Finite Group Databasebeta

← C2×#20289104 #28291794

Subgroups — C2×#20289104 #28291794

Order 13568.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289104C2132yesmaximal, direct product factor
2C2×#16811368C214yesmaximal, complemented
3C2×#16811338C211yesmaximal, characteristic, complemented
4C2×#16811337C212yesmaximal, complemented
5C2×#16811330C211yesmaximal, characteristic, complemented
6C2×#16811320C212yesmaximal, complemented
7C2×#16811313C212yesmaximal, complemented
8C2×D4×Dic106C211yesmaximal, characteristic, complemented
9C2×#16811282C212yesmaximal, complemented
10C2×#16811278C211yesmaximal, characteristic, complemented
11C2×#16811250C212yesmaximal, complemented
12C2×#16811237C214yesmaximal, complemented
13C2×#16811227C212yesmaximal, complemented
14C2×#16811201C212yesmaximal, complemented
15C2×#16811194C212yesmaximal, complemented
16C2×#16811180C211yesmaximal, characteristic, complemented
17C2×#16811157C211yesmaximal, characteristic, complemented
18C2×C53×#532C211yesmaximal, characteristic, complemented
19C22×#11719945C2212yes—
20C23×Dic106C2212yes—
21#16811368C22164yescomplemented
22#16811338C22116yescomplemented
23#16811337C22132yescomplemented
24#16811330C22116yescomplemented
25#16811320C22132yescomplemented
26#16811313C22132yescomplemented
27D4×Dic106C22116yescomplemented
28#16811282C22132yescomplemented
29#16811278C22116yescomplemented
30#16811250C22132yescomplemented
31#16811237C22164yescomplemented
32#16811227C22132yescomplemented
33#16811201C22132yescomplemented
34#16811194C22132yescomplemented
35#16811180C22116yescomplemented
36C2×#13133217C2211yescharacteristic
37C2×#13133217C2211yescharacteristic
38C2×#13133216C2212yes—
39C2×#13133215C2214yes—
40#16811157C22116yescomplemented
41C2×#13133211C2212yes—
42C2×#13133210C2214yes—
43C2×#13133209C2212yes—
44C2×#13133209C2211yescharacteristic
45C2×#13133208C2212yes—
46C2×#13133207C2214yes—
47C2×#13133205C2211yescharacteristic
48C2×#13133204C2214yes—
49C2×#13133203C2214yes—
50C2×#13133203C2214yes—
51C2×#13133200C2212yes—
52C2×#13133199C2214yes—
53C2×#13133198C2214yes—
54C2×#13133198C2214yes—
55C2×#13133198C2214yes—
56C2×#13133196C2212yes—
57C2×#13133196C2212yes—
58C2×#13133196C2211yescharacteristic
59C2×#13133196C2212yes—
60C2×#13133196C2212yes—
61C2×#13133196C2212yes—
62C2×#13133195C2214yes—
63C2×#13133194C2214yes—
64C2×#13133194C2214yes—
65C2×#13133193C2214yes—
66C2×#13133191C2211yescharacteristic
67C2×#13133191C2212yes—
68C2×#13133189C2214yes—
69C2×#13133189C2214yes—
70C2×#13133189C2214yes—
71C2×#13133188C2214yes—
72C2×#13133188C2212yes—
73C2×#13133188C2212yes—
74C2×C4×Dic106C2212yes—
75C2×C4×Dic106C2212yes—
