Finite Group Databasebeta

← C2×#19148503 #26004969

Subgroups — C2×#19148503 #26004969

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148503C2132yesmaximal, direct product factor
2C2×#14583620C212yesmaximal, complemented
3C2×#14583615C211yesmaximal, characteristic, complemented
4C2×#14583614C211yesmaximal, characteristic, complemented
5C2×#14583609C211yesmaximal, characteristic, complemented
6C2×#14583602C212yesmaximal, complemented
7C2×#14583599C212yesmaximal, complemented
8C2×#14583559C214yesmaximal, complemented
9C2×#14583550C212yesmaximal, complemented
10C2×#14583519C214yesmaximal, complemented
11C2×#14583479C212yesmaximal, complemented
12C2×#14583455C212yesmaximal, complemented
13C2×#14583446C212yesmaximal, complemented
14C2×#14583446C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583380C212yesmaximal, complemented
17C2×C4×#10621902C211yesmaximal, characteristic, complemented
18C2×C43×#554C211yesmaximal, characteristic, complemented
19C22×#10621902C2211yescharacteristic
20C22×#10621898C2212yes—
21C22×#10621898C2214yes—
22C22×Q8×D43C2212yes—
23#14583620C22132yescomplemented
24#14583615C22116yescomplemented
25#14583614C22116yescomplemented
26#14583609C22116yescomplemented
27#14583602C22132yescomplemented
28#14583599C22132yescomplemented
29#14583559C22164yescomplemented
30#14583550C22132yescomplemented
31#14583519C22164yescomplemented
32#14583479C22132yescomplemented
33#14583455C22132yescomplemented
34#14583446C22132yescomplemented
35#14583446C22116yescomplemented
36C2×#13063325C2211yescharacteristic
37C2×#13063324C2212yes—
38C2×#13063324C2212yes—
39C2×#13063324C2211yescharacteristic
40C2×#13063323C2212yes—
41C4⋊Q8×D43C22116yescomplemented
42C2×#13063321C2211yescharacteristic
43C2×#13063320C2214yes—
44C2×#13063318C2214yes—
45C2×#13063317C2212yes—
46C2×#13063314C2214yes—
47C2×#13063311C2214yes—
48C2×#13063311C2214yes—
49C2×#13063311C2212yes—
50C2×#13063310C2214yes—
51C2×#13063308C2214yes—
52C2×#13063303C2214yes—
53C2×#13063303C2214yes—
54C2×#13063303C2214yes—
55C2×#13063301C2212yes—
56C2×#13063300C2212yes—
57C2×#13063300C2214yes—
58C2×#13063300C2211yescharacteristic
59C2×#13063300C2212yes—
60C2×#13063299C2212yes—
61C2×#13063298C2212yes—
62C2×#13063298C2214yes—
63C2×#13063298C2214yes—
64C2×#13063296C2211yescharacteristic
65C2×#13063296C2212yes—
66#14583380C22132yescomplemented
67C4×#10621902C22116yescomplemented
68C2×Q8×Dic43C2211yescharacteristic
69C2×#13063290C2214yes—
70C2×#13063290C2214yes—
71C2×C4×D172C2212yes—
72C2×C4×D172C2211yescharacteristic
73C2×C4×D172C2212yes—
74C2×C4×D172C2211yescharacteristic
75C2×#13063287C2211yescharacteristic
