Finite Group Databasebeta

← C2×#20289106 #28291786

Subgroups — C2×#20289106 #28291786

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#20289106C2132yesmaximal, direct product factor
2C2×#16811370C214yesmaximal, complemented
3C2×#16811338C211yesmaximal, characteristic, complemented
4C2×#16811338C212yesmaximal, complemented
5C2×#16811333C211yesmaximal, characteristic, complemented
6C2×#16811319C212yesmaximal, complemented
7C2×#16811311C212yesmaximal, complemented
8C2×Q8×D212C211yesmaximal, characteristic, complemented
9C2×#16811281C212yesmaximal, complemented
10C2×#16811277C211yesmaximal, characteristic, complemented
11C2×#16811251C212yesmaximal, complemented
12C2×#16811239C214yesmaximal, complemented
13C2×#16811228C212yesmaximal, complemented
14C2×#16811202C212yesmaximal, complemented
15C2×#16811196C212yesmaximal, complemented
16C2×#16811180C211yesmaximal, characteristic, complemented
17C2×#16811173C211yesmaximal, characteristic, complemented
18C2×C53×#529C211yesmaximal, characteristic, complemented
19C22×#11719945C2212yes—
20C22×#11719947C2212yes—
21C22×Q8×D53C2212yes—
22#16811370C22164yescomplemented
23#16811338C22116yescomplemented
24#16811338C22132yescomplemented
25#16811333C22116yescomplemented
26#16811319C22132yescomplemented
27#16811311C22132yescomplemented
28Q8×D212C22116yescomplemented
29#16811281C22132yescomplemented
30#16811277C22116yescomplemented
31#16811251C22132yescomplemented
32#16811239C22164yescomplemented
33#16811228C22132yescomplemented
34#16811202C22132yescomplemented
35#16811196C22132yescomplemented
36#16811180C22116yescomplemented
37#16811173C22116yescomplemented
38C2×#13133217C2211yescharacteristic
39C2×#13133217C2211yescharacteristic
40C2×#13133217C2211yescharacteristic
41C2×#13133217C2212yes—
42C2×#13133216C2214yes—
43C2×#13133214C2211yescharacteristic
44C2×#13133212C2214yes—
45C2×#13133209C2212yes—
46C2×#13133209C2212yes—
47C2×#13133208C2214yes—
48C2×#13133205C2212yes—
49C2×#13133203C2214yes—
50C2×#13133203C2214yes—
51C2×#13133203C2214yes—
52C2×#13133202C2214yes—
53C2×#13133202C2214yes—
54C2×#13133201C2214yes—
55C2×#13133199C2214yes—
56C2×#13133197C2212yes—
57C2×#13133197C2212yes—
58C2×#13133197C2214yes—
59C2×#13133196C2212yes—
60C2×#13133196C2212yes—
61C2×#13133195C2214yes—
62C2×#13133194C2214yes—
63C2×#13133194C2214yes—
64C2×#13133193C2212yes—
65C2×#13133191C2212yes—
66C2×#13133191C2212yes—
67C2×#13133191C2212yes—
68C2×#13133191C2211yescharacteristic
69C2×#13133191C2211yescharacteristic
70C2×#13133190C2214yes—
71C2×#13133190C2214yes—
72C2×#13133189C2214yes—
73C2×#13133188C2214yes—
74C2×#13133188C2212yes—
75C2×C4×Dic106C2212yes—
76C2×C4×Dic106C2212yes—
77C2×C4×D212C2212yes—
78C2×C4×D212C2212yes—
79C2×C4×D212C2211yescharacteristic
80C2×C4×D212C2212yes—
81C2×C4×D212C2211yescharacteristic
82C2×#13133177C2214yes—
83C2×#13133176C2212yes—
84C2×#13133176C2212yes—
85C2×#13133175C2212yes—