76C2×C4×Dic106C2211yescharacteristic
77C2×C4×D212C2211yescharacteristic
78C2×D4×Dic53C2212yes—
79C2×D4×Dic53C2212yes—
80C2×C4×C22⋊D53C2212yes—
81C2×#13133177C2214yes—
82C2×#13133176C2212yes—
83C2×#13133176C2212yes—
84C2×#13133175C2212yes—
85C2×#13133174C2212yes—
86C2×#13133173C2214yes—
87C22×C4⋊Dic53C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C22×#41×C53C2212yes—
90C53×#532C22116yescomplemented
91C2×C4⋊Q8×C53C2211yescharacteristic
92C2×#127×C53C2211yescharacteristic
93C2×#124×C53C2212yes—
94C2×#121×C53C2212yes—
95C2×#121×C53C2211yescharacteristic
96C2×#121×C53C2211yescharacteristic
97C2×C4×D4×C53C2211yescharacteristic
98C2×C4×D4×C53C2212yes—
99C2×C4×D4×C53C2211yescharacteristic
100C22×C42×C53C2211yescharacteristic
101C2×#11719945—48no—
102C2×#11719945C23116yes—
103C22×Dic106—48no—
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2312yes—
106C22×Dic106C23116yes—
107C22×Dic106C2312yes—
108C22×Dic106C2314yes—
109C22×D212C2311yescharacteristic
110C22×C22⋊D53C2314yes—
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2314yes—
113C23×Dic53C2314yes—
114C23×Dic53C2314yes—
115C22×C4×D53C2312yes—
116C22×C4×D53C2314yes—
117#13133217C2318yes—
118#13133217C2318yes—
119#13133216C23116yes—
120#13133215C23132yes—
121#13133211C23116yes—
122#13133210C23132yes—
123#13133209C2318yes—
124#13133209C23116yes—
125#13133208C23116yes—
126#13133207C23132yes—
127#13133205C2318yes—
128#13133204C23132yes—
129#13133203C23132yes—
130#13133203C23132yes—
131#13133200C23116yes—
132#13133199C23132yes—
133#13133198C23132yes—
134#13133198C23132yes—
135#13133198C23132yes—
136#13133196C23116yes—
137#13133196C23116yes—
138#13133196C23116yes—
139#13133196C23116yes—
140#13133196C2318yes—
141#13133196C23116yes—
142#13133195C23132yes—
143#13133194C23132yes—
144#13133194C23132yes—
145#13133193C23132yes—
146#13133191C23116yes—
147#13133191C2318yes—
148#13133189C23132yes—
149#13133189C23132yes—
150#13133189C23132yes—
151#13133188C23116yes—
152#13133188C23116yes—
153#13133188C23132yes—
154C4×Dic106C23116yes—
155C4×Dic106C2318yes—
156C4×Dic106C23116yes—
157C4×D212C2318yes—
158D4×Dic53C23116yes—
159D4×Dic53C23116yes—
160C4×C22⋊D53C23116yes—
161#13133177C23132yes—
162#13133176C23116yes—
163#13133176C23116yes—
164#13133175C23116yes—
165#13133174C23116yes—
166#13133173C23132yes—
167C2×C4⋊Dic53C23116yes—
168C2×C4⋊Dic53C2312yes—
169C2×C4⋊Dic53C2311yescharacteristic
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2314yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2311yescharacteristic
174C2×C4⋊Dic53C2312yes—
175C2×#11719919C2314yes—
176C2×#11719919C2312yes—
177C2×#11719919C2314yes—
178C2×#11719919C2312yes—
