Finite Group Databasebeta

← C2×#19148994 #26004393

Subgroups — C2×#19148994 #26004393

Order 11008.

7810 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148994C2132yesmaximal, direct product factor
2C2×#14583645C214yesmaximal, complemented
3C2×#14583610C211yesmaximal, characteristic, complemented
4C2×#14583605C212yesmaximal, complemented
5C2×#14583571C211yesmaximal, characteristic, complemented
6C2×#14583570C211yesmaximal, characteristic, complemented
7C2×#14583570C212yesmaximal, complemented
8C2×#14583551C212yesmaximal, complemented
9C2×#14583550C212yesmaximal, complemented
10C2×#14583505C212yesmaximal, complemented
11C2×#14583500C212yesmaximal, complemented
12C2×#14583480C212yesmaximal, complemented
13C2×#14583479C212yesmaximal, complemented
14C2×#14583479C214yesmaximal, complemented
15C2×#14583453C211yesmaximal, characteristic, complemented
16C2×#14583450C211yesmaximal, characteristic, complemented
17C2×#14583446C211yesmaximal, characteristic, complemented
18C2×C43×#554C211yesmaximal, characteristic, complemented
19C22×#10621902C2212yes—
20C22×#10621902C2212yes—
21C22×#10621898C2214yes—
22C22×#10621898C2212yes—
23C22×#10621898C2212yes—
24#14583645C22164yescomplemented
25#14583610C22116yescomplemented
26#14583605C22132yescomplemented
27#14583571C22116yescomplemented
28#14583570C22116yescomplemented
29#14583570C22132yescomplemented
30#14583551C22132yescomplemented
31#14583550C22132yescomplemented
32#14583505C22132yescomplemented
33#14583500C22132yescomplemented
34#14583480C22132yescomplemented
35#14583479C22164yescomplemented
36#14583479C22132yescomplemented
37#14583453C22116yescomplemented
38#14583450C22116yescomplemented
39#14583446C22116yescomplemented
40C2×#13063324C2211yescharacteristic
41C2×#13063324C2211yescharacteristic
42C2×#13063323C2211yescharacteristic
43C2×#13063322C2211yescharacteristic
44C2×#13063322C2212yes—
45C2×#13063321C2211yescharacteristic
46C2×#13063321C2212yes—
47C2×#13063316C2212yes—
48C2×#13063315C2212yes—
49C2×#13063314C2212yes—
50C2×#13063311C2212yes—
51C2×#13063310C2214yes—
52C2×#13063310C2214yes—
53C2×#13063308C2214yes—
54C2×#13063307C2214yes—
55C2×#13063305C2212yes—
56C2×#13063305C2214yes—
57C2×#13063305C2211yescharacteristic
58C2×#13063303C2214yes—
59C2×#13063303C2214yes—
60C2×#13063303C2212yes—
61C2×#13063301C2214yes—
62C2×#13063301C2211yescharacteristic
63C2×#13063300C2212yes—
64C2×#13063300C2214yes—
65C2×#13063300C2211yescharacteristic
66C2×#13063300C2212yes—
67C2×#13063300C2212yes—
68C2×#13063300C2214yes—
69C2×#13063300C2214yes—
70C2×#13063299C2212yes—
71C2×#13063299C2214yes—
72C2×#13063299C2214yes—
73C2×#13063298C2214yes—
74C2×#13063298C2214yes—
75C2×#13063298C2214yes—