76C2×#13063287C2212yes—
77C2×#13063287C2214yes—
78C2×C4×C22⋊D43C2214yes—
79C2×C4×C22⋊D43C2214yes—
80C2×C4×C22⋊D43C2212yes—
81C2×#13063284C2212yes—
82C2×#13063283C2211yescharacteristic
83C2×#13063283C2212yes—
84C2×#13063283C2212yes—
85C2×#13063283C2212yes—
86C2×#13063283C2212yes—
87C2×C4⋊C4×D43C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C42×D43C2211yescharacteristic
91C2×C42×D43C2212yes—
92C43×#554C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#125×C43C2212yes—
95C2×C22⋊Q8×C43C2214yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×D4×C43C2212yes—
99C2×C4×D4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yes—
101C2×#10621902—28no—
102C2×#10621902C2318yes—
103C2×#10621898—216no—
104C2×#10621898—416no—
105C2×#10621898C23116yes—
106C2×#10621898C23132yes—
107C22×Dic86C2312yes—
108C22×Dic86C2314yes—
109C22×Dic86C2312yes—
110C2×Q8×D43—48no—
111C2×Q8×D43C23116yes—
112C22×D172C2312yes—
113C22×D172C2312yes—
114C22×D172C2311yescharacteristic
115C22×D172C2311yescharacteristic
116C22×D172C2314yes—
117C22×C22⋊D43C2312yes—
118C22×C22⋊D43C2312yes—
119C22×C22⋊D43C2312yes—
120C22×C22⋊D43C2314yes—
121C22×C4×D43C2311yescharacteristic
122C22×C4×D43C2312yes—
123C22×C4×D43C2312yes—
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C2312yes—
126C22×C4×D43C2312yes—
127C22×C4×D43C2314yes—
128C22×C4×D43C2314yes—
129C22×C4×D43C2311yescharacteristic
130#13063325C2318yes—
131#13063324C23116yes—
132#13063324C23116yes—
133#13063324C2318yes—
134#13063323C23116yes—
135#13063321C2318yes—
136#13063320C23132yes—
137#13063318C23132yes—
138#13063317C23116yes—
139#13063314C23132yes—
140#13063311C23132yes—
141#13063311C23132yes—
142#13063311C23116yes—
143#13063310C23132yes—
144#13063308C23132yes—
145#13063303C23132yes—
146#13063303C23132yes—
147#13063303C23132yes—
148#13063301C23116yes—
149#13063300C23132yes—
150#13063300C2318yes—
151#13063300C23116yes—
152#13063300C23116yes—
153#13063299C23116yes—
154#13063298C23116yes—
155#13063298C23132yes—
156#13063298C23132yes—
157#13063296C2318yes—
158#13063296C23116yes—
159Q8×Dic43C2318yes—
160#13063290C23132yes—
161#13063290C23132yes—
162C4×D172C23116yes—
163C4×D172C23116yes—
164C4×D172C2318yes—
165C4×D172C2318yes—
166#13063287C23116yes—
167#13063287C23132yes—
168#13063287C2318yes—
169C4×C22⋊D43C23132yes—
170C4×C22⋊D43C23116yes—
171C4×C22⋊D43C23132yes—
172#13063284C23116yes—
173#13063283C23116yes—
174#13063283C23116yes—
175#13063283C23116yes—
176#13063283C2318yes—
177#13063283C23116yes—
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2311yescharacteristic
181C2×C4⋊Dic43C2311yescharacteristic
182C2×C4⋊Dic43C2312yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2314yes—
