Finite Group Databasebeta

← C2×#20285565 #28254743

Subgroups — C2×#20285565 #28254743

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×#16811202C211yesmaximal, characteristic, complemented
2C2×#16811192C211yesmaximal, characteristic, complemented
3#20285565C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810964C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810875C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810858C211yesmaximal, characteristic, complemented
10C2×#16810853C211yesmaximal, characteristic, complemented
11C2×#16810769C211yesmaximal, characteristic, complemented
12C2×#16810769C211yesmaximal, characteristic, complemented
13C2×#16810776C211yesmaximal, characteristic, complemented
14C2×#16810756C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic, complemented
19C23×D212C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719912C2211yescharacteristic, complemented
25C22×C8×D53C2211yescharacteristic, complemented
26#16811202—24no—
27#16811202C2218yescomplemented
28#16811192—24no—
29#16811192C2218yescomplemented
30C2×#13133214—21no—
31C2×#13133205—21no—
32C2×#13133197C2211yescharacteristic, complemented
33C2×#13133196C2211yescharacteristic
34C2×#13133194—21no—
35C2×#13133192C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×#13133190—21no—
40C2×#13133189—21no—
41C2×#13133188—21no—
42C2×#13133188C2211yescharacteristic, complemented
43C2×#13133187—21no—
44C2×#13133187—21no—
45C2×C4⋊C4×D53C2211yescharacteristic, complemented
46#16810964C2218yescomplemented
47#16810943C2218yescomplemented
48#16810938C2218yescomplemented
49#16810875C2218yescomplemented
50#16810870C2218yescomplemented
51#16810858C2218yescomplemented
52#16810853C2218yescomplemented
53#16810776C2218yescomplemented
54#16810769C2218yescomplemented
55#16810769C2218yescomplemented
56#16810756C2218yescomplemented
57C2×#13133150C2211yescharacteristic, complemented
58C2×#13133148C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic, complemented
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945D414yes—
81C2×#11719945C2314yes—
82C2×#11719947—22no—
83C2×#11719947—42no—
84C2×#11719947—42no—
85C2×#11719947C2314yescomplemented
86C22×Dic106D411yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212—22no—
90C22×D212—21no—
91C22×D212—21no—
92C22×D212—21no—
93C22×D212—21no—
94C22×D212—42no—
95C22×D212—42no—
96C22×D212D411yescharacteristic
97C22×D212C2311yescharacteristic
98C22×D212C2311yescharacteristic
99C22×D212C2314yes—
100C22×C22⋊D53—21no—
101C22×C22⋊D53—21no—
102C22×C22⋊D53D411yescharacteristic
103C22×C22⋊D53D411yescharacteristic
104C23×Dic53—21no—
105C22×C4×D53—21no—
106C22×C4×D53C2311yescharacteristic
107C22×C4×D53C2311yescharacteristic
108C2×#11719913—42no—
109C2×#11719913—42no—
110C2×#11719913C2314yes—
111C2×#11719913C2314yes—
112C2×#11719922—42no—
113C2×#11719922—42no—
114C2×#11719922C2314yes—
115C2×#11719922C2314yes—
116C2×#11719912—42no—
117C2×#11719912C2314yescomplemented
118C22×#88322C2311yescharacteristic
119C22×#88322C2311yescharacteristic
120C2×C8×D53—42no—
121C2×C8×D53C2314yescomplemented
122#13133214—28no—
123#13133205—28no—
124#13133197—22no—
125#13133197C2314yescomplemented
126#13133196—22no—
127#13133196C2314yes—
128#13133194—28no—
129#13133192—22no—
130#13133192—22no—
131#13133192—22no—
132#13133192—22no—
133#13133192C2314yes—
134#13133192C2314yes—
135#13133192C2314yes—
136#13133192C2314yes—
137#13133190—28no—
138#13133189—28no—
139#13133188—28no—
140#13133188—22no—
141#13133188C2314yescomplemented
142#13133187—28no—
143#13133187—28no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53C2311yescharacteristic
146C2×#11719919—21no—
147C2×#11719919—21no—
148C4⋊C4×D53—22no—
149C4⋊C4×D53C2314yescomplemented
150C2×C22⋊Dic53—21no—
151C2×C22⋊Dic53—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157#13133150C2314yescomplemented
158#13133148C2314yescomplemented
159#13133140C2314yescomplemented
160#13133140C2314yescomplemented
161#13133139C2314yes—
162#13133139C2314yes—
163#13133137C2314yes—
164#13133137C2314yes—
165C22⋊#88322C2314yes—
166#13133129C2314yescomplemented
167#13133129C2314yescomplemented
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173#121×C53—22no—
174#121×C53C2314yes—
175#117×C53—22no—
176#117×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C42×C53—21no—
