Finite Group Databasebeta

← C2×#19148935 #26004279

Subgroups — C2×#19148935 #26004279

Order 11008.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148935C2132yesmaximal, direct product factor
2C2×#14583651C214yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583614C211yesmaximal, characteristic, complemented
5C2×#14583609C211yesmaximal, characteristic, complemented
6C2×#14583606C211yesmaximal, characteristic, complemented
7C2×#14583591C212yesmaximal, complemented
8C2×#14583589C212yesmaximal, complemented
9C2×#14583553C212yesmaximal, complemented
10C2×#14583549C212yesmaximal, complemented
11C2×#14583529C212yesmaximal, complemented
12C2×#14583527C212yesmaximal, complemented
13C2×#14583520C212yesmaximal, complemented
14C2×#14583518C212yesmaximal, complemented
15C2×#14583471C214yesmaximal, complemented
16C22×#13063325C211yesmaximal, characteristic, complemented
17C2×#14583433C211yesmaximal, characteristic, complemented
18C2×C43×#529C211yesmaximal, characteristic, complemented
19C22×#10621900C2214yes—
20C23×Dic86C2212yes—
21#14583651C22164yescomplemented
22Q8×Dic86C22116yescomplemented
23#14583614C22116yescomplemented
24#14583609C22116yescomplemented
25#14583606C22116yescomplemented
26#14583591C22132yescomplemented
27#14583589C22132yescomplemented
28#14583553C22132yescomplemented
29#14583549C22132yescomplemented
30#14583529C22132yescomplemented
31#14583527C22132yescomplemented
32#14583520C22132yescomplemented
33#14583518C22132yescomplemented
34#14583471C22164yescomplemented
35C2×#13063325C2212yes—
36C2×#13063325C2211yescharacteristic
37C2×#13063325C2211yescharacteristic
38C2×#13063325C2212yes—
39C2×#13063325C2212yes—
40C2×#13063325C2212yes—
41C2×#13063325C22116yescomplemented
42C2×#13063324C2212yes—
43C2×#13063324C2214yes—
44C2×#13063324C2214yes—
45#14583433C22116yescomplemented
46C2×#13063320C2214yes—
47C2×#13063319C2212yes—
48C2×#13063318C2214yes—
49C2×#13063317C2212yes—
50C2×#13063317C2211yescharacteristic
51C2×#13063316C2212yes—
52C2×#13063316C2214yes—
53C2×#13063315C2214yes—
54C2×#13063313C2211yescharacteristic
55C2×#13063311C2214yes—
56C2×#13063311C2214yes—
57C2×#13063309C2214yes—
58C2×#13063309C2214yes—
59C2×#13063308C2212yes—
60C2×#13063307C2214yes—
61C2×#13063306C2214yes—
62C2×#13063305C2214yes—
63C2×#13063304C2211yescharacteristic
64C2×#13063304C2212yes—
65C2×#13063303C2214yes—
66C2×#13063303C2214yes—
67C2×#13063302C2214yes—
68C2×#13063302C2214yes—
69C2×#13063302C2214yes—
70C2×#13063301C2212yes—
71C2×#13063299C2211yescharacteristic
72C2×#13063299C2212yes—
73C2×#13063296C2212yes—
74C2×Q8×Dic43C2212yes—
75C2×C4×Dic86C2212yes—
76C2×C4×Dic86C2211yescharacteristic
77C2×C4×D172C2212yes—
78C2×C4×D172C2211yescharacteristic
79C2×D4×Dic43C2212yes—
80C2×C4×C22⋊D43C2212yes—
81C2×#13063284C2212yes—
82C2×#13063283C2212yes—
83C2×#13063282C2212yes—
84C2×#13063281C2214yes—
85C22×C4⋊Dic43C2212yes—