76C2×#13063298C2212yes—
77C2×#13063298C2214yes—
78C2×#13063296C2211yescharacteristic
79C2×C4×Dic86C2212yes—
80C2×C4×Dic86C2211yescharacteristic
81C2×C4×D172C2212yes—
82C2×C4×D172C2211yescharacteristic
83C2×#13063287C2212yes—
84C2×#13063287C2212yes—
85C2×#13063287C2212yes—
86C2×#13063287C2212yes—
87C2×C4×C22⋊D43C2212yes—
88C2×#13063282C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×D43C2214yes—
91C2×C42×D43C2211yescharacteristic
92C43×#554C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#125×C43C2212yes—
95C2×C22⋊Q8×C43C2212yes—
96C2×C22⋊Q8×C43C2214yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×D4×C43C2211yescharacteristic
99C2×C4×D4×C43C2212yes—
100C22×C4⋊C4×C43C2212yes—
101C2×#10621902—48no—
102C2×#10621902—48no—
103C2×#10621902C23116yes—
104C2×#10621902C23116yes—
105C2×#10621898—416no—
106C2×#10621898—48no—
107C2×#10621898—48no—
108C2×#10621898C23132yes—
109C2×#10621898C23116yes—
110C2×#10621898C23116yes—
111C22×Dic86C2312yes—
112C22×Dic86C2311yescharacteristic
113C22×Dic86C2312yes—
114C22×D172C2312yes—
115C22×D172C2311yescharacteristic
116C22×D172C2312yes—
117C22×D172C2314yes—
118C22×D172C2312yes—
119C22×D172C2314yes—
120C22×D172C2312yes—
121C22×D172C2314yes—
122C22×C22⋊D43C2312yes—
123C22×C22⋊D43C2312yes—
124C22×C22⋊D43C2314yes—
125C22×C22⋊D43C2314yes—
126C22×C22⋊D43C2312yes—
127C22×C4×D43C2311yescharacteristic
128C22×C4×D43C2311yescharacteristic
129C22×C4×D43C2311yescharacteristic
130C22×C4×D43C2312yes—
131C22×C4×D43C2314yes—
132C22×C4×D43C2314yes—
133C22×C4×D43C2314yes—
134C22×C4×D43C2314yes—
135#13063324C2318yes—
136#13063324C2318yes—
137#13063323C2318yes—
138#13063322C2318yes—
139#13063322C23116yes—
140#13063321C2318yes—
141#13063321C23116yes—
142#13063316C23116yes—
143#13063315C23116yes—
144#13063314C23116yes—
145#13063311C23116yes—
146#13063310C23132yes—
147#13063310C23132yes—
148#13063308C23132yes—
149#13063307C23132yes—
150#13063305C23132yes—
151#13063305C23116yes—
152#13063305C2318yes—
153#13063303C23132yes—
154#13063303C23132yes—
155#13063303C23116yes—
156#13063301C23132yes—
157#13063301C2318yes—
158#13063300C23132yes—
159#13063300C23116yes—
160#13063300C2318yes—
161#13063300C23116yes—
162#13063300C23116yes—
163#13063300C23132yes—
164#13063300C23132yes—
165#13063299C23132yes—
166#13063299C23116yes—
167#13063299C23132yes—
168#13063298C23132yes—
169#13063298C23132yes—
170#13063298C23132yes—
171#13063298C23116yes—
172#13063298C23132yes—
173#13063296C2318yes—
174C4×Dic86C23116yes—
175C4×Dic86C2318yes—
176C4×D172C23116yes—
177C4×D172C2318yes—
178#13063287C23116yes—
179#13063287C23116yes—
180#13063287C23116yes—
181#13063287C23116yes—
182C4×C22⋊D43C23116yes—
183#13063282C23116yes—
184C2×C4⋊Dic43C2311yescharacteristic