188C4⋊C4×D43C23116yes—
189C4⋊C4×D43C23116yes—
190C4⋊C4×D43C23116yes—
191C2×C22⋊Dic43C2314yes—
192C2×C22⋊Dic43C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2314yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2314yes—
209C42×D43C2318yes—
210C42×D43C23116yes—
211C22×Q8×C43C2311yescharacteristic
212C22×Q8×C43C2312yes—
213C22×D4×C43C2311yescharacteristic
214C23×C4×C43C2312yes—
215C23×C4×C43C2314yes—
216C4⋊Q8×C43C2318yes—
217#125×C43C23116yes—
218C22⋊Q8×C43C23132yes—
219C22⋊Q8×C43C23116yes—
220C4×Q8×C43C2318yes—
221C4×D4×C43C23116yes—
222C4×D4×C43C2318yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2314yes—
225C2×C4⋊C4×C43C2312yes—
226C2×C4⋊C4×C43C23116yes—
227C2×C4⋊C4×C43C2311yescharacteristic
228C2×C4⋊C4×C43C2312yes—
229C2×C4⋊C4×C43C2312yes—
230C2×C4⋊C4×C43C2314yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C22⋊C4×C43C2312yes—
233C2×C42×C43C2312yes—
234C2×C42×C43C2311yescharacteristic
235C24×C43C2412yes—
236C23×D43C2412yes—
237C23×D43C2412yes—
238C23×D43C2411yescharacteristic
239C2×Q8×C43—24no—
240C2×Q8×C43—44no—
241C2×Q8×C43C2414yes—
242C2×Q8×C43C2418yes—
243C2×D4×C43—24no—
244C2×D4×C43C2414yes—
245C22×C4×C43—28no—
246C22×C4×C43—48no—
247C22×C4×C43C2412yes—
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2412yes—
250C22×C4×C43C2412yes—
251C22×C4×C43C2414yes—
252C22×C4×C43C2418yes—
253C22×C4×C43C24116yes—
254C22×C4×C43C2411yescharacteristic
255C22×C4×C43C2411yescharacteristic
256C2×C22⋊D43—28no—
257C2×C22⋊D43—28no—
258C2×C22⋊D43—28no—
259C2×C22⋊D43—48no—
260C2×C22⋊D43C2418yes—
261C2×C22⋊D43C2418yes—
262C2×C22⋊D43C2418yes—
263C2×C22⋊D43C24116yes—
264C22×Dic43C2412yes—
265C22×Dic43C2411yescharacteristic
266C22×Dic43C2412yes—
267C22×Dic43C2414yes—
268C22×Dic43C2411yescharacteristic
269C22×Dic43C2411yescharacteristic
270#10621902—232no—
271Q8×D43—432no—
272#10621898—264no—
273#10621898—464no—
274C2×D172—24no—
275C2×D172—24no—
276C2×D172—28no—
277C2×D172—28no—
278C2×D172—48no—
279C2×D172C2418yes—
280C2×D172C2418yes—
281C2×D172C2414yes—
282C2×D172C2414yes—
283C2×D172C24116yes—
284C2×C4×D43—28no—
285C2×C4×D43—24no—
286C2×C4×D43—28no—
287C2×C4×D43—28no—
288C2×C4×D43—24no—
289C2×C4×D43—28no—
290C2×C4×D43—48no—
291C2×C4×D43—48no—
292C2×C4×D43#4118yescomplemented
293C2×C4×D43C2414yes—
294C2×C4×D43C2418yes—
295C2×C4×D43C2418yes—
296C2×C4×D43C2414yes—
297C2×C4×D43C2418yes—
298C2×C4×D43C2418yes—
299C2×C4×D43C24116yes—
300C2×C4×D43C24116yes—
301C2×C4×D43C2414yes—
302C2×Dic86—28no—
303C2×Dic86—216no—
304C2×Dic86—44no—
305C2×Dic86C2418yes—
306C2×Dic86C24116yes—
307C2×Dic86C2418yes—
308C4⋊C4×C43C2414yes—
309C4⋊C4×C43C24116yes—
