Finite Group Databasebeta

← C2×#20285569 #28254747

Subgroups — C2×#20285569 #28254747

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic, complemented
2C2×#16811187C211yesmaximal, characteristic, complemented
3#20285569C2116yesmaximal, direct product factor
4C2×#16810942C211yesmaximal, characteristic, complemented
5C2×#16810965C211yesmaximal, characteristic, complemented
6C2×#16810948C211yesmaximal, characteristic, complemented
7C2×#16810937C211yesmaximal, characteristic, complemented
8C2×#16810876C211yesmaximal, characteristic, complemented
9C2×#16810869C211yesmaximal, characteristic, complemented
10C2×#16810859C211yesmaximal, characteristic, complemented
11C2×#16810852C211yesmaximal, characteristic, complemented
12C2×#16810770C211yesmaximal, characteristic, complemented
13C2×#16810770C211yesmaximal, characteristic, complemented
14C2×#16810776C211yesmaximal, characteristic, complemented
15C2×#16810759C211yesmaximal, characteristic, complemented
16C2×C53×#408C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic, complemented
18C23×D212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×D424C2211yescharacteristic
23#16811201—24no—
24#16811201C2218yescomplemented
25#16811187—24no—
26#16811187C2218yescomplemented
27C2×#13133213—21no—
28C2×#13133206—21no—
29C2×#13133196C2211yescharacteristic
30C2×#13133196C2211yescharacteristic, complemented
31C2×#13133193—21no—
32C2×#13133191C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic
37C2×#13133191C2211yescharacteristic, complemented
38C2×#13133189—21no—
39C2×#13133189—21no—
40C2×#13133188—21no—
41C2×#13133185—21no—
42C2×#13133185—21no—
43C2×#13133176C2211yescharacteristic
44C22×C4⋊Dic53C2211yescharacteristic, complemented
45#16810965C2218yescomplemented
46#16810948C2218yescomplemented
47#16810942C2218yescomplemented
48#16810937C2218yescomplemented
49#16810876C2218yescomplemented
50#16810869C2218yescomplemented
51#16810859C2218yescomplemented
52#16810852C2218yescomplemented
53#16810776C2218yescomplemented
54#16810770C2218yescomplemented
55#16810770C2218yescomplemented
56#16810759C2218yescomplemented
57C2×#13133151C2211yescharacteristic, complemented
58C2×#13133151C2211yescharacteristic, complemented
59C2×#13133149C2211yescharacteristic, complemented
60C2×#13133149C2211yescharacteristic, complemented
61C2×#13133142C2211yescharacteristic, complemented
62C2×#13133142C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic, complemented
68C2×#13133139C2211yescharacteristic, complemented
69C22×#41×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic, complemented
71C23×C8×C53C2211yescharacteristic, complemented
72C53×#408C2218yescomplemented
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—42no—
80C2×#11719945—42no—
81C2×#11719945C2314yescomplemented
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212—22no—
85C22×D212—42no—
86C22×D212—42no—
87C22×D212C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×D212C2314yes—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C22×C22⋊D53—21no—
98C23×Dic53—21no—
99C22×C4×D53—21no—
100C2×#11719913—42no—
101C2×#11719913—42no—
102C2×#11719913C2314yes—
103C2×#11719913C2314yes—
104C2×D424—42no—
105C2×D424—42no—
106C2×D424C2314yes—
107C2×D424C2314yes—
108#13133213—28no—
109#13133206—28no—
110#13133196—22no—
111#13133196—22no—
112#13133196C2314yes—
113#13133196C2314yescomplemented
114#13133193—28no—
115#13133191—22no—
116#13133191—22no—
117#13133191—22no—
118#13133191—22no—
119#13133191—22no—
120#13133191—22no—
121#13133191C2314yes—
122#13133191C2314yes—
123#13133191C2314yes—
124#13133191C2314yes—
125#13133191C2314yes—
126#13133191C2314yescomplemented
127#13133189—28no—
128#13133189—28no—
129#13133188—28no—
130#13133185—28no—
131#13133185—28no—
132#13133176—22no—
133#13133176C2314yes—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53—22no—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×C4⋊Dic53C2311yescharacteristic