183#107×C53C2314yescomplemented
184#106×C53C2314yescomplemented
185#102×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C23×D53C2×D411yescharacteristic
198C2×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—82no—
203C2×D4×C53C2412yes—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—42no—
216C2×C22⋊D53—42no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53—82no—
219C2×C22⋊D53C2×D414yes—
220C2×C22⋊D53C2×D414yes—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—24no—
224C22×Dic53—44no—
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227#11719947—44no—
228#11719947—44no—
229#11719947—48no—
230#11719945—48no—
231#11719945—44no—
232#11719945—44no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—24no—
240C2×D212—24no—
241C2×D212—24no—
242C2×D212—24no—
243C2×D212—24no—
244C2×D212—44no—
245C2×D212—44no—
246C2×D212—42no—
247C2×D212—44no—
248C2×D212—48no—
249C2×D212—82no—
250C2×D212—82no—
251C2×D212—82no—
252C2×D212—82no—
253C2×D212C2×D414yes—
254C2×D212C2412yes—
255C2×D212C2412yes—
256C2×C4×D53—22no—
257C2×C4×D53—22no—
258C2×C4×D53—22no—
259C2×C4×D53—22no—
260C2×C4×D53—24no—
261C2×C4×D53—82no—
262C2×C4×D53C2×D412yes—
263C2×C4×D53C2×D412yes—
264C2×C4×D53C2412yes—
265C2×C4×D53C2412yes—
266C2×Dic106—22no—
267C2×Dic106—22no—
268C2×Dic106—21no—
269C2×Dic106—42no—
270C2×Dic106C2×D414yes—
271C2×Dic106C2412yes—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53C2412yes—
280C4⋊C4×C53C2412yes—
281C4⋊C4×C53C2412yes—
282C22⋊C4×C53—24no—
283C22⋊C4×C53—24no—
284C42×C53—24no—
285C22⋊Dic53—24no—
286C22⋊Dic53—24no—
287#11719922—44no—
288#11719922—44no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294C4⋊Dic53—21no—
295C4⋊Dic53—24no—
296C4⋊Dic53C2412yes—
297#11719919—24no—
298#11719919—24no—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303#11719913—44no—
304#11719913—44no—
305#11719912—44no—
306C8×D53—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53C22×D412yes—
315C23×C53C22×D411yescharacteristic
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—48no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—84no—
332C22×D53—84no—
333C22×D53—816no—
334C22×D53C22×D412yes—
335C22×D53C22×D412yes—
336D4×C53—22no—
337D4×C53—22no—
338D4×C53—42no—
339D4×C53—84no—
340C2×C4×C53—22no—
341C2×C4×C53—24no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D411yescharacteristic
352C2×C4×C53H(5,𝔽2)12yes—
353C2×C4×C53H(5,𝔽2)12yes—
354C2×C4×C53C2511yescharacteristic
355C22⋊D53—44no—
356C22⋊D53—44no—
357C22⋊D53—48no—
358C22⋊D53—84no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—48no—
364C2×Dic53—42no—
365C2×Dic53—42no—
366C2×Dic53C22×D412yes—
367C2×Dic53C22×D412yes—
368D212—22no—
369D212—22no—
370D212—22no—
371D212—22no—
372D212—44no—
373D212—48no—
374D212—42no—
375D212—42no—
376D212—84no—
377D212—84no—
378D212—84no—
379D212—84no—
380C4×D53—24no—
381C4×D53—24no—
382C4×D53—22no—
383C4×D53—22no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—84no—
387Dic106—22no—
388Dic106—22no—
389Dic106—44no—
390Dic106—42no—
391C8×C53—22no—
392C8×C53—22no—
393#88322—22no—
394#88322—22no—
395C2×#3198—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—44no—
400C22×C53—42no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—84no—
404C22×C53#53412yes—
405C22×C53#57612yes—
406C22×C53#57712yes—
407C22×C53C23×D411yescharacteristic
408C2×D53—22no—
409C2×D53—22no—
410C2×D53—22no—
411C2×D53—22no—
412C2×D53—22no—
413C2×D53—22no—
414C2×D53—44no—
415C2×D53—44no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—816no—
423C2×D53—84no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53—42no—
428C4×C53—42no—
429C4×C53#53412yes—
430C4×C53C2×H(5,𝔽2)11yescharacteristic
431C4×C53C2×H(5,𝔽2)11yescharacteristic
432Dic53—22no—
433Dic53—22no—
434Dic53—42no—
435Dic53—42no—
436C2×#537—531no—
437C2×#535—531no—
438#3198—5316no—
439C2×#481—531no—
440C2×#485—531no—
441C2×#482D5311yescharacteristic, complemented
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×#408—531no—
452C2×C53—42no—
453C2×C53—82no—
454C2×C53#319814yescomplemented
455C2×C53C2×#53411yescharacteristic
456C2×C53C2×#57611yescharacteristic
457C2×C53C2×#57711yescharacteristic
458D53—42no—
459D53—42no—
460D53—82no—
461D53—82no—
462C22×#41—531no—
463C22×#41—531no—
