Finite Group Databasebeta

← C2×#19149133 #26003959

Subgroups — C2×#19149133 #26003959

Order 11008.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149133C2132yesmaximal, direct product factor
2C2×#14583649C212yesmaximal, complemented
3C2×#14583643C212yesmaximal, complemented
4C2×#14583608C212yesmaximal, complemented
5C2×#14583601C212yesmaximal, complemented
6C2×#14583599C212yesmaximal, complemented
7C2×#14583549C212yesmaximal, complemented
8C2×#14583548C214yesmaximal, complemented
9C2×#14583526C212yesmaximal, complemented
10C2×#14583503C212yesmaximal, complemented
11C2×#14583494C212yesmaximal, complemented
12C2×#14583491C214yesmaximal, complemented
13C2×#14583476C212yesmaximal, complemented
14C2×#14583433C211yesmaximal, characteristic, complemented
15C22×#13063317C211yesmaximal, characteristic, complemented
16C2×C43×#532C211yesmaximal, characteristic, complemented
17C22×#10621900C2214yes—
18#14583649C22132yescomplemented
19#14583643C22132yescomplemented
20#14583608C22132yescomplemented
21#14583601C22132yescomplemented
22#14583599C22132yescomplemented
23#14583549C22132yescomplemented
24#14583548C22164yescomplemented
25#14583526C22132yescomplemented
26#14583503C22132yescomplemented
27#14583494C22132yescomplemented
28#14583491C22164yescomplemented
29#14583476C22132yescomplemented
30C2×#13063324C2212yes—
31C2×#13063323C2214yes—
32#14583433C22116yescomplemented
33C2×#13063319C2212yes—
34C2×#13063318C2214yes—
35C2×#13063318C2214yes—
36C2×#13063317C2212yes—
37C2×#13063317C2212yes—
38C2×#13063317C2212yes—
39C2×#13063317C2212yes—
40C2×#13063317C2211yescharacteristic
41C2×#13063317C22116yescomplemented
42C2×#13063316C2212yes—
43C2×#13063315C2214yes—
44C2×#13063313C2211yescharacteristic
45C2×#13063309C2214yes—
46C2×#13063308C2212yes—
47C2×#13063308C2214yes—
48C2×#13063307C2214yes—
49C2×#13063306C2214yes—
50C2×#13063306C2214yes—
51C2×#13063306C2214yes—
52C2×#13063304C2214yes—
53C2×#13063304C2211yescharacteristic
54C2×#13063303C2214yes—
55C2×#13063302C2214yes—
56C2×#13063302C2214yes—
57C2×#13063302C2214yes—
58C2×#13063301C2214yes—
59C2×#13063299C2211yescharacteristic
60C2×#13063298C2214yes—
61C2×#13063297C2214yes—
62C2×#13063297C2214yes—
63C2×#13063297C2214yes—
64C2×#13063296C2212yes—
65C2×#13063296C2212yes—
66C2×C4×Dic86C2211yescharacteristic
67C2×C4×D172C2211yescharacteristic
68C2×D4×Dic43C2214yes—
69C2×D4×Dic43C2212yes—
70C2×D4×Dic43C2212yes—
71C2×C4×C22⋊D43C2214yes—
72C2×C4×C22⋊D43C2212yes—
73C2×#13063283C2212yes—
74C2×#13063282C2212yes—
75C22×C4⋊Dic43C2211yescharacteristic
76C22×C4⋊Dic43C2211yescharacteristic
77C22×Dic43⋊C4C2212yes—
78C22×Dic43⋊C4C2214yes—
79C22×Dic43⋊C4C2212yes—
80C2×C4⋊C4×D43C2212yes—
81C22×#41×C43C2212yes—
