Finite Group Databasebeta

← C2×#19148214 #26003692

Subgroups — C2×#19148214 #26003692

Order 11008.

7706 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#19148214C2132yesmaximal, direct product factor
2C2×#14583627C211yesmaximal, characteristic, complemented
3C2×#14583617C212yesmaximal, complemented
4C2×#14583590C212yesmaximal, complemented
5C2×#14583585C214yesmaximal, complemented
6C2×#14583564C211yesmaximal, characteristic, complemented
7C2×#14583557C212yesmaximal, complemented
8C2×#14583554C211yesmaximal, characteristic, complemented
9C2×#14583551C212yesmaximal, complemented
10C2×#14583454C211yesmaximal, characteristic, complemented
11C2×#14583451C212yesmaximal, complemented
12C2×#14583432C214yesmaximal, complemented
13C2×#14583428C212yesmaximal, complemented
14C2×C4×#10621902C211yesmaximal, characteristic, complemented
15C2×#14583367C212yesmaximal, complemented
16C2×C4×#10621900C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D43C212yesmaximal, complemented
18C2×C43×#556C211yesmaximal, characteristic, complemented
19C22×#10621902C2211yescharacteristic
20C22×#10621898C2212yes—
21C22×#10621900C2211yescharacteristic
22C22×Q8×D43C2212yes—
23#14583627C22116yescomplemented
24#14583617C22132yescomplemented
25#14583590C22132yescomplemented
26#14583585C22164yescomplemented
27#14583564C22116yescomplemented
28#14583557C22132yescomplemented
29#14583554C22116yescomplemented
30#14583551C22132yescomplemented
31#14583454C22116yescomplemented
32#14583451C22132yescomplemented
33C2×#13063325C2211yescharacteristic
34C2×#13063324C2212yes—
35C2×#13063323C2212yes—
36#14583432C22164yescomplemented
37#14583428C22132yescomplemented
38C2×#13063319C2214yes—
39C2×#13063318C2214yes—
40C2×#13063317C2212yes—
41C2×#13063316C2212yes—
42C2×#13063315C2214yes—
43C2×#13063315C2214yes—
44C2×#13063311C2214yes—
45C2×#13063310C2214yes—
46C2×#13063307C2214yes—
47C2×#13063307C2214yes—
48C2×#13063305C2212yes—
49C2×#13063304C2212yes—
50C2×#13063303C2214yes—
51C2×#13063302C2214yes—
52C2×#13063301C2212yes—
53C2×#13063301C2212yes—
54C2×#13063298C2214yes—
55C2×#13063296C2212yes—
56C4×#10621902C22116yescomplemented
57#14583367C22132yescomplemented
58C4×#10621900C22116yescomplemented
59C2×Q8×Dic43C2211yescharacteristic
60C2×Q8×Dic43C2212yes—
61C2×C4×Dic86C2212yes—
62C2×C4×Dic86C2211yescharacteristic
63C2×C4×Dic86C2214yes—
64C2×#13063290C2214yes—
65C2×#13063290C2212yes—
66C2×#13063290C2212yes—
67C2×#13063290C2211yescharacteristic
68C4×Q8×D43C22132yescomplemented
69C2×C4×D172C2211yescharacteristic
70C2×C4×D172C2212yes—
71C2×D4×Dic43C2211yescharacteristic
72C2×#13063287C2212yes—
73C2×#13063287C2211yescharacteristic
74C2×#13063287C2212yes—
75C2×C4×C22⋊D43C2212yes—
76C2×(C22⋊D43)⋊C4C2214yes—
77C2×(C22⋊D43)⋊C4C2214yes—
78C2×(C22⋊D43)⋊C4C2212yes—
79C2×#13063283C2212yes—
80C2×#13063283C2211yescharacteristic
81C2×#13063283C2211yescharacteristic
82C2×#13063283C2212yes—
83C2×#13063282C2214yes—
84C2×#13063281C2212yes—