86C22×C4⋊Dic43C2212yes—
87C22×C4⋊Dic43C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C43×#529C22116yescomplemented
90C2×#126×C43C2212yes—
91C2×#125×C43C2211yescharacteristic
92C2×#124×C43C2211yescharacteristic
93C2×#123×C43C2212yes—
94C2×C22⋊Q8×C43C2211yescharacteristic
95C2×#121×C43C2211yescharacteristic
96C2×C4×Q8×C43C2211yescharacteristic
97C2×C4×D4×C43C2212yes—
98C2×C4×D4×C43C2211yescharacteristic
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C2×#10621900—416no—
102C2×#10621900C23132yes—
103C22×Dic86—48no—
104C22×Dic86C2311yescharacteristic
105C22×Dic86C2312yes—
106C22×Dic86C2314yes—
107C22×Dic86C2314yes—
108C22×Dic86C2312yes—
109C22×Dic86C23116yes—
110C22×D172C2311yescharacteristic
111C22×C22⋊D43C2312yes—
112C22×C22⋊D43C2314yes—
113C23×Dic43C2314yes—
114C23×Dic43C2314yes—
115C22×C4×D43C2312yes—
116C22×C4×D43C2314yes—
117#13063325C23116yes—
118#13063325C2318yes—
119#13063325C2318yes—
120#13063325C23116yes—
121#13063325C23116yes—
122#13063325C23116yes—
123#13063324C23132yes—
124#13063324C23116yes—
125#13063324C23132yes—
126#13063320C23132yes—
127#13063319C23116yes—
128#13063318C23132yes—
129#13063317C23116yes—
130#13063317C2318yes—
131#13063316C23116yes—
132#13063316C23132yes—
133#13063315C23132yes—
134#13063313C2318yes—
135#13063311C23132yes—
136#13063311C23132yes—
137#13063309C23132yes—
138#13063309C23132yes—
139#13063308C23116yes—
140#13063307C23132yes—
141#13063306C23132yes—
142#13063305C23132yes—
143#13063304C2318yes—
144#13063304C23116yes—
145#13063303C23132yes—
146#13063303C23132yes—
147#13063302C23132yes—
148#13063302C23132yes—
149#13063302C23132yes—
150#13063301C23116yes—
151#13063299C2318yes—
152#13063299C23116yes—
153#13063296C23116yes—
154Q8×Dic43C23116yes—
155C4×Dic86C23116yes—
156C4×Dic86C2318yes—
157C4×D172C23116yes—
158C4×D172C2318yes—
159D4×Dic43C23116yes—
160C4×C22⋊D43C23116yes—
161#13063284C23116yes—
162#13063283C23116yes—
163#13063282C23116yes—
164#13063281C23132yes—
165C2×C4⋊Dic43C23116yes—
166C2×C4⋊Dic43C23116yes—
167C2×C4⋊Dic43C23116yes—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2314yes—
174C2×C4⋊Dic43C2314yes—
175C2×C4⋊Dic43C2314yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C4⋊Dic43C2314yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2314yes—
186C4⋊C4×D43C23116yes—
187C2×C22⋊Dic43C2312yes—
188C2×C22⋊Dic43C2314yes—
189C2×C22⋊Dic43C2314yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×C4×Dic43C2314yes—
197C2×C4×Dic43C2314yes—
198C2×C4×Dic43C2312yes—
199C22×Q8×C43C2311yescharacteristic
200C22×D4×C43C2312yes—
201C22×D4×C43C2311yescharacteristic
202C23×C4×C43C2311yescharacteristic
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C23×C4×C43C2312yes—
206#126×C43C23116yes—
207#125×C43C2318yes—
208#124×C43C2318yes—
209#123×C43C23116yes—
210C22⋊Q8×C43C2318yes—
211#121×C43C2318yes—
212C4×Q8×C43C2318yes—
213C4×D4×C43C23116yes—
214C4×D4×C43C2318yes—