185C2×C4⋊Dic43C2314yes—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×C4⋊Dic43C2312yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2312yes—
190C2×Dic43⋊C4C2314yes—
191C2×Dic43⋊C4C2312yes—
192C2×Dic43⋊C4C2312yes—
193C2×Dic43⋊C4C2312yes—
194C2×Dic43⋊C4C2312yes—
195C4⋊C4×D43C23132yes—
196C4⋊C4×D43C23116yes—
197C2×C22⋊Dic43C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2314yes—
202C2×(C2×D43)⋊C4C2314yes—
203C2×(C2×D43)⋊C4C2314yes—
204C2×(C2×D43)⋊C4C2314yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2314yes—
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2312yes—
211C42×D43C2318yes—
212C22×Q8×C43C2311yescharacteristic
213C22×Q8×C43C2312yes—
214C22×D4×C43C2311yescharacteristic
215C23×C4×C43C2312yes—
216C23×C4×C43C2314yes—
217C4⋊Q8×C43C2318yes—
218#125×C43C23116yes—
219C22⋊Q8×C43C23132yes—
220C22⋊Q8×C43C23116yes—
221C4×Q8×C43C2318yes—
222C4×D4×C43C2318yes—
223C4×D4×C43C23116yes—
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2314yes—
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C23116yes—
228C2×C4⋊C4×C43C2311yescharacteristic
229C2×C4⋊C4×C43C2312yes—
230C2×C4⋊C4×C43C2312yes—
231C2×C4⋊C4×C43C2314yes—
232C2×C22⋊C4×C43C2314yes—
233C2×C22⋊C4×C43C2312yes—
234C2×C42×C43C2312yes—
235C2×C42×C43C2311yescharacteristic
236C24×C43C2412yes—
237C23×D43C2411yescharacteristic
238C23×D43C2414yes—
239C23×D43C2412yes—
240C2×Q8×C43—24no—
241C2×Q8×C43—44no—
242C2×Q8×C43C2414yes—
243C2×Q8×C43C2418yes—
244C2×D4×C43—24no—
245C2×D4×C43C2414yes—
246C22×C4×C43—28no—
247C22×C4×C43—48no—
248C22×C4×C43C2412yes—
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2412yes—
251C22×C4×C43C2412yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2418yes—
254C22×C4×C43C24116yes—
255C22×C4×C43C2411yescharacteristic
256C22×C4×C43C2411yescharacteristic
257C2×C22⋊D43—28no—
258C2×C22⋊D43—48no—
259C2×C22⋊D43—44no—
260C2×C22⋊D43—44no—
261C2×C22⋊D43—48no—
262C2×C22⋊D43C2418yes—
263C2×C22⋊D43C2418yes—
264C2×C22⋊D43C24116yes—
265C2×C22⋊D43C24116yes—
266C2×C22⋊D43C2418yes—
267C22×Dic43C2411yescharacteristic
268C22×Dic43C2411yescharacteristic
269C22×Dic43C2412yes—
270C22×Dic43C2412yes—
271C22×Dic43C2412yes—
272C22×Dic43C2411yescharacteristic
273#10621902—432no—
274#10621902—432no—
275#10621898—464no—
276#10621898—432no—
277#10621898—432no—
278C2×D172—28no—
279C2×D172—28no—
280C2×D172—24no—
281C2×D172—44no—
282C2×D172—48no—
283C2×D172—48no—
284C2×D172—44no—
285C2×D172—48no—
286C2×D172C2418yes—
287C2×D172C2414yes—
288C2×D172C2418yes—
289C2×D172C24116yes—
290C2×D172C2418yes—
291C2×D172C24116yes—
292C2×D172C2418yes—
293C2×D172C24116yes—
294C2×C4×D43—24no—
295C2×C4×D43—28no—
296C2×C4×D43—24no—
297C2×C4×D43—216no—
298C2×C4×D43—24no—