179C2×#11719919C2312yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2312yes—
184C4⋊C4×D53C23116yes—
185C2×C22⋊Dic53C2314yes—
186C2×C22⋊Dic53C2314yes—
187C2×C22⋊Dic53C2314yes—
188C2×C22⋊Dic53C2312yes—
189C2×C22⋊Dic53C2314yes—
190C2×C22⋊Dic53C2314yes—
191C2×#11719921C2312yes—
192C2×#11719921C2312yes—
193C2×#11719921C2314yes—
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×C4×Dic53C2314yes—
197C2×C4×Dic53C2314yes—
198C2×C4×Dic53C2312yes—
199C2×#41×C53—48no—
200C2×#41×C53C23116yes—
201C22×Q8×C53C2312yes—
202C22×D4×C53C2311yescharacteristic
203C22×D4×C53C2311yescharacteristic
204C22×D4×C53C2312yes—
205C22×D4×C53C2312yes—
206C22×D4×C53C2312yes—
207C22×D4×C53C2312yes—
208C23×C4×C53C2311yescharacteristic
209C23×C4×C53C2311yescharacteristic
210C23×C4×C53C2312yes—
211C23×C4×C53C2312yes—
212C23×C4×C53C2311yescharacteristic
213C4⋊Q8×C53C2318yes—
214#127×C53C2318yes—
215#124×C53C23116yes—
216#121×C53C2318yes—
217#121×C53C2318yes—
218#121×C53C23116yes—
219C4×D4×C53C2318yes—
220C4×D4×C53C23116yes—
221C4×D4×C53C2318yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2312yes—
225C2×C22⋊C4×C53C2312yes—
226C2×C22⋊C4×C53C2312yes—
227C2×C22⋊C4×C53C2312yes—
228C2×C22⋊C4×C53C2312yes—
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2318yes—
234C24×C53C2412yes—
235C24×C53C2412yes—
236C24×C53C2411yescharacteristic
237C23×D53C2412yes—
238#41×C53—432no—
239C2×Q8×C53—44no—
240C2×Q8×C53C2418yes—
241C2×D4×C53—24no—
242C2×D4×C53—24no—
243C2×D4×C53—44no—
244C2×D4×C53—44no—
245C2×D4×C53—44no—
246C2×D4×C53—44no—
247C2×D4×C53C2414yes—
248C2×D4×C53C2414yes—
249C2×D4×C53C2418yes—
250C2×D4×C53C2418yes—
251C2×D4×C53C2418yes—
252C2×D4×C53C2418yes—
253C22×C4×C53—24no—
254C22×C4×C53—28no—
255C22×C4×C53—28no—
256C22×C4×C53—24no—
257C22×C4×C53—42no—
258C22×C4×C53C2411yescharacteristic
259C22×C4×C53C2411yescharacteristic
260C22×C4×C53C2411yescharacteristic
261C22×C4×C53C2414yes—
262C22×C4×C53C2411yescharacteristic
263C22×C4×C53C2414yes—
264C22×C4×C53C2412yes—
265C22×C4×C53C2412yes—
266C22×C4×C53C2418yes—
267C22×C4×C53C2418yes—
268C22×C4×C53C2414yes—
269C22×C4×C53C2411yescharacteristic
270C22×C4×C53C2411yescharacteristic
271C2×C22⋊D53—48no—
272C2×C22⋊D53—44no—
273C2×C22⋊D53—48no—
274C2×C22⋊D53C24116yes—
275C2×C22⋊D53C2418yes—
276C2×C22⋊D53C24116yes—
277C22×Dic53—48no—
278C22×Dic53—48no—
279C22×Dic53C2412yes—
280C22×Dic53C2414yes—
281C22×Dic53C2412yes—
282C22×Dic53C2412yes—
283C22×Dic53C2414yes—
284C22×Dic53C24116yes—
285C22×Dic53C24116yes—
286#11719945—432no—
287C2×D212—24no—
288C2×D212C2414yes—
289C2×C4×D53—28no—
290C2×C4×D53—48no—
291C2×C4×D53C2418yes—
292C2×C4×D53C24116yes—
293C2×Dic106—24no—
294C2×Dic106—28no—
295C2×Dic106—432no—