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16—531no—
467C22×D8—531no—
468C22×D8—531no—
469C22×M16—531no—
470C23×C8—531no—
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—1061no—
486C2×#121—1061no—
487C2×#121—1061no—
488C2×#121C2×D5311yescharacteristic
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117C2×D5311yescharacteristic
492C22×C4⋊C4—531no—
493#485—538no—
494#482C2×D5318yescomplemented
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×#107C2×D5311yescharacteristic, complemented
507C2×#106—531no—
508C2×#106C2×D5311yescharacteristic, complemented
509C2×#103—531no—
510C2×#103—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102C2×D5311yescharacteristic, complemented
516C2×#102C2×D5311yescharacteristic, complemented
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8C2×D5311yescharacteristic
522C53C2×#319811yescharacteristic, complemented, Sylow
523C25—1061no—
524C2×#41—534no—
525C2×#41—534no—
526C2×#41—534no—
527C2×#41—1062no—
528C2×#41—2122no—
529C2×#41—2122no—
530C2×#41—2122no—
531C2×#41—2122no—
532C22×Q8—531no—
533C22×Q8—531no—
534C22×D4—21no—
535C22×D4—531no—
536C22×D4—531no—
537C22×D4—531no—
538C22×D4—531no—
539C22×D4—531no—
540C22×D4—534no—
541C22×D4—1061no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—1062no—
549C22×D4—2122no—
550C22×D4—2122no—
551C22×D4C22×D5311yescharacteristic
552C23×C4—531no—
553C23×C4—531no—
554C23×C4—1061no—
555C23×C4—1061no—
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—534no—
566C2×M16—2122no—
567C22×C8—531no—
568C22×C8—531no—
569C22×C8—534no—
570C22×C8—2122no—
571C22×C8C22×D5311yescharacteristic
572C22×C8C22×D5311yescharacteristic
573#127—1068no—
574#124—1068no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1068no—
578C22⋊Q8—1062no—
579C22⋊Q8—1062no—
580#121—22no—
581#121—534no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1068no—
587#121—1062no—
588#121—1062no—
589#121—1062no—
590#121—1062no—
591#121—1062no—
592#121—1068no—
593#121—1068no—
594#121C22×D5314yes—
595#120—1068no—
596#120—1068no—
597#117—22no—
598#117C22×D5314yes—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—1062no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C4⋊C4C22×D5311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
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—21no—
618#107—534no—
619#107C22×D5314yescomplemented
620#106—534no—
621#106C22×D5314yescomplemented
622#103—534no—
623#103—534no—
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102C22×D5314yescomplemented
629#102C22×D5314yescomplemented
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8C22×D5314yes—
634C24—21no—
635C24—531no—
636C24—531no—
637C24—1064no—
638C24—1061no—
639C24—1061no—
640C24—4242no—
641C24—4242no—
642C24—2124no—
643C24D4×D5311yescharacteristic
644#41—2128no—
645#41—2124no—
646#41—2124no—
647#41—2124no—
648#41—2124no—
649#41—2128no—
650C2×Q8—534no—
651C2×Q8—532no—
652C2×Q8—1061no—
653C2×Q8—1062no—
654C2×Q8—1062no—
655C2×Q8—2122no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—534no—
662C2×D4—534no—
663C2×D4—534no—
664C2×D4—532no—
665C2×D4—532no—
666C2×D4—1064no—
667C2×D4—1064no—
668C2×D4—1064no—
669C2×D4—1064no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1061no—
673C2×D4—1061no—
674C2×D4—1064no—
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—2124no—
685C2×D4—2124no—
686C2×D4—2122no—
687C2×D4—2124no—
688C2×D4—2128no—
689C2×D4—2122no—
690C2×D4—2122no—
691C2×D4—2124no—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—531no—
699C22×C4—531no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—1064no—
705C22×C4—1064no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1062no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—4242no—
713C22×C4—2124no—
714C22×C4D4×D5312yes—
715C22×C4D4×D5311yescharacteristic
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718SD16—2124no—
719SD16—2124no—
720D8—2124no—
721D8—2124no—
722M16—2124no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—1062no—
728C2×C8—1062no—
729C2×C8—2124no—
730C2×C8C23×D5312yes—
731C2×C8C23×D5312yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—532no—
736C4⋊C4—1064no—
737C4⋊C4—1064no—
738C4⋊C4—1061no—
739C4⋊C4—1064no—
740C4⋊C4C23×D5312yes—
741C4⋊C4C23×D5312yes—
742C4⋊C4C23×D5312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—532no—