85C2×#13063281C2214yes—
86C2×C4⋊C4×D43C2214yes—
87C2×C4⋊C4×D43C2212yes—
88C22×C4×Dic43C2212yes—
89C2×C42×D43C2212yes—
90C2×C42×D43C2211yescharacteristic
91C2×C42×D43C2214yes—
92C43×#556C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#126×C43C2214yes—
95C2×#124×C43C2212yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×Q8×C43C2212yes—
99C2×C4×D4×C43C2211yescharacteristic
100C2×#117×C43C2212yes—
101C2×#10621902—28no—
102C2×#10621902C2318yes—
103C2×#10621898—216no—
104C2×#10621898C23116yes—
105C2×#10621900—28no—
106C2×#10621900C2318yes—
107C22×Dic86C2312yes—
108C22×Dic86C2314yes—
109C22×Dic86C2311yescharacteristic
110C2×Q8×D43—216no—
111C2×Q8×D43C23116yes—
112C22×D172C2312yes—
113C22×D172C2311yescharacteristic
114C22×C22⋊D43C2314yes—
115C22×C22⋊D43C2312yes—
116C23×Dic43C2312yes—
117C23×Dic43C2312yes—
118C22×C4×D43C2312yes—
119C22×C4×D43C2314yes—
120C22×C4×D43C2312yes—
121C22×C4×D43C2314yes—
122C22×C4×D43C2312yes—
123C22×C4×D43C2311yescharacteristic
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C2311yescharacteristic
126#13063325C2318yes—
127#13063324C23116yes—
128#13063323C23116yes—
129#13063319C23132yes—
130#13063318C23132yes—
131#13063317C23116yes—
132#13063316C23116yes—
133#13063315C23132yes—
134#13063315C23132yes—
135#13063311C23132yes—
136#13063310C23132yes—
137#13063307C23132yes—
138#13063307C23132yes—
139#13063305C23116yes—
140#13063304C23116yes—
141#13063303C23132yes—
142#13063302C23132yes—
143#13063301C23116yes—
144#13063301C23116yes—
145#13063298C23132yes—
146#13063296C23116yes—
147Q8×Dic43C23116yes—
148Q8×Dic43C2318yes—
149C4×Dic86C23116yes—
150C4×Dic86C2318yes—
151C4×Dic86C23132yes—
152#13063290C23116yes—
153#13063290C2318yes—
154#13063290C23132yes—
155#13063290C23116yes—
156C4×D172C2318yes—
157C4×D172C23116yes—
158D4×Dic43C2318yes—
159#13063287C23116yes—
160#13063287C2318yes—
161#13063287C23116yes—
162C4×C22⋊D43C23116yes—
163(C22⋊D43)⋊C4C23132yes—
164(C22⋊D43)⋊C4C23116yes—
165(C22⋊D43)⋊C4C23132yes—
166#13063283C23116yes—
167#13063283C2318yes—
168#13063283C2318yes—
169#13063283C23116yes—
170#13063282C23132yes—
171#13063281C23116yes—
172#13063281C23132yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2314yes—
175C2×C4⋊Dic43C2311yescharacteristic
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2311yescharacteristic
178C2×C4⋊Dic43C2312yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2314yes—
187C4⋊C4×D43C23116yes—
188C4⋊C4×D43C23132yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2314yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×C4×Dic43C2311yescharacteristic
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2312yes—
202C2×C4×Dic43C2314yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2314yes—
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C23116yes—
208C42×D43C23132yes—
209C42×D43C23116yes—
210C42×D43C2318yes—
211C22×Q8×C43C2311yescharacteristic
212C22×Q8×C43C2312yes—
213C22×D4×C43C2311yescharacteristic
