Finite Group Databasebeta

← C2×#19149005 #26004404

Subgroups — C2×#19149005 #26004404

Order 11008.

7074 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149005C2132yesmaximal, direct product factor
2C2×#14583653C212yesmaximal, complemented
3C2×#14583649C211yesmaximal, characteristic, complemented
4C2×#14583633C212yesmaximal, complemented
5C2×#14583629C212yesmaximal, complemented
6C2×#14583616C214yesmaximal, complemented
7C2×#14583562C214yesmaximal, complemented
8C2×#14583519C214yesmaximal, complemented
9C2×#14583515C214yesmaximal, complemented
10C2×#14583474C212yesmaximal, complemented
11C2×#14583471C212yesmaximal, complemented
12C2×#14583455C212yesmaximal, complemented
13C2×#14583448C211yesmaximal, characteristic
14C2×C43×#563C211yesmaximal, characteristic, complemented
15C22×#10621902C2211yescharacteristic
16C22×#10621900C2211yescharacteristic
17C23×Dic86C2212yes—
18C22×Q8×D43C2212yes—
19#14583653C22132yescomplemented
20#14583649C22116yescomplemented
21#14583633C22132yescomplemented
22#14583629C22132yescomplemented
23#14583616C22164yescomplemented
24#14583562C22164yescomplemented
25#14583519C22164yescomplemented
26#14583515C22164yescomplemented
27#14583474C22132yescomplemented
28#14583471C22132yescomplemented
29#14583455C22132yescomplemented
30#14583448C22116yes—
31C2×#13063324C2212yes—
32C2×#13063324C2214yes—
33C2×#13063324C2212yes—
34C2×#13063324C2214yes—
35C2×#13063323C2214yes—
36C2×#13063323C2211yescharacteristic
37C2×#13063323C2212yes—
38C2×#13063321C2211yescharacteristic
39C2×#13063320C2214yes—
40C2×#13063320C2214yes—
41C2×#13063318C2214yes—
42C2×#13063317C2212yes—
43C2×#13063314C2212yes—
44C2×#13063313C2211yescharacteristic
45C2×#13063313C2212yes—
46C2×#13063311C2214yes—
47C2×#13063311C2214yes—
48C2×#13063311C2214yes—
49C2×#13063310C2214yes—
50C2×#13063310C2214yes—
51C2×#13063309C2212yes—
52C2×#13063308C2212yes—
53C2×#13063306C2212yes—
54C2×#13063305C2214yes—
55C2×#13063303C2214yes—
56C2×#13063303C2214yes—
57C2×#13063303C2214yes—
58C2×#13063303C2214yes—
59C2×#13063302C2214yes—
60C2×#13063302C2214yes—
61C2×#13063298C2214yes—
62C2×C4×Dic86C2214yes—
63C2×#13063290C2214yes—
64C2×#13063290C2214yes—
65C2×#13063290C2214yes—
66C2×C4×C22⋊D43C2214yes—
67C2×(C22⋊D43)⋊C4C2214yes—
68C2×(C22⋊D43)⋊C4C2214yes—
69C2×#13063283C2212yes—
70C2×#13063283C2212yes—
71C2×#13063282C2212yes—
72C2×#13063281C2212yes—
73C2×C42×D43C2211yescharacteristic
74C43×#563C22116yescomplemented
75C2×C4⋊Q8×C43C2212yes—
76C2×#126×C43C2214yes—
77C2×#125×C43C2212yes—
78C2×#124×C43C2211yescharacteristic
79C2×#123×C43C2212yes—
80C2×C22⋊Q8×C43C2214yes—
81C2×#10621902—44no—
82C2×#10621902C2318yes—
83C2×#10621900—44no—
84C2×#10621900C2318yes—
85C22×Dic86—48no—
86C22×Dic86C2314yes—
87C22×Dic86C2314yes—
88C22×Dic86C23116yes—
89C22×Dic86C2312yes—
90C22×Dic86C2314yes—
91C22×Dic86C2311yescharacteristic
92C2×Q8×D43—48no—
93C2×Q8×D43C23116yes—
94C22×D172C2312yes—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43C2314yes—
97C22×C22⋊D43C2312yes—
98C23×Dic43C2312yes—
99C23×Dic43C2312yes—
100C22×C4×D43C2312yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2312yes—
103C22×C4×D43C2314yes—
104#13063324C23116yes—
105#13063324C23132yes—
106#13063324C23116yes—
107#13063324C23132yes—
108#13063323C23132yes—
109#13063323C2318yes—
110#13063323C23116yes—
111#13063321C2318yes—
112#13063320C23132yes—
113#13063320C23132yes—
114#13063318C23132yes—
115#13063317C23116yes—
116#13063314C23116yes—
117#13063313C2318yes—
118#13063313C23116yes—