310C4⋊C4×C43C2418yes—
311C4⋊C4×C43C2414yes—
312C4⋊C4×C43C2418yes—
313C4⋊C4×C43C2418yes—
314C4⋊C4×C43C24116yes—
315C22⋊C4×C43C24116yes—
316C22⋊C4×C43C2418yes—
317C42×C43C2418yes—
318C42×C43C2414yes—
319C22⋊Dic43C24116yes—
320C22⋊Dic43C2418yes—
321(C2×D43)⋊C4C2418yes—
322(C2×D43)⋊C4C24116yes—
323(C2×D43)⋊C4C2418yes—
324(C2×D43)⋊C4C2418yes—
325(C2×D43)⋊C4C24116yes—
326(C2×D43)⋊C4C24116yes—
327(C2×D43)⋊C4C2418yes—
328(C2×D43)⋊C4C24116yes—
329(C2×D43)⋊C4C2418yes—
330C4⋊Dic43C2418yes—
331C4⋊Dic43C2418yes—
332C4⋊Dic43C2414yes—
333C4⋊Dic43C2414yes—
334C4⋊Dic43C2418yes—
335Dic43⋊C4C24116yes—
336Dic43⋊C4C24116yes—
337Dic43⋊C4C24116yes—
338Dic43⋊C4C2418yes—
339Dic43⋊C4C24116yes—
340C4×Dic43C2414yes—
341C4×Dic43C2418yes—
342C4×Dic43C2414yes—
343C4×Dic43C2414yes—
344C4×Dic43C2418yes—
345C4×Dic43C24116yes—
346C4×Dic43C24116yes—
347C23×C43—24no—
348C23×C43—24no—
349C23×C43—24no—
350C23×C43C2514yes—
351C23×C43C2511yescharacteristic
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—24no—
355C22×D43—24no—
356C22×D43—24no—
357C22×D43—24no—
358C22×D43—24no—
359C22×D43—24no—
360C22×D43C2×#4114yes—
361C22×D43C2514yes—
362C22×D43C2514yes—
363C22×D43C2512yes—
364Q8×C43—28no—
365Q8×C43—48no—
366D4×C43—28no—
367C2×C4×C43—24no—
368C2×C4×C43—24no—
369C2×C4×C43—28no—
370C2×C4×C43—22no—
371C2×C4×C43—24no—
372C2×C4×C43—216no—
373C2×C4×C43—416no—
374C2×C4×C43C2×#4114yes—
375C2×C4×C432−1+414yes—
376C2×C4×C43C2514yes—
377C2×C4×C43C2514yes—
378C2×C4×C43C2514yes—
379C2×C4×C43C2518yes—
380C2×C4×C43C2512yes—
381C2×C4×C43C2512yes—
382C2×C4×C43C2512yes—
383C22⋊D43—216no—
384C22⋊D43—216no—
385C22⋊D43—216no—
386C22⋊D43—416no—
387C2×Dic43—24no—
388C2×Dic43—28no—
389C2×Dic43—24no—
390C2×Dic43—22no—
391C2×Dic43C2×#4114yes—
392C2×Dic43H(5,𝔽2)14yes—
393C2×Dic43C2514yes—
394C2×Dic43C2514yes—
395C2×Dic43C2512yes—
396C2×Dic43C2518yes—
397C2×Dic43C2512yes—
398C2×Dic43C2512yes—
399D172—216no—
400D172—216no—
401D172—28no—
402D172—28no—
403D172—416no—
404C4×D43—216no—
405C4×D43—28no—
406C4×D43—216no—
407C4×D43—216no—
408C4×D43—216no—
409C4×D43—28no—
410C4×D43—416no—
411C4×D43—416no—
412C4×D43C2×#41116yescomplemented
413Dic86—216no—
414Dic86—232no—
415Dic86—48no—
416C2×#3511—431nomaximal, Sylow
417C22×C43—24no—
418C22×C43—24no—
419C22×C43—24no—
420C22×C43—48no—
421C22×C43C22×#4112yes—
422C22×C43C2×H(5,𝔽2)12yes—
423C22×C43C2×2−1+412yes—
424C22×C43C2611yescharacteristic
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—28no—
428C2×D43—24no—
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—24no—
432C2×D43—24no—
433C2×D43—24no—
434C2×D43—48no—
435C2×D43—48no—
436C2×D43C22×#4114yes—
437C4×C43—24no—