82C43×#532C22116yescomplemented
83C2×C4⋊Q8×C43C2211yescharacteristic
84C2×#127×C43C2211yescharacteristic
85C2×#124×C43C2212yes—
86C2×#121×C43C2212yes—
87C2×#121×C43C2212yes—
88C2×C4×D4×C43C2212yes—
89C2×C4×D4×C43C2212yes—
90C22×C42×C43C2211yescharacteristic
91C2×#10621900—416no—
92C2×#10621900C23132yes—
93C22×Dic86C2311yescharacteristic
94C22×Dic86C2314yes—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43C2312yes—
97C22×C22⋊D43C2314yes—
98C22×C22⋊D43C2314yes—
99C23×Dic43C2312yes—
100C23×Dic43C2312yes—
101C23×Dic43C2314yes—
102C23×Dic43C2314yes—
103C22×C4×D43C2312yes—
104C22×C4×D43C2314yes—
105#13063324C23116yes—
106#13063323C23132yes—
107#13063319C23116yes—
108#13063318C23132yes—
109#13063318C23132yes—
110#13063317C23116yes—
111#13063317C23116yes—
112#13063317C2318yes—
113#13063317C23116yes—
114#13063317C23116yes—
115#13063316C23116yes—
116#13063315C23132yes—
117#13063313C2318yes—
118#13063309C23132yes—
119#13063308C23132yes—
120#13063308C23116yes—
121#13063307C23132yes—
122#13063306C23132yes—
123#13063306C23132yes—
124#13063306C23132yes—
125#13063304C23132yes—
126#13063304C2318yes—
127#13063303C23132yes—
128#13063302C23132yes—
129#13063302C23132yes—
130#13063302C23132yes—
131#13063301C23132yes—
132#13063299C2318yes—
133#13063298C23132yes—
134#13063297C23132yes—
135#13063297C23132yes—
136#13063297C23132yes—
137#13063296C23116yes—
138#13063296C23116yes—
139C4×Dic86C2318yes—
140C4×D172C2318yes—
141D4×Dic43C23116yes—
142D4×Dic43C23132yes—
143D4×Dic43C23116yes—
144C4×C22⋊D43C23132yes—
145C4×C22⋊D43C23116yes—
146#13063283C23116yes—
147#13063282C23116yes—
148C2×C4⋊Dic43C2318yes—
149C2×C4⋊Dic43C2312yes—
150C2×C4⋊Dic43C2312yes—
151C2×C4⋊Dic43C2312yes—
152C2×C4⋊Dic43C2312yes—
153C2×C4⋊Dic43C2318yes—
154C2×C4⋊Dic43C2314yes—
155C2×C4⋊Dic43C2311yescharacteristic
156C2×C4⋊Dic43C2311yescharacteristic
157C2×Dic43⋊C4C2314yes—
158C2×Dic43⋊C4C2314yes—
159C2×Dic43⋊C4C2312yes—
160C2×Dic43⋊C4C23132yes—
161C2×Dic43⋊C4C2314yes—
162C2×Dic43⋊C4C2314yes—
163C2×Dic43⋊C4C2314yes—
164C2×Dic43⋊C4C2314yes—
165C2×Dic43⋊C4C2314yes—
166C2×Dic43⋊C4C23116yes—
167C2×Dic43⋊C4C23116yes—
168C2×Dic43⋊C4C2312yes—
169C2×Dic43⋊C4C2312yes—
170C2×Dic43⋊C4C2312yes—
171C4⋊C4×D43C23116yes—
172C2×C22⋊Dic43C2312yes—
173C2×C22⋊Dic43C2314yes—
174C2×C22⋊Dic43C2314yes—
175C2×C22⋊Dic43C2314yes—
176C2×C22⋊Dic43C2314yes—
177C2×(C2×D43)⋊C4C2312yes—
178C2×(C2×D43)⋊C4C2312yes—
179C2×(C2×D43)⋊C4C2314yes—
180C2×(C2×D43)⋊C4C2312yes—
181C2×(C2×D43)⋊C4C2312yes—
182C2×C4×Dic43C2312yes—
183C2×C4×Dic43C2314yes—
184C2×#41×C43—48no—
185C2×#41×C43C23116yes—
186C22×Q8×C43C2312yes—
187C22×D4×C43C2312yes—
188C22×D4×C43C2314yes—
189C22×D4×C43C2312yes—
190C22×D4×C43C2312yes—