299C2×C4×D43—48no—
300C2×C4×D43—48no—
301C2×C4×D43—48no—
302C2×C4×D43C2414yes—
303C2×C4×D43C2414yes—
304C2×C4×D43C2414yes—
305C2×C4×D43C2418yes—
306C2×C4×D43C24116yes—
307C2×C4×D43C24116yes—
308C2×C4×D43C24116yes—
309C2×C4×D43C24116yes—
310C2×Dic86—24no—
311C2×Dic86—28no—
312C2×Dic86—44no—
313C2×Dic86C2418yes—
314C2×Dic86C2414yes—
315C2×Dic86C2418yes—
316C4⋊C4×C43C2414yes—
317C4⋊C4×C43C24116yes—
318C4⋊C4×C43C2418yes—
319C4⋊C4×C43C2414yes—
320C4⋊C4×C43C2418yes—
321C4⋊C4×C43C2418yes—
322C4⋊C4×C43C24116yes—
323C22⋊C4×C43C24116yes—
324C22⋊C4×C43C2418yes—
325C42×C43C2418yes—
326C42×C43C2414yes—
327C22⋊Dic43C2418yes—
328(C2×D43)⋊C4C2418yes—
329(C2×D43)⋊C4C2418yes—
330(C2×D43)⋊C4C2418yes—
331(C2×D43)⋊C4C24116yes—
332(C2×D43)⋊C4C24116yes—
333(C2×D43)⋊C4C24116yes—
334(C2×D43)⋊C4C24116yes—
335(C2×D43)⋊C4C2418yes—
336(C2×D43)⋊C4C24116yes—
337C4⋊Dic43C2414yes—
338C4⋊Dic43C24116yes—
339C4⋊Dic43C2414yes—
340C4⋊Dic43C2418yes—
341Dic43⋊C4C2418yes—
342Dic43⋊C4C2418yes—
343Dic43⋊C4C24116yes—
344Dic43⋊C4C2418yes—
345Dic43⋊C4C2418yes—
346Dic43⋊C4C2418yes—
347Dic43⋊C4C2418yes—
348C4×Dic43C2414yes—
349C4×Dic43C2414yes—
350C4×Dic43C2414yes—
351C4×Dic43C2418yes—
352C23×C43—24no—
353C23×C43—24no—
354C23×C43—24no—
355C23×C43C2514yes—
356C23×C43C2511yescharacteristic
357C22×D43—22no—
358C22×D43—28no—
359C22×D43—24no—
360C22×D43—22no—
361C22×D43—28no—
362C22×D43—24no—
363C22×D43—22no—
364C22×D43—28no—
365C22×D43—24no—
366C22×D43C2512yes—
367C22×D43C2518yes—
368C22×D43C2514yes—
369Q8×C43—28no—
370Q8×C43—48no—
371D4×C43—28no—
372C2×C4×C43—24no—
373C2×C4×C43—24no—
374C2×C4×C43—28no—
375C2×C4×C43—22no—
376C2×C4×C43—24no—
377C2×C4×C43—216no—
378C2×C4×C43—416no—
379C2×C4×C43H(5,𝔽2)14yes—
380C2×C4×C432−1+414yes—
381C2×C4×C43C2512yes—
382C2×C4×C43C2514yes—
383C2×C4×C43C2514yes—
384C2×C4×C43C2518yes—
385C2×C4×C43C2514yes—
386C2×C4×C43C2512yes—
387C2×C4×C43C2512yes—
388C22⋊D43—216no—
389C22⋊D43—416no—
390C22⋊D43—416no—
391C22⋊D43—48no—
392C22⋊D43—48no—
393C2×Dic43—24no—
394C2×Dic43—24no—
395C2×Dic43—22no—
396C2×Dic43—24no—
397C2×Dic43—22no—
398C2×Dic43H(5,𝔽2)14yes—
399C2×Dic43C2512yes—
400C2×Dic43C2512yes—
401C2×Dic43C2514yes—
402C2×Dic43C2514yes—
403C2×Dic43C2514yes—
404C2×Dic43C2512yes—
405D172—216no—
406D172—216no—
407D172—28no—
408D172—416no—
409D172—48no—
410D172—416no—
411D172—48no—
412D172—416no—
413C4×D43—28no—
414C4×D43—216no—
415C4×D43—28no—
416C4×D43—232no—
417C4×D43—28no—
418C4×D43—416no—
419C4×D43—416no—
420C4×D43—416no—
421Dic86—28no—
422Dic86—216no—
423Dic86—48no—
424C2×#3548—431nomaximal, Sylow
425C22×C43—24no—
426C22×C43—24no—
427C22×C43—24no—
428C22×C43—48no—
429C22×C43C2×H(5,𝔽2)12yes—
430C22×C43C2×H(5,𝔽2)12yes—
431C22×C43C2×2−1+412yes—