296C2×Dic106—48no—
297C2×Dic106—44no—
298C2×Dic106C2414yes—
299C2×Dic106C2418yes—
300C2×Dic106C2418yes—
301C2×Dic106C24116yes—
302C4⋊C4×C53C2414yes—
303C4⋊C4×C53C2414yes—
304C4⋊C4×C53C2418yes—
305C22⋊C4×C53C2418yes—
306C22⋊C4×C53C2418yes—
307C22⋊C4×C53C2418yes—
308C22⋊C4×C53C2418yes—
309C42×C53C2414yes—
310C42×C53C2414yes—
311C42×C53C2414yes—
312C42×C53C2414yes—
313C22⋊Dic53C24116yes—
314C22⋊Dic53C24116yes—
315C22⋊Dic53C24116yes—
316C22⋊Dic53C2418yes—
317C22⋊Dic53C24116yes—
318C22⋊Dic53C24116yes—
319#11719921C2418yes—
320#11719921C2418yes—
321#11719921C24116yes—
322#11719921C2418yes—
323#11719921C2418yes—
324C4⋊Dic53C2418yes—
325C4⋊Dic53C2414yes—
326C4⋊Dic53C2418yes—
327C4⋊Dic53C24116yes—
328C4⋊Dic53C2418yes—
329C4⋊Dic53C2414yes—
330C4⋊Dic53C2418yes—
331#11719919C24116yes—
332#11719919C2418yes—
333#11719919C24116yes—
334#11719919C2418yes—
335#11719919C2418yes—
336#11719919C24116yes—
337#11719919C24116yes—
338#11719919C24116yes—
339#11719919C2418yes—
340C4×Dic53C24116yes—
341C4×Dic53C24116yes—
342C4×Dic53C2418yes—
343C23×C53—24no—
344C23×C53—24no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—24no—
348C23×C53—24no—
349C23×C53—24no—
350C23×C53—22no—
351C23×C53—24no—
352C23×C53C2514yes—
353C23×C53C2514yes—
354C23×C53C2512yes—
355C23×C53C2511yescharacteristic
356C22×D53—24no—
357C22×D53—24no—
358C22×D53—24no—
359C22×D53C2514yes—
360Q8×C53—48no—
361D4×C53—28no—
362D4×C53—28no—
363D4×C53—48no—
364D4×C53—48no—
365D4×C53—48no—
366D4×C53—48no—
367C2×C4×C53—24no—
368C2×C4×C53—24no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—216no—
374C2×C4×C53—216no—
375C2×C4×C53—28no—
376C2×C4×C53—28no—
377C2×C4×C53—44no—
378C2×C4×C53H(5,𝔽2)14yes—
379C2×C4×C532−1+414yes—
380C2×C4×C53C2514yes—
381C2×C4×C53C2512yes—
382C2×C4×C53C2514yes—
383C2×C4×C53C2512yes—
384C2×C4×C53C2512yes—
385C2×C4×C53C2512yes—
386C2×C4×C53C2512yes—
387C2×C4×C53C2512yes—
388C22⋊D53—416no—
389C22⋊D53—416no—
390C22⋊D53—48no—
391C2×Dic53—24no—
392C2×Dic53—28no—
393C2×Dic53—24no—
394C2×Dic53—28no—
395C2×Dic53—24no—
396C2×Dic53—416no—
397C2×Dic53—416no—
398C2×Dic53C2514yes—
399C2×Dic53C2518yes—
400C2×Dic53C2518yes—
401C2×Dic53C2514yes—
402C2×Dic53C2514yes—
403D212—28no—
404C4×D53—216no—
405C4×D53—416no—
406Dic106—28no—
407Dic106—216no—
408Dic106—416no—
409Dic106—48no—
410C2×#3547—531nomaximal, Sylow
411C22×C53—24no—
412C22×C53—24no—
413C22×C53—22no—
414C22×C53—22no—
415C22×C53—24no—
416C22×C53—24no—
417C22×C53—24no—
418C22×C53—22no—
419C22×C53—24no—
420C22×C53—48no—
421C22×C53—48no—
422C22×C53—44no—
423C22×C53C2×H(5,𝔽2)12yes—
424C22×C53C2×2−1+412yes—
425C22×C53#58512yes—
426C22×C53C2611yescharacteristic
427C2×D53—24no—
428C2×D53—24no—