86C2×#13133175C2214yes—
87C22×C4⋊Dic53C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C53×#529C22116yescomplemented
90C2×#126×C53C2212yes—
91C2×#125×C53C2211yescharacteristic
92C2×#124×C53C2211yescharacteristic
93C2×#123×C53C2212yes—
94C2×C22⋊Q8×C53C2211yescharacteristic
95C2×#121×C53C2211yescharacteristic
96C2×C4×Q8×C53C2211yescharacteristic
97C2×C4×D4×C53C2211yescharacteristic
98C2×C4×D4×C53C2212yes—
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719945—48no—
102C2×#11719945C23116yes—
103C2×#11719947—48no—
104C2×#11719947C23116yes—
105C22×Dic106C2312yes—
106C22×Dic106C2312yes—
107C22×Dic106C2312yes—
108C22×Dic106C2314yes—
109C2×Q8×D53—48no—
110C2×Q8×D53C23116yes—
111C22×D212C2311yescharacteristic
112C22×D212C2311yescharacteristic
113C22×D212C2312yes—
114C22×D212C2312yes—
115C22×C22⋊D53C2314yes—
116C22×C22⋊D53C2312yes—
117C22×C22⋊D53C2314yes—
118C22×C22⋊D53C2312yes—
119C23×Dic53C2314yes—
120C22×C4×D53C2312yes—
121C22×C4×D53C2312yes—
122C22×C4×D53C2314yes—
123C22×C4×D53C2314yes—
124#13133217C2318yes—
125#13133217C23116yes—
126#13133217C2318yes—
127#13133217C2318yes—
128#13133216C23132yes—
129#13133214C2318yes—
130#13133212C23132yes—
131#13133209C23116yes—
132#13133209C23116yes—
133#13133208C23132yes—
134#13133205C23116yes—
135#13133203C23132yes—
136#13133203C23132yes—
137#13133203C23132yes—
138#13133202C23132yes—
139#13133202C23132yes—
140#13133201C23132yes—
141#13133199C23132yes—
142#13133197C23116yes—
143#13133197C23116yes—
144#13133197C23132yes—
145#13133196C23116yes—
146#13133196C23116yes—
147#13133195C23132yes—
148#13133194C23132yes—
149#13133194C23132yes—
150#13133193C23116yes—
151#13133191C23116yes—
152#13133191C2318yes—
153#13133191C23116yes—
154#13133191C2318yes—
155#13133191C23116yes—
156#13133190C23132yes—
157#13133190C23132yes—
158#13133189C23132yes—
159#13133188C23116yes—
160#13133188C23132yes—
161C4×Dic106C23116yes—
162C4×Dic106C23116yes—
163C4×D212C2318yes—
164C4×D212C23116yes—
165C4×D212C23116yes—
166C4×D212C2318yes—
167C4×D212C23116yes—
168#13133177C23132yes—
169#13133176C23116yes—
170#13133176C23116yes—
171#13133175C23116yes—
172#13133175C23132yes—
173C2×C4⋊Dic53C23116yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2314yes—
178C2×C4⋊Dic53C2314yes—
179C2×C4⋊Dic53C2312yes—
180C2×C4⋊Dic53C2311yescharacteristic
181C2×C4⋊Dic53C2312yes—
182C2×C4⋊Dic53C2312yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C2×#11719919C2314yes—
187C4⋊C4×D53C23116yes—
188C2×C22⋊Dic53C2314yes—
189C2×C22⋊Dic53C2314yes—
190C2×#11719921C2312yes—
191C2×#11719921C2314yes—
192C2×#11719921C2314yes—
193C2×#11719921C2312yes—
194C2×#11719921C2314yes—
195C2×#11719921C2314yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×C4×Dic53C2314yes—
199C2×C4×Dic53C2314yes—
200C22×Q8×C53C2311yescharacteristic
201C22×D4×C53C2311yescharacteristic
202C22×D4×C53C2312yes—
203C23×C4×C53C2311yescharacteristic
204C23×C4×C53C2311yescharacteristic