432C22×C43C2611yescharacteristic
433C2×D43—22no—
434C2×D43—28no—
435C2×D43—24no—
436C2×D43—22no—
437C2×D43—28no—
438C2×D43—24no—
439C2×D43—22no—
440C2×D43—28no—
441C2×D43—24no—
442C2×D43—44no—
443C2×D43—416no—
444C2×D43—48no—
445C4×C43—24no—
446C4×C43—24no—
447C4×C43—28no—
448C4×C43—22no—
449C4×C43—24no—
450C4×C43C2×H(5,𝔽2)14yes—
451C4×C43C2×2−1+414yes—
452Dic43—24no—
453Dic43—24no—
454Dic43—22no—
455Dic43—24no—
456Dic43—22no—
457Dic43C2×H(5,𝔽2)14yes—
458#3548—4332no—
459C2×#562—434no—
460C2×#554—431no—
461C2×#554—432no—
462C2×#554D4311yescharacteristic, complemented
463C2×#550—431no—
464C2×#550—432no—
465C2×#550—431no—
466C2×#547—432no—
467C2×#547—432no—
468C2×#540—432no—
469C2×#540—432no—
470C2×#537—434no—
471C2×#537—432no—
472C2×#537—432no—
473C2×#533—431no—
474C2×#532—431no—
475C2×#532—431no—
476C2×C43—44no—
477C2×C43#354814yescomplemented
478C2×C43C22×H(5,𝔽2)11yescharacteristic
479C2×C43C22×H(5,𝔽2)11yescharacteristic
480C2×C43C22×2−1+411yescharacteristic
481D43—42no—
482D43—48no—
483D43—44no—
484C22×#41—432no—
485C22×#41—432no—
486C22×#41—432no—
487C22×#41—434no—
488C22×#41—432no—
489#562—4364no—
490#554—4316no—
491#554—4332no—
492#554C2×D43116yescomplemented
493#550—4316no—
494#550—4332no—
495#550—4316no—
496#547—4332no—
497#547—4332no—
498#540—4332no—
499#540—4332no—
500#537—4364no—
501#537—4332no—
502#537—4332no—
503#533—4316no—
504#532—4316no—
505#532—4316no—
506C2×C4⋊Q8—431no—
507C2×C4⋊Q8—431no—
508C2×C4⋊Q8—431no—
509C2×C4⋊Q8C2×D4311yescharacteristic
510C2×#127—431no—
511C2×#127—432no—
512C2×#127—431no—
513C2×#127—432no—
514C2×#125—432no—
515C2×#125—432no—
516C2×#125C2×D4312yes—
517C2×#124—432no—
518C2×#124—432no—
519C2×#123—434no—
520C2×#123—434no—
521C2×#123—434no—
522C2×#123—434no—
523C2×C22⋊Q8—431no—
524C2×C22⋊Q8—434no—
525C2×C22⋊Q8—432no—
526C2×C22⋊Q8—434no—
527C2×C22⋊Q8—434no—
528C2×C22⋊Q8—431no—
529C2×C22⋊Q8—432no—
530C2×C22⋊Q8—434no—
531C2×C22⋊Q8C2×D4312yes—
532C2×C22⋊Q8C2×D4314yes—
533C2×#121—431no—
534C2×#121—434no—
535C2×#121—432no—
536C2×#121—434no—
537C2×#121—432no—
538C2×#121—432no—
539C2×#121—431no—
540C2×#121—434no—
541C2×#121—434no—
542C2×#121—432no—
543C2×#121—434no—
544C2×#121—432no—
545C2×#121—434no—
546C2×#121—434no—
547C2×#121—434no—
548C2×#121—434no—
549C2×C4×Q8—431no—
550C2×C4×Q8—432no—
551C2×C4×Q8C2×D4311yescharacteristic
552C2×C4×D4—432no—
553C2×C4×D4—432no—
554C2×C4×D4—432no—
555C2×C4×D4—432no—
556C2×C4×D4—432no—
557C2×C4×D4—431no—
558C2×C4×D4—432no—
559C2×C4×D4C2×D4311yescharacteristic
560C2×C4×D4C2×D4312yes—
561C2×#117—432no—
562C22×C4⋊C4—434no—
563C22×C4⋊C4—432no—
564C22×C4⋊C4C2×D4312yes—
565C22×C42—431no—
566C43C2×#354811yescharacteristic, complemented, Sylow
567C2×#41—4316no—
568C2×#41—4316no—