119#13063311C23132yes—
120#13063311C23132yes—
121#13063311C23132yes—
122#13063310C23132yes—
123#13063310C23132yes—
124#13063309C23116yes—
125#13063308C23116yes—
126#13063306C23116yes—
127#13063305C23132yes—
128#13063303C23132yes—
129#13063303C23132yes—
130#13063303C23132yes—
131#13063303C23132yes—
132#13063302C23132yes—
133#13063302C23132yes—
134#13063298C23132yes—
135C4×Dic86C23132yes—
136#13063290C23132yes—
137#13063290C23132yes—
138#13063290C23132yes—
139C4×C22⋊D43C23132yes—
140(C22⋊D43)⋊C4C23132yes—
141(C22⋊D43)⋊C4C23132yes—
142#13063283C23116yes—
143#13063283C23116yes—
144#13063282C23116yes—
145#13063281C23116yes—
146C2×C4⋊Dic43C2312yes—
147C2×C4⋊Dic43C2312yes—
148C2×C4⋊Dic43C2314yes—
149C2×Dic43⋊C4C2314yes—
150C2×Dic43⋊C4C2314yes—
151C2×Dic43⋊C4C2314yes—
152C2×Dic43⋊C4C2314yes—
153C2×Dic43⋊C4C2314yes—
154C2×Dic43⋊C4C2314yes—
155C2×Dic43⋊C4C2314yes—
156C2×C22⋊Dic43C2312yes—
157C2×C22⋊Dic43C2314yes—
158C2×(C2×D43)⋊C4C2314yes—
159C2×(C2×D43)⋊C4C2314yes—
160C2×(C2×D43)⋊C4C2314yes—
161C2×(C2×D43)⋊C4C2314yes—
162C2×(C2×D43)⋊C4C2314yes—
163C2×(C2×D43)⋊C4C2314yes—
164C2×C4×Dic43C2312yes—
165C2×C4×Dic43C2311yescharacteristic
166C2×C4×Dic43C2314yes—
167C2×C4×Dic43C2312yes—
168C2×C4×Dic43C2314yes—
169C2×C4×Dic43C2314yes—
170C42×D43C2318yes—
171C22×Q8×C43C2312yes—
172C22×Q8×C43C2311yescharacteristic
173C22×D4×C43C2311yescharacteristic
174C23×C4×C43C2312yes—
175C4⋊Q8×C43C23116yes—
176#126×C43C23132yes—
177#125×C43C23116yes—
178#124×C43C2318yes—
179#123×C43C23116yes—
180C22⋊Q8×C43C23132yes—
181C2×C4⋊C4×C43C2312yes—
182C2×C4⋊C4×C43C2314yes—
183C2×C4⋊C4×C43C2314yes—
184C2×C4⋊C4×C43C2314yes—
185C2×C4⋊C4×C43C2312yes—
186C2×C22⋊C4×C43C2314yes—
187C2×C22⋊C4×C43C2314yes—
188C2×C22⋊C4×C43C2312yes—
189C2×C42×C43C2311yescharacteristic
190C2×C42×C43C2312yes—
191C24×C43C2412yes—
192C23×D43C2412yes—
193C23×D43C2411yescharacteristic
194C2×Q8×C43—44no—
195C2×Q8×C43—42no—
196C2×Q8×C43C2418yes—
197C2×Q8×C43C2414yes—
198C2×D4×C43—42no—
199C2×D4×C43C2414yes—
200C22×C4×C43—44no—
201C22×C4×C43C2414yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C22×C4×C43C2414yes—
206C22×C4×C43C2418yes—
207C2×C22⋊D43—216no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43C24116yes—
210C2×C22⋊D43C2418yes—
211C22×Dic43—28no—
212C22×Dic43—44no—
213C22×Dic43C2414yes—
214C22×Dic43C2412yes—
215C22×Dic43C2414yes—
216C22×Dic43C2418yes—
217C22×Dic43C2418yes—
218C22×Dic43C2411yescharacteristic
219C22×Dic43C2412yes—
220#10621902—416no—
221Q8×D43—432no—
222#10621900—416no—
223C2×D172—42no—
224C2×D172—44no—
225C2×D172C2418yes—
226C2×D172C2414yes—
227C2×C4×D43—28no—
228C2×C4×D43—24no—
229C2×C4×D43—28no—
230C2×C4×D43—48no—
231C2×C4×D43C2418yes—
232C2×C4×D43C2414yes—
233C2×C4×D43C2418yes—
234C2×C4×D43C24116yes—
235C2×Dic86—216no—
236C2×Dic86—216no—
237C2×Dic86—432no—
238C2×Dic86—44no—
239C2×Dic86—48no—
240C2×Dic86—42no—
241C2×Dic86C24116yes—
242C2×Dic86C24116yes—
243C2×Dic86C2418yes—
244C2×Dic86C24116yes—
245C2×Dic86C2414yes—
246C4⋊C4×C43C2418yes—
247C4⋊C4×C43C24116yes—
248C4⋊C4×C43C24116yes—
249C4⋊C4×C43C24116yes—
250C4⋊C4×C43C2418yes—
251C22⋊C4×C43C24116yes—
252C22⋊C4×C43C24116yes—
253C22⋊C4×C43C2418yes—
254C42×C43C2414yes—
255C42×C43C2418yes—
256C22⋊Dic43C2418yes—
257C22⋊Dic43C24116yes—
258(C2×D43)⋊C4C24116yes—
259(C2×D43)⋊C4C24116yes—
260(C2×D43)⋊C4C24116yes—
261(C2×D43)⋊C4C24116yes—
262(C2×D43)⋊C4C24116yes—
263(C2×D43)⋊C4C24116yes—
264C4⋊Dic43C2418yes—
265C4⋊Dic43C2418yes—
266C4⋊Dic43C24116yes—
267Dic43⋊C4C24116yes—
268Dic43⋊C4C24116yes—
269