Finite Group Databasebeta

← C2×#19148505 #26004962

Subgroups — C2×#19148505 #26004962

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148505C2132yesmaximal, direct product factor
2C2×#14583623C211yesmaximal, characteristic, complemented
3C2×#14583619C211yesmaximal, characteristic, complemented
4C2×#14583613C212yesmaximal, complemented
5C2×#14583604C212yesmaximal, complemented
6C2×#14583594C214yesmaximal, complemented
7C2×#14583559C212yesmaximal, complemented
8C2×#14583556C212yesmaximal, complemented
9C2×#14583554C211yesmaximal, characteristic, complemented
10C2×#14583517C214yesmaximal, complemented
11C2×#14583478C212yesmaximal, complemented
12C2×#14583451C212yesmaximal, complemented
13C2×#14583446C211yesmaximal, characteristic, complemented
14C2×#14583445C212yesmaximal, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583380C212yesmaximal, complemented
17C2×C4×#10621900C211yesmaximal, characteristic, complemented
18C2×C43×#547C211yesmaximal, characteristic, complemented
19C22×#10621898C2212yes—
20C22×#10621898C2212yes—
21C22×#10621900C2211yescharacteristic
22C22×Q8×D43C2212yes—
23#14583623C22116yescomplemented
24#14583619C22116yescomplemented
25#14583613C22132yescomplemented
26#14583604C22132yescomplemented
27#14583594C22164yescomplemented
28#14583559C22132yescomplemented
29#14583556C22132yescomplemented
30#14583554C22116yescomplemented
31#14583517C22164yescomplemented
32#14583478C22132yescomplemented
33#14583451C22132yescomplemented
34#14583446C22116yescomplemented
35#14583445C22132yescomplemented
36C2×#13063325C2211yescharacteristic
37C2×#13063324C2212yes—
38C2×#13063324C2212yes—
39C2×#13063324C2211yescharacteristic
40C2×#13063323C2212yes—
41C4⋊Q8×D43C22116yescomplemented
42C2×#13063321C2211yescharacteristic
43C2×#13063320C2214yes—
44C2×#13063318C2214yes—
45C2×#13063315C2214yes—
46C2×#13063314C2212yes—
47C2×#13063312C2212yes—
48C2×#13063312C2214yes—
49C2×#13063311C2214yes—
50C2×#13063311C2212yes—
51C2×#13063307C2214yes—
52C2×#13063305C2212yes—
53C2×#13063304C2212yes—
54C2×#13063304C2214yes—
55C2×#13063304C2212yes—
56C2×#13063303C2214yes—
57C2×#13063302C2214yes—
58C2×#13063300C2211yescharacteristic
59C2×#13063298C2214yes—
60C2×#13063298C2212yes—
61C2×#13063297C2214yes—
62C2×#13063297C2214yes—
63C2×#13063296C2212yes—
64C2×#13063296C2211yescharacteristic
65C2×#13063296C2214yes—
66#14583380C22132yescomplemented
67C4×#10621900C22116yescomplemented
68C2×Q8×Dic43C2212yes—
69C2×C4×Dic86C2211yescharacteristic
70C2×#13063290C2214yes—
71C2×#13063290C2212yes—
72C2×#13063290C2211yescharacteristic
73C2×C4×D172C2211yescharacteristic
74C2×D4×Dic43C2211yescharacteristic