429C2×D53—24no—
430C2×D53—48no—
431C4×C53—24no—
432C4×C53—24no—
433C4×C53—22no—
434C4×C53—22no—
435C4×C53—22no—
436C4×C53—22no—
437C4×C53C2×H(5,𝔽2)14yes—
438C4×C53C2×2−1+414yes—
439Dic53—24no—
440Dic53—28no—
441Dic53—24no—
442Dic53—28no—
443Dic53—24no—
444#3547—5332no—
445C2×#562—534no—
446C2×#555—532no—
447C2×#555—531no—
448C2×#554—531no—
449C2×#553—532no—
450C2×#552—532no—
451C2×D4×Q8—531no—
452C2×#548—532no—
453C2×#547—531no—
454C2×#544—532no—
455C2×#542—534no—
456C2×#540—532no—
457C2×#537—532no—
458C2×#536—532no—
459C2×#533—531no—
460C2×#532D5311yescharacteristic, complemented
461C2×#529—531no—
462C2×C53—44no—
463C2×C53—44no—
464C2×C53—42no—
465C2×C53#354714yescomplemented
466C2×C53C22×H(5,𝔽2)11yescharacteristic
467C2×C53C22×2−1+411yescharacteristic
468C2×C53C2×#58511yescharacteristic
469D53—44no—
470C22×#41—532no—
471C22×#41C2×D5312yes—
472C23×Q8—532no—
473#562—5364no—
474#555—5332no—
475#555—5316no—
476#554—5316no—
477#553—5332no—
478#552—5332no—
479D4×Q8—5316no—
480#548—5332no—
481#547—5316no—
482#544—5332no—
483#542—5364no—
484#540—5332no—
485#537—5332no—
486#536—5332no—
487#533—5316no—
488#532C2×D53116yescomplemented
489C2×C4⋊Q8—534no—
490C2×C4⋊Q8—532no—
491C2×C4⋊Q8—531no—
492C2×C4⋊Q8—531no—
493C2×C4⋊Q8C2×D5311yescharacteristic
494C2×#127C2×D5311yescharacteristic
495#529—5316no—
496C2×#126—534no—
497C2×#126—532no—
498C2×#125—534no—
499C2×#125—532no—
500C2×#125—531no—
501C2×#125—532no—
502C2×#124—534no—
503C2×#124—534no—
504C2×#124—534no—
505C2×#124—531no—
506C2×#124C2×D5312yes—
507C2×#123—534no—
508C2×#123—534no—
509C2×#123—534no—
510C2×#123—532no—
511C2×#123—534no—
512C2×C22⋊Q8—534no—
513C2×C22⋊Q8—531no—
514C2×C22⋊Q8—532no—
515C2×C22⋊Q8—532no—
516C2×C22⋊Q8—532no—
517C2×C22⋊Q8—532no—
518C2×C22⋊Q8—532no—
519C2×C22⋊Q8—534no—
520C2×C22⋊Q8—534no—
521C2×C22⋊Q8—534no—
522C2×#121—534no—
523C2×#121—532no—
524C2×#121—532no—
525C2×#121—534no—
526C2×#121—534no—
527C2×#121—534no—
528C2×#121—531no—
529C2×#121—532no—
530C2×#121C2×D5311yescharacteristic
531C2×#121C2×D5311yescharacteristic
532C2×#121C2×D5312yes—
533C2×C4×Q8—531no—
534C2×C4×Q8—532no—
535C2×C4×Q8—532no—
536C2×C4×D4—532no—
537C2×C4×D4—532no—
538C2×C4×D4—532no—
539C2×C4×D4—534no—
540C2×C4×D4—531no—
541C2×C4×D4C2×D5311yescharacteristic
542C2×C4×D4C2×D5312yes—
543C2×C4×D4C2×D5311yescharacteristic
544C2×#117—532no—
545C2×#117—532no—
546C2×#117—532no—
547C2×#117—534no—
548C2×#117—532no—
549C22×C4⋊C4—532no—
550C22×C4⋊C4—532no—
551C22×C42C2×D5311yescharacteristic
552C53C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—48no—
554C2×#41—5316no—
555C2×#41—2128no—
556C2×#41C22×D53116yes—
557C22×Q8—531no—
558C22×Q8—532no—
559C22×Q8—532no—
