Finite Group Databasebeta

← C2×#19149066 #26004226

Subgroups — C2×#19149066 #26004226

Order 11008.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149066C2132yesmaximal, direct product factor
2C2×#14583645C214yesmaximal, complemented
3C2×#14583634C211yesmaximal, characteristic, complemented
4C2×#14583634C212yesmaximal, complemented
5C2×#14583627C211yesmaximal, characteristic, complemented
6C2×#14583609C212yesmaximal, complemented
7C2×#14583571C211yesmaximal, characteristic, complemented
8C2×Q8×D172C211yesmaximal, characteristic, complemented
9C2×#14583559C212yesmaximal, complemented
10C2×#14583551C212yesmaximal, complemented
11C2×#14583523C212yesmaximal, complemented
12C2×#14583520C212yesmaximal, complemented
13C2×#14583504C212yesmaximal, complemented
14C2×#14583497C214yesmaximal, complemented
15C2×#14583474C212yesmaximal, complemented
16C2×#14583449C211yesmaximal, characteristic, complemented
17C2×#14583433C211yesmaximal, characteristic, complemented
18C2×C43×#533C211yesmaximal, characteristic, complemented
19C22×#10621902C2212yes—
20C22×#10621898C2212yes—
21C22×Q8×D43C2212yes—
22#14583645C22164yescomplemented
23#14583634C22116yescomplemented
24#14583634C22132yescomplemented
25#14583627C22116yescomplemented
26#14583609C22132yescomplemented
27#14583571C22116yescomplemented
28Q8×D172C22116yescomplemented
29#14583559C22132yescomplemented
30#14583551C22132yescomplemented
31#14583523C22132yescomplemented
32#14583520C22132yescomplemented
33#14583504C22132yescomplemented
34#14583497C22164yescomplemented
35#14583474C22132yescomplemented
36#14583449C22116yescomplemented
37C2×#13063325C2212yes—
38C2×#13063325C2211yescharacteristic
39C2×#13063323C2212yes—
40C2×#13063322C2211yescharacteristic
41C2×#13063322C2212yes—
42#14583433C22116yescomplemented
43C2×#13063320C2214yes—
44C2×#13063319C2212yes—
45C2×#13063317C2211yescharacteristic
46C2×#13063317C2212yes—
47C2×#13063315C2214yes—
48C2×#13063314C2212yes—
49C2×#13063314C2214yes—
50C2×#13063313C2211yescharacteristic
51C2×#13063313C2212yes—
52C2×#13063313C2212yes—
53C2×#13063311C2214yes—
54C2×#13063310C2214yes—
55C2×#13063310C2214yes—
56C2×#13063310C2214yes—
57C2×#13063310C2214yes—
58C2×#13063310C2214yes—
59C2×#13063308C2212yes—
60C2×#13063307C2214yes—
61C2×#13063305C2212yes—
62C2×#13063305C2214yes—
63C2×#13063304C2211yescharacteristic
64C2×#13063303C2214yes—
65C2×#13063303C2214yes—
66C2×#13063303C2214yes—
67C2×#13063301C2214yes—
68C2×#13063300C2212yes—
69C2×#13063300C2214yes—
70C2×#13063299C2211yescharacteristic
71C2×#13063299C2212yes—
72C2×#13063299C2212yes—
73C2×#13063298C2214yes—
74C2×#13063298C2214yes—
75C2×C4×Dic86C2211yescharacteristic
76C2×C4×Dic86C2212yes—
77C2×#13063290C2212yes—
78C2×C4×D172C2211yescharacteristic
79C2×C4×D172C2212yes—
80C2×C4×D172C2212yes—
81C2×C4×D172C2212yes—
82C2×C4×D172C2212yes—
83C2×C4×D172C2212yes—
84C2×#13063287C2212yes—
85C2×#13063287C2214yes—