75C2×#13063287C2214yes—
76C2×C4×C22⋊D43C2214yes—
77C2×C4×C22⋊D43C2214yes—
78C2×C4×C22⋊D43C2212yes—
79C2×C4×C22⋊D43C2214yes—
80C2×C4×C22⋊D43C2212yes—
81C2×(C22⋊D43)⋊C4C2212yes—
82C2×#13063284C2212yes—
83C2×#13063283C2211yescharacteristic
84C2×#13063283C2212yes—
85C2×#13063281C2214yes—
86C2×#13063281C2212yes—
87C2×C4⋊C4×D43C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C22×C4×Dic43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C22×#41×C43C2212yes—
93C43×#547C22116yescomplemented
94C2×C4⋊Q8×C43C2211yescharacteristic
95C2×#123×C43C2214yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×#121×C43C2212yes—
98C2×C4×D4×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yes—
101C2×#10621898—216no—
102C2×#10621898—48no—
103C2×#10621898C23116yes—
104C2×#10621898C23116yes—
105C2×#10621900—28no—
106C2×#10621900C2318yes—
107C22×Dic86C2312yes—
108C22×Dic86C2311yescharacteristic
109C22×Dic86C2312yes—
110C22×Dic86C2314yes—
111C2×Q8×D43—48no—
112C2×Q8×D43C23116yes—
113C22×D172C2312yes—
114C22×D172C2311yescharacteristic
115C22×C22⋊D43C2312yes—
116C22×C22⋊D43C2312yes—
117C22×C22⋊D43C2312yes—
118C22×C22⋊D43C2312yes—
119C22×C22⋊D43C2314yes—
120C23×Dic43C2312yes—
121C23×Dic43C2312yes—
122C22×C4×D43C2311yescharacteristic
123C22×C4×D43C2311yescharacteristic
124C22×C4×D43C2312yes—
125C22×C4×D43C2314yes—
126C22×C4×D43C2314yes—
127C22×C4×D43C2311yescharacteristic
128#13063325C2318yes—
129#13063324C23116yes—
130#13063324C23116yes—
131#13063324C2318yes—
132#13063323C23116yes—
133#13063321C2318yes—
134#13063320C23132yes—
135#13063318C23132yes—
136#13063315C23132yes—
137#13063314C23116yes—
138#13063312C23132yes—
139#13063312C23116yes—
140#13063311C23132yes—
141#13063311C23116yes—
142#13063307C23132yes—
143#13063305C23116yes—
144#13063304C23116yes—
145#13063304C23132yes—
146#13063304C23116yes—
147#13063303C23132yes—
148#13063302C23132yes—
149#13063300C2318yes—
150#13063298C23132yes—
151#13063298C23116yes—
152#13063297C23132yes—
153#13063297C23132yes—
154#13063296C23116yes—
155#13063296C2318yes—
156#13063296C23132yes—
157Q8×Dic43C23116yes—
158C4×Dic86C2318yes—
159#13063290C23116yes—
160#13063290C2318yes—
161#13063290C23132yes—
162C4×D172C2318yes—
163D4×Dic43C2318yes—
164#13063287C23132yes—
165C4×C22⋊D43C23116yes—
166C4×C22⋊D43C23132yes—
167C4×C22⋊D43C23132yes—
168C4×C22⋊D43C23116yes—
169C4×C22⋊D43C23132yes—
170(C22⋊D43)⋊C4C23116yes—
171#13063284C23116yes—
172#13063283C23116yes—
173#13063283C2318yes—
174#13063281C23132yes—
175#13063281C23116yes—
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2311yescharacteristic
180C2×C4⋊Dic43C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2314yes—