569C2×#41—4316no—
570C2×#41—4332no—
571C2×#41—4316no—
572C2×#41—1728no—
573C2×#41—1728no—
574C2×#41—17216no—
575C2×#41—1728no—
576C2×#41—1728no—
577C22×Q8—432no—
578C22×Q8—431no—
579C22×Q8—432no—
580C22×Q8C22×D4311yescharacteristic
581C22×Q8C22×D4312yes—
582C22×D4—432no—
583C22×D4—432no—
584C22×D4—434no—
585C22×D4—434no—
586C22×D4—432no—
587C22×D4—432no—
588C22×D4—431no—
589C22×D4—432no—
590C22×D4—434no—
591C22×D4—432no—
592C22×D4—434no—
593C22×D4—434no—
594C22×D4—432no—
595C22×D4C22×D4311yescharacteristic
596C23×C4—434no—
597C23×C4—432no—
598C23×C4—431no—
599C23×C4—431no—
600C23×C4—431no—
601C23×C4—434no—
602C23×C4—434no—
603C23×C4—434no—
604C23×C4C22×D4312yes—
605C23×C4C22×D4314yes—
606C4⋊Q8—438no—
607C4⋊Q8—438no—
608C4⋊Q8—438no—
609C4⋊Q8C22×D4318yes—
610#127—438no—
611#127—4316no—
612#127—438no—
613#127—4316no—
614#125—4316no—
615#125—4316no—
616#125C22×D43116yes—
617#124—4316no—
618#124—4316no—
619#123—4332no—
620#123—4332no—
621#123—4332no—
622#123—4332no—
623C22⋊Q8—438no—
624C22⋊Q8—4332no—
625C22⋊Q8—4316no—
626C22⋊Q8—438no—
627C22⋊Q8—4332no—
628C22⋊Q8—4316no—
629C22⋊Q8—4332no—
630C22⋊Q8—4332no—
631C22⋊Q8C22×D43116yes—
632C22⋊Q8C22×D43132yes—
633#121—438no—
634#121—4332no—
635#121—4316no—
636#121—4332no—
637#121—4316no—
638#121—4316no—
639#121—438no—
640#121—4332no—
641#121—4332no—
642#121—4316no—
643#121—4332no—
644#121—4316no—
645#121—4332no—
646#121—4332no—
647#121—4332no—
648#121—4332no—
649C4×Q8—4316no—
650C4×Q8—438no—
651C4×Q8C22×D4318yes—
652C4×D4—4316no—
653C4×D4—4316no—
654C4×D4—4316no—
655C4×D4—4316no—
656C4×D4—4316no—
657C4×D4—438no—
658C4×D4—4316no—
659C4×D4C22×D4318yes—
660C4×D4C22×D43116yes—
661#117—4316no—
662C2×C4⋊C4—432no—
663C2×C4⋊C4—432no—
664C2×C4⋊C4—431no—
665C2×C4⋊C4—434no—
666C2×C4⋊C4—434no—
667C2×C4⋊C4—432no—
668C2×C4⋊C4—432no—
669C2×C4⋊C4—431no—
670C2×C4⋊C4—432no—
671C2×C4⋊C4—432no—
672C2×C4⋊C4—432no—
673C2×C4⋊C4—4332no—
674C2×C4⋊C4—4316no—
675C2×C4⋊C4C22×D4312yes—
676C2×C4⋊C4C22×D4314yes—
677C2×C4⋊C4C22×D4311yescharacteristic
678C2×C4⋊C4C22×D4314yes—
679C2×C4⋊C4C22×D43116yes—
680C2×C4⋊C4C22×D4312yes—
681C2×C4⋊C4C22×D4311yescharacteristic
682C2×C4⋊C4C22×D4312yes—
683C2×C22⋊C4—432no—
684C2×C22⋊C4—432no—
685C2×C22⋊C4—432no—
686C2×C22⋊C4—434no—
687C2×C22⋊C4—434no—
688C2×C22⋊C4—434no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—432no—
691C2×C22⋊C4—434no—
692C2×C22⋊C4—432no—
693C2×C22⋊C4C22×D4314yes—
694C2×C22⋊C4C22×D4312yes—
695C2×C42—432no—
696C2×C42—431no—
697C2×C42—431no—
698C2×C42—431no—
699C2×C42—438no—
700C2×C42C22×D4312yes—
701C2×C42C22×D4311yescharacteristic
702C24—431no—
703C24—434no—
704C24—432no—
705C24C23×D4312yes—
706#41—17232no—
707#41—17232no—
708#41—17264no—
709#41—17232no—