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2314yescomplemented
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×C4×Dic53—21no—
153#13133151C2314yescomplemented
154#13133151C2314yescomplemented
155#13133149C2314yescomplemented
156#13133149C2314yescomplemented
157#13133142C2314yescomplemented
158#13133142C2314yescomplemented
159#13133139C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yescomplemented
164#13133139C2314yescomplemented
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53D414yes—
168C2×#41×C53C2314yes—
169C22×Q8×C53D411yescharacteristic
170C22×D4×C53D411yescharacteristic
171C22×D4×C53D411yescharacteristic
172C22×D4×C53D411yescharacteristic
173C23×C4×C53C2311yescharacteristic
174C23×C4×C53C2311yescharacteristic
175C23×C4×C53C2311yescharacteristic
176C2×M16×C53—42no—
177C2×M16×C53C2314yescomplemented
178C22×C8×C53—42no—
179C22×C8×C53C2311yescharacteristic
180C22×C8×C53C2311yescharacteristic
181C22×C8×C53C2311yescharacteristic
182C22×C8×C53C2311yescharacteristic
183C22×C8×C53C2314yescomplemented
184C22⋊C8×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C22⋊C8×C53C2314yescomplemented
187C22⋊C8×C53C2314yescomplemented
188C24×C53C2×D411yescharacteristic
189C24×C53C2×D411yescharacteristic
190C24×C53C2×D411yescharacteristic
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—24no—
195C23×D53—44no—
196C23×D53—82no—
197C23×D53—82no—
198#41×C53—48no—
199#41×C53—44no—
200#41×C53—44no—
201C2×Q8×C53—42no—
202C2×Q8×C53C2×D414yes—
203C2×D4×C53—42no—
204C2×D4×C53—42no—
205C2×D4×C53—42no—
206C2×D4×C53C2×D414yes—
207C2×D4×C53C2×D414yes—
208C2×D4×C53C2×D414yes—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—22no—
213C22×C4×C53—22no—
214C22×C4×C53—22no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D412yes—
219C22×C4×C53C2×D412yes—
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2412yes—
223C22×C4×C53C2412yes—
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—24no—
228C2×C22⋊D53—24no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—44no—
233C2×C22⋊D53—82no—
234C2×C22⋊D53—82no—
235C2×C22⋊D53—82no—
236C2×C22⋊D53—82no—
237C2×C22⋊D53—82no—
238C2×C22⋊D53—82no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—24no—
245C22×Dic53—82no—
246#11719945—44no—
247#11719945—44no—
248#11719945—48no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—22no—
252C2×D212—22no—
253C2×D212—22no—
254C2×D212—22no—
255C2×D212—21no—
256C2×D212—21no—
257C2×D212—21no—
258C2×D212—24no—
259C2×D212—44no—
260C2×D212—44no—
261C2×D212—44no—
262C2×D212—48no—
263C2×D212C2412yes—
264C2×D212C2412yes—
265C2×D212C2412yes—
266C2×C4×D53—24no—
267C2×C4×D53—44no—
268C2×Dic106—22no—
269C2×Dic106—22no—
270C2×Dic106—21no—
271C2×Dic106C2412yes—
272M16×C53—44no—
273C2×C8×C53—22no—
274C2×C8×C53—22no—
275C2×C8×C53—22no—
276C2×C8×C53—22no—
277C2×C8×C53—44no—
278C2×C8×C53C2412yes—
279C2×C8×C53C2412yes—
280C2×C8×C53C2412yes—
281C2×C8×C53C2412yes—
282C22⋊Dic53—24no—
283C22⋊Dic53—24no—
284C22⋊Dic53—24no—
285#11719921—24no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291C4⋊Dic53—21no—
292C4⋊Dic53—21no—
293C4⋊Dic53—24no—
294C4⋊Dic53—21no—
295C4⋊Dic53—21no—
296C4⋊Dic53C2412yes—
297C4⋊Dic53C2412yes—
298C4⋊Dic53C2412yes—
299C4⋊Dic53C2412yes—
300#11719919—24no—
301#11719919—24no—
302C4×Dic53—24no—
303D424—44no—
304D424—44no—
305#11719913—44no—
306#11719913—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53C22×D412yes—
317C23×C53C22×D412yes—
318C23×C53C22×D412yes—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—48no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—42no—
332C22×D53—42no—
333C22×D53—84no—
334C22×D53—84no—
335C22×D53—816no—
336Q8×C53—44no—
337D4×C53—44no—
338D4×C53—44no—
339D4×C53—44no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—24no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D412yes—