438C4×C43—24no—
439C4×C43—28no—
440C4×C43—22no—
441C4×C43—24no—
442C4×C43C22×#4114yes—
443C4×C43C2×2−1+414yes—
444Dic43—24no—
445Dic43—28no—
446Dic43—24no—
447Dic43—22no—
448Dic43C22×#4114yes—
449Dic43C2×H(5,𝔽2)14yes—
450#3511—4332no—
451C2×#556—432no—
452C2×#555—431no—
453C2×#555—431no—
454C2×#554—431no—
455C2×#554D4311yescharacteristic, complemented
456C2×#553—432no—
457C2×#553—432no—
458C2×#548—434no—
459C2×#547—432no—
460C2×#542—434no—
461C2×#537—432no—
462C2×#533—432no—
463C2×#532—432no—
464C2×#532—431no—
465C22×C4⋊Q8—431no—
466C2×#520—432no—
467C2×C4×#41—431no—
468C2×C43—44no—
469C2×C43#351114yescomplemented
470C2×C43C23×#4111yescharacteristic
471C2×C43C22×H(5,𝔽2)11yescharacteristic
472C2×C43C22×2−1+411yescharacteristic
473D43—24no—
474D43—44no—
475D43—44no—
476C22×#41—431no—
477C22×#41—432no—
478C22×#41—434no—
479C23×Q8—432no—
480#556—4332no—
481#555—4316no—
482#555—4316no—
483#554—4316no—
484#554C2×D43116yescomplemented
485#553—4332no—
486#553—4332no—
487#548—4364no—
488#547—4332no—
489#542—4364no—
490#537—4332no—
491#533—4332no—
492#532—4316no—
493#532—4332no—
494C2×C4⋊Q8—432no—
495C2×C4⋊Q8—4316no—
496C2×C4⋊Q8—432no—
497C2×C4⋊Q8—432no—
498C2×C4⋊Q8—431no—
499C2×C4⋊Q8—431no—
500C2×C4⋊Q8C2×D4311yescharacteristic
501C2×#127—431no—
502C2×#126—434no—
503C2×#126—434no—
504C2×#125—432no—
505C2×#125C2×D4312yes—
506C2×#124—434no—
507C2×#124—432no—
508C2×#124—434no—
509C2×#124—434no—
510C2×#123—434no—
511C2×#123—434no—
512C2×C22⋊Q8—432no—
513C2×C22⋊Q8—434no—
514C2×C22⋊Q8—434no—
515C2×C22⋊Q8—434no—
516C2×C22⋊Q8C2×D4312yes—
517C2×C22⋊Q8C2×D4314yes—
518C2×#121—431no—
519C2×#121—432no—
520C2×#121—432no—
521C2×#121—431no—
522C2×#121—432no—
523C2×#121—432no—
524C2×#121—434no—
525C2×#121—434no—
526C2×#121—432no—
527C2×#121—434no—
528#520—4332no—
529C4×#41—4316no—
530C2×C4×Q8—431no—
531C2×C4×Q8—434no—
532C2×C4×Q8—434no—
533C2×C4×Q8C2×D4311yescharacteristic
534C2×C4×D4—434no—
535C2×C4×D4—434no—
536C2×C4×D4—432no—
537C2×C4×D4—431no—
538C2×C4×D4—432no—
539C2×C4×D4—434no—
540C2×C4×D4—432no—
541C2×C4×D4—431no—
542C2×C4×D4—432no—
543C2×C4×D4—431no—
544C2×C4×D4C2×D4312yes—
545C2×C4×D4C2×D4311yescharacteristic
546C2×#117—432no—
547C2×#117—431no—
548C2×#117—432no—
549C2×#117—432no—
550C2×#117—432no—
551C2×#117—432no—
552C22×C4⋊C4—432no—
553C22×C4⋊C4—432no—
554C22×C4⋊C4—432no—
555C22×C4⋊C4C2×D4312yes—
556C22×C42—431no—
557C22×C42—432no—
558C43C2×#351111yescharacteristic, complemented, Sylow
559C2×#41—438no—
560C2×#41—4316no—
561C2×#41—4332no—
562C2×#41—8616no—
563C2×#41—868no—
564C2×#41—17216no—
565C22×Q8—4316no—
566C22×Q8—432no—
567C22×Q8—434no—
568C22×Q8—432no—
569C22×Q8—1728no—