191C23×C4×C43C2311yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C23×C4×C43C2311yescharacteristic
194C23×C4×C43C2314yes—
195C4⋊Q8×C43C2318yes—
196#127×C43C2318yes—
197#124×C43C23116yes—
198#121×C43C23116yes—
199#121×C43C23116yes—
200C4×D4×C43C23116yes—
201C4×D4×C43C23116yes—
202C2×C4⋊C4×C43C2312yes—
203C2×C4⋊C4×C43C2312yes—
204C2×C22⋊C4×C43C2314yes—
205C2×C22⋊C4×C43C2314yes—
206C2×C42×C43C2311yescharacteristic
207C2×C42×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209C2×C42×C43C2311yescharacteristic
210C2×C42×C43C2318yes—
211C24×C43C2414yes—
212C24×C43C2411yescharacteristic
213C23×D43C2412yes—
214#41×C43—432no—
215C2×Q8×C43—44no—
216C2×Q8×C43C2418yes—
217C2×D4×C43—28no—
218C2×D4×C43—216no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43C2418yes—
222C2×D4×C43C24116yes—
223C2×D4×C43C2418yes—
224C2×D4×C43C2418yes—
225C22×C4×C43—24no—
226C22×C4×C43—24no—
227C22×C4×C43—42no—
228C22×C4×C43—48no—
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C22×C4×C43C2414yes—
233C22×C4×C43C2411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C22×C4×C43C2414yes—
236C22×C4×C43C2414yes—
237C22×C4×C43C2414yes—
238C22×C4×C43C24116yes—
239C22×C4×C43C2411yescharacteristic
240C2×C22⋊D43—28no—
241C2×C22⋊D43—48no—
242C2×C22⋊D43—48no—
243C2×C22⋊D43C2418yes—
244C2×C22⋊D43C24116yes—
245C2×C22⋊D43C24116yes—
246C22×Dic43—28no—
247C22×Dic43—44no—
248C22×Dic43—48no—
249C22×Dic43—48no—
250C22×Dic43C2412yes—
251C22×Dic43C2412yes—
252C22×Dic43C2414yes—
253C22×Dic43C2412yes—
254C22×Dic43C2414yes—
255C22×Dic43C2418yes—
256C22×Dic43C2418yes—
257C22×Dic43C24116yes—
258C22×Dic43C24116yes—
259#10621900—464no—
260C2×D172—42no—
261C2×D172C2414yes—
262C2×C4×D43—28no—
263C2×C4×D43—48no—
264C2×C4×D43C2418yes—
265C2×C4×D43C24116yes—
266C2×Dic86—42no—
267C2×Dic86—48no—
268C2×Dic86C2414yes—
269C2×Dic86C24116yes—
270C4⋊C4×C43C2418yes—
271C4⋊C4×C43C2418yes—
272C22⋊C4×C43C24116yes—
273C22⋊C4×C43C24116yes—
274C42×C43C2414yes—
275C42×C43C2414yes—
276C42×C43C2414yes—
277C42×C43C2414yes—
278C22⋊Dic43C2418yes—
279C22⋊Dic43C24116yes—
280C22⋊Dic43C24116yes—
281C22⋊Dic43C24116yes—
282C22⋊Dic43C24116yes—
283(C2×D43)⋊C4C2418yes—
284(C2×D43)⋊C4C2418yes—
285(C2×D43)⋊C4C24116yes—
286(C2×D43)⋊C4C2418yes—
287(C2×D43)⋊C4C2418yes—
288C4⋊Dic43C2418yes—
289C4⋊Dic43C2418yes—
290C4⋊Dic43C2418yes—
291C4⋊Dic43C2418yes—
292C4⋊Dic43C24116yes—
293C4⋊Dic43C2414yes—
294C4⋊Dic43C2414yes—
295Dic43⋊C4C24116yes—
296Dic43⋊C4C24116yes—
297Dic43⋊C4C2418yes—
298Dic43⋊C4C24116yes—
299Dic43⋊C4C24116yes—
300Dic43⋊C4C24116yes—
301Dic43⋊C4C24116yes—
302Dic43⋊C4C24116yes—
303Dic43⋊C4C2418yes—
304Dic43⋊C4C2418yes—
305Dic43⋊C4C2418yes—
306C4×Dic43C2418yes—
307C4×Dic43C24116yes—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—28no—