188C4⋊C4×D43C23116yes—
189C4⋊C4×D43C23116yes—
190C4⋊C4×D43C23116yes—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2314yes—
193C2×C22⋊Dic43C2314yes—
194C2×C22⋊Dic43C2314yes—
195C2×C22⋊Dic43C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C23116yes—
208C2×C4×Dic43C2314yes—
209C2×C4×Dic43C2314yes—
210C42×D43C2318yes—
211C2×#41×C43—48no—
212C2×#41×C43C23116yes—
213C22×Q8×C43C2312yes—
214C22×D4×C43C2311yescharacteristic
215C22×D4×C43C2311yescharacteristic
216C22×D4×C43C2314yes—
217C23×C4×C43C2312yes—
218C23×C4×C43C2312yes—
219C23×C4×C43C2314yes—
220C4⋊Q8×C43C2318yes—
221#123×C43C23132yes—
222C22⋊Q8×C43C23116yes—
223#121×C43C23116yes—
224C4×D4×C43C2318yes—
225C4×D4×C43C2318yes—
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C4⋊C4×C43C23116yes—
230C2×C4⋊C4×C43C2311yescharacteristic
231C2×C4⋊C4×C43C2312yes—
232C2×C22⋊C4×C43C2312yes—
233C2×C22⋊C4×C43C2312yes—
234C2×C22⋊C4×C43C2314yes—
235C2×C42×C43C2311yescharacteristic
236C24×C43C2412yes—
237C24×C43C2412yes—
238C23×D43C2412yes—
239C23×D43C2411yescharacteristic
240#41×C43—432no—
241C2×Q8×C43—28no—
242C2×Q8×C43C2418yes—
243C2×D4×C43—24no—
244C2×D4×C43—24no—
245C2×D4×C43—48no—
246C2×D4×C43C2414yes—
247C2×D4×C43C2414yes—
248C2×D4×C43C24116yes—
249C22×C4×C43—28no—
250C22×C4×C43—28no—
251C22×C4×C43—48no—
252C22×C4×C43C2411yescharacteristic
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2414yes—
256C22×C4×C43C2418yes—
257C22×C4×C43C2418yes—
258C22×C4×C43C24116yes—
259C22×C4×C43C2411yescharacteristic
260C22×C4×C43C2411yescharacteristic
261C2×C22⋊D43—28no—
262C2×C22⋊D43—28no—
263C2×C22⋊D43—28no—
264C2×C22⋊D43—28no—
265C2×C22⋊D43—48no—
266C2×C22⋊D43C2418yes—
267C2×C22⋊D43C2418yes—
268C2×C22⋊D43C2418yes—
269C2×C22⋊D43C2418yes—
270C2×C22⋊D43C24116yes—
271C22×Dic43—28no—
272C22×Dic43—28no—
273C22×Dic43C2412yes—
274C22×Dic43C2411yescharacteristic
275C22×Dic43C2412yes—
276C22×Dic43C2412yes—
277C22×Dic43C2418yes—
278C22×Dic43C2418yes—
279C22×Dic43C2414yes—
280C22×Dic43C2411yescharacteristic
281C22×Dic43C2411yescharacteristic
282Q8×D43—432no—
283#10621900—232no—
284#10621898—264no—
285#10621898—432no—
286C2×D172—24no—
287C2×D172—28no—
288C2×D172C2418yes—
289C2×D172C2414yes—
290C2×C4×D43—28no—
291C2×C4×D43—24no—
292C2×C4×D43—24no—
293C2×C4×D43—48no—
294C2×C4×D43—48no—
295C2×C4×D43#4118yescomplemented
296C2×C4×D43C2414yes—
297C2×C4×D43C2414yes—
298C2×C4×D43C2418yes—
299C2×C4×D43C24116yes—
300C2×C4×D43C24116yes—
301C2×C4×D43C2414yes—
302C2×Dic86—24no—
303C2×Dic86—28no—
304C2×Dic86—28no—
305C2×Dic86—48no—
306C2×Dic86C2418yes—
307C2×Dic86C2414yes—
308C2×Dic86C2418yes—
309C2×Dic86C24116yes—
310C4⋊C4×C43C2414yes—