86C2×C4×C22⋊D43C2212yes—
87C2×#13063282C2212yes—
88C2×C4⋊C4×D43C2214yes—
89C43×#533C22116yescomplemented
90C2×C4⋊Q8×C43C2211yescharacteristic
91C2×C4⋊Q8×C43C2211yescharacteristic
92C2×#125×C43C2212yes—
93C2×C22⋊Q8×C43C2211yescharacteristic
94C2×C22⋊Q8×C43C2211yescharacteristic
95C2×C22⋊Q8×C43C2212yes—
96C2×C4×Q8×C43C2211yescharacteristic
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×Q8×C43C2212yes—
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C2×#10621902—48no—
102C2×#10621902C23116yes—
103C2×#10621898—48no—
104C2×#10621898C23116yes—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C2314yes—
108C2×Q8×D43—48no—
109C2×Q8×D43C23116yes—
110C22×D172C2312yes—
111C22×D172C2311yescharacteristic
112C22×D172C2312yes—
113C22×D172C2314yes—
114C22×D172C2312yes—
115C22×D172C2314yes—
116C22×C22⋊D43C2312yes—
117C22×C22⋊D43C2314yes—
118C22×C4×D43C2312yes—
119C22×C4×D43C2314yes—
120C22×C4×D43C2314yes—
121C22×C4×D43C2314yes—
122C22×C4×D43C2314yes—
123#13063325C23116yes—
124#13063325C2318yes—
125#13063323C23116yes—
126#13063322C2318yes—
127#13063322C23116yes—
128#13063320C23132yes—
129#13063319C23116yes—
130#13063317C2318yes—
131#13063317C23116yes—
132#13063315C23132yes—
133#13063314C23116yes—
134#13063314C23132yes—
135#13063313C2318yes—
136#13063313C23116yes—
137#13063313C23116yes—
138#13063311C23132yes—
139#13063310C23132yes—
140#13063310C23132yes—
141#13063310C23132yes—
142#13063310C23132yes—
143#13063310C23132yes—
144#13063308C23116yes—
145#13063307C23132yes—
146#13063305C23132yes—
147#13063305C23116yes—
148#13063304C2318yes—
149#13063303C23132yes—
150#13063303C23132yes—
151#13063303C23132yes—
152#13063301C23132yes—
153#13063300C23116yes—
154#13063300C23132yes—
155#13063299C23116yes—
156#13063299C2318yes—
157#13063299C23116yes—
158#13063298C23132yes—
159#13063298C23132yes—
160C4×Dic86C2318yes—
161C4×Dic86C23116yes—
162#13063290C23116yes—
163C4×D172C2318yes—
164C4×D172C23116yes—
165C4×D172C23116yes—
166C4×D172C23116yes—
167C4×D172C23116yes—
168C4×D172C23116yes—
169#13063287C23132yes—
170#13063287C23116yes—
171C4×C22⋊D43C23116yes—
172#13063282C23116yes—
173C2×C4⋊Dic43C2314yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2311yescharacteristic
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2312yes—
185C4⋊C4×D43C23132yes—
186C2×C22⋊Dic43C2312yes—
187C2×(C2×D43)⋊C4C2312yes—
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2314yes—
191C2×(C2×D43)⋊C4C2314yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2314yes—
200C22×Q8×C43C2311yescharacteristic
201C22×Q8×C43C2311yescharacteristic
202C22×Q8×C43C2312yes—
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C23×C4×C43C2311yescharacteristic
206C4⋊Q8×C43C2318yes—
207C4⋊Q8×C43C2318yes—
208#125×C43C23116yes—
209C22⋊Q8×C43C2318yes—
210C22⋊Q8×C43C23116yes—
211C22⋊Q8×C43C2318yes—
212C4×Q8×C43C2318yes—
213C4×Q8×C43C2318yes—
214C4×Q8×C43C23116yes—
215#117×C43C23116yes—