215#117×C43C23116yes—
216C2×C4⋊C4×C43C2312yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2311yescharacteristic
219C2×C4⋊C4×C43C2312yes—
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C4⋊C4×C43C2312yes—
222C2×C22⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C22⋊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—
233C24×C43C2412yes—
234C24×C43C2411yescharacteristic
235C23×D43C2412yes—
236C2×Q8×C43—24no—
237C2×Q8×C43C2414yes—
238C2×D4×C43—24no—
239C2×D4×C43—28no—
240C2×D4×C43C2418yes—
241C2×D4×C43C2414yes—
242C22×C4×C43—24no—
243C22×C4×C43—24no—
244C22×C4×C43—28no—
245C22×C4×C43—24no—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2414yes—
251C22×C4×C43C2414yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2418yes—
257C22×C4×C43C2411yescharacteristic
258C22×C4×C43C2411yescharacteristic
259C2×C22⋊D43—28no—
260C2×C22⋊D43—48no—
261C2×C22⋊D43C2418yes—
262C2×C22⋊D43C24116yes—
263C22×Dic43—216no—
264C22×Dic43—48no—
265C22×Dic43C2412yes—
266C22×Dic43C2412yes—
267C22×Dic43C2414yes—
268C22×Dic43C2412yes—
269C22×Dic43C2414yes—
270C22×Dic43C24116yes—
271C22×Dic43C24116yes—
272#10621900—464no—
273C2×D172—24no—
274C2×D172C2414yes—
275C2×C4×D43—28no—
276C2×C4×D43—48no—
277C2×C4×D43C2418yes—
278C2×C4×D43C24116yes—
279C2×Dic86—24no—
280C2×Dic86—44no—
281C2×Dic86—48no—
282C2×Dic86—44no—
283C2×Dic86—432no—
284C2×Dic86—48no—
285C2×Dic86C2414yes—
286C2×Dic86C2418yes—
287C2×Dic86C24116yes—
288C2×Dic86C24116yes—
289C2×Dic86C2418yes—
290C4⋊C4×C43C2418yes—
291C4⋊C4×C43C2418yes—
292C4⋊C4×C43C2414yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C2418yes—
296C22⋊C4×C43C2418yes—
297C22⋊C4×C43C2418yes—
298C22⋊C4×C43C2418yes—
299C22⋊C4×C43C2418yes—
300C22⋊C4×C43C2418yes—
301C42×C43C2414yes—
302C42×C43C2414yes—
303C42×C43C2414yes—
304C42×C43C2414yes—
305C42×C43C2418yes—
306C22⋊Dic43C2418yes—
307C22⋊Dic43C24116yes—
308C22⋊Dic43C24116yes—
309(C2×D43)⋊C4C2418yes—
310(C2×D43)⋊C4C2418yes—
311(C2×D43)⋊C4C24116yes—
312(C2×D43)⋊C4C2418yes—
313(C2×D43)⋊C4C24116yes—
314(C2×D43)⋊C4C2418yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C2418yes—
317C4⋊Dic43C2414yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C24116yes—
321C4⋊Dic43C24116yes—
322C4⋊Dic43C24116yes—
323C4⋊Dic43C2414yes—
324C4⋊Dic43C24116yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C24116yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C2418yes—
330Dic43⋊C4C2418yes—
331Dic43⋊C4C2418yes—
332Dic43⋊C4C24116yes—
333C4×Dic43C24116yes—
334C4×Dic43C24116yes—
335C4×Dic43C2418yes—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—24no—
339C23×C43—24no—
340C23×C43—24no—
341C23×C43H(5,𝔽2)14yes—
342C23×C43C2514yes—
343C23×C43C2512yes—
344C23×C43C2511yescharacteristic
345C22×D43—24no—
346C22×D43—24no—
347C22×D43—24no—
348C22×D43C2514yes—
349Q8×C43—28no—
350D4×C43—216no—
351D4×C43—28no—