311C4⋊C4×C43C2418yes—
312C4⋊C4×C43C24116yes—
313C4⋊C4×C43C2414yes—
314C4⋊C4×C43C2418yes—
315C22⋊C4×C43C2418yes—
316C22⋊C4×C43C2418yes—
317C22⋊C4×C43C24116yes—
318C42×C43C2414yes—
319C22⋊Dic43C2418yes—
320C22⋊Dic43C24116yes—
321C22⋊Dic43C24116yes—
322C22⋊Dic43C24116yes—
323C22⋊Dic43C2418yes—
324(C2×D43)⋊C4C2418yes—
325(C2×D43)⋊C4C24116yes—
326(C2×D43)⋊C4C24116yes—
327(C2×D43)⋊C4C2418yes—
328(C2×D43)⋊C4C2418yes—
329C4⋊Dic43C2418yes—
330C4⋊Dic43C2418yes—
331C4⋊Dic43C2414yes—
332C4⋊Dic43C2414yes—
333C4⋊Dic43C24116yes—
334Dic43⋊C4C24116yes—
335Dic43⋊C4C24116yes—
336Dic43⋊C4C24116yes—
337Dic43⋊C4C2418yes—
338Dic43⋊C4C2418yes—
339Dic43⋊C4C2418yes—
340Dic43⋊C4C24116yes—
341C4×Dic43C2414yes—
342C4×Dic43C2414yes—
343C4×Dic43C2414yes—
344C4×Dic43C2418yes—
345C4×Dic43C2418yes—
346C4×Dic43C2418yes—
347C4×Dic43C24116yes—
348C4×Dic43C24116yes—
349C23×C43—24no—
350C23×C43—24no—
351C23×C43—24no—
352C23×C43—24no—
353C23×C43—24no—
354C23×C43—24no—
355C23×C43C2514yes—
356C23×C43C2514yes—
357C23×C43C2511yescharacteristic
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—24no—
361C22×D43—24no—
362C22×D43—24no—
363C22×D43C2×#4114yes—
364C22×D43C2514yes—
365C22×D43C2512yes—
366Q8×C43—216no—
367D4×C43—28no—
368D4×C43—28no—
369D4×C43—416no—
370C2×C4×C43—24no—
371C2×C4×C43—28no—
372C2×C4×C43—24no—
373C2×C4×C43—22no—
374C2×C4×C43—216no—
375C2×C4×C43—216no—
376C2×C4×C43—416no—
377C2×C4×C43C2×#4114yes—
378C2×C4×C43H(5,𝔽2)14yes—
379C2×C4×C43C2514yes—
380C2×C4×C43C2514yes—
381C2×C4×C43C2512yes—
382C2×C4×C43C2518yes—
383C2×C4×C43C2512yes—
384C2×C4×C43C2512yes—
385C22⋊D43—216no—
386C22⋊D43—216no—
387C22⋊D43—216no—
388C22⋊D43—216no—
389C22⋊D43—416no—
390C2×Dic43—24no—
391C2×Dic43—24no—
392C2×Dic43—28no—
393C2×Dic43—22no—
394C2×Dic43—24no—
395C2×Dic43—216no—
396C2×Dic43—216no—
397C2×Dic43C2×#4114yes—
398C2×Dic432−1+414yes—
399C2×Dic43C2514yes—
400C2×Dic43C2514yes—
401C2×Dic43C2514yes—
402C2×Dic43C2512yes—
403C2×Dic43C2518yes—
404C2×Dic43C2512yes—
405C2×Dic43C2512yes—
406D172—216no—
407D172—28no—
408C4×D43—216no—
409C4×D43—28no—
410C4×D43—28no—
411C4×D43—416no—
412C4×D43—416no—
413C4×D43C2×#41116yescomplemented
414Dic86—28no—
415Dic86—216no—
416Dic86—216no—
417Dic86—416no—
418C2×#3511—431nomaximal, Sylow
419C22×C43—24no—
420C22×C43—24no—
421C22×C43—24no—
422C22×C43—24no—
423C22×C43—24no—
424C22×C43—24no—
425C22×C43—48no—
426C22×C43—48no—
427C22×C43C22×#4112yes—
428C22×C43C2×H(5,𝔽2)12yes—
429C22×C43C2×2−1+412yes—
430C22×C43C2611yescharacteristic
431C2×D43—22no—
432C2×D43—22no—
433C2×D43—28no—
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—24no—
437C2×D43—48no—
438C2×D43C22×#4114yes—
439C4×C43—24no—