216C2×C4⋊C4×C43C2312yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2312yes—
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2312yes—
222C2×C4⋊C4×C43C2311yescharacteristic
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2312yes—
225C2×C22⋊C4×C43C2312yes—
226C2×C22⋊C4×C43C2312yes—
227C2×C42×C43C2311yescharacteristic
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2318yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2312yes—
234C24×C43C2411yescharacteristic
235C23×D43C2412yes—
236C23×D43C2414yes—
237C2×Q8×C43—24no—
238C2×Q8×C43—24no—
239C2×Q8×C43—44no—
240C2×Q8×C43C2414yes—
241C2×Q8×C43C2414yes—
242C2×Q8×C43C2418yes—
243C22×C4×C43—24no—
244C22×C4×C43—24no—
245C22×C4×C43—42no—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2414yes—
251C22×C4×C43C2414yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2414yes—
257C22×C4×C43C2411yescharacteristic
258C22×C4×C43C2411yescharacteristic
259C2×C22⋊D43—44no—
260C2×C22⋊D43—48no—
261C2×C22⋊D43C2418yes—
262C2×C22⋊D43C24116yes—
263C22×Dic43C2412yes—
264C22×Dic43C2412yes—
265C22×Dic43C2414yes—
266C22×Dic43C2412yes—
267#10621902—432no—
268Q8×D43—432no—
269#10621898—432no—
270C2×D172—28no—
271C2×D172—24no—
272C2×D172—28no—
273C2×D172—44no—
274C2×D172—48no—
275C2×D172—48no—
276C2×D172C2418yes—
277C2×D172C2414yes—
278C2×D172C2418yes—
279C2×D172C24116yes—
280C2×D172C2418yes—
281C2×D172C24116yes—
282C2×C4×D43—28no—
283C2×C4×D43—48no—
284C2×C4×D43—48no—
285C2×C4×D43—48no—
286C2×C4×D43—48no—
287C2×C4×D43C2418yes—
288C2×C4×D43C24116yes—
289C2×C4×D43C24116yes—
290C2×C4×D43C24116yes—
291C2×C4×D43C24116yes—
292C2×Dic86—28no—
293C2×Dic86—24no—
294C2×Dic86—48no—
295C2×Dic86C2418yes—
296C2×Dic86C2414yes—
297C2×Dic86C24116yes—
298C4⋊C4×C43C2418yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C2418yes—
301C4⋊C4×C43C2418yes—
302C4⋊C4×C43C2418yes—
303C4⋊C4×C43C2418yes—
304C4⋊C4×C43C2414yes—
305C4⋊C4×C43C2414yes—
306C4⋊C4×C43C2418yes—
307C22⋊C4×C43C2418yes—
308C22⋊C4×C43C2418yes—
309C42×C43C2414yes—
310C42×C43C2414yes—
311C42×C43C2414yes—
312C42×C43C2414yes—
313C42×C43C2418yes—
314C42×C43C2418yes—
315C22⋊Dic43C2418yes—
316(C2×D43)⋊C4C2418yes—
317(C2×D43)⋊C4C2418yes—
318(C2×D43)⋊C4C2418yes—
319(C2×D43)⋊C4C24116yes—
320(C2×D43)⋊C4C24116yes—
321(C2×D43)⋊C4C24116yes—
322(C2×D43)⋊C4C24116yes—
323(C2×D43)⋊C4C24116yes—
324(C2×D43)⋊C4C24116yes—
325(C2×D43)⋊C4C24116yes—
326(C2×D43)⋊C4C2418yes—
327C4⋊Dic43C24116yes—
328C4⋊Dic43C2414yes—
329C4⋊Dic43C2414yes—
330C4⋊Dic43C2418yes—
331C4⋊Dic43C2418yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C24116yes—
334Dic43⋊C4C2418yes—
335Dic43⋊C4C2418yes—
336Dic43⋊C4C24116yes—
337Dic43⋊C4C24116yes—
338Dic43⋊C4C2418yes—
339C4×Dic43C2418yes—
340C4×Dic43C24116yes—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43C2512yes—
345C23×C43C2511yescharacteristic
346C22×D43—24no—
347C22×D43—28no—
348C22×D43—24no—
349C22×D43—28no—
350C22×D43—28no—
351C22×D43—24no—