214C23×C4×C43C2312yes—
215C4⋊Q8×C43C2318yes—
216#126×C43C23132yes—
217#124×C43C23116yes—
218C22⋊Q8×C43C23116yes—
219C4×Q8×C43C23116yes—
220C4×Q8×C43C2318yes—
221C4×D4×C43C2318yes—
222#117×C43C23116yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2314yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2312yes—
229C2×C22⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C42×C43C2314yes—
233C2×C42×C43C2311yescharacteristic
234C2×C42×C43C2312yes—
235C24×C43C2412yes—
236C23×D43C2411yescharacteristic
237C23×D43C2412yes—
238C2×Q8×C43—28no—
239C2×Q8×C43—24no—
240C2×Q8×C43C2414yes—
241C2×Q8×C43C2418yes—
242C2×D4×C43—24no—
243C2×D4×C43C2414yes—
244C22×C4×C43—28no—
245C22×C4×C43C2412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2414yes—
249C22×C4×C43C2412yes—
250C22×C4×C43C2418yes—
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—28no—
254C2×C22⋊D43—216no—
255C2×C22⋊D43C24116yes—
256C2×C22⋊D43C2418yes—
257C22×Dic43—28no—
258C22×Dic43—28no—
259C22×Dic43C2411yescharacteristic
260C22×Dic43C2411yescharacteristic
261C22×Dic43C2412yes—
262C22×Dic43C2412yes—
263C22×Dic43C2414yes—
264C22×Dic43C2418yes—
265C22×Dic43C2418yes—
266C22×Dic43C2412yes—
267C22×Dic43C2411yescharacteristic
268#10621902—232no—
269Q8×D43—264no—
270#10621900—232no—
271#10621898—264no—
272C2×D172—28no—
273C2×D172#4118yescomplemented
274C2×D172C2418yes—
275C2×D172C2414yes—
276C2×C4×D43—28no—
277C2×C4×D43—24no—
278C2×C4×D43—24no—
279C2×C4×D43—216no—
280C2×C4×D43—28no—
281C2×C4×D43—24no—
282C2×C4×D43—216no—
283C2×C4×D43—28no—
284C2×C4×D43C2418yes—
285C2×C4×D43C24116yes—
286C2×C4×D43C2418yes—
287C2×C4×D43C24116yes—
288C2×C4×D43C2418yes—
289C2×C4×D43C2414yes—
290C2×C4×D43C2414yes—
291C2×C4×D43C2414yes—
292C2×Dic86—28no—
293C2×Dic86—216no—
294C2×Dic86#4118yescomplemented
295C2×Dic86C2418yes—
296C2×Dic86C24116yes—
297C2×Dic86C2414yes—
298C4⋊C4×C43C2414yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C2414yes—
301C4⋊C4×C43C24116yes—
302C4⋊C4×C43C2418yes—
303C4⋊C4×C43C2418yes—
304C22⋊C4×C43C24116yes—
305C22⋊C4×C43C2418yes—
306C22⋊C4×C43C24116yes—
307C42×C43C24116yes—
308C42×C43C2414yes—
309C42×C43C2418yes—
310C22⋊Dic43C2418yes—
311C22⋊Dic43C24116yes—
312(C2×D43)⋊C4C2418yes—
313(C2×D43)⋊C4C24116yes—
314(C2×D43)⋊C4C2418yes—
315(C2×D43)⋊C4C2418yes—
316(C2×D43)⋊C4C2418yes—
317(C2×D43)⋊C4C24116yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C24116yes—
320C4⋊Dic43C2414yes—
321C4⋊Dic43C2418yes—
322C4⋊Dic43C2414yes—
323C4⋊Dic43C2418yes—
324Dic43⋊C4C2418yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C24116yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C24116yes—
331Dic43⋊C4C24116yes—
332C4×Dic43C2414yes—
333C4×Dic43C2418yes—
334C4×Dic43C2414yes—
335C4×Dic43C2414yes—
336C4×Dic43C2418yes—
337C4×Dic43C24116yes—
338C4×Dic43C2418yes—
339C4×Dic43C24116yes—
340C4×Dic43C2418yes—
341C4×Dic43C2418yes—
342C23×C43—24no—
343C23×C43—24no—
344C23×C43—24no—
345C23×C43C2514yes—
346C23×C43C2511yescharacteristic