440C4×C43—28no—
441C4×C43—24no—
442C4×C43—22no—
443C4×C43C22×#4114yes—
444C4×C43C2×H(5,𝔽2)14yes—
445Dic43—24no—
446Dic43—24no—
447Dic43—28no—
448Dic43—22no—
449Dic43—24no—
450Dic43C22×#4114yes—
451Dic43C2×2−1+414yes—
452#3511—4332no—
453C2×#556—431no—
454C2×#556—431no—
455C2×#555—432no—
456C2×#554—432no—
457C2×#553—434no—
458C2×#548—432no—
459C2×#548—432no—
460C2×#547—431no—
461C2×#547D4311yescharacteristic, complemented
462C2×#542—434no—
463C2×#537—432no—
464C2×#533—432no—
465C2×#532—432no—
466C2×#532—431no—
467C22×C4⋊Q8—431no—
468C2×#520—432no—
469C2×C4×#41—431no—
470C2×C43—44no—
471C2×C43—44no—
472C2×C43#351114yescomplemented
473C2×C43C23×#4111yescharacteristic
474C2×C43C22×H(5,𝔽2)11yescharacteristic
475C2×C43C22×2−1+411yescharacteristic
476D43—24no—
477D43—44no—
478C22×#41—431no—
479C22×#41—432no—
480C22×#41—432no—
481C22×#41C2×D4312yes—
482C23×Q8—432no—
483#556—4316no—
484#556—4316no—
485#555—4332no—
486#554—4332no—
487#553—4364no—
488#548—4332no—
489#548—4332no—
490#547—4316no—
491#547C2×D43116yescomplemented
492#542—4364no—
493#537—4332no—
494#533—4332no—
495#532—4332no—
496#532—4316no—
497C2×C4⋊Q8—432no—
498C2×C4⋊Q8—4316no—
499C2×C4⋊Q8—432no—
500C2×C4⋊Q8—432no—
501C2×C4⋊Q8—431no—
502C2×C4⋊Q8—431no—
503C2×C4⋊Q8C2×D4311yescharacteristic
504C2×#127—431no—
505C2×#126—434no—
506C2×#126—434no—
507C2×#125—434no—
508C2×#124—432no—
509C2×#124—432no—
510C2×#124—434no—
511C2×#124—432no—
512C2×#124—434no—
513C2×#123—434no—
514C2×#123C2×D4314yes—
515C2×C22⋊Q8—432no—
516C2×C22⋊Q8—432no—
517C2×C22⋊Q8—434no—
518C2×C22⋊Q8—434no—
519C2×C22⋊Q8—432no—
520C2×C22⋊Q8—434no—
521C2×C22⋊Q8C2×D4312yes—
522C2×#121—431no—
523C2×#121—432no—
524C2×#121—434no—
525C2×#121—434no—
526C2×#121—434no—
527C2×#121—431no—
528C2×#121—432no—
529C2×#121—434no—
530C2×#121C2×D4312yes—
531#520—4332no—
532C4×#41—4316no—
533C2×C4×Q8—432no—
534C2×C4×Q8—431no—
535C2×C4×Q8—434no—
536C2×C4×Q8—432no—
537C2×C4×Q8—431no—
538C2×C4×D4—431no—
539C2×C4×D4—432no—
540C2×C4×D4—434no—
541C2×C4×D4—434no—
542C2×C4×D4—434no—
543C2×C4×D4—432no—
544C2×C4×D4—434no—
545C2×C4×D4—432no—
546C2×C4×D4—431no—
547C2×C4×D4C2×D4311yescharacteristic
548C2×C4×D4C2×D4311yescharacteristic
549C2×#117—432no—
550C2×#117—431no—
551C2×#117—432no—
552C2×#117—432no—
553C2×#117—434no—
554C22×C4⋊C4—432no—
555C22×C4⋊C4—432no—
556C22×C4⋊C4—432no—
557C22×C4⋊C4C2×D4312yes—
558C22×C42—432no—
559C22×C42—431no—
560C43C2×#351111yescharacteristic, complemented, Sylow
561C2×#41—48no—
562C2×#41—438no—
563C2×#41—4316no—
564C2×#41—4316no—
565C2×#41—8616no—
566C2×#41—868no—
567C2×#41—1728no—
568C2×#41C22×D43116yes—
569C22×Q8—4316no—
570C22×Q8—431no—
571C22×Q8—432no—