560C22×Q8—534no—
561C22×Q8—5316no—
562C22×Q8—2128no—
563C22×Q8C22×D5312yes—
564C22×D4—532no—
565C22×D4—534no—
566C22×D4—534no—
567C22×D4—531no—
568C22×D4C22×D5311yescharacteristic
569C22×D4C22×D5311yescharacteristic
570C22×D4C22×D5312yes—
571C22×D4C22×D5312yes—
572C22×D4C22×D5312yes—
573C22×D4C22×D5312yes—
574C23×C4—534no—
575C23×C4—534no—
576C23×C4—532no—
577C23×C4—534no—
578C23×C4C22×D5312yes—
579C23×C4C22×D5311yescharacteristic
580C23×C4C22×D5312yes—
581C23×C4C22×D5311yescharacteristic
582C23×C4C22×D5311yescharacteristic
583C4⋊Q8—5332no—
584C4⋊Q8—5316no—
585C4⋊Q8—538no—
586C4⋊Q8—538no—
587C4⋊Q8C22×D5318yes—
588#127C22×D5318yes—
589#126—5332no—
590#126—5316no—
591#125—5332no—
592#125—5316no—
593#125—538no—
594#125—5316no—
595#124—5332no—
596#124—5332no—
597#124—5332no—
598#124—538no—
599#124C22×D53116yes—
600#123—5332no—
601#123—5332no—
602#123—5332no—
603#123—5316no—
604#123—5332no—
605C22⋊Q8—5332no—
606C22⋊Q8—538no—
607C22⋊Q8—5316no—
608C22⋊Q8—5316no—
609C22⋊Q8—5316no—
610C22⋊Q8—5316no—
611C22⋊Q8—5316no—
612C22⋊Q8—5332no—
613C22⋊Q8—5332no—
614C22⋊Q8—5332no—
615#121—5332no—
616#121—5332no—
617#121—5332no—
618#121—5316no—
619#121—5332no—
620#121—5316no—
621#121—538no—
622#121—5316no—
623#121C22×D5318yes—
624#121C22×D5318yes—
625#121C22×D53116yes—
626C4×Q8—538no—
627C4×Q8—5316no—
628C4×Q8—5316no—
629C4×D4—5316no—
630C4×D4—5316no—
631C4×D4—5316no—
632C4×D4—5332no—
633C4×D4—538no—
634C4×D4C22×D5318yes—
635C4×D4C22×D53116yes—
636C4×D4C22×D5318yes—
637#117—5316no—
638#117—5316no—
639#117—5316no—
640#117—5332no—
641#117—5316no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—532no—
644C2×C4⋊C4—532no—
645C2×C4⋊C4—534no—
646C2×C4⋊C4—534no—
647C2×C4⋊C4—5316no—
648C2×C4⋊C4—532no—
649C2×C4⋊C4—531no—
650C2×C4⋊C4—532no—
651C2×C4⋊C4—534no—
652C2×C4⋊C4—532no—
653C2×C4⋊C4—532no—
654C2×C4⋊C4—534no—
655C2×C4⋊C4—534no—
656C2×C4⋊C4—534no—
657C2×C4⋊C4—532no—
658C2×C4⋊C4—532no—
659C2×C4⋊C4—5316no—
660C2×C4⋊C4C22×D5311yescharacteristic
661C2×C4⋊C4C22×D5311yescharacteristic
662C2×C4⋊C4C22×D5312yes—
663C2×C22⋊C4—534no—
664C2×C22⋊C4—534no—
665C2×C22⋊C4—534no—
666C2×C22⋊C4—534no—
667C2×C22⋊C4—534no—
668C2×C22⋊C4—532no—
669C2×C22⋊C4—532no—
670C2×C22⋊C4—532no—
671C2×C22⋊C4—534no—
672C2×C22⋊C4—532no—
673C2×C22⋊C4—532no—
674C2×C22⋊C4C22×D5312yes—
675C2×C22⋊C4C22×D5312yes—
676C2×C22⋊C4C22×D5312yes—
677C2×C22⋊C4C22×D5312yes—
678C2×C42—534no—
679C2×C42—534no—
680C2×C42—532no—
681C2×C42C22×D5311yescharacteristic
682C2×C42C22×D5311yescharacteristic
683C2×C42C22×D5311yescharacteristic
684C2×C42C22×D5311yescharacteristic
685C2×C42C22×D5318yes—
686C24—532no—
687C24C23×D5311yescharacteristic
688C24C23×D5312yes—
689C24C23×D5312yes—