710#41—17232no—
711C2×Q8—24no—
712C2×Q8—44no—
713C2×Q8—438no—
714C2×Q8—434no—
715C2×Q8—438no—
716C2×Q8—868no—
717C2×Q8—864no—
718C2×Q8—1724no—
719C2×Q8C23×D4314yes—
720C2×Q8C23×D4318yes—
721C2×D4—24no—
722C2×D4—438no—
723C2×D4—438no—
724C2×D4—4316no—
725C2×D4—4316no—
726C2×D4—438no—
727C2×D4—438no—
728C2×D4—434no—
729C2×D4—438no—
730C2×D4—4316no—
731C2×D4—438no—
732C2×D4—4316no—
733C2×D4—4316no—
734C2×D4—438no—
735C2×D4—868no—
736C2×D4—868no—
737C2×D4—868no—
738C2×D4—864no—
739C2×D4—1728no—
740C2×D4—1728no—
741C2×D4—1724no—
742C2×D4—1724no—
743C2×D4—1728no—
744C2×D4—1728no—
745C2×D4—1724no—
746C2×D4—1724no—
747C2×D4—1728no—
748C2×D4C23×D4314yes—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—432no—
757C22×C4—434no—
758C22×C4—434no—
759C22×C4—434no—
760C22×C4—4316no—
761C22×C4—438no—
762C22×C4—4316no—
763C22×C4—4316no—
764C22×C4—4316no—
765C22×C4—8616no—
766C22×C4—864no—
767C22×C4—868no—
768C22×C4—864no—
769C22×C4—864no—
770C22×C4—1728no—
771C22×C4—1728no—
772C22×C4—1728no—
773C22×C4C23×D4318yes—
774C22×C4C23×D4311yescharacteristic
775C22×C4C23×D4312yes—
776C22×C4C23×D4312yes—
777C22×C4C23×D4314yes—
778C22×C4C23×D4312yes—
779C22×C4C23×D43116yes—
780C22×C4C23×D4311yescharacteristic
781C22×C4C23×D4311yescharacteristic
782C4⋊C4—438no—
783C4⋊C4—438no—
784C4⋊C4—434no—
785C4⋊C4—4316no—
786C4⋊C4—4316no—
787C4⋊C4—438no—
788C4⋊C4—438no—
789C4⋊C4—434no—
790C4⋊C4—438no—
791C4⋊C4—438no—
792C4⋊C4—438no—
793C4⋊C4C23×D4318yes—
794C4⋊C4C23×D43116yes—
795C4⋊C4C23×D4314yes—
796C4⋊C4C23×D43116yes—
797C4⋊C4C23×D4318yes—
798C4⋊C4C23×D4314yes—
799C4⋊C4C23×D4318yes—
800C22⋊C4—438no—
801C22⋊C4—438no—
802C22⋊C4—438no—
803C22⋊C4—4316no—
804C22⋊C4—4316no—
805C22⋊C4—4316no—
806C22⋊C4—4316no—
807C22⋊C4—438no—
808C22⋊C4—4316no—
809C22⋊C4—438no—
810C22⋊C4C23×D43116yes—
811C22⋊C4C23×D4318yes—
812C42—434no—
813C42—434no—
814C42—434no—
815C42—438no—
816C42C23×D4314yes—
817C42C23×D4318yes—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—432no—
822C23—438no—
823C23—434no—
824C23—862no—
825C23—868no—
826C23—864no—
827C23—864no—
828C23—862no—
829C23—868no—
830C23—862no—
831C23—868no—
832C23—864no—
833C23C24×D4314yes—
834C23C24×D4311yescharacteristic
835Q8—28no—
836Q8—48no—
837Q8—8616no—
838Q8—868no—
839Q8—1728no—
840D4—28no—
841D4—8616no—
842D4—8616no—
843D4—8616no—
844D4—868no—
845D4—17216no—
846D4—17216no—
847D4—1728no—
848D4—1728no—
849D4—17216no—
850D4—17216no—
851D4—1728no—
852D4—1728no—
853D4—17216no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—216no—
860C2×C4—416no—
861C2×C4—434no—
862C2×C4—432no—
863C2×C4—432no—
864C2×C4—432no—
865C2×C4—434no—
866C2×C4—434no—
867C2×C4—434no—
868C2×C4—8632no—
869C2×C4—868no—
870C2×C4—864no—
871C2×C4—864no—