352C22×D43C2514yes—
353C22×D43C2518yes—
354Q8×C43—28no—
355Q8×C43—28no—
356Q8×C43—48no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—24no—
360C2×C4×C43—22no—
361C2×C4×C43—24no—
362C2×C4×C43—22no—
363C2×C4×C43—24no—
364C2×C4×C43—22no—
365C2×C4×C43—28no—
366C2×C4×C43—28no—
367C2×C4×C43—44no—
368C2×C4×C43H(5,𝔽2)14yes—
369C2×C4×C432−1+414yes—
370C2×C4×C43C2514yes—
371C2×C4×C43C2514yes—
372C2×C4×C43C2512yes—
373C2×C4×C43C2512yes—
374C2×C4×C43C2512yes—
375C2×C4×C43C2512yes—
376C2×C4×C43C2514yes—
377C2×C4×C43C2514yes—
378C2×C4×C43C2512yes—
379C2×C4×C43C2512yes—
380C22⋊D43—416no—
381C22⋊D43—48no—
382C2×Dic43—28no—
383C2×Dic43—24no—
384C2×Dic43—24no—
385C2×Dic43—24no—
386C2×Dic43C2514yes—
387C2×Dic43C2514yes—
388C2×Dic43C2518yes—
389C2×Dic43C2514yes—
390D172—216no—
391D172—28no—
392D172—216no—
393D172—48no—
394D172—416no—
395D172—416no—
396C4×D43—216no—
397C4×D43—416no—
398C4×D43—416no—
399C4×D43—416no—
400C4×D43—416no—
401Dic86—216no—
402Dic86—28no—
403Dic86—416no—
404C2×#3554—431nomaximal, Sylow
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—44no—
409C22×C43C2×H(5,𝔽2)12yes—
410C22×C43C2×2−1+412yes—
411C22×C43#58512yes—
412C22×C43C2611yescharacteristic
413C2×D43—24no—
414C2×D43—28no—
415C2×D43—24no—
416C2×D43—28no—
417C2×D43—28no—
418C2×D43—24no—
419C2×D43—48no—
420C2×D43—416no—
421C4×C43—24no—
422C4×C43—22no—
423C4×C43—24no—
424C4×C43—22no—
425C4×C43—24no—
426C4×C43—22no—
427C4×C43—24no—
428C4×C43—22no—
429C4×C43C2×H(5,𝔽2)14yes—
430C4×C43C2×2−1+414yes—
431Dic43—28no—
432Dic43—24no—
433Dic43—24no—
434Dic43—24no—
435#3554—4332no—
436C2×#562—434no—
437C2×#559—432no—
438C2×#559—431no—
439C2×#557—431no—
440C2×#554—432no—
441C2×#550—431no—
442C2×D4×Q8—431no—
443C2×#548—432no—
444C2×#547—432no—
445C2×#542—432no—
446C2×#542—432no—
447C2×#540—432no—
448C2×#539—434no—
449C2×#536—432no—
450C2×#533D4311yescharacteristic, complemented
451C2×#532—431no—
452C2×#529—431no—
453C2×C43—42no—
454C2×C43#355414yescomplemented
455C2×C43C22×H(5,𝔽2)11yescharacteristic
456C2×C43C22×2−1+411yescharacteristic
457C2×C43C2×#58511yescharacteristic
458D43—44no—
459D43—48no—
460C22×#41—432no—
461C22×#41—432no—
462C23×Q8—432no—
463#562—4364no—
464#559—4332no—
465#559—4316no—
466#557—4316no—
467#554—4332no—
468#550—4316no—
469D4×Q8—4316no—
470#548—4332no—
471#547—4332no—
472#542—4332no—
473#542—4332no—
474#540—4332no—
475#539—4364no—
476#536—4332no—
477#533C2×D43116yescomplemented
478#532—4316no—
479C2×C4⋊Q8—432no—
480C2×C4⋊Q8—431no—
481C2×C4⋊Q8—432no—
482C2×C4⋊Q8C2×D4311yescharacteristic
483C2×C4⋊Q8C2×D4311yescharacteristic
484C2×#127—431no—
485C2×#127—432no—
486#529—4316no—
487C2×#126—434no—
488C2×#126—432no—
489C2×#125—434no—
490C2×#125—431no—
491C2×#125—432no—
492C2×#125C2×D4312yes—
493C2×#124—432no—
494C2×#124—434no—
495C2×#124—434no—
496C2×#124—431no—
497C2×#124—432no—
498C2×#124—432no—
499C2×#123—432no—
500C2×#123—434no—
501C2×#123—434no—