352C2×C4×C43—28no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—24no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—24no—
359C2×C4×C43—24no—
360C2×C4×C43—28no—
361C2×C4×C43—216no—
362C2×C4×C43—28no—
363C2×C4×C432−1+414yes—
364C2×C4×C432−1+414yes—
365C2×C4×C43C2514yes—
366C2×C4×C43C2514yes—
367C2×C4×C43C2514yes—
368C2×C4×C43C2512yes—
369C2×C4×C43C2512yes—
370C2×C4×C43C2512yes—
371C2×C4×C43C2512yes—
372C2×C4×C43C2512yes—
373C2×C4×C43C2512yes—
374C22⋊D43—216no—
375C22⋊D43—416no—
376C2×Dic43—28no—
377C2×Dic43—28no—
378C2×Dic43—232no—
379C2×Dic43—24no—
380C2×Dic43—24no—
381C2×Dic43—24no—
382C2×Dic43—416no—
383C2×Dic43C2514yes—
384C2×Dic43C2514yes—
385C2×Dic43C2518yes—
386C2×Dic43C2514yes—
387C2×Dic43C2518yes—
388D172—28no—
389C4×D43—216no—
390C4×D43—416no—
391Dic86—28no—
392Dic86—48no—
393Dic86—416no—
394Dic86—48no—
395Dic86—416no—
396C2×#3544—431nomaximal, Sylow
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—28no—
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—24no—
403C22×C43—48no—
404C22×C43C2×H(5,𝔽2)14yes—
405C22×C43C2×H(5,𝔽2)12yes—
406C22×C43C2×2−1+412yes—
407C22×C43C2×2−1+412yes—
408C22×C43C2611yescharacteristic
409C2×D43—24no—
410C2×D43—24no—
411C2×D43—24no—
412C2×D43—48no—
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—24no—
416C4×C43—24no—
417C4×C43—22no—
418C4×C43—22no—
419C4×C43—24no—
420C4×C43C2×2−1+414yes—
421C4×C43C2×2−1+414yes—
422Dic43—28no—
423Dic43—28no—
424Dic43—24no—
425Dic43—24no—
426Dic43—24no—
427#3544—4332no—
428C2×#563—434no—
429C2×Q82—431no—
430C2×#555—431no—
431C2×#554—431no—
432C2×#554—431no—
433C2×#552—432no—
434C2×#552—432no—
435C2×#547—432no—
436C2×#547—432no—
437C2×#544—432no—
438C2×#544—432no—
439C2×#542—432no—
440C2×#542—432no—
441C2×#536—434no—
442C22×C4⋊Q8—431no—
443C2×#529—431no—
444C2×#529D4311yescharacteristic, complemented
445C2×C43—24no—
446C2×C43—44no—
447C2×C43#354414yescomplemented
448C2×C43C22×H(5,𝔽2)11yescharacteristic
449C2×C43C22×2−1+411yescharacteristic
450C2×C43C22×2−1+411yescharacteristic
451D43—44no—
452C22×#41—434no—
453C23×Q8—432no—
454#563—4364no—
455Q82—4316no—
456#555—4316no—
457#554—4316no—
458#554—4316no—
459#552—4332no—
460#552—4332no—
461#547—4332no—
462#547—4332no—
463#544—4332no—
464#544—4332no—
465#542—4332no—
466#542—4332no—
467#536—4364no—
468C2×C4⋊Q8—434no—
469C2×C4⋊Q8—434no—
470C2×C4⋊Q8—432no—
471C2×C4⋊Q8—432no—
472C2×C4⋊Q8—432no—
473C2×C4⋊Q8—431no—
474C2×C4⋊Q8—431no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—4316no—
477C2×C4⋊Q8—432no—
478#529—4316no—
479#529C2×D43116yescomplemented
480C2×#126—434no—
481C2×#126—434no—
482C2×#126—432no—
483C2×#126C2×D4312yes—
484C2×#125—434no—
485C2×#125—432no—
486C2×#125—434no—
487C2×#125—431no—
488C2×#125—432no—
489C2×#125C2×D4311yescharacteristic
490C2×#124—434no—
491C2×#124—434no—
492C2×#124—431no—
493C2×#124C2×D4311yescharacteristic
494C2×#123—434no—
495C2×#123—432no—
496C2×#123—434no—