572C22×Q8—432no—
573C22×Q8—434no—
574C22×Q8—1728no—
575C22×Q8C22×D4312yes—
576C22×D4—432no—
577C22×D4—432no—
578C22×D4—432no—
579C22×D4—432no—
580C22×D4—434no—
581C22×D4—432no—
582C22×D4—431no—
583C22×D4C22×D4311yescharacteristic
584C22×D4C22×D4311yescharacteristic
585C22×D4C22×D4314yes—
586C23×C4—431no—
587C23×C4—432no—
588C23×C4—432no—
589C23×C4—431no—
590C23×C4—432no—
591C23×C4—431no—
592C23×C4—434no—
593C23×C4—434no—
594C23×C4C22×D4312yes—
595C23×C4C22×D4312yes—
596C23×C4C22×D4314yes—
597C4⋊Q8—4316no—
598C4⋊Q8—4316no—
599C4⋊Q8—4316no—
600C4⋊Q8—438no—
601C4⋊Q8—438no—
602C4⋊Q8C22×D4318yes—
603#127—438no—
604#126—4332no—
605#126—4332no—
606#125—4332no—
607#124—4316no—
608#124—4316no—
609#124—4332no—
610#124—4316no—
611#124—4332no—
612#123—4332no—
613#123C22×D43132yes—
614C22⋊Q8—4316no—
615C22⋊Q8—4316no—
616C22⋊Q8—4332no—
617C22⋊Q8—4316no—
618C22⋊Q8—4332no—
619C22⋊Q8—4332no—
620C22⋊Q8C22×D43116yes—
621#121—4332no—
622#121—438no—
623#121—4332no—
624#121—4316no—
625#121—4332no—
626#121—438no—
627#121—4316no—
628#121—4332no—
629#121C22×D43116yes—
630C4×Q8—4316no—
631C4×Q8—438no—
632C4×Q8—4332no—
633C4×Q8—4316no—
634C4×Q8—438no—
635C4×D4—438no—
636C4×D4—4316no—
637C4×D4—4332no—
638C4×D4—4332no—
639C4×D4—4332no—
640C4×D4—4316no—
641C4×D4—4332no—
642C4×D4—4316no—
643C4×D4—438no—
644C4×D4C22×D4318yes—
645C4×D4C22×D4318yes—
646#117—4316no—
647#117—438no—
648#117—4316no—
649#117—4316no—
650#117—4332no—
651C2×C4⋊C4—432no—
652C2×C4⋊C4—434no—
653C2×C4⋊C4—434no—
654C2×C4⋊C4—434no—
655C2×C4⋊C4—432no—
656C2×C4⋊C4—431no—
657C2×C4⋊C4—432no—
658C2×C4⋊C4—432no—
659C2×C4⋊C4—432no—
660C2×C4⋊C4—431no—
661C2×C4⋊C4—434no—
662C2×C4⋊C4—434no—
663C2×C4⋊C4—4316no—
664C2×C4⋊C4—4316no—
665C2×C4⋊C4—4316no—
666C2×C4⋊C4C22×D4311yescharacteristic
667C2×C4⋊C4C22×D4312yes—
668C2×C4⋊C4C22×D4312yes—
669C2×C4⋊C4C22×D4314yes—
670C2×C4⋊C4C22×D43116yes—
671C2×C4⋊C4C22×D4311yescharacteristic
672C2×C22⋊C4—434no—
673C2×C22⋊C4—432no—
674C2×C22⋊C4—434no—
675C2×C22⋊C4—434no—
676C2×C22⋊C4—432no—
677C2×C22⋊C4—432no—
678C2×C22⋊C4—434no—
679C2×C22⋊C4—434no—
680C2×C22⋊C4—432no—
681C2×C22⋊C4—432no—
682C2×C22⋊C4C22×D4312yes—
683C2×C22⋊C4C22×D4314yes—
684C2×C22⋊C4C22×D4312yes—
685C2×C42—432no—
686C2×C42—434no—
687C2×C42—434no—
688C2×C42—431no—
689C2×C42—432no—
690C2×C42—431no—
691C2×C42—432no—
692C2×C42—4316no—
693C2×C42—431no—
694C2×C42—438no—
695C2×C42C22×D4311yescharacteristic
696C24—431no—
697C24—432no—
698C24C23×D4312yes—
699C24C23×D4312yes—
700#41—432no—
701#41—8664no—
702#41—8632no—
703#41—17232no—
704C2×Q8—28no—
705C2×Q8—434no—
706C2×Q8—438no—
707C2×Q8—438no—
708C2×Q8—4316no—
709C2×Q8—868no—
710C2×Q8—864no—