502C2×#123—434no—
503C2×#123—434no—
504C2×#123—434no—
505C2×#123—434no—
506C2×C22⋊Q8—434no—
507C2×C22⋊Q8—431no—
508C2×C22⋊Q8—434no—
509C2×C22⋊Q8—434no—
510C2×C22⋊Q8—434no—
511C2×C22⋊Q8—434no—
512C2×C22⋊Q8—432no—
513C2×C22⋊Q8C2×D4311yescharacteristic
514C2×C22⋊Q8C2×D4311yescharacteristic
515C2×C22⋊Q8C2×D4312yes—
516C2×#121—431no—
517C2×#121—432no—
518C2×#121—432no—
519C2×#121—434no—
520C2×#121—432no—
521C2×#121—434no—
522C2×#121—434no—
523C2×C4×Q8—432no—
524C2×C4×Q8—431no—
525C2×C4×Q8—432no—
526C2×C4×Q8C2×D4311yescharacteristic
527C2×C4×Q8C2×D4311yescharacteristic
528C2×C4×Q8C2×D4312yes—
529C2×C4×D4—432no—
530C2×C4×D4—434no—
531C2×C4×D4—432no—
532C2×C4×D4—431no—
533C2×C4×D4—432no—
534C2×C4×D4—432no—
535C2×C4×D4—432no—
536C2×C4×D4—432no—
537C2×C4×D4—432no—
538C2×#117—432no—
539C2×#117C2×D4312yes—
540C22×C4⋊C4—434no—
541C22×C42C2×D4311yescharacteristic
542C43C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—4316no—
544C2×#41—4316no—
545C2×#41—1728no—
546C2×#41—1728no—
547C22×Q8—4316no—
548C22×Q8—431no—
549C22×Q8—432no—
550C22×Q8—434no—
551C22×Q8—1728no—
552C22×Q8C22×D4311yescharacteristic
553C22×Q8C22×D4311yescharacteristic
554C22×Q8C22×D4312yes—
555C22×D4—432no—
556C22×D4—434no—
557C22×D4—431no—
558C22×D4—432no—
559C22×D4—432no—
560C22×D4—432no—
561C22×D4—434no—
562C22×D4—434no—
563C23×C4—432no—
564C23×C4—434no—
565C23×C4—434no—
566C23×C4—434no—
567C23×C4—434no—
568C23×C4C22×D4311yescharacteristic
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571C4⋊Q8—4316no—
572C4⋊Q8—438no—
573C4⋊Q8—4316no—
574C4⋊Q8C22×D4318yes—
575C4⋊Q8C22×D4318yes—
576#127—438no—
577#127—4316no—
578#126—4332no—
579#126—4316no—
580#125—4332no—
581#125—438no—
582#125—4316no—
583#125C22×D43116yes—
584#124—4316no—
585#124—4332no—
586#124—4332no—
587#124—438no—
588#124—4316no—
589#124—4316no—
590#123—4316no—
591#123—4332no—
592#123—4332no—
593#123—4332no—
594#123—4332no—
595#123—4332no—
596#123—4332no—
597C22⋊Q8—4332no—
598C22⋊Q8—438no—
599C22⋊Q8—4332no—
600C22⋊Q8—4332no—
601C22⋊Q8—4332no—
602C22⋊Q8—4332no—
603C22⋊Q8—4316no—
604C22⋊Q8C22×D4318yes—
605C22⋊Q8C22×D4318yes—
606C22⋊Q8C22×D43116yes—
607#121—438no—
608#121—4316no—
609#121—4316no—
610#121—4332no—
611#121—4316no—
612#121—4332no—
613#121—4332no—
614C4×Q8—4316no—
615C4×Q8—438no—
616C4×Q8—4316no—
617C4×Q8C22×D4318yes—
618C4×Q8C22×D4318yes—
619C4×Q8C22×D43116yes—
620C4×D4—4316no—
621C4×D4—4332no—
622C4×D4—4316no—
623C4×D4—438no—
624C4×D4—4316no—
625C4×D4—4316no—
626C4×D4—4316no—
627C4×D4—4316no—
628C4×D4—4316no—
629#117—4316no—
630#117C22×D43116yes—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—434no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—432no—
636C2×C4⋊C4—431no—
637C2×C4⋊C4—431no—
638C2×C4⋊C4—432no—
639C2×C4⋊C4—432no—
640C2×C4⋊C4—434no—
641C2×C4⋊C4—434no—
642C2×C4⋊C4—432no—
643C2×C4⋊C4—4332no—
644C2×C4⋊C4C22×D4312yes—
645C2×C4⋊C4C22×D4312yes—
646C2×C4⋊C4C22×D4312yes—
647C2×C4⋊C4C22×D4312yes—