311C23×C43—28no—
312C23×C43—28no—
313C23×C43H(5,𝔽2)14yes—
314C23×C43C2518yes—
315C23×C43C2512yes—
316C23×C43C2511yescharacteristic
317C22×D43—24no—
318C22×D43—24no—
319C22×D43—24no—
320C22×D43C2514yes—
321Q8×C43—48no—
322D4×C43—232no—
323D4×C43—216no—
324D4×C43—48no—
325D4×C43—48no—
326C2×C4×C43—28no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—28no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—28no—
334C2×C4×C43—44no—
335C2×C4×C43—416no—
336C2×C4×C432−1+414yes—
337C2×C4×C43C2518yes—
338C2×C4×C43C2512yes—
339C2×C4×C43C2512yes—
340C2×C4×C43C2512yes—
341C2×C4×C43C2512yes—
342C2×C4×C43C2512yes—
343C2×C4×C43C2512yes—
344C22⋊D43—216no—
345C22⋊D43—416no—
346C22⋊D43—416no—
347C2×Dic43—24no—
348C2×Dic43—28no—
349C2×Dic43—216no—
350C2×Dic43—24no—
351C2×Dic43—24no—
352C2×Dic43—28no—
353C2×Dic43—416no—
354C2×Dic43—416no—
355C2×Dic43—48no—
356C2×Dic43C2514yes—
357C2×Dic43C2518yes—
358C2×Dic43C2514yes—
359C2×Dic43C2514yes—
360C2×Dic43C2518yes—
361D172—44no—
362C4×D43—216no—
363C4×D43—416no—
364Dic86—44no—
365Dic86—416no—
366C2×#3559—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—28no—
370C22×C43—28no—
371C22×C43—28no—
372C22×C43—28no—
373C22×C43—416no—
374C22×C43C2×H(5,𝔽2)14yes—
375C22×C43C2×H(5,𝔽2)12yes—
376C22×C43C2×2−1+412yes—
377C22×C43#58512yes—
378C22×C43C2611yescharacteristic
379C2×D43—24no—
380C2×D43—24no—
381C2×D43—24no—
382C2×D43—48no—
383C4×C43—28no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43C2×2−1+414yes—
390Dic43—24no—
391Dic43—28no—
392Dic43—24no—
393Dic43—24no—
394Dic43—28no—
395#3559—4332no—
396C2×#563—432no—
397C2×#562—432no—
398C2×#554—432no—
399C2×#553—432no—
400C2×#553—432no—
401C2×#547—434no—
402C2×#547—432no—
403C2×#544—432no—
404C2×#540—432no—
405C2×#539—432no—
406C2×#539—434no—
407C2×#537—432no—
408C2×#532D4311yescharacteristic, complemented
409C2×#529—431no—
410C22×#125—431no—
411C2×C43—24no—
412C2×C43—48no—
413C2×C43#355914yescomplemented
414C2×C43C22×H(5,𝔽2)11yescharacteristic
415C2×C43C22×2−1+411yescharacteristic
416C2×C43C2×#58511yescharacteristic
417D43—44no—
418C22×#41—434no—
419C22×#41C2×D4312yes—
420#563—4332no—
421#562—4332no—
422#554—4332no—
423#553—4332no—
424#553—4332no—
425#547—4364no—
426#547—4332no—
427#544—4332no—
428#540—4332no—
429#539—4332no—
430#539—4364no—
431#537—4332no—
432#532C2×D43116yescomplemented
433C2×C4⋊Q8—434no—
434C2×C4⋊Q8—432no—
435C2×C4⋊Q8C2×D4311yescharacteristic
436C2×#127C2×D4311yescharacteristic
437#529—4316no—
438C2×#126—434no—
439C2×#126—434no—
440C2×#126—432no—
441C2×#125—434no—
442C2×#125—432no—
443C2×#125—432no—
444C2×#125—432no—
445C2×#125—432no—
446C2×#125—432no—
447C2×#125—4316no—
448C2×#125—431no—