497C2×#123—434no—
498C2×#123—434no—
499C2×#123C2×D4312yes—
500C2×C22⋊Q8—432no—
501C2×C22⋊Q8—431no—
502C2×C22⋊Q8—432no—
503C2×C22⋊Q8—434no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—434no—
506C2×C22⋊Q8—434no—
507C2×C22⋊Q8—434no—
508C2×C22⋊Q8—434no—
509C2×C22⋊Q8C2×D4311yescharacteristic
510C2×#121—432no—
511C2×#121—431no—
512C2×#121—432no—
513C2×#121C2×D4311yescharacteristic
514C2×C4×Q8—432no—
515C2×C4×Q8—431no—
516C2×C4×Q8—432no—
517C2×C4×Q8C2×D4311yescharacteristic
518C2×C4×D4—432no—
519C2×C4×D4—432no—
520C2×C4×D4—431no—
521C2×C4×D4—432no—
522C2×C4×D4C2×D4312yes—
523C2×C4×D4C2×D4311yescharacteristic
524C2×#117—432no—
525C2×#117—432no—
526C2×#117—434no—
527C2×#117—432no—
528C2×#117C2×D4312yes—
529C22×C4⋊C4—432no—
530C22×C4⋊C4—432no—
531C22×C4⋊C4—432no—
532C22×C4⋊C4—432no—
533C22×C42C2×D4311yescharacteristic
534C43C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—4332no—
536C2×#41—17216no—
537C22×Q8—431no—
538C22×Q8—432no—
539C22×Q8—434no—
540C22×Q8—434no—
541C22×Q8—432no—
542C22×Q8—4316no—
543C22×Q8—1728no—
544C22×Q8C22×D4311yescharacteristic
545C22×D4—432no—
546C22×D4—434no—
547C22×D4—431no—
548C22×D4C22×D4311yescharacteristic
549C22×D4C22×D4312yes—
550C23×C4—434no—
551C23×C4—434no—
552C23×C4—432no—
553C23×C4—434no—
554C23×C4C22×D4311yescharacteristic
555C23×C4C22×D4311yescharacteristic
556C23×C4C22×D4312yes—
557C23×C4C22×D4311yescharacteristic
558C4⋊Q8—4332no—
559C4⋊Q8—4332no—
560C4⋊Q8—4316no—
561C4⋊Q8—4316no—
562C4⋊Q8—4316no—
563C4⋊Q8—438no—
564C4⋊Q8—438no—
565C4⋊Q8—4316no—
566C4⋊Q8—4316no—
567#126—4332no—
568#126—4332no—
569#126—4316no—
570#126C22×D43116yes—
571#125—4316no—
572#125—4332no—
573#125—4332no—
574#125—438no—
575#125—4316no—
576#125C22×D4318yes—
577#124—4332no—
578#124—4332no—
579#124—438no—
580#124C22×D4318yes—
581#123—4332no—
582#123—4316no—
583#123—4332no—
584#123—4332no—
585#123—4332no—
586#123C22×D43116yes—
587C22⋊Q8—4316no—
588C22⋊Q8—438no—
589C22⋊Q8—4316no—
590C22⋊Q8—4332no—
591C22⋊Q8—4332no—
592C22⋊Q8—4332no—
593C22⋊Q8—4332no—
594C22⋊Q8—4332no—
595C22⋊Q8—4332no—
596C22⋊Q8C22×D4318yes—
597#121—4316no—
598#121—438no—
599#121—4316no—
600#121C22×D4318yes—
601C4×Q8—4316no—
602C4×Q8—438no—
603C4×Q8—4316no—
604C4×Q8C22×D4318yes—
605C4×D4—4316no—
606C4×D4—4316no—
607C4×D4—438no—
608C4×D4—4316no—
609C4×D4C22×D43116yes—
610C4×D4C22×D4318yes—
611#117—4316no—
612#117—4316no—
613#117—4332no—
614#117—4316no—
615#117C22×D43116yes—
616C2×C4⋊C4—432no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—432no—
620C2×C4⋊C4—432no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—434no—
625C2×C4⋊C4—4316no—
626C2×C4⋊C4—4316no—
627C2×C4⋊C4—4316no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—434no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—432no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—434no—
636C2×C4⋊C4—434no—
637C2×C4⋊C4—4316no—
638C2×C4⋊C4C22×D4311yescharacteristic