711C2×Q8—868no—
712C2×Q8—1728no—
713C2×Q8—17232no—
714C2×Q8C23×D4318yes—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—48no—
718C2×D4—438no—
719C2×D4—438no—
720C2×D4—438no—
721C2×D4—438no—
722C2×D4—4316no—
723C2×D4—438no—
724C2×D4—434no—
725C2×D4—868no—
726C2×D4—868no—
727C2×D4—868no—
728C2×D4—868no—
729C2×D4—868no—
730C2×D4—864no—
731C2×D4—1728no—
732C2×D4C23×D4314yes—
733C2×D4C23×D4314yes—
734C2×D4C23×D43116yes—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—48no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—438no—
741C22×C4—434no—
742C22×C4—438no—
743C22×C4—438no—
744C22×C4—432no—
745C22×C4—431no—
746C22×C4—432no—
747C22×C4—432no—
748C22×C4—434no—
749C22×C4—434no—
750C22×C4—434no—
751C22×C4—438no—
752C22×C4—4316no—
753C22×C4—4316no—
754C22×C4—864no—
755C22×C4—868no—
756C22×C4—868no—
757C22×C4—868no—
758C22×C4—864no—
759C22×C4—1728no—
760C22×C4—1728no—
761C22×C4C23×D4318yes—
762C22×C4C23×D4318yes—
763C22×C4C23×D4312yes—
764C22×C4C23×D4312yes—
765C22×C4C23×D4311yescharacteristic
766C22×C4C23×D4314yes—
767C22×C4C23×D43116yes—
768C22×C4C23×D4311yescharacteristic
769C22×C4C23×D4311yescharacteristic
770C4⋊C4—438no—
771C4⋊C4—4316no—
772C4⋊C4—4316no—
773C4⋊C4—4316no—
774C4⋊C4—438no—
775C4⋊C4—434no—
776C4⋊C4—438no—
777C4⋊C4—438no—
778C4⋊C4—438no—
779C4⋊C4—434no—
780C4⋊C4—4316no—
781C4⋊C4—4316no—
782C4⋊C4C23×D4314yes—
783C4⋊C4C23×D4318yes—
784C4⋊C4C23×D4318yes—
785C4⋊C4C23×D43116yes—
786C4⋊C4C23×D4314yes—
787C22⋊C4—4316no—
788C22⋊C4—438no—
789C22⋊C4—4316no—
790C22⋊C4—4316no—
791C22⋊C4—438no—
792C22⋊C4—438no—
793C22⋊C4—4316no—
794C22⋊C4—4316no—
795C22⋊C4—438no—
796C22⋊C4—438no—
797C22⋊C4C23×D4318yes—
798C22⋊C4C23×D43116yes—
799C22⋊C4C23×D4318yes—
800C42—434no—
801C42—438no—
802C42—434no—
803C42—438no—
804C42—434no—
805C42—438no—
806C42—4316no—
807C42—4316no—
808C42C23×D4314yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—434no—
816C23—432no—
817C23—434no—
818C23—862no—
819C23—862no—
820C23—864no—
821C23—864no—
822C23—864no—
823C23C24×D4314yes—
824C23C24×D4314yes—
825C23C24×D4311yescharacteristic
826Q8—216no—
827Q8—8616no—
828Q8—868no—
829Q8—8616no—
830Q8—17216no—
831D4—28no—
832D4—28no—
833D4—416no—
834D4—8616no—
835D4—8616no—
836D4—8616no—
837D4—8616no—
838D4—8616no—
839D4—868no—
840D4—17216no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—22no—
845C2×C4—216no—
846C2×C4—216no—
847C2×C4—416no—
848C2×C4—434no—
849C2×C4—434no—
850C2×C4—432no—
851C2×C4—432no—
852C2×C4—4316no—
853C2×C4—434no—
854C2×C4—432no—
855C2×C4—434no—
856C2×C4—434no—
857C2×C4—438no—
858C2×C4—868no—
859C2×C4—8616no—
860C2×C4—8616no—
861C2×C4—864no—
862C2×C4—864no—
863C2×C4—862no—