570C22×Q8C22×D4311yescharacteristic
571C22×Q8C22×D4312yes—
572C22×D4—432no—
573C22×D4—432no—
574C22×D4—432no—
575C22×D4—434no—
576C22×D4—431no—
577C22×D4—432no—
578C22×D4—432no—
579C22×D4—431no—
580C22×D4—434no—
581C22×D4C22×D4311yescharacteristic
582C23×C4—431no—
583C23×C4—431no—
584C23×C4—432no—
585C23×C4—432no—
586C23×C4—432no—
587C23×C4—431no—
588C23×C4—432no—
589C23×C4—434no—
590C23×C4—434no—
591C23×C4C22×D4312yes—
592C23×C4C22×D4314yes—
593C4⋊Q8—4316no—
594C4⋊Q8—4316no—
595C4⋊Q8—4316no—
596C4⋊Q8—438no—
597C4⋊Q8—438no—
598C4⋊Q8C22×D4318yes—
599#127—438no—
600#126—4332no—
601#126—4332no—
602#125—4316no—
603#125C22×D43116yes—
604#124—4332no—
605#124—4316no—
606#124—4332no—
607#124—4332no—
608#123—4332no—
609#123—4332no—
610C22⋊Q8—4316no—
611C22⋊Q8—4332no—
612C22⋊Q8—4332no—
613C22⋊Q8—4332no—
614C22⋊Q8C22×D43116yes—
615C22⋊Q8C22×D43132yes—
616#121—438no—
617#121—4316no—
618#121—4316no—
619#121—438no—
620#121—4316no—
621#121—4316no—
622#121—4332no—
623#121—4332no—
624#121—4316no—
625#121—4332no—
626C4×Q8—438no—
627C4×Q8—4332no—
628C4×Q8—4332no—
629C4×Q8C22×D4318yes—
630C4×D4—4332no—
631C4×D4—4332no—
632C4×D4—4316no—
633C4×D4—438no—
634C4×D4—4316no—
635C4×D4—4332no—
636C4×D4—4316no—
637C4×D4—438no—
638C4×D4—4316no—
639C4×D4—438no—
640C4×D4C22×D43116yes—
641C4×D4C22×D4318yes—
642#117—4316no—
643#117—438no—
644#117—4316no—
645#117—4316no—
646#117—4316no—
647#117—4316no—
648C2×C4⋊C4—432no—
649C2×C4⋊C4—432no—
650C2×C4⋊C4—434no—
651C2×C4⋊C4—434no—
652C2×C4⋊C4—434no—
653C2×C4⋊C4—431no—
654C2×C4⋊C4—431no—
655C2×C4⋊C4—432no—
656C2×C4⋊C4—432no—
657C2×C4⋊C4—434no—
658C2×C4⋊C4—4316no—
659C2×C4⋊C4—4316no—
660C2×C4⋊C4—4316no—
661C2×C4⋊C4C22×D4311yescharacteristic
662C2×C4⋊C4C22×D4312yes—
663C2×C4⋊C4C22×D4312yes—
664C2×C4⋊C4C22×D4314yes—
665C2×C4⋊C4C22×D43116yes—
666C2×C4⋊C4C22×D4311yescharacteristic
667C2×C4⋊C4C22×D4312yes—
668C2×C4⋊C4C22×D4314yes—
669C2×C22⋊C4—434no—
670C2×C22⋊C4—432no—
671C2×C22⋊C4—432no—
672C2×C22⋊C4—434no—
673C2×C22⋊C4—432no—
674C2×C22⋊C4—432no—
675C2×C22⋊C4—434no—
676C2×C22⋊C4—434no—
677C2×C22⋊C4—434no—
678C2×C22⋊C4—432no—
679C2×C22⋊C4—432no—
680C2×C22⋊C4C22×D4314yes—
681C2×C22⋊C4C22×D4312yes—
682C2×C42—432no—
683C2×C42—434no—
684C2×C42—434no—
685C2×C42—431no—
686C2×C42—431no—
687C2×C42—432no—
688C2×C42—431no—
689C2×C42—438no—
690C2×C42—4316no—
691C2×C42C22×D4312yes—
692C2×C42C22×D4311yescharacteristic
693C24—431no—
694C24—432no—
695C24—432no—
696C24C23×D4312yes—
697#41—8664no—
698#41—8632no—
699#41—17264no—
700C2×Q8—24no—
701C2×Q8—44no—
702C2×Q8—438no—
703C2×Q8—4316no—
704C2×Q8—438no—
705C2×Q8—8616no—
706C2×Q8—868no—
707C2×Q8—1724no—
708C2×Q8—17232no—