354C2×C4×C53C22×D412yes—
355C2×C4×C53C22×D411yescharacteristic
356C2×C4×C53H(5,𝔽2)12yes—
357C2×C4×C53H(5,𝔽2)12yes—
358C2×C4×C53C2511yescharacteristic
359C22⋊D53—48no—
360C22⋊D53—84no—
361C22⋊D53—84no—
362C22⋊D53—84no—
363C22⋊D53—84no—
364C22⋊D53—84no—
365C22⋊D53—84no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—42no—
372C2×Dic53—42no—
373C2×Dic53—42no—
374C2×Dic53—42no—
375C2×Dic53—42no—
376C2×Dic53—84no—
377D212—22no—
378D212—22no—
379D212—22no—
380D212—22no—
381D212—22no—
382D212—22no—
383D212—48no—
384D212—42no—
385D212—42no—
386D212—42no—
387C4×D53—48no—
388Dic106—22no—
389Dic106—22no—
390Dic106—42no—
391C8×C53—22no—
392C8×C53—22no—
393C8×C53—22no—
394C8×C53—22no—
395C2×#3198—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—22no—
400C22×C53—22no—
401C22×C53—22no—
402C22×C53—22no—
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—44no—
406C22×C53—44no—
407C22×C53—44no—
408C22×C53#53412yes—
409C22×C53#57612yes—
410C22×C53#57712yes—
411C22×C53C23×D411yescharacteristic
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—816no—
422C2×D53—84no—
423C2×D53—84no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—22no—
427C4×C53—22no—
428C4×C53#53412yes—
429C4×C53C2×H(5,𝔽2)11yescharacteristic
430C4×C53C2×H(5,𝔽2)11yescharacteristic
431Dic53—42no—
432Dic53—42no—
433Dic53—42no—
434Dic53—42no—
435Dic53—42no—
436C2×#537—531no—
437C2×#535—531no—
438#3198—5316no—
439C2×#481—531no—
440C2×#485—531no—
441C2×#482—531no—
442C2×#480—531no—
443C2×#469—531no—
444C2×#468—531no—
445C2×#466—531no—
446C2×#465—531no—
447C2×#449—531no—
448C2×#449—531no—
449C2×#450—531no—
450C2×#447—531no—
451C2×#408D5311yescharacteristic, complemented
452C2×C53—42no—
453C2×C53—42no—
454C2×C53—42no—
455C2×C53#319814yescomplemented
456C2×C53C2×#53411yescharacteristic
457C2×C53C2×#57611yescharacteristic
458C2×C53C2×#57711yescharacteristic
459D53—82no—
460D53—82no—
461D53—82no—
462C22×#41—531no—
463C22×#41C2×D5311yescharacteristic
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16—531no—
467C22×D8—531no—
468C22×D8—531no—
469C22×M16C2×D5311yescharacteristic, complemented
470C23×C8C2×D5311yescharacteristic, complemented
471#537—538no—
472#537—1064no—
473#535—538no—
474#535—1064no—
475C2×#127—1061no—
476C2×#124—1061no—
477C2×C22⋊Q8—531no—
478C2×C22⋊Q8—531no—
479C2×C22⋊Q8—1061no—
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—531no—
484C2×#121—531no—
485C2×#121—531no—
486C2×#121—1061no—
487C2×#121—1061no—
488C2×#121—1061no—
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117—531no—
492C22×C4⋊C4—531no—
493#485—538no—
494#482—538no—
495#481—538no—
496#480—538no—
497#469—538no—
498#468—538no—
499#466—538no—
500#465—538no—
501#450—538no—
502#449—538no—
503#449—538no—
504#447—538no—
505C2×#107—531no—
506C2×#107—531no—
507C2×#106—531no—
508C2×#106—531no—
509C2×#103—531no—
510C2×#103—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102—531no—
516C2×#102—531no—
517#408C2×D5318yescomplemented
518C2×C22⋊C8C2×D5311yescharacteristic
519C2×C22⋊C8C2×D5311yescharacteristic
520C2×C22⋊C8C2×D5311yescharacteristic, complemented
521C2×C22⋊C8C2×D5311yescharacteristic, complemented
522C53C2×#319811yescharacteristic, complemented, Sylow
523C25—1061no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—534no—
527C2×#41—1062no—
528C2×#41—2122no—
529C2×#41—2122no—
530C2×#41D21214yes—
531C2×#41C22×D5314yes—
532C22×Q8—531no—
533C22×Q8D21211yescharacteristic
534C22×D4—531no—
535C22×D4—531no—
536C22×D4—531no—
537C22×D4—534no—
538C22×D4—1061no—
539C22×D4—1061no—
540C22×D4—1061no—
541C22×D4—1061no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1061no—
546C22×D4—1062no—
547C22×D4—2122no—
548C22×D4—2122no—
549C22×D4D21211yescharacteristic
550C22×D4D21211yescharacteristic
551C22×D4D21211yescharacteristic
552C23×C4—1061no—
553C23×C4—1061no—
554C23×C4C22×D5311yescharacteristic