347C22×D43—24no—
348C22×D43—24no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43C2×#4118yes—
353C22×D43C2512yes—
354C22×D43C2514yes—
355Q8×C43—216no—
356Q8×C43—28no—
357D4×C43—28no—
358C2×C4×C43—28no—
359C2×C4×C43—24no—
360C2×C4×C43—24no—
361C2×C4×C43—24no—
362C2×C4×C43—22no—
363C2×C4×C43—216no—
364C2×C4×C43C2×#4114yes—
365C2×C4×C43C2×#4114yes—
366C2×C4×C43C2514yes—
367C2×C4×C43C2514yes—
368C2×C4×C43C2514yes—
369C2×C4×C43C2512yes—
370C2×C4×C43C2518yes—
371C2×C4×C43C2512yes—
372C2×C4×C43C2512yes—
373C22⋊D43—232no—
374C22⋊D43—216no—
375C2×Dic43—24no—
376C2×Dic43—28no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—24no—
380C2×Dic43—216no—
381C2×Dic43—216no—
382C2×Dic43C2×#4118yes—
383C2×Dic432−1+414yes—
384C2×Dic43C2512yes—
385C2×Dic43C2512yes—
386C2×Dic43C2514yes—
387C2×Dic43C2518yes—
388C2×Dic43C2514yes—
389C2×Dic43C2514yes—
390C2×Dic43C2512yes—
391D172—216no—
392D172C2×#41116yescomplemented
393C4×D43—232no—
394C4×D43—216no—
395C4×D43—28no—
396C4×D43—216no—
397C4×D43—28no—
398C4×D43—232no—
399C4×D43—216no—
400C4×D43—28no—
401Dic86—216no—
402Dic86—232no—
403Dic86C2×#41116yescomplemented
404C2×#3482—431nomaximal, Sylow
405C22×C43—24no—
406C22×C43—24no—
407C22×C43—24no—
408C22×C43—48no—
409C22×C43C22×#4112yes—
410C22×C43C22×#4112yes—
411C22×C43C2×2−1+412yes—
412C22×C43C2611yescharacteristic
413C2×D43—24no—
414C2×D43—24no—
415C2×D43—216no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—44no—
420C2×D43C22×#4118yes—
421C4×C43—28no—
422C4×C43—24no—
423C4×C43—24no—
424C4×C43—24no—
425C4×C43—22no—
426C4×C43C22×#4114yes—
427C4×C43C22×#4114yes—
428Dic43—24no—
429Dic43—28no—
430Dic43—22no—
431Dic43—22no—
432Dic43—24no—
433Dic43C22×#4118yes—
434Dic43C2×2−1+414yes—
435#3482—4332no—
436C2×#557—431no—
437C2×#556—432no—
438C2×#556D4311yescharacteristic, complemented
439C2×#552—434no—
440C2×#552—432no—
441C2×D4×Q8—431no—
442C2×#548—432no—
443C2×#547—432no—
444C2×#547—431no—
445C2×#533—431no—
446C2×#533—432no—
447C2×#529—434no—
448C2×#529—432no—
449C2×C4×#41—431no—
450C2×C4×#41—431no—
451C2×C4×#41—432no—
452C22×C4×Q8—432no—
453C2×C43—44no—
454C2×C43#348214yescomplemented
455C2×C43C23×#4111yescharacteristic
456C2×C43C23×#4111yescharacteristic
457C2×C43C22×2−1+411yescharacteristic
458D43—28no—
459D43—42no—
460C22×#41—431no—
461C22×#41—431no—
462C22×#41—432no—
463C23×Q8—432no—
464#557—4316no—
465#556—4332no—
466#556C2×D43116yescomplemented
467#552—4364no—
468#552—4332no—
469D4×Q8—4316no—
470#548—4332no—
471#547—4332no—
472#547—4316no—
473#533—4316no—
474#533—4332no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—432no—
477C2×C4⋊Q8—431no—
478C2×C4⋊Q8C2×D4311yescharacteristic
479#529—4364no—
480#529—4332no—
481C2×#126—434no—
482C2×#126—434no—
483C2×#126C2×D4314yes—
484C2×#125—434no—
485C2×#125—434no—
486C2×#125—432no—
487C2×#125—432no—
488C2×#124—434no—
489C2×#124C2×D4312yes—
490C2×#123—434no—
491C2×#123—434no—
492C2×#123—434no—
493C2×C22⋊Q8—432no—
494C2×C22⋊Q8—432no—