709C2×Q8C23×D4314yes—
710C2×Q8C23×D4318yes—
711C2×D4—24no—
712C2×D4—438no—
713C2×D4—438no—
714C2×D4—438no—
715C2×D4—4316no—
716C2×D4—434no—
717C2×D4—438no—
718C2×D4—438no—
719C2×D4—434no—
720C2×D4—4316no—
721C2×D4—868no—
722C2×D4—868no—
723C2×D4—868no—
724C2×D4—868no—
725C2×D4—868no—
726C2×D4—864no—
727C2×D4—864no—
728C2×D4—1728no—
729C2×D4—1728no—
730C2×D4C23×D4314yes—
731C22×C4—28no—
732C22×C4—48no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—438no—
736C22×C4—434no—
737C22×C4—432no—
738C22×C4—431no—
739C22×C4—432no—
740C22×C4—434no—
741C22×C4—434no—
742C22×C4—438no—
743C22×C4—438no—
744C22×C4—434no—
745C22×C4—438no—
746C22×C4—438no—
747C22×C4—4316no—
748C22×C4—4316no—
749C22×C4—864no—
750C22×C4—868no—
751C22×C4—868no—
752C22×C4—868no—
753C22×C4—864no—
754C22×C4—868no—
755C22×C4—1728no—
756C22×C4—1728no—
757C22×C4C23×D4318yes—
758C22×C4C23×D4312yes—
759C22×C4C23×D4311yescharacteristic
760C22×C4C23×D4312yes—
761C22×C4C23×D4312yes—
762C22×C4C23×D4314yes—
763C22×C4C23×D43116yes—
764C22×C4C23×D4311yescharacteristic
765C22×C4C23×D4311yescharacteristic
766C4⋊C4—438no—
767C4⋊C4—438no—
768C4⋊C4—4316no—
769C4⋊C4—4316no—
770C4⋊C4—4316no—
771C4⋊C4—434no—
772C4⋊C4—434no—
773C4⋊C4—438no—
774C4⋊C4—438no—
775C4⋊C4—4316no—
776C4⋊C4C23×D4314yes—
777C4⋊C4C23×D4318yes—
778C4⋊C4C23×D4318yes—
779C4⋊C4C23×D43116yes—
780C4⋊C4C23×D4314yes—
781C4⋊C4C23×D4318yes—
782C4⋊C4C23×D43116yes—
783C22⋊C4—4316no—
784C22⋊C4—438no—
785C22⋊C4—438no—
786C22⋊C4—4316no—
787C22⋊C4—438no—
788C22⋊C4—438no—
789C22⋊C4—4316no—
790C22⋊C4—4316no—
791C22⋊C4—4316no—
792C22⋊C4—438no—
793C22⋊C4—438no—
794C22⋊C4C23×D43116yes—
795C22⋊C4C23×D4318yes—
796C42—434no—
797C42—438no—
798C42—434no—
799C42—434no—
800C42—438no—
801C42—4316no—
802C42—4316no—
803C42C23×D4318yes—
804C42C23×D4314yes—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—434no—
809C23—432no—
810C23—434no—
811C23—434no—
812C23—862no—
813C23—862no—
814C23—864no—
815C23—864no—
816C23—864no—
817C23—864no—
818C23—864no—
819C23—864no—
820C23C24×D4314yes—
821C23C24×D4311yescharacteristic
822Q8—28no—
823Q8—48no—
824Q8—8632no—
825Q8—8616no—
826Q8—1728no—
827D4—28no—
828D4—8616no—
829D4—8616no—
830D4—8616no—
831D4—8616no—
832D4—8616no—
833D4—868no—
834D4—868no—
835D4—17216no—
836D4—17216no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—216no—
843C2×C4—416no—
844C2×C4—434no—
845C2×C4—434no—
846C2×C4—432no—
847C2×C4—432no—
848C2×C4—4316no—
849C2×C4—434no—
850C2×C4—432no—
851C2×C4—434no—
852C2×C4—438no—
853C2×C4—868no—
854C2×C4—8616no—
855C2×C4—8616no—
856C2×C4—864no—
857C2×C4—868no—
858C2×C4—864no—
859C2×C4—862no—
860C2×C4—8616no—
861C2×C4—868no—
862C2×C4—8616no—