872C2×C4—862no—
873C2×C4—864no—
874C2×C4—862no—
875C2×C4—8616no—
876C2×C4—868no—
877C2×C4—868no—
878C2×C4—17216no—
879C2×C4—17216no—
880C2×C4—17216no—
881C2×C4#1306337114yes—
882C2×C4#1306337314yes—
883C2×C4C24×D4312yes—
884C2×C4C24×D4314yes—
885C2×C4C24×D4314yes—
886C2×C4C24×D4318yes—
887C2×C4C24×D4314yes—
888C2×C4C24×D4312yes—
889C2×C4C24×D4312yes—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—48no—
894C22—862no—
895C22—868no—
896C22—864no—
897C22—864no—
898C22—862no—
899C22—868no—
900C22—862no—
901C22—868no—
902C22—864no—
903C22—1724no—
904C22—17216no—
905C22—1728no—
906C22H(5,𝔽2)×D4312yes—
907C22C2×#1306337112yes—
908C22C2×#1306337312yes—
909C22C25×D4311yescharacteristic
910C4—24no—
911C4—28no—
912C4—22no—
913C4—24no—
914C4—24no—
915C4—434no—
916C4—864no—
917C4—864no—
918C4—862no—
919C4—864no—
920C4—862no—
921C4C2×#1306337114yes—
922C4C2×#1306337314yes—
923C2—44no—
924C2—1722no—
925C2—1728no—
926C2—1724no—
927C2#1914899414yesdirect product factor
928C2C2×H(5,𝔽2)×D4311yescharacteristic
929C2C22×#1306337111yescharacteristic
930C2C22×#1306337311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#554C2
socleC23×C43C25
hypercenterC2×#554D43
hypocenterC43C2×#3548
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19148994C2direct (N × H)
2. C2×#14583645C2semidirect
3. C2×#14583610C2semidirect
4. C2×#14583605C2semidirect
5. C2×#14583571C2semidirect
6. C2×#14583570C2semidirect
7. C2×#14583570C2semidirect
8. C2×#14583551C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583505C2semidirect
11. C2×#14583500C2semidirect
12. C2×#14583480C2semidirect
13. C2×#14583479C2semidirect
14. C2×#14583479C2semidirect
15. C2×#14583453C2semidirect
16. C2×#14583450C2semidirect
17. C2×#14583446C2semidirect
18. C2×C43×#554C2semidirect
24. #14583645C22semidirect
25. #14583610C22semidirect
26. #14583605C22semidirect
27. #14583571C22semidirect
28. #14583570C22semidirect
29. #14583570C22semidirect
30. #14583551C22semidirect
31. #14583550C22semidirect
32. #14583505C22semidirect
33. #14583500C22semidirect
34. #14583480C22semidirect
35. #14583479C22semidirect
36. #14583479C22semidirect
37. #14583453C22semidirect
38. #14583450C22semidirect
39. #14583446C22semidirect
92. C43×#554C22semidirect
462. C2×#554D43semidirect
477. C2×C43#3548semidirect
492. #554C2×D43semidirect
566. C43C2×#3548semidirect
927. C2#19148994direct (N × H)

Maximal subgroups

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

subgroupindex
#191489942
C2×#145836452
C2×#145836102
C2×#145836052
C2×#145835712
C2×#145835702
C2×#145835512
C2×#145835502
C2×#145835052
C2×#145835002
C2×#145834802
C2×#145834792
C2×#145834532
C2×#145834502
C2×#145834462
C2×C43×#5542
C2×#354843