648C2×C4⋊C4C22×D4311yescharacteristic
649C2×C4⋊C4C22×D4311yescharacteristic
650C2×C4⋊C4C22×D4312yes—
651C2×C4⋊C4C22×D4312yes—
652C2×C4⋊C4C22×D4312yes—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4—432no—
657C2×C22⋊C4—432no—
658C2×C22⋊C4—434no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4—434no—
663C2×C22⋊C4—434no—
664C2×C22⋊C4—434no—
665C2×C22⋊C4C22×D4312yes—
666C2×C22⋊C4C22×D4312yes—
667C2×C42—432no—
668C2×C42—434no—
669C2×C42C22×D4311yescharacteristic
670C2×C42C22×D4312yes—
671C2×C42C22×D4312yes—
672C2×C42C22×D4311yescharacteristic
673C2×C42C22×D4311yescharacteristic
674C2×C42C22×D4311yescharacteristic
675C2×C42C22×D4318yes—
676C24—432no—
677C24—434no—
678C24C23×D4311yescharacteristic
679#41—17232no—
680#41—17232no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—434no—
685C2×Q8—438no—
686C2×Q8—4316no—
687C2×Q8—868no—
688C2×Q8—864no—
689C2×Q8—1728no—
690C2×Q8—17232no—
691C2×Q8C23×D4314yes—
692C2×Q8C23×D4314yes—
693C2×Q8C23×D4318yes—
694C2×D4—438no—
695C2×D4—4316no—
696C2×D4—434no—
697C2×D4—438no—
698C2×D4—438no—
699C2×D4—438no—
700C2×D4—4316no—
701C2×D4—4316no—
702C2×D4—868no—
703C2×D4—864no—
704C2×D4—868no—
705C2×D4—1728no—
706C2×D4—1724no—
707C2×D4—1728no—
708C2×D4—1728no—
709C2×D4—1724no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—434no—
716C22×C4—432no—
717C22×C4—438no—
718C22×C4—4316no—
719C22×C4—4316no—
720C22×C4—4316no—
721C22×C4—4316no—
722C22×C4—868no—
723C22×C4—1728no—
724C22×C4—1728no—
725C22×C4—1728no—
726C22×C4—1728no—
727C22×C4C23×D4314yes—
728C22×C4C23×D4314yes—
729C22×C4C23×D4312yes—
730C22×C4C23×D4311yescharacteristic
731C22×C4C23×D4311yescharacteristic
732C22×C4C23×D4311yescharacteristic
733C22×C4C23×D4311yescharacteristic
734C22×C4C23×D4312yes—
735C22×C4C23×D4312yes—
736C22×C4C23×D4312yes—
737C22×C4C23×D4314yes—
738C22×C4C23×D4311yescharacteristic
739C22×C4C23×D4311yescharacteristic
740C4⋊C4—438no—
741C4⋊C4—4316no—
742C4⋊C4—4316no—
743C4⋊C4—438no—
744C4⋊C4—438no—
745C4⋊C4—434no—
746C4⋊C4—434no—
747C4⋊C4—438no—
748C4⋊C4—438no—
749C4⋊C4—4316no—
750C4⋊C4—4316no—
751C4⋊C4—438no—
752C4⋊C4C23×D4318yes—
753C4⋊C4C23×D4318yes—
754C4⋊C4C23×D4318yes—
755C4⋊C4C23×D4318yes—
756C4⋊C4C23×D4314yes—
757C4⋊C4C23×D4314yes—
758C4⋊C4C23×D4318yes—
759C4⋊C4C23×D4318yes—
760C4⋊C4C23×D4318yes—
761C22⋊C4—438no—
762C22⋊C4—438no—
763C22⋊C4—438no—
764C22⋊C4—438no—
765C22⋊C4—438no—
766C22⋊C4—4316no—
767C22⋊C4—4316no—
768C22⋊C4—4316no—
769C22⋊C4—4316no—
770C22⋊C4—4316no—
771C22⋊C4—4316no—
772C22⋊C4—4316no—
773C22⋊C4C23×D4318yes—
774C22⋊C4C23×D4318yes—
775C42—438no—
776C42—4316no—
777C42C23×D4314yes—
778C42C23×D4314yes—
779C42C23×D4314yes—
780C42C23×D4314yes—
781C42C23×D4318yes—
782C42C23×D4318yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—434no—
787C23—438no—
788C23—864no—
789C23—868no—
790C23—864no—
791C23—868no—
792C23—868no—
793C23—864no—
794C23C24×D4312yes—