690#41—432no—
691#41—21232no—
692C2×Q8—44no—
693C2×Q8—534no—
694C2×Q8—538no—
695C2×Q8—538no—
696C2×Q8—5316no—
697C2×Q8—1064no—
698C2×Q8—1068no—
699C2×Q8—2124no—
700C2×Q8—2128no—
701C2×Q8—21232no—
702C2×Q8C23×D5318yes—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—538no—
710C2×D4—5316no—
711C2×D4—5316no—
712C2×D4—534no—
713C2×D4—1064no—
714C2×D4—2124no—
715C2×D4—2128no—
716C2×D4—2128no—
717C2×D4C23×D5314yes—
718C2×D4C23×D5314yes—
719C2×D4C23×D5318yes—
720C2×D4C23×D5318yes—
721C2×D4C23×D5318yes—
722C2×D4C23×D5318yes—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—24no—
727C22×C4—42no—
728C22×C4—532no—
729C22×C4—534no—
730C22×C4—532no—
731C22×C4—532no—
732C22×C4—534no—
733C22×C4—5316no—
734C22×C4—5316no—
735C22×C4—538no—
736C22×C4—5316no—
737C22×C4—1068no—
738C22×C4—2128no—
739C22×C4—2128no—
740C22×C4—2128no—
741C22×C4C23×D5314yes—
742C22×C4C23×D5314yes—
743C22×C4C23×D5318yes—
744C22×C4C23×D5318yes—
745C22×C4C23×D5311yescharacteristic
746C22×C4C23×D5312yes—
747C22×C4C23×D5311yescharacteristic
748C22×C4C23×D5311yescharacteristic
749C22×C4C23×D5311yescharacteristic
750C22×C4C23×D5312yes—
751C22×C4C23×D5314yes—
752C22×C4C23×D5311yescharacteristic
753C22×C4C23×D5311yescharacteristic
754C4⋊C4—534no—
755C4⋊C4—538no—
756C4⋊C4—538no—
757C4⋊C4—5316no—
758C4⋊C4—5316no—
759C4⋊C4—538no—
760C4⋊C4—534no—
761C4⋊C4—538no—
762C4⋊C4—5316no—
763C4⋊C4—538no—
764C4⋊C4—538no—
765C4⋊C4—5316no—
766C4⋊C4—5316no—
767C4⋊C4—5316no—
768C4⋊C4—538no—
769C4⋊C4—538no—
770C4⋊C4C23×D5314yes—
771C4⋊C4C23×D5314yes—
772C4⋊C4C23×D5318yes—
773C22⋊C4—5316no—
774C22⋊C4—5316no—
775C22⋊C4—5316no—
776C22⋊C4—5316no—
777C22⋊C4—5316no—
778C22⋊C4—538no—
779C22⋊C4—538no—
780C22⋊C4—538no—
781C22⋊C4—5316no—
782C22⋊C4—538no—
783C22⋊C4—538no—
784C22⋊C4C23×D5318yes—
785C22⋊C4C23×D5318yes—
786C22⋊C4C23×D5318yes—
787C22⋊C4C23×D5318yes—
788C42—5316no—
789C42—5316no—
790C42—538no—
791C42C23×D5314yes—
792C42C23×D5314yes—
793C42C23×D5314yes—
794C42C23×D5314yes—
795C23—24no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—534no—
805C23—1064no—
806C23—1064no—
807C23—1064no—
808C23C24×D5312yes—
809C23C24×D5314yes—
810C23C24×D5314yes—
811C23C24×D5311yescharacteristic
812Q8—48no—
813Q8—1068no—
814Q8—10616no—
815Q8—2128no—
816Q8—21216no—
817D4—28no—
818D4—28no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—48no—
823D4—1068no—
824D4—2128no—
825D4—21216no—
826D4—21216no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—216no—
834C2×C4—28no—
835C2×C4—216no—
836C2×C4—28no—
837C2×C4—44no—
838C2×C4—534no—
839C2×C4—538no—
840C2×C4—534no—
841C2×C4—534no—
842C2×C4—538no—
843C2×C4—1068no—
844C2×C4—1064no—
845C2×C4—1064no—
846C2×C4—1064no—