863C2×C4—17216no—
864C2×C4—17216no—
865C2×C4#41×D4314yes—
866C2×C4#1306337314yes—
867C2×C4C24×D4314yes—
868C2×C4C24×D4312yes—
869C2×C4C24×D4314yes—
870C2×C4C24×D4314yes—
871C2×C4C24×D4318yes—
872C2×C4C24×D4312yes—
873C2×C4C24×D4312yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—48no—
878C22—434no—
879C22—862no—
880C22—862no—
881C22—868no—
882C22—864no—
883C22—864no—
884C22—864no—
885C22—864no—
886C22—864no—
887C22—864no—
888C22—1728no—
889C22—1728no—
890C22C2×#41×D4312yes—
891C22H(5,𝔽2)×D4312yes—
892C22C2×#1306337312yes—
893C22C25×D4311yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—434no—
900C4—434no—
901C4—864no—
902C4—868no—
903C4—864no—
904C4—862no—
905C4C2×#41×D4314yes—
906C4C2×#1306337314yes—
907C2—44no—
908C2—864no—
909C2—1724no—
910C2—1724no—
911C2#1914850314yesdirect product factor
912C2C22×#41×D4311yescharacteristic
913C2C2×H(5,𝔽2)×D4311yescharacteristic
914C2C22×#1306337311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#554C2
socleC23×C43C25
hypercenterC2×#554D43
hypocenterC43C2×#3511
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19148503C2direct (N × H)
2. C2×#14583620C2semidirect
3. C2×#14583615C2semidirect
4. C2×#14583614C2semidirect
5. C2×#14583609C2semidirect
6. C2×#14583602C2semidirect
7. C2×#14583599C2semidirect
8. C2×#14583559C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583519C2semidirect
11. C2×#14583479C2semidirect
12. C2×#14583455C2semidirect
13. C2×#14583446C2semidirect
14. C2×#14583446C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
16. C2×#14583380C2semidirect
17. C2×C4×#10621902C2semidirect
18. C2×C43×#554C2semidirect
23. #14583620C22semidirect
24. #14583615C22semidirect
25. #14583614C22semidirect
26. #14583609C22semidirect
27. #14583602C22semidirect
28. #14583599C22semidirect
29. #14583559C22semidirect
30. #14583550C22semidirect
31. #14583519C22semidirect
32. #14583479C22semidirect
33. #14583455C22semidirect
34. #14583446C22semidirect
35. #14583446C22semidirect
41. C4⋊Q8×D43C22semidirect
66. #14583380C22semidirect
67. C4×#10621902C22semidirect
92. C43×#554C22semidirect
292. C2×C4×D43#41semidirect
412. C4×D43C2×#41semidirect
455. C2×#554D43semidirect
469. C2×C43#3511semidirect
484. #554C2×D43semidirect
558. C43C2×#3511semidirect
911. C2#19148503direct (N × H)

Maximal subgroups

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

subgroupindex
#191485032
C2×#145836202
C2×#145836152
C2×#145836142
C2×#145836092
C2×#145836022
C2×#145835992
C2×#145835592
C2×#145835502
C2×#145835192
C2×#145834792
C2×#145834552
C2×#145834462
C2×C4⋊Q8×D432
C2×#145833802
C2×C4×#106219022
C2×C43×#5542
C2×#351143