639C2×C4⋊C4C22×D4311yescharacteristic
640C2×C4⋊C4C22×D4312yes—
641C2×C4⋊C4C22×D4312yes—
642C2×C4⋊C4C22×D4312yes—
643C2×C4⋊C4C22×D4312yes—
644C2×C22⋊C4—432no—
645C2×C22⋊C4—434no—
646C2×C22⋊C4—434no—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—434no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—434no—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—432no—
653C2×C22⋊C4C22×D4312yes—
654C2×C22⋊C4C22×D4312yes—
655C2×C22⋊C4C22×D4312yes—
656C2×C22⋊C4C22×D4312yes—
657C2×C22⋊C4C22×D4312yes—
658C2×C42—434no—
659C2×C42—432no—
660C2×C42—434no—
661C2×C42C22×D4311yescharacteristic
662C2×C42C22×D4311yescharacteristic
663C2×C42C22×D4312yes—
664C2×C42C22×D4311yescharacteristic
665C2×C42C22×D4311yescharacteristic
666C2×C42C22×D4318yes—
667C24—432no—
668C24C23×D4312yes—
669C24C23×D4311yescharacteristic
670#41—17264no—
671C2×Q8—24no—
672C2×Q8—434no—
673C2×Q8—438no—
674C2×Q8—4316no—
675C2×Q8—4316no—
676C2×Q8—438no—
677C2×Q8—864no—
678C2×Q8—1724no—
679C2×Q8—1728no—
680C2×Q8—1724no—
681C2×Q8—17232no—
682C2×Q8—1728no—
683C2×Q8C23×D4314yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—438no—
687C2×D4—4316no—
688C2×D4—434no—
689C2×D4—868no—
690C2×D4—864no—
691C2×D4—1728no—
692C2×D4C23×D4314yes—
693C2×D4C23×D4318yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—4316no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—434no—
702C22×C4—432no—
703C22×C4—434no—
704C22×C4—4316no—
705C22×C4—438no—
706C22×C4—4316no—
707C22×C4—8616no—
708C22×C4—868no—
709C22×C4—1728no—
710C22×C4—1728no—
711C22×C4C23×D4314yes—
712C22×C4C23×D4314yes—
713C22×C4C23×D4314yes—
714C22×C4C23×D4318yes—
715C22×C4C23×D4312yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718C22×C4C23×D4311yescharacteristic
719C22×C4C23×D4311yescharacteristic
720C22×C4C23×D4311yescharacteristic
721C22×C4C23×D4312yes—
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C4⋊C4—438no—
725C4⋊C4—438no—
726C4⋊C4—434no—
727C4⋊C4—438no—
728C4⋊C4—438no—
729C4⋊C4—4316no—
730C4⋊C4—4316no—
731C4⋊C4—4316no—
732C4⋊C4—4316no—
733C4⋊C4—434no—
734C4⋊C4—4316no—
735C4⋊C4—4316no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—438no—
739C4⋊C4—438no—
740C4⋊C4—4316no—
741C4⋊C4—4316no—
742C4⋊C4C23×D4314yes—
743C4⋊C4C23×D4314yes—
744C4⋊C4C23×D4318yes—
745C4⋊C4C23×D4318yes—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D4318yes—
748C22⋊C4—438no—
749C22⋊C4—4316no—
750C22⋊C4—4316no—
751C22⋊C4—438no—
752C22⋊C4—4316no—
753C22⋊C4—438no—
754C22⋊C4—4316no—
755C22⋊C4—438no—
756C22⋊C4—438no—
757C22⋊C4C23×D4318yes—
758C22⋊C4C23×D4318yes—
759C22⋊C4C23×D4318yes—
760C22⋊C4C23×D4318yes—
761C22⋊C4C23×D4318yes—
762C42—4316no—
763C42—438no—
764C42—4316no—
765C42C23×D4314yes—
766C42C23×D4314yes—
767C42C23×D4314yes—
768C42C23×D4314yes—
769C42C23×D4318yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—434no—
776C23—864no—
777C23—864no—
778C23—864no—
779C23#1306337114yes—