795C23C24×D4311yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—8616no—
800Q8—868no—
801Q8—17216no—
802D4—8616no—
803D4—868no—
804D4—8616no—
805D4—17216no—
806D4—1728no—
807D4—17216no—
808D4—17216no—
809D4—1728no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—434no—
822C2×C4—434no—
823C2×C4—438no—
824C2×C4—434no—
825C2×C4—864no—
826C2×C4—868no—
827C2×C4—864no—
828C2×C4—864no—
829C2×C4—8616no—
830C2×C4—17216no—
831C2×C4—17216no—
832C2×C4—17216no—
833C2×C4—17216no—
834C2×C4#1306337114yes—
835C2×C4#1306337314yes—
836C2×C4C24×D4314yes—
837C2×C4C24×D4312yes—
838C2×C4C24×D4312yes—
839C2×C4C24×D4312yes—
840C2×C4C24×D4312yes—
841C2×C4C24×D4314yes—
842C2×C4C24×D4314yes—
843C2×C4C24×D4314yes—
844C2×C4C24×D4312yes—
845C2×C4C24×D4312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—864no—
851C22—868no—
852C22—864no—
853C22—868no—
854C22—868no—
855C22—864no—
856C22—1728no—
857C22—17216no—
858C22C2×#1306337112yes—
859C22C2×#1306337312yes—
860C22#1458373512yes—
861C22C25×D4311yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—864no—
871C4—868no—
872C4—864no—
873C4—864no—
874C4C2×#1306337114yes—
875C4C2×#1306337314yes—
876C2—42no—
877C2—1724no—
878C2—1728no—
879C2#1914906614yesdirect product factor
880C2C22×#1306337111yescharacteristic
881C2C22×#1306337311yescharacteristic
882C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#533C2
socleC23×C43C25
hypercenterC2×#533D43
hypocenterC43C2×#3554
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #19149066C2direct (N × H)
2. C2×#14583645C2semidirect
3. C2×#14583634C2semidirect
4. C2×#14583634C2semidirect
5. C2×#14583627C2semidirect
6. C2×#14583609C2semidirect
7. C2×#14583571C2semidirect
8. C2×Q8×D172C2semidirect
9. C2×#14583559C2semidirect
10. C2×#14583551C2semidirect
11. C2×#14583523C2semidirect
12. C2×#14583520C2semidirect
13. C2×#14583504C2semidirect
14. C2×#14583497C2semidirect
15. C2×#14583474C2semidirect
16. C2×#14583449C2semidirect
17. C2×#14583433C2semidirect
18. C2×C43×#533C2semidirect
22. #14583645C22semidirect
23. #14583634C22semidirect
24. #14583634C22semidirect
25. #14583627C22semidirect
26. #14583609C22semidirect
27. #14583571C22semidirect
28. Q8×D172C22semidirect
29. #14583559C22semidirect
30. #14583551C22semidirect
31. #14583523C22semidirect
32. #14583520C22semidirect
33. #14583504C22semidirect
34. #14583497C22semidirect
35. #14583474C22semidirect
36. #14583449C22semidirect
42. #14583433C22semidirect
89. C43×#533C22semidirect
450. C2×#533D43semidirect
454. C2×C43#3554semidirect
477. #533C2×D43semidirect
542. C43C2×#3554semidirect
879. C2#19149066direct (N × H)

Maximal subgroups

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

subgroupindex
#191490662
C2×#145836452
C2×#145836342
C2×#145836272
C2×#145836092
C2×#145835712
C2×Q8×D1722
C2×#145835592
C2×#145835512
C2×#145835232
C2×#145835202
C2×#145835042
C2×#145834972
C2×#145834742
C2×#145834492
C2×#145834332
C2×C43×#5332
C2×#355443