761C23—532no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—4244no—
771C23—4244no—
772C23—42416no—
773C23—2128no—
774C23—2122no—
775C23—2122no—
776C23—2122no—
777C23—2122no—
778C23—2122no—
779C23—2122no—
780C23C2×D4×D5312yes—
781C23C2×D4×D5311yescharacteristic
782Q8—1062no—
783Q8—1062no—
784Q8—2124no—
785Q8—2122no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1062no—
791D4—1062no—
792D4—1062no—
793D4—1062no—
794D4—4244no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—2124no—
800D4—2128no—
801D4—2124no—
802D4—2124no—
803D4—2128no—
804D4—2122no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—532no—
817C2×C4—532no—
818C2×C4—1062no—
819C2×C4—1062no—
820C2×C4—1064no—
821C2×C4—1064no—
822C2×C4—1062no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—4244no—
829C2×C4—2128no—
830C2×C4—2122no—
831C2×C4—2122no—
832C2×C4C2×D4×D5312yes—
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4#1313326312yes—
835C2×C4#1313326312yes—
836C2×C4C24×D5311yescharacteristic
837C8—22no—
838C8—22no—
839C8—1062no—
840C8—1062no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—1062no—
850C22—1062no—
851C22—1062no—
852C22—1062no—
853C22—1062no—
854C22—1062no—
855C22—42416no—
856C22—4244no—
857C22—4244no—
858C22—2122no—
859C22—2122no—
860C22—2122no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2124no—
865C22—2124no—
866C22#1681118412yes—
867C22#1681142712yes—
868C22#1681143012yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1062no—
875C4—1062no—
876C4—2122no—
877C4—2122no—
878C4#1681118412yes—
879C4C2×#1313326311yescharacteristic
880C4C2×#1313326311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4242no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028556514yesdirect product factor
888C2C2×#1681118411yescharacteristic
889C2C2×#1681142711yescharacteristic
890C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
hypercenterC2×#482D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811202C2semidirect
2. C2×#16811192C2semidirect
3. #20285565C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810964C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810875C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810858C2semidirect
10. C2×#16810853C2semidirect
11. C2×#16810769C2semidirect
12. C2×#16810769C2semidirect
13. C2×#16810776C2semidirect
14. C2×#16810756C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#482C2semidirect
18. C22×#11719947C22semidirect
24. C22×#11719912C22semidirect
25. C22×C8×D53C22semidirect
27. #16811202C22semidirect
29. #16811192C22semidirect
32. C2×#13133197C22semidirect
42. C2×#13133188C22semidirect
45. C2×C4⋊C4×D53C22semidirect
46. #16810964C22semidirect
47. #16810943C22semidirect
48. #16810938C22semidirect
49. #16810875C22semidirect
50. #16810870C22semidirect
51. #16810858C22semidirect
52. #16810853C22semidirect
53. #16810776C22semidirect
54. #16810769C22semidirect
55. #16810769C22semidirect
56. #16810756C22semidirect
57. C2×#13133150C22semidirect
58. C2×#13133148C22semidirect
59. C2×#13133140C22semidirect
60. C2×#13133140C22semidirect
65. #16810588C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
71. C53×#482C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
85. C2×#11719947C23semidirect
117. C2×#11719912C23semidirect
121. C2×C8×D53C23semidirect
125. #13133197C23semidirect
141. #13133188C23semidirect
149. C4⋊C4×D53C23semidirect
157. #13133150C23semidirect
158. #13133148C23semidirect
159. #13133140C23semidirect
160. #13133140C23semidirect
166. #13133129C23semidirect
167. #13133129C23semidirect
183. #107×C53C23semidirect
184. #106×C53C23semidirect
185. #102×C53C23semidirect
186. #102×C53C23semidirect
441. C2×#482D53semidirect
454. C2×C53#3198semidirect
494. #482C2×D53semidirect
506. C2×#107C2×D53semidirect
508. C2×#106C2×D53semidirect
515. C2×#102C2×D53semidirect
516. C2×#102C2×D53semidirect
522. C53C2×#3198semidirect
619. #107C22×D53semidirect
621. #106C22×D53semidirect
628. #102C22×D53semidirect
629. #102C22×D53semidirect
887. C2#20285565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112022
C2×#168111922
#202855652
C2×#168109432
C2×#168109642
C2×#168109382
C2×#168108752
C2×#168108702
C2×#168108582
C2×#168108532
C2×#168107692
C2×#168107762
C2×#168107562
C2×#168105882
C2×C53×#4822
C2×#319853