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5311yescharacteristic
557C2×SD16—534no—
558C2×SD16—534no—
559C2×SD16—2122no—
560C2×SD16—2122no—
561C2×D8—534no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8—2122no—
565C2×M16—42no—
566C2×M16C22×D5314yescomplemented
567C22×C8—42no—
568C22×C8C22×D5311yescharacteristic
569C22×C8C22×D5311yescharacteristic
570C22×C8C22×D5311yescharacteristic
571C22×C8C22×D5311yescharacteristic
572C22×C8C22×D5314yescomplemented
573#127—1068no—
574#124—1068no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1068no—
578C22⋊Q8—1062no—
579C22⋊Q8—1062no—
580#121—534no—
581#121—534no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1068no—
587#121—1068no—
588#121—1068no—
589#121—1062no—
590#121—1062no—
591#121—1062no—
592#121—1062no—
593#121—1062no—
594#121—1062no—
595#120—1068no—
596#120—1068no—
597#117—534no—
598#117—1062no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—531no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1062no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C22⋊C4—1061no—
609C2×C22⋊C4—1061no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C42—1061no—
618#107—534no—
619#107—534no—
620#106—534no—
621#106—534no—
622#103—534no—
623#103—534no—
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102—534no—
629#102—534no—
630C22⋊C8C22×D5314yes—
631C22⋊C8C22×D5314yes—
632C22⋊C8C22×D5314yescomplemented
633C22⋊C8C22×D5314yescomplemented
634C24—1064no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—4242no—
639C24—4242no—
640C24—2124no—
641C24C2×D21211yescharacteristic
642C24C2×D21211yescharacteristic
643C24C2×D21211yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—2124no—
648#41—2124no—
649#41—2128no—
650C2×Q8—42no—
651C2×Q8—532no—
652C2×Q8—1061no—
653C2×Q8—1062no—
654C2×Q8—1062no—
655C2×Q8C2×D21214yes—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—532no—
660C2×D4—532no—
661C2×D4—532no—
662C2×D4—1064no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1064no—
668C2×D4—1064no—
669C2×D4—1061no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4—1064no—
673C2×D4—1062no—
674C2×D4—1062no—
675C2×D4—1062no—
676C2×D4—1062no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—4242no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2124no—
688C2×D4—2128no—
689C2×D4—2124no—
690C2×D4C2×D21214yes—
691C2×D4C2×D21214yes—
692C2×D4C2×D21214yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—1064no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—1061no—
704C22×C4—1061no—
705C22×C4—1064no—
706C22×C4—4242no—
707C22×C4—2124no—
708C22×C4C2×D21212yes—
709C22×C4C2×D21212yes—
710C22×C4C2×D21212yes—
711C22×C4C2×D21211yescharacteristic
712C22×C4C2×D21211yescharacteristic
713C22×C4C2×D21211yescharacteristic
714C22×C4C23×D5312yes—
715C22×C4C23×D5312yes—
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718SD16—2124no—
719SD16—2124no—
720D8—2124no—
721D8—2124no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—44no—
728C2×C8C23×D5312yes—
729C2×C8C23×D5312yes—
730C2×C8C23×D5312yes—
731C2×C8C23×D5312yes—
732C4⋊C4—532no—
733C4⋊C4—532no—
734C4⋊C4—532no—
735C4⋊C4—532no—
736C4⋊C4—1064no—
737C4⋊C4—1061no—
738C4⋊C4—1061no—
739C4⋊C4—1061no—
740C4⋊C4—1061no—
741C4⋊C4—1064no—
742C4⋊C4—1064no—
743C22⋊C4—1064no—
744C22⋊C4—1064no—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C42—1064no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—4244no—
766C23—4244no—
767C23—42416no—
768C23—2128no—
769C23—2122no—
770C23—2122no—
771C23—2122no—
772C23—2122no—
773C23—2122no—
774C23—2122no—
775C23—2122no—
776C23—2122no—
777C23—2122no—
778C23C22×D21212yes—
779C23C22×D21212yes—
780C23C22×D21212yes—
781C23C22×D21211yescharacteristic
782Q8—44no—
783Q8—1062no—
784Q8—1062no—
785Q8—2122no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—1062no—
790D4—1062no—
791D4—1062no—
792D4—1062no—
793D4—1062no—