495C2×C22⋊Q8—432no—
496C2×C22⋊Q8—434no—
497C2×C22⋊Q8—432no—
498C2×C22⋊Q8—434no—
499C2×C22⋊Q8C2×D4312yes—
500C2×#121—432no—
501C2×#121—434no—
502C4×#41—4316no—
503C4×#41—4316no—
504C4×#41—4332no—
505C2×C4×Q8—432no—
506C2×C4×Q8—431no—
507C2×C4×Q8—4332no—
508C2×C4×Q8—431no—
509C2×C4×Q8—434no—
510C2×C4×Q8—432no—
511C2×C4×Q8—432no—
512C2×C4×Q8—432no—
513C2×C4×Q8—434no—
514C2×C4×Q8—431no—
515C2×C4×Q8C2×D4312yes—
516C2×C4×Q8C2×D4311yescharacteristic
517C2×C4×D4—431no—
518C2×C4×D4—432no—
519C2×C4×D4—431no—
520C2×C4×D4—432no—
521C2×C4×D4—432no—
522C2×C4×D4—434no—
523C2×C4×D4—432no—
524C2×C4×D4—434no—
525C2×C4×D4—431no—
526C2×C4×D4—432no—
527C2×C4×D4C2×D4311yescharacteristic
528C2×#117—431no—
529C2×#117—432no—
530C2×#117—431no—
531C2×#117—432no—
532C2×#117—432no—
533C2×#117—434no—
534C2×#117—434no—
535C2×#117C2×D4312yes—
536C22×C4⋊C4—434no—
537C22×C4⋊C4—432no—
538C22×C42—432no—
539C22×C42—432no—
540C22×C42—434no—
541C22×C42—431no—
542C43C2×#348211yescharacteristic, complemented, Sylow
543C2×#41—438no—
544C2×#41—438no—
545C2×#41—4316no—
546C2×#41—8616no—
547C2×#41—868no—
548C2×#41—868no—
549C22×Q8—4316no—
550C22×Q8—431no—
551C22×Q8—434no—
552C22×Q8—432no—
553C22×Q8—8616no—
554C22×Q8C22×D4312yes—
555C22×Q8C22×D4311yescharacteristic
556C22×D4—434no—
557C22×D4—432no—
558C22×D4—431no—
559C22×D4—432no—
560C22×D4C22×D4311yescharacteristic
561C23×C4—432no—
562C23×C4—432no—
563C23×C4—432no—
564C23×C4—434no—
565C23×C4—434no—
566C23×C4—432no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—432no—
571C23×C4C22×D4312yes—
572C4⋊Q8—4316no—
573C4⋊Q8—4316no—
574C4⋊Q8—438no—
575C4⋊Q8C22×D4318yes—
576#126—4332no—
577#126—4332no—
578#126C22×D43132yes—
579#125—4332no—
580#125—4332no—
581#125—4316no—
582#125—4316no—
583#124—4332no—
584#124C22×D43116yes—
585#123—4332no—
586#123—4332no—
587#123—4332no—
588C22⋊Q8—4316no—
589C22⋊Q8—4316no—
590C22⋊Q8—4316no—
591C22⋊Q8—4332no—
592C22⋊Q8—4316no—
593C22⋊Q8—4332no—
594C22⋊Q8C22×D43116yes—
595#121—4316no—
596#121—4332no—
597C4×Q8—4316no—
598C4×Q8—438no—
599C4×Q8—438no—
600C4×Q8—4332no—
601C4×Q8—4316no—
602C4×Q8—4316no—
603C4×Q8—4316no—
604C4×Q8—4332no—
605C4×Q8—438no—
606C4×Q8C22×D43116yes—
607C4×Q8C22×D4318yes—
608C4×D4—438no—
609C4×D4—4316no—
610C4×D4—438no—
611C4×D4—4316no—
612C4×D4—4316no—
613C4×D4—4316no—
614C4×D4—4332no—
615C4×D4—4332no—
616C4×D4—438no—
617C4×D4—4316no—
618C4×D4C22×D4318yes—
619#117—438no—
620#117—4316no—
621#117—438no—
622#117—4316no—
623#117—4316no—
624#117—4332no—
625#117—4332no—
626#117C22×D43116yes—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—434no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—434no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—431no—
636C2×C4⋊C4—431no—
637C2×C4⋊C4—434no—
638C2×C4⋊C4—434no—
639C2×C4⋊C4—434no—
640C2×C4⋊C4—432no—
641C2×C4⋊C4—4332no—
642C2×C4⋊C4—4316no—
643C2×C4⋊C4C22×D4311yescharacteristic
644C2×C4⋊C4C22×D4314yes—
645C2×C4⋊C4C22×D4311yescharacteristic
646C2×C4⋊C4C22×D4312yes—