847C2×C4—1068no—
848C2×C4—10616no—
849C2×C4—21216no—
850C2×C4—21216no—
851C2×C4—21216no—
852C2×C4#1313326214yes—
853C2×C4#1313326414yes—
854C2×C4C24×D5312yes—
855C2×C4C24×D5314yes—
856C2×C4C24×D5312yes—
857C2×C4C24×D5312yes—
858C2×C4C24×D5312yes—
859C2×C4C24×D5314yes—
860C2×C4C24×D5312yes—
861C2×C4C24×D5312yes—
862C22—24no—
863C22—22no—
864C22—24no—
865C22—22no—
866C22—24no—
867C22—24no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—48no—
872C22—44no—
873C22—48no—
874C22—1064no—
875C22—1064no—
876C22—1064no—
877C22—2128no—
878C22C2×#1313326212yes—
879C22C2×#1313326412yes—
880C22#1681145912yes—
881C22C25×D5311yescharacteristic
882C4—24no—
883C4—22no—
884C4—24no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—1068no—
889C4—1064no—
890C4—1064no—
891C4—1064no—
892C4—1068no—
893C4C2×#1313326214yes—
894C4C2×#1313326414yes—
895C2—44no—
896C2—42no—
897C2—44no—
898C2—2124no—
899C2#2028910414yesdirect product factor
900C2C22×#1313326211yescharacteristic
901C2C22×#1313326411yescharacteristic
902C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#532C2
socleC23×C53C25
hypercenterC2×#532D53
hypocenterC53C2×#3547
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20289104C2direct (N × H)
2. C2×#16811368C2semidirect
3. C2×#16811338C2semidirect
4. C2×#16811337C2semidirect
5. C2×#16811330C2semidirect
6. C2×#16811320C2semidirect
7. C2×#16811313C2semidirect
8. C2×D4×Dic106C2semidirect
9. C2×#16811282C2semidirect
10. C2×#16811278C2semidirect
11. C2×#16811250C2semidirect
12. C2×#16811237C2semidirect
13. C2×#16811227C2semidirect
14. C2×#16811201C2semidirect
15. C2×#16811194C2semidirect
16. C2×#16811180C2semidirect
17. C2×#16811157C2semidirect
18. C2×C53×#532C2semidirect
21. #16811368C22semidirect
22. #16811338C22semidirect
23. #16811337C22semidirect
24. #16811330C22semidirect
25. #16811320C22semidirect
26. #16811313C22semidirect
27. D4×Dic106C22semidirect
28. #16811282C22semidirect
29. #16811278C22semidirect
30. #16811250C22semidirect
31. #16811237C22semidirect
32. #16811227C22semidirect
33. #16811201C22semidirect
34. #16811194C22semidirect
35. #16811180C22semidirect
40. #16811157C22semidirect
90. C53×#532C22semidirect
460. C2×#532D53semidirect
465. C2×C53#3547semidirect
488. #532C2×D53semidirect
552. C53C2×#3547semidirect
899. C2#20289104direct (N × H)

Maximal subgroups

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

subgroupindex
#202891042
C2×#168113682
C2×#168113382
C2×#168113372
C2×#168113302
C2×#168113202
C2×#168113132
C2×D4×Dic1062
C2×#168112822
C2×#168112782
C2×#168112502
C2×#168112372
C2×#168112272
C2×#168112012
C2×#168111942
C2×#168111802
C2×#168111572
C2×C53×#5322
C2×#354753