794D4—1062no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—4244no—
800D4—4244no—
801D4—2128no—
802D4—2128no—
803D4—2122no—
804D4—2122no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—1062no—
819C2×C4—1062no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—1062no—
823C2×C4—4244no—
824C2×C4—2128no—
825C2×C4—2122no—
826C2×C4—2122no—
827C2×C4—2122no—
828C2×C4—2122no—
829C2×C4—2122no—
830C2×C4C22×D21212yes—
831C2×C4C22×D21212yes—
832C2×C4C22×D21212yes—
833C2×C4C22×D21211yescharacteristic
834C2×C4#1313326212yes—
835C2×C4#1313326212yes—
836C2×C4C24×D5311yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42416no—
854C22—4244no—
855C22—4244no—
856C22—4244no—
857C22—2122no—
858C22—2122no—
859C22—2122no—
860C22—2122no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2122no—
865C22—2122no—
866C22#1681118512yes—
867C22#1681142812yes—
868C22#1681143512yes—
869C22C23×D21211yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—2122no—
874C4—2122no—
875C4—2122no—
876C4—2122no—
877C4—2122no—
878C4#1681118512yes—
879C4C2×#1313326211yescharacteristic
880C4C2×#1313326211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—4242no—
885C2—4242no—
886C2—4242no—
887C2#2028556914yesdirect product factor
888C2C2×#1681118511yescharacteristic
889C2C2×#1681142811yescharacteristic
890C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#408C2
socleC23×C53C22×D4
hypercenterC2×#408D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#16811201C2semidirect
2. C2×#16811187C2semidirect
3. #20285569C2direct (N × H)
4. C2×#16810942C2semidirect
5. C2×#16810965C2semidirect
6. C2×#16810948C2semidirect
7. C2×#16810937C2semidirect
8. C2×#16810876C2semidirect
9. C2×#16810869C2semidirect
10. C2×#16810859C2semidirect
11. C2×#16810852C2semidirect
12. C2×#16810770C2semidirect
13. C2×#16810770C2semidirect
14. C2×#16810776C2semidirect
15. C2×#16810759C2semidirect
16. C2×C53×#408C2semidirect
17. C22×#11719945C22semidirect
24. #16811201C22semidirect
26. #16811187C22semidirect
30. C2×#13133196C22semidirect
37. C2×#13133191C22semidirect
44. C22×C4⋊Dic53C22semidirect
45. #16810965C22semidirect
46. #16810948C22semidirect
47. #16810942C22semidirect
48. #16810937C22semidirect
49. #16810876C22semidirect
50. #16810869C22semidirect
51. #16810859C22semidirect
52. #16810852C22semidirect
53. #16810776C22semidirect
54. #16810770C22semidirect
55. #16810770C22semidirect
56. #16810759C22semidirect
57. C2×#13133151C22semidirect
58. C2×#13133151C22semidirect
59. C2×#13133149C22semidirect
60. C2×#13133149C22semidirect
61. C2×#13133142C22semidirect
62. C2×#13133142C22semidirect
67. C2×#13133139C22semidirect
68. C2×#13133139C22semidirect
70. C22×M16×C53C22semidirect
71. C23×C8×C53C22semidirect
72. C53×#408C22semidirect
75. C2×C22⋊C8×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
81. C2×#11719945C23semidirect
113. #13133196C23semidirect
126. #13133191C23semidirect
140. C2×C4⋊Dic53C23semidirect
153. #13133151C23semidirect
154. #13133151C23semidirect
155. #13133149C23semidirect
156. #13133149C23semidirect
157. #13133142C23semidirect
158. #13133142C23semidirect
163. #13133139C23semidirect
164. #13133139C23semidirect
177. C2×M16×C53C23semidirect
183. C22×C8×C53C23semidirect
186. C22⋊C8×C53C23semidirect
187. C22⋊C8×C53C23semidirect
451. C2×#408D53semidirect
455. C2×C53#3198semidirect
469. C22×M16C2×D53semidirect
470. C23×C8C2×D53semidirect
517. #408C2×D53semidirect
520. C2×C22⋊C8C2×D53semidirect
521. C2×C22⋊C8C2×D53semidirect
522. C53C2×#3198semidirect
566. C2×M16C22×D53semidirect
572. C22×C8C22×D53semidirect
632. C22⋊C8C22×D53semidirect
633. C22⋊C8C22×D53semidirect
887. C2#20285569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112012
C2×#168111872
#202855692
C2×#168109422
C2×#168109652
C2×#168109482
C2×#168109372
C2×#168108762
C2×#168108692
C2×#168108592
C2×#168108522
C2×#168107702
C2×#168107762
C2×#168107592
C2×C53×#4082
C2×#319853