780C23C24×D4314yes—
781C23C24×D4312yes—
782C23C24×D4311yescharacteristic
783Q8—28no—
784Q8—868no—
785Q8—1728no—
786Q8—17216no—
787Q8—1728no—
788Q8—17216no—
789D4—216no—
790D4—28no—
791D4—8616no—
792D4—868no—
793D4—17216no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—434no—
806C2×C4—434no—
807C2×C4—438no—
808C2×C4—434no—
809C2×C4—438no—
810C2×C4—868no—
811C2×C4—868no—
812C2×C4—8632no—
813C2×C4—864no—
814C2×C4—864no—
815C2×C4—864no—
816C2×C4—8616no—
817C2×C4—17216no—
818C2×C4—17216no—
819C2×C4#1306337214yes—
820C2×C4#1306337214yes—
821C2×C4C24×D4314yes—
822C2×C4C24×D4314yes—
823C2×C4C24×D4312yes—
824C2×C4C24×D4312yes—
825C2×C4C24×D4312yes—
826C2×C4C24×D4312yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—864no—
838C22—864no—
839C22—864no—
840C22—1728no—
841C22C2×#1306337114yes—
842C22C2×#1306337112yes—
843C22C2×#1306337212yes—
844C22C2×#1306337212yes—
845C22C25×D4311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—868no—
854C4—868no—
855C4—864no—
856C4—864no—
857C4—864no—
858C4C2×#1306337214yes—
859C4C2×#1306337214yes—
860C2—24no—
861C2—44no—
862C2—1724no—
863C2#1914893514yesdirect product factor
864C2C22×#1306337111yescharacteristic
865C2C22×#1306337211yescharacteristic
866C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#529C2
socleC23×C43C25
hypercenterC2×#529D43
hypocenterC43C2×#3544
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #19148935C2direct (N × H)
2. C2×#14583651C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583614C2semidirect
5. C2×#14583609C2semidirect
6. C2×#14583606C2semidirect
7. C2×#14583591C2semidirect
8. C2×#14583589C2semidirect
9. C2×#14583553C2semidirect
10. C2×#14583549C2semidirect
11. C2×#14583529C2semidirect
12. C2×#14583527C2semidirect
13. C2×#14583520C2semidirect
14. C2×#14583518C2semidirect
15. C2×#14583471C2semidirect
16. C22×#13063325C2semidirect
17. C2×#14583433C2semidirect
18. C2×C43×#529C2semidirect
21. #14583651C22semidirect
22. Q8×Dic86C22semidirect
23. #14583614C22semidirect
24. #14583609C22semidirect
25. #14583606C22semidirect
26. #14583591C22semidirect
27. #14583589C22semidirect
28. #14583553C22semidirect
29. #14583549C22semidirect
30. #14583529C22semidirect
31. #14583527C22semidirect
32. #14583520C22semidirect
33. #14583518C22semidirect
34. #14583471C22semidirect
41. C2×#13063325C22semidirect
45. #14583433C22semidirect
89. C43×#529C22semidirect
444. C2×#529D43semidirect
447. C2×C43#3544semidirect
479. #529C2×D43semidirect
534. C43C2×#3544semidirect
863. C2#19148935direct (N × H)

Maximal subgroups

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

subgroupindex
#191489352
C2×#145836512
C2×Q8×Dic862
C2×#145836142
C2×#145836092
C2×#145836062
C2×#145835912
C2×#145835892
C2×#145835532
C2×#145835492
C2×#145835292
C2×#145835272
C2×#145835202
C2×#145835182
C2×#145834712
C22×#130633252
C2×#145834332
C2×C43×#5292
C2×#354443