647C2×C4⋊C4C22×D4312yes—
648C2×C4⋊C4C22×D4312yes—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—434no—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—434no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4C22×D4312yes—
658C2×C22⋊C4C22×D4314yes—
659C2×C22⋊C4C22×D4314yes—
660C2×C42—431no—
661C2×C42—432no—
662C2×C42—432no—
663C2×C42—434no—
664C2×C42—432no—
665C2×C42—432no—
666C2×C42—434no—
667C2×C42—432no—
668C2×C42—431no—
669C2×C42—431no—
670C2×C42—4316no—
671C2×C42—4316no—
672C2×C42—4332no—
673C2×C42—438no—
674C2×C42C22×D4314yes—
675C2×C42C22×D4311yescharacteristic
676C2×C42C22×D4312yes—
677C24—432no—
678C24—431no—
679C24C23×D4312yes—
680#41—8664no—
681#41—8632no—
682#41—8632no—
683C2×Q8—28no—
684C2×Q8—24no—
685C2×Q8—438no—
686C2×Q8—434no—
687C2×Q8—4316no—
688C2×Q8—438no—
689C2×Q8—8616no—
690C2×Q8—8664no—
691C2×Q8—868no—
692C2×Q8C23×D4318yes—
693C2×Q8C23×D4314yes—
694C2×D4—24no—
695C2×D4—4316no—
696C2×D4—438no—
697C2×D4—438no—
698C2×D4—434no—
699C2×D4—438no—
700C2×D4—868no—
701C2×D4—868no—
702C2×D4—8616no—
703C2×D4C23×D4314yes—
704C22×C4—28no—
705C22×C4—431no—
706C22×C4—432no—
707C22×C4—438no—
708C22×C4—438no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—434no—
714C22×C4—438no—
715C22×C4—438no—
716C22×C4—4316no—
717C22×C4—4316no—
718C22×C4—438no—
719C22×C4—434no—
720C22×C4—434no—
721C22×C4—434no—
722C22×C4—8616no—
723C22×C4—868no—
724C22×C4—864no—
725C22×C4—8616no—
726C22×C4—868no—
727C22×C4—868no—
728C22×C4—868no—
729C22×C4—868no—
730C22×C4—864no—
731C22×C4—864no—
732C22×C4C23×D4318yes—
733C22×C4C23×D4312yes—
734C22×C4C23×D4312yes—
735C22×C4C23×D4311yescharacteristic
736C22×C4C23×D4314yes—
737C22×C4C23×D4312yes—
738C22×C4C23×D4311yescharacteristic
739C22×C4C23×D4311yescharacteristic
740C4⋊C4—438no—
741C4⋊C4—4316no—
742C4⋊C4—438no—
743C4⋊C4—4316no—
744C4⋊C4—4316no—
745C4⋊C4—438no—
746C4⋊C4—4316no—
747C4⋊C4—438no—
748C4⋊C4—434no—
749C4⋊C4—434no—
750C4⋊C4—4316no—
751C4⋊C4—4316no—
752C4⋊C4—4316no—
753C4⋊C4—438no—
754C4⋊C4C23×D4314yes—
755C4⋊C4C23×D43116yes—
756C4⋊C4C23×D4314yes—
757C4⋊C4C23×D4318yes—
758C4⋊C4C23×D4318yes—
759C4⋊C4C23×D4318yes—
760C22⋊C4—438no—
761C22⋊C4—4316no—
762C22⋊C4—438no—
763C22⋊C4—4316no—
764C22⋊C4—438no—
765C22⋊C4—438no—
766C22⋊C4—438no—
767C22⋊C4—4316no—
768C22⋊C4C23×D4318yes—
769C22⋊C4C23×D43116yes—
770C22⋊C4C23×D43116yes—
771C42—438no—
772C42—434no—
773C42—434no—
774C42—434no—
775C42—438no—
776C42—438no—
777C42—4316no—
778C42—438no—
779C42—438no—
780C42—4316no—
781C42C23×D43116yes—
782C42C23×D4314yes—
783C42C23×D4318yes—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—438no—
788C23—434no—
789C23—432no—
790C23—864no—
791C23—864no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23C24×D4314yes—
796C23C24×D4311yescharacteristic
797Q8—216no—
798Q8—28no—
799Q8—4316no—
800Q8—8632no—
801Q8—8616no—
802D4—28no—
803D4—4316no—
804D4—8616no—
805D4—8616no—
806D4—8632no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—216no—