205C23×C4×C53C2312yes—
206C23×C4×C53C2311yescharacteristic
207#126×C53C23116yes—
208#125×C53C2318yes—
209#124×C53C2318yes—
210#123×C53C23116yes—
211C22⋊Q8×C53C2318yes—
212#121×C53C2318yes—
213C4×Q8×C53C2318yes—
214C4×D4×C53C2318yes—
215C4×D4×C53C23116yes—
216#117×C53C23116yes—
217C2×C4⋊C4×C53C2312yes—
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2311yescharacteristic
220C2×C4⋊C4×C53C2312yes—
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2312yes—
223C2×C22⋊C4×C53C2312yes—
224C2×C22⋊C4×C53C2312yes—
225C2×C22⋊C4×C53C2312yes—
226C2×C22⋊C4×C53C2312yes—
227C2×C22⋊C4×C53C2312yes—
228C2×C42×C53C2311yescharacteristic
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2318yes—
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C24×C53C2411yescharacteristic
236C23×D53C2412yes—
237C23×D53C2412yes—
238C2×Q8×C53—24no—
239C2×Q8×C53C2414yes—
240C2×D4×C53—24no—
241C2×D4×C53—44no—
242C2×D4×C53C2414yes—
243C2×D4×C53C2418yes—
244C22×C4×C53—24no—
245C22×C4×C53—24no—
246C22×C4×C53—28no—
247C22×C4×C53—42no—
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2411yescharacteristic
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2414yes—
253C22×C4×C53C2414yes—
254C22×C4×C53C2412yes—
255C22×C4×C53C2412yes—
256C22×C4×C53C2412yes—
257C22×C4×C53C2418yes—
258C22×C4×C53C2414yes—
259C22×C4×C53C2411yescharacteristic
260C22×C4×C53C2411yescharacteristic
261C2×C22⋊D53—48no—
262C2×C22⋊D53—48no—
263C2×C22⋊D53—44no—
264C2×C22⋊D53—44no—
265C2×C22⋊D53C24116yes—
266C2×C22⋊D53C2418yes—
267C2×C22⋊D53C24116yes—
268C2×C22⋊D53C2418yes—
269C22×Dic53—48no—
270C22×Dic53C2414yes—
271C22×Dic53C2412yes—
272C22×Dic53C2414yes—
273C22×Dic53C2412yes—
274C22×Dic53C24116yes—
275Q8×D53—432no—
276#11719947—432no—
277#11719945—432no—
278C2×D212—24no—
279C2×D212—24no—
280C2×D212—44no—
281C2×D212—44no—
282C2×D212C2414yes—
283C2×D212C2414yes—
284C2×D212C2418yes—
285C2×D212C2418yes—
286C2×C4×D53—28no—
287C2×C4×D53—28no—
288C2×C4×D53—48no—
289C2×C4×D53—48no—
290C2×C4×D53C2418yes—
291C2×C4×D53C2418yes—
292C2×C4×D53C24116yes—
293C2×C4×D53C24116yes—
294C2×Dic106—28no—
295C2×Dic106—48no—
296C2×Dic106—44no—
297C2×Dic106—44no—
298C2×Dic106C2418yes—
299C2×Dic106C2418yes—
300C2×Dic106C2418yes—
301C2×Dic106C24116yes—
302C4⋊C4×C53C2418yes—
303C4⋊C4×C53C2418yes—
304C4⋊C4×C53C2414yes—
305C4⋊C4×C53C2418yes—
306C4⋊C4×C53C2414yes—
307C4⋊C4×C53C2418yes—
308C22⋊C4×C53C2418yes—
309C22⋊C4×C53C2418yes—
310C22⋊C4×C53C2418yes—
311C22⋊C4×C53C2418yes—
312C22⋊C4×C53C2418yes—
313C42×C53C2414yes—
314C42×C53C2414yes—
315C42×C53C2414yes—
316C42×C53C2414yes—
317C42×C53C2418yes—
318C22⋊Dic53C24116yes—
319C22⋊Dic53C24116yes—
320#11719921C2418yes—
321#11719921C24116yes—
322#11719921C24116yes—
323#11719921C2418yes—
324#11719921C24116yes—
325#11719921C24116yes—
326#11719921C2418yes—
327#11719921C2418yes—
328C4⋊Dic53C2418yes—
329C4⋊Dic53C2414yes—
330C4⋊Dic53C2418yes—
331C4⋊Dic53C24116yes—
332C4⋊Dic53C24116yes—
