4C22×C22⋊D5312yes—
828C2×C4#1313326212yes—
829C2×C4C24×D5311yescharacteristic
830C8—22no—
831C8—1062no—
832C8—1062no—
833C8C22×C22⋊D5314yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—1062no—
838C22—1062no—
839C22—1062no—
840C22—4244no—
841C22—2122no—
842C22—2122no—
843C22—2122no—
844C22—2124no—
845C22D4×C22⋊D5312yes—
846C22C2×#1313324912yes—
847C22C2×#1313324914yescomplemented
848C22#1681143612yes—
849C22C22×D4×D5311yescharacteristic
850C4—22no—
851C4—24no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—1062no—
856C4—1062no—
857C4—1062no—
858C4—2122no—
859C4—2122no—
860C4—2122no—
861C4D4×C22⋊D5312yes—
862C4C23×C22⋊D5311yescharacteristic
863C4C2×#1313326211yescharacteristic
864C2—24no—
865C2—4242no—
866C2—2122no—
867C2#2028628514yesdirect product factor
868C2C2×D4×C22⋊D5311yescharacteristic
869C2C22×#1313324911yescharacteristic
870C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC23×Q16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811284C2
hypercenterC23×Q16D53
hypocenterC53C2×#3270
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C2×Q8×C22⋊D53C2semidirect
4. #20286285C2direct (N × H)
5. C2×#16811016C2semidirect
6. C2×#16810878C2semidirect
7. C2×#16810852C2semidirect
8. C2×#16810847C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810784C2semidirect
11. C2×#16810779C2semidirect
12. C2×#16810777C2semidirect
13. C2×#16810762C2semidirect
14. C2×#16810730C2semidirect
15. C2×#16810694C2semidirect
16. C23×Q16×C53C2semidirect
20. C2×#13133249C22semidirect
28. Q8×C22⋊D53C22semidirect
48. #16811016C22semidirect
49. #16810878C22semidirect
50. #16810852C22semidirect
51. #16810847C22semidirect
52. #16810831C22semidirect
53. #16810784C22semidirect
54. #16810779C22semidirect
55. #16810777C22semidirect
56. #16810762C22semidirect
57. #16810730C22semidirect
58. #16810694C22semidirect
77. C22×Q16×C53C22semidirect
190. C2×Q16×C53D4semidirect
281. Q16×C53C2×D4semidirect
323. C23×C53#137semidirect
404. C22×C53C2×#137semidirect
430. C23×Q16D53semidirect
446. C2×C53#3270semidirect
465. C22×Q16C2×D53semidirect
514. C53C2×#3270semidirect
558. C2×Q16C22⋊D53semidirect
719. Q16C2×C22⋊D53semidirect
767. C23#13133249semidirect
847. C22C2×#13133249semidirect
867. C2#20286285direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C2×Q8×C22⋊D532
C2×#168112842
#202862852
C2×#168110162
C2×#168108782
C2×#168108522
C2×#168108472
C2×#168108312
C2×#168107842
C2×#168107792
C2×#168107772
C2×#168107622
C2×#168107302
C2×#168106942
C23×Q16×C532
C2×#327053