449C2×#124—431no—
450C2×#124C2×D4312yes—
451C2×#123—434no—
452C2×#123—434no—
453C2×#123—434no—
454C2×#123—432no—
455C2×#123—434no—
456C2×#123—434no—
457C2×#123—434no—
458C2×C22⋊Q8—434no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8—434no—
461C2×C22⋊Q8—434no—
462C2×C22⋊Q8—434no—
463C2×C22⋊Q8—434no—
464C2×C22⋊Q8—434no—
465C2×#121—432no—
466C2×#121—432no—
467C2×#121—434no—
468C2×#121—434no—
469C2×#121—434no—
470C2×#121—431no—
471C2×#121—434no—
472C2×#121C2×D4312yes—
473C2×#121C2×D4312yes—
474C2×C4×Q8—431no—
475C2×C4×D4—434no—
476C2×C4×D4—432no—
477C2×C4×D4—432no—
478C2×C4×D4—432no—
479C2×C4×D4—434no—
480C2×C4×D4—431no—
481C2×C4×D4C2×D4312yes—
482C2×C4×D4C2×D4312yes—
483C2×#117—432no—
484C2×#117—432no—
485C22×C4⋊C4—432no—
486C22×C4⋊C4—432no—
487C22×C4⋊C4—434no—
488C22×C4⋊C4—431no—
489C22×C4⋊C4—431no—
490C22×C4⋊C4—432no—
491C22×C42C2×D4311yescharacteristic
492C43C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—48no—
494C2×#41—4332no—
495C2×#41—17216no—
496C2×#41C22×D43116yes—
497C22×Q8—431no—
498C22×Q8—434no—
499C22×Q8C22×D4312yes—
500C22×D4—432no—
501C22×D4—434no—
502C22×D4—434no—
503C22×D4—431no—
504C22×D4C22×D4312yes—
505C22×D4C22×D4314yes—
506C22×D4C22×D4312yes—
507C22×D4C22×D4312yes—
508C23×C4—432no—
509C23×C4—432no—
510C23×C4—434no—
511C23×C4—434no—
512C23×C4—432no—
513C23×C4—434no—
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4314yes—
518C4⋊Q8—4332no—
519C4⋊Q8—4316no—
520C4⋊Q8C22×D4318yes—
521#127C22×D4318yes—
522#126—4332no—
523#126—4332no—
524#126—4316no—
525#125—4332no—
526#125—4316no—
527#125—4316no—
528#125—4316no—
529#125—4316no—
530#125—4316no—
531#125—438no—
532#124—438no—
533#124C22×D43116yes—
534#123—4332no—
535#123—4332no—
536#123—4332no—
537#123—4316no—
538#123—4332no—
539#123—4332no—
540#123—4332no—
541C22⋊Q8—4332no—
542C22⋊Q8—438no—
543C22⋊Q8—4332no—
544C22⋊Q8—4332no—
545C22⋊Q8—4332no—
546C22⋊Q8—4332no—
547C22⋊Q8—4332no—
548#121—4332no—
549#121—4332no—
550#121—4316no—
551#121—4332no—
552#121—4316no—
553#121—438no—
554#121—4332no—
555#121C22×D43116yes—
556#121C22×D43116yes—
557C4×Q8—438no—
558C4×D4—4332no—
559C4×D4—4316no—
560C4×D4—4316no—
561C4×D4—4316no—
562C4×D4—4332no—
563C4×D4—438no—
564C4×D4C22×D43116yes—
565C4×D4C22×D43116yes—
566#117—4316no—
567#117—4316no—
568C2×C4⋊C4—432no—
569C2×C4⋊C4—434no—
570C2×C4⋊C4—432no—
571C2×C4⋊C4—432no—
572C2×C4⋊C4—434no—
573C2×C4⋊C4—434no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—434no—
576C2×C4⋊C4—432no—
577C2×C4⋊C4—434no—
578C2×C4⋊C4—434no—
579C2×C4⋊C4—432no—
580C2×C4⋊C4—4316no—
581C2×C4⋊C4—4316no—
582C2×C4⋊C4—438no—
583C2×C4⋊C4—438no—
584C2×C4⋊C4—4332no—
585C2×C4⋊C4—432no—
586C2×C4⋊C4—432no—
587C2×C4⋊C4—434no—