333C4⋊Dic53C2418yes—
334C4⋊Dic53C2414yes—
335C4⋊Dic53C2418yes—
336C4⋊Dic53C2418yes—
337#11719919C24116yes—
338#11719919C24116yes—
339#11719919C24116yes—
340#11719919C24116yes—
341C4×Dic53C24116yes—
342C4×Dic53C24116yes—
343C23×C53—24no—
344C23×C53—22no—
345C23×C53—24no—
346C23×C53—22no—
347C23×C53—24no—
348C23×C53—22no—
349C23×C53C2514yes—
350C23×C53C2512yes—
351C23×C53C2511yescharacteristic
352C22×D53—24no—
353C22×D53—24no—
354C22×D53—24no—
355C22×D53—24no—
356C22×D53—24no—
357C22×D53—24no—
358C22×D53C2514yes—
359C22×D53C2514yes—
360Q8×C53—28no—
361D4×C53—28no—
362D4×C53—48no—
363C2×C4×C53—24no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—24no—
367C2×C4×C53—22no—
368C2×C4×C53—24no—
369C2×C4×C53—22no—
370C2×C4×C53—28no—
371C2×C4×C53—28no—
372C2×C4×C53—216no—
373C2×C4×C53—44no—
374C2×C4×C53H(5,𝔽2)14yes—
375C2×C4×C532−1+414yes—
376C2×C4×C53C2514yes—
377C2×C4×C53C2512yes—
378C2×C4×C53C2512yes—
379C2×C4×C53C2514yes—
380C2×C4×C53C2512yes—
381C2×C4×C53C2512yes—
382C2×C4×C53C2514yes—
383C2×C4×C53C2512yes—
384C2×C4×C53C2512yes—
385C22⋊D53—48no—
386C22⋊D53—48no—
387C22⋊D53—416no—
388C22⋊D53—416no—
389C2×Dic53—28no—
390C2×Dic53—24no—
391C2×Dic53—24no—
392C2×Dic53—28no—
393C2×Dic53—416no—
394C2×Dic53C2514yes—
395C2×Dic53C2518yes—
396C2×Dic53C2514yes—
397C2×Dic53C2518yes—
398D212—28no—
399D212—28no—
400D212—48no—
401D212—48no—
402C4×D53—216no—
403C4×D53—216no—
404C4×D53—416no—
405C4×D53—416no—
406Dic106—216no—
407Dic106—48no—
408Dic106—48no—
409Dic106—416no—
410C2×#3547—531nomaximal, Sylow
411C22×C53—24no—
412C22×C53—22no—
413C22×C53—24no—
414C22×C53—22no—
415C22×C53—24no—
416C22×C53—22no—
417C22×C53—48no—
418C22×C53—44no—
419C22×C53C2×H(5,𝔽2)12yes—
420C22×C53C2×2−1+412yes—
421C22×C53#58512yes—
422C22×C53C2611yescharacteristic
423C2×D53—24no—
424C2×D53—24no—
425C2×D53—24no—
426C2×D53—24no—
427C2×D53—24no—
428C2×D53—24no—
429C2×D53—48no—
430C2×D53—48no—
431C4×C53—24no—
432C4×C53—22no—
433C4×C53—22no—
434C4×C53—24no—
435C4×C53—22no—
436C4×C53—24no—
437C4×C53—22no—
438C4×C53C2×H(5,𝔽2)14yes—
439C4×C53C2×2−1+414yes—
440Dic53—28no—
441Dic53—24no—
442Dic53—24no—
443Dic53—28no—
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×#532—531no—
461C2×#529D5311yescharacteristic, complemented
462C2×C53—44no—
463C2×C53—42no—
464C2×C53#354714yescomplemented
465C2×C53C22×H(5,𝔽2)11yescharacteristic
466C2×C53C22×2−1+411yescharacteristic
467C2×C53C2×#58511yescharacteristic
468D53—44no—
469D53—44no—
470C22×#41—532no—
471C22×#41—532no—
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#532—5316no—
489C2×C4⋊Q8—534no—
490C2×C4⋊Q8—531no—
491C2×C4⋊Q8—531no—
492C2×C4⋊Q8—531no—
493C2×C4⋊Q8—532no—
494C2×#127—531no—
495#529C2×D53116yescomplemented
496C2×#126—534no—
497C2×#126C2×D5312yes—
498C2×#125—534no—
499C2×#125—532no—
500C2×#125—532no—
501C2×#125C2×D5311yescharacteristic
502C2×#124—534no—
503C2×#124—534no—
504C2×#124—534no—
505C2×#124—532no—