864C2×C4—868no—
865C2×C4—864no—
866C2×C4—8616no—
867C2×C4—868no—
868C2×C4—17216no—
869C2×C4—17216no—
870C2×C4#41×D4314yes—
871C2×C4#1306337014yes—
872C2×C4C24×D4314yes—
873C2×C4C24×D4314yes—
874C2×C4C24×D4312yes—
875C2×C4C24×D4318yes—
876C2×C4C24×D4312yes—
877C2×C4C24×D4312yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—48no—
885C22—48no—
886C22—434no—
887C22—862no—
888C22—862no—
889C22—868no—
890C22—864no—
891C22—864no—
892C22—864no—
893C22—1728no—
894C22C2×#41×D4312yes—
895C22C2×#1306337012yes—
896C222−1+4×D4312yes—
897C22C25×D4311yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—22no—
902C4—434no—
903C4—434no—
904C4—864no—
905C4—864no—
906C4—862no—
907C4—868no—
908C4—864no—
909C4C2×#41×D4314yes—
910C4C2×#1306337014yes—
911C2—44no—
912C2—44no—
913C2—864no—
914C2—1724no—
915C2#1914850514yesdirect product factor
916C2C22×#41×D4311yescharacteristic
917C2C22×#1306337011yescharacteristic
918C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#547C2
socleC23×C43C25
hypercenterC2×#547D43
hypocenterC43C2×#3511
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #19148505C2direct (N × H)
2. C2×#14583623C2semidirect
3. C2×#14583619C2semidirect
4. C2×#14583613C2semidirect
5. C2×#14583604C2semidirect
6. C2×#14583594C2semidirect
7. C2×#14583559C2semidirect
8. C2×#14583556C2semidirect
9. C2×#14583554C2semidirect
10. C2×#14583517C2semidirect
11. C2×#14583478C2semidirect
12. C2×#14583451C2semidirect
13. C2×#14583446C2semidirect
14. C2×#14583445C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
16. C2×#14583380C2semidirect
17. C2×C4×#10621900C2semidirect
18. C2×C43×#547C2semidirect
23. #14583623C22semidirect
24. #14583619C22semidirect
25. #14583613C22semidirect
26. #14583604C22semidirect
27. #14583594C22semidirect
28. #14583559C22semidirect
29. #14583556C22semidirect
30. #14583554C22semidirect
31. #14583517C22semidirect
32. #14583478C22semidirect
33. #14583451C22semidirect
34. #14583446C22semidirect
35. #14583445C22semidirect
41. C4⋊Q8×D43C22semidirect
66. #14583380C22semidirect
67. C4×#10621900C22semidirect
93. C43×#547C22semidirect
295. C2×C4×D43#41semidirect
413. C4×D43C2×#41semidirect
461. C2×#547D43semidirect
472. C2×C43#3511semidirect
491. #547C2×D43semidirect
560. C43C2×#3511semidirect
915. C2#19148505direct (N × H)

Maximal subgroups

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

subgroupindex
#191485052
C2×#145836232
C2×#145836192
C2×#145836132
C2×#145836042
C2×#145835942
C2×#145835592
C2×#145835562
C2×#145835542
C2×#145835172
C2×#145834782
C2×#145834512
C2×#145834462
C2×#145834452
C2×C4⋊Q8×D432
C2×#145833802
C2×C4×#106219002
C2×C43×#5472
C2×#351143