588C2×C4⋊C4—432no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—4316no—
592C2×C4⋊C4C22×D4312yes—
593C2×C4⋊C4C22×D4312yes—
594C2×C22⋊C4—432no—
595C2×C22⋊C4—434no—
596C2×C22⋊C4—434no—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—434no—
599C2×C22⋊C4—432no—
600C2×C22⋊C4—434no—
601C2×C22⋊C4—432no—
602C2×C22⋊C4—432no—
603C2×C22⋊C4—432no—
604C2×C22⋊C4C22×D4314yes—
605C2×C22⋊C4C22×D4314yes—
606C2×C42—432no—
607C2×C42—434no—
608C2×C42C22×D4311yescharacteristic
609C2×C42C22×D4311yescharacteristic
610C2×C42C22×D4311yescharacteristic
611C2×C42C22×D4311yescharacteristic
612C2×C42C22×D4318yes—
613C24—432no—
614C24C23×D4314yes—
615C24C23×D4311yescharacteristic
616#41—432no—
617#41—17264no—
618C2×Q8—44no—
619C2×Q8—434no—
620C2×Q8—4316no—
621C2×Q8—1728no—
622C2×Q8—1722no—
623C2×Q8C23×D4318yes—
624C2×D4—216no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—438no—
629C2×D4—4316no—
630C2×D4—4316no—
631C2×D4—434no—
632C2×D4—868no—
633C2×D4—1722no—
634C2×D4—1728no—
635C2×D4—1728no—
636C2×D4C23×D4318yes—
637C2×D4C23×D43116yes—
638C2×D4C23×D4318yes—
639C2×D4C23×D4318yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—48no—
643C22×C4—42no—
644C22×C4—438no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—434no—
648C22×C4—432no—
649C22×C4—434no—
650C22×C4—438no—
651C22×C4—4316no—
652C22×C4—4316no—
653C22×C4—438no—
654C22×C4—4316no—
655C22×C4—868no—
656C22×C4—868no—
657C22×C4—1728no—
658C22×C4—1728no—
659C22×C4—1724no—
660C22×C4—1728no—
661C22×C4C23×D4314yes—
662C22×C4C23×D4314yes—
663C22×C4C23×D4314yes—
664C22×C4C23×D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666C22×C4C23×D4311yescharacteristic
667C22×C4C23×D4311yescharacteristic
668C22×C4C23×D4311yescharacteristic
669C22×C4C23×D4314yes—
670C22×C4C23×D43116yes—
671C22×C4C23×D4311yescharacteristic
672C4⋊C4—438no—
673C4⋊C4—4316no—
674C4⋊C4—438no—
675C4⋊C4—438no—
676C4⋊C4—4316no—
677C4⋊C4—4316no—
678C4⋊C4—4316no—
679C4⋊C4—4316no—
680C4⋊C4—438no—
681C4⋊C4—4316no—
682C4⋊C4—4316no—
683C4⋊C4—438no—
684C4⋊C4—438no—
685C4⋊C4—438no—
686C4⋊C4—4316no—
687C4⋊C4—438no—
688C4⋊C4—434no—
689C4⋊C4—434no—
690C4⋊C4C23×D4318yes—
691C4⋊C4C23×D4318yes—
692C22⋊C4—438no—
693C22⋊C4—4316no—
694C22⋊C4—4316no—
695C22⋊C4—4316no—
696C22⋊C4—4316no—
697C22⋊C4—438no—
698C22⋊C4—4316no—
699C22⋊C4—438no—
700C22⋊C4—438no—
701C22⋊C4—438no—
702C22⋊C4C23×D43116yes—
703C22⋊C4C23×D43116yes—
704C42—438no—
705C42—4316no—
706C42C23×D4314yes—
707C42C23×D4314yes—
708C42C23×D4314yes—
709C42C23×D4314yes—
710C23—22no—
711C23—22no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—434no—
716C23—864no—
717C23—864no—
718C23—864no—
719C23#1306337014yes—
720C23C24×D4318yes—
721C23C24×D4312yes—
722C23C24×D4311yescharacteristic
723Q8—48no—