506C2×#124C2×D5311yescharacteristic
507C2×#123—534no—
508C2×#123—534no—
509C2×#123—534no—
510C2×#123—534no—
511C2×#123C2×D5312yes—
512C2×C22⋊Q8—532no—
513C2×C22⋊Q8—532no—
514C2×C22⋊Q8—532no—
515C2×C22⋊Q8—534no—
516C2×C22⋊Q8—532no—
517C2×C22⋊Q8—532no—
518C2×C22⋊Q8—534no—
519C2×C22⋊Q8—534no—
520C2×C22⋊Q8—534no—
521C2×C22⋊Q8C2×D5311yescharacteristic
522C2×#121—532no—
523C2×#121—534no—
524C2×#121—534no—
525C2×#121—531no—
526C2×#121—531no—
527C2×#121—532no—
528C2×#121—532no—
529C2×#121—532no—
530C2×#121—534no—
531C2×#121—534no—
532C2×#121C2×D5311yescharacteristic
533C2×C4×Q8—532no—
534C2×C4×Q8—532no—
535C2×C4×Q8C2×D5311yescharacteristic
536C2×C4×D4—534no—
537C2×C4×D4—531no—
538C2×C4×D4—532no—
539C2×C4×D4—531no—
540C2×C4×D4—532no—
541C2×C4×D4—532no—
542C2×C4×D4C2×D5311yescharacteristic
543C2×C4×D4C2×D5312yes—
544C2×#117—532no—
545C2×#117—532no—
546C2×#117—532no—
547C2×#117—534no—
548C2×#117C2×D5312yes—
549C22×C4⋊C4—532no—
550C22×C4⋊C4—532no—
551C22×C42C2×D5311yescharacteristic
552C53C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—5316no—
554C2×#41—5316no—
555C2×#41—2128no—
556C2×#41—2128no—
557C22×Q8—5316no—
558C22×Q8—532no—
559C22×Q8—532no—
560C22×Q8—534no—
561C22×Q8—532no—
562C22×Q8—2128no—
563C22×Q8C22×D5311yescharacteristic
564C22×D4—534no—
565C22×D4—532no—
566C22×D4—534no—
567C22×D4—532no—
568C22×D4—531no—
569C22×D4—531no—
570C22×D4—532no—
571C22×D4—532no—
572C22×D4C22×D5311yescharacteristic
573C22×D4C22×D5312yes—
574C23×C4—534no—
575C23×C4—532no—
576C23×C4—532no—
577C23×C4—534no—
578C23×C4—534no—
579C23×C4C22×D5312yes—
580C23×C4C22×D5311yescharacteristic
581C23×C4C22×D5311yescharacteristic
582C23×C4C22×D5311yescharacteristic
583C4⋊Q8—5332no—
584C4⋊Q8—538no—
585C4⋊Q8—538no—
586C4⋊Q8—538no—
587C4⋊Q8—5316no—
588#127—538no—
589#126—5332no—
590#126C22×D53116yes—
591#125—5332no—
592#125—5316no—
593#125—5316no—
594#125C22×D5318yes—
595#124—5332no—
596#124—5332no—
597#124—5332no—
598#124—5316no—
599#124C22×D5318yes—
600#123—5332no—
601#123—5332no—
602#123—5332no—
603#123—5332no—
604#123C22×D53116yes—
605C22⋊Q8—5316no—
606C22⋊Q8—5316no—
607C22⋊Q8—5316no—
608C22⋊Q8—5316no—
609C22⋊Q8—5316no—
610C22⋊Q8—5332no—
611C22⋊Q8—5332no—
612C22⋊Q8—5332no—
613C22⋊Q8—5332no—
614C22⋊Q8C22×D5318yes—
615#121—5316no—
616#121—5332no—
617#121—5332no—
618#121—538no—
619#121—538no—
620#121—5316no—
621#121—5316no—
622#121—5316no—
623#121—5332no—
624#121—5332no—
625#121C22×D5318yes—
626C4×Q8—5316no—
627C4×Q8—5316no—
628C4×Q8C22×D5318yes—
629C4×D4—5332no—
630C4×D4—538no—
631C4×D4—5316no—
632C4×D4—538no—
633C4×D4—5316no—
634C4×D4—5316no—
635C4×D4C22×D5318yes—
636C4×D4C22×D53116yes—
637#117—5316no—
638#117—5316no—
639#117—5316no—
640#117—5332no—
641#117C22×D53116yes—
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—534no—
651C2×C4⋊C4—532no—
652C2×C4⋊C4—534no—
653C2×C4⋊C4—534no—
654C2×C4⋊C4—534no—
655C2×C4⋊C4—532no—
656C2×C4⋊C4—5316no—