813C2×C4—438no—
814C2×C4—434no—
815C2×C4—432no—
816C2×C4—434no—
817C2×C4—432no—
818C2×C4—432no—
819C2×C4—434no—
820C2×C4—434no—
821C2×C4—438no—
822C2×C4—8632no—
823C2×C4—8616no—
824C2×C4—868no—
825C2×C4—8632no—
826C2×C4—8616no—
827C2×C4—8616no—
828C2×C4—8616no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—868no—
832C2×C4—864no—
833C2×C4—864no—
834C2×C4—8616no—
835C2×C4—868no—
836C2×C4—868no—
837C2×C4#41×D4314yes—
838C2×C4#41×D4314yes—
839C2×C4C24×D4314yes—
840C2×C4C24×D4314yes—
841C2×C4C24×D4312yes—
842C2×C4C24×D4318yes—
843C2×C4C24×D4314yes—
844C2×C4C24×D4312yes—
845C2×C4C24×D4312yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—438no—
851C22—864no—
852C22—864no—
853C22—8616no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—1724no—
858C22C2×#41×D4312yes—
859C22C2×#41×D4312yes—
860C222−1+4×D4312yes—
861C22C25×D4311yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—438no—
868C4—434no—
869C4—862no—
870C4—862no—
871C4—868no—
872C4—864no—
873C4—864no—
874C4C2×#41×D4314yes—
875C4C2×#41×D4314yes—
876C2—44no—
877C2—868no—
878C2—1722no—
879C2#1914821414yesdirect product factor
880C2C22×#41×D4311yescharacteristic
881C2C22×#41×D4311yescharacteristic
882C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
hypercenterC2×#556D43
hypocenterC43C2×#3482
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19148214C2direct (N × H)
2. C2×#14583627C2semidirect
3. C2×#14583617C2semidirect
4. C2×#14583590C2semidirect
5. C2×#14583585C2semidirect
6. C2×#14583564C2semidirect
7. C2×#14583557C2semidirect
8. C2×#14583554C2semidirect
9. C2×#14583551C2semidirect
10. C2×#14583454C2semidirect
11. C2×#14583451C2semidirect
12. C2×#14583432C2semidirect
13. C2×#14583428C2semidirect
14. C2×C4×#10621902C2semidirect
15. C2×#14583367C2semidirect
16. C2×C4×#10621900C2semidirect
17. C2×C4×Q8×D43C2semidirect
18. C2×C43×#556C2semidirect
23. #14583627C22semidirect
24. #14583617C22semidirect
25. #14583590C22semidirect
26. #14583585C22semidirect
27. #14583564C22semidirect
28. #14583557C22semidirect
29. #14583554C22semidirect
30. #14583551C22semidirect
31. #14583454C22semidirect
32. #14583451C22semidirect
36. #14583432C22semidirect
37. #14583428C22semidirect
56. C4×#10621902C22semidirect
57. #14583367C22semidirect
58. C4×#10621900C22semidirect
68. C4×Q8×D43C22semidirect
92. C43×#556C22semidirect
273. C2×D172#41semidirect
294. C2×Dic86#41semidirect
392. D172C2×#41semidirect
403. Dic86C2×#41semidirect
438. C2×#556D43semidirect
454. C2×C43#3482semidirect
466. #556C2×D43semidirect
542. C43C2×#3482semidirect
879. C2#19148214direct (N × H)

Maximal subgroups

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

subgroupindex
#191482142
C2×#145836272
C2×#145836172
C2×#145835902
C2×#145835852
C2×#145835642
C2×#145835572
C2×#145835542
C2×#145835512
C2×#145834542
C2×#145834512
C2×#145834322
C2×#145834282
C2×C4×#106219022
C2×#145833672
C2×C4×#106219002
C2×C4×Q8×D432
C2×C43×#5562
C2×#348243