724Q8—17216no—
725Q8—1724no—
726D4—232no—
727D4—216no—
728D4—48no—
729D4—48no—
730D4—8616no—
731D4—1724no—
732D4—17216no—
733D4—17216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—416no—
743C2×C4—44no—
744C2×C4—434no—
745C2×C4—434no—
746C2×C4—438no—
747C2×C4—434no—
748C2×C4—438no—
749C2×C4—868no—
750C2×C4—8616no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—868no—
754C2×C4—864no—
755C2×C4—8616no—
756C2×C4—17216no—
757C2×C4—17216no—
758C2×C4—1728no—
759C2×C4—17216no—
760C2×C4#1306337214yes—
761C2×C4C24×D4318yes—
762C2×C4C24×D4312yes—
763C2×C4C24×D4312yes—
764C2×C4C24×D4312yes—
765C2×C4C24×D4312yes—
766C2×C4C24×D4312yes—
767C2×C4C24×D4312yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—416no—
775C22—864no—
776C22—864no—
777C22—864no—
778C22—1728no—
779C22C2×#1306337014yes—
780C22C2×#1306337012yes—
781C22C2×#1306337212yes—
782C22#1458373512yes—
783C22C25×D4311yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—868no—
791C4—864no—
792C4—864no—
793C4—868no—
794C4—864no—
795C4C2×#1306337214yes—
796C2—24no—
797C2—48no—
798C2—1724no—
799C2#1914913314yesdirect product factor
800C2C22×#1306337011yescharacteristic
801C2C22×#1306337211yescharacteristic
802C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#532C2
socleC23×C43C25
hypercenterC2×#532D43
hypocenterC43C2×#3559
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #19149133C2direct (N × H)
2. C2×#14583649C2semidirect
3. C2×#14583643C2semidirect
4. C2×#14583608C2semidirect
5. C2×#14583601C2semidirect
6. C2×#14583599C2semidirect
7. C2×#14583549C2semidirect
8. C2×#14583548C2semidirect
9. C2×#14583526C2semidirect
10. C2×#14583503C2semidirect
11. C2×#14583494C2semidirect
12. C2×#14583491C2semidirect
13. C2×#14583476C2semidirect
14. C2×#14583433C2semidirect
15. C22×#13063317C2semidirect
16. C2×C43×#532C2semidirect
18. #14583649C22semidirect
19. #14583643C22semidirect
20. #14583608C22semidirect
21. #14583601C22semidirect
22. #14583599C22semidirect
23. #14583549C22semidirect
24. #14583548C22semidirect
25. #14583526C22semidirect
26. #14583503C22semidirect
27. #14583494C22semidirect
28. #14583491C22semidirect
29. #14583476C22semidirect
32. #14583433C22semidirect
41. C2×#13063317C22semidirect
82. C43×#532C22semidirect
408. C2×#532D43semidirect
413. C2×C43#3559semidirect
432. #532C2×D43semidirect
492. C43C2×#3559semidirect
799. C2#19149133direct (N × H)

Maximal subgroups

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

subgroupindex
#191491332
C2×#145836492
C2×#145836432
C2×#145836082
C2×#145836012
C2×#145835992
C2×#145835492
C2×#145835482
C2×#145835262
C2×#145835032
C2×#145834942
C2×#145834912
C2×#145834762
C2×#145834332
C22×#130633172
C2×C43×#5322
C2×#355943