657C2×C4⋊C4C22×D5311yescharacteristic
658C2×C4⋊C4C22×D5311yescharacteristic
659C2×C4⋊C4C22×D5312yes—
660C2×C4⋊C4C22×D5312yes—
661C2×C4⋊C4C22×D5312yes—
662C2×C4⋊C4C22×D5312yes—
663C2×C22⋊C4—534no—
664C2×C22⋊C4—534no—
665C2×C22⋊C4—532no—
666C2×C22⋊C4—534no—
667C2×C22⋊C4—534no—
668C2×C22⋊C4—532no—
669C2×C22⋊C4—534no—
670C2×C22⋊C4—532no—
671C2×C22⋊C4—534no—
672C2×C22⋊C4—532no—
673C2×C22⋊C4C22×D5312yes—
674C2×C22⋊C4C22×D5312yes—
675C2×C22⋊C4C22×D5312yes—
676C2×C22⋊C4C22×D5312yes—
677C2×C22⋊C4C22×D5312yes—
678C2×C42—534no—
679C2×C42—534no—
680C2×C42C22×D5311yescharacteristic
681C2×C42C22×D5312yes—
682C2×C42C22×D5311yescharacteristic
683C2×C42C22×D5311yescharacteristic
684C2×C42C22×D5311yescharacteristic
685C2×C42C22×D5318yes—
686C24—532no—
687C24—532no—
688C24C23×D5311yescharacteristic
689C24C23×D5312yes—
690#41—21232no—
691#41—21232no—
692C2×Q8—24no—
693C2×Q8—538no—
694C2×Q8—538no—
695C2×Q8—5316no—
696C2×Q8—538no—
697C2×Q8—1068no—
698C2×Q8—2124no—
699C2×Q8—2128no—
700C2×Q8—2124no—
701C2×Q8—21232no—
702C2×Q8C23×D5314yes—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—5316no—
706C2×D4—538no—
707C2×D4—5316no—
708C2×D4—538no—
709C2×D4—534no—
710C2×D4—534no—
711C2×D4—538no—
712C2×D4—538no—
713C2×D4—1064no—
714C2×D4—1064no—
715C2×D4—2124no—
716C2×D4—2124no—
717C2×D4—2128no—
718C2×D4—2124no—
719C2×D4—2124no—
720C2×D4—2128no—
721C2×D4C23×D5314yes—
722C2×D4C23×D5318yes—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—534no—
728C22×C4—532no—
729C22×C4—534no—
730C22×C4—532no—
731C22×C4—5316no—
732C22×C4—538no—
733C22×C4—538no—
734C22×C4—5316no—
735C22×C4—5316no—
736C22×C4—1068no—
737C22×C4—1068no—
738C22×C4—2128no—
739C22×C4—2128no—
740C22×C4—2128no—
741C22×C4C23×D5314yes—
742C22×C4C23×D5314yes—
743C22×C4C23×D5318yes—
744C22×C4C23×D5311yescharacteristic
745C22×C4C23×D5312yes—
746C22×C4C23×D5311yescharacteristic
747C22×C4C23×D5311yescharacteristic
748C22×C4C23×D5311yescharacteristic
749C22×C4C23×D5312yes—
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—5316no—
762C4⋊C4—538no—
763C4⋊C4—5316no—
764C4⋊C4—5316no—
765C4⋊C4—5316no—
766C4⋊C4—538no—
767C4⋊C4C23×D5314yes—
768C4⋊C4C23×D5314yes—
769C4⋊C4C23×D5318yes—
770C4⋊C4C23×D5318yes—
771C4⋊C4C23×D5318yes—
772C4⋊C4C23×D5318yes—
773C22⋊C4—5316no—
774C22⋊C4—5316no—
775C22⋊C4—538no—
776C22⋊C4—5316no—
777C22⋊C4—5316no—
778C22⋊C4—538no—
779C22⋊C4—5316no—
780C22⋊C4—538no—
781C22⋊C4—5316no—
782C22⋊C4—538no—
783C22⋊C4C23×D5318yes—
784C22⋊C4C23×D5318yes—
785C22⋊C4C23×D5318yes—
786C22⋊C4C23×D5318yes—
787C22⋊C4C23×D5318yes—
788C42—5316no—
789C42—5316no—
790C42C23×D5314yes—
791C42C23×D5314yes—
792C42C23×D5314yes—
793C42C23×D5314yes—
794C42C23×D5318yes—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—534no—
802C23—534no—
803C23—1064no—
804C23—1064no—
805C23—1064no—
806C23—1064no—
807C23—1064no—
808C23—1064no—
809C23C24×D5312yes—
810C23C24×D5314yes—
811C23C24×D5311yescharacteristic
812Q8—28no—
813Q8—10616no—
814Q8—2128no—
815Q8—21216no—
816Q8—2128no—
817D4—28no—
818D4—48no—
819D4—1068no—
820D4—1068no—
821D4—2128no—
822D4—2128no—
823D4—21216no—
824D4—2128no—
825D4—2128no—
826D4—21216no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—538no—
839C2×C4—534no—
840C2×C4—538no—
841C2×C4—534no—
842C2×C4—1064no—
843C2×C4—1064no—
844C2×C4—1068no—
845C2×C4—1068no—
846C2×C4—10616no—
847C2×C4—10616no—
848C2×C4—21216no—
849C2×C4—21216no—
850C2×C4—21216no—
851C2×C4#1313326314yes—
852C2×C4#1313326414yes—
853C2×C4C24×D5312yes—
854C2×C4C24×D5314yes—
855C2×C4C24×D5312yes—
856C2×C4C24×D5312yes—
857C2×C4C24×D5312yes—
858C2×C4C24×D5314yes—
859C2×C4C24×D5314yes—
860C2×C4C24×D5312yes—
861C2×C4C24×D5312yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—1064no—
871C22—1064no—
872C22—1064no—
873C22—1064no—
874C22—1064no—
875C22—1064no—
876C22—2128no—
877C22—2128no—
878C22C2×#1313326312yes—
879C22C2×#1313326412yes—
880C22#1681145912yes—
881C22C25×D5311yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—1064no—
890C4—1064no—
891C4—1068no—
892C4—1068no—
893C4C2×#1313326314yes—
894C4C2×#1313326414yes—
895C2—42no—
896C2—44no—
897C2—2124no—
898C2—2124no—
899C2#2028910614yesdirect product factor
900C2C22×#1313326311yescharacteristic
901C2C22×#1313326411yescharacteristic
902C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#529C2
socleC23×C53C25
hypercenterC2×#529D53
hypocenterC53C2×#3547
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #20289106C2direct (N × H)
2. C2×#16811370C2semidirect
3. C2×#16811338C2semidirect
4. C2×#16811338C2semidirect
5. C2×#16811333C2semidirect
6. C2×#16811319C2semidirect
7. C2×#16811311C2semidirect
8. C2×Q8×D212C2semidirect
9. C2×#16811281C2semidirect
10. C2×#16811277C2semidirect
11. C2×#16811251C2semidirect
12. C2×#16811239C2semidirect
13. C2×#16811228C2semidirect
14. C2×#16811202C2semidirect
15. C2×#16811196C2semidirect
16. C2×#16811180C2semidirect
17. C2×#16811173C2semidirect
18. C2×C53×#529C2semidirect
22. #16811370C22semidirect
23. #16811338C22semidirect
24. #16811338C22semidirect
25. #16811333C22semidirect
26. #16811319C22semidirect
27. #16811311C22semidirect
28. Q8×D212C22semidirect
29. #16811281C22semidirect
30. #16811277C22semidirect
31. #16811251C22semidirect
32. #16811239C22semidirect
33. #16811228C22semidirect
34. #16811202C22semidirect
35. #16811196C22semidirect
36. #16811180C22semidirect
37. #16811173C22semidirect
89. C53×#529C22semidirect
461. C2×#529D53semidirect
464. C2×C53#3547semidirect
495. #529C2×D53semidirect
552. C53C2×#3547semidirect
899. C2#20289106direct (N × H)

Maximal subgroups

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

subgroupindex
#202891062
C2×#168113702
C2×#168113382
C2×#168113332
C2×#168113192
C2×#168113112
C2×Q8×D2122
C2×#168112812
C2×#168112772
C2×#168112512
C2×#168112392
C2×#168112282
C2×#168112022
C2×#168111962
C2×#168111802
C2×#168111732
C2×C53×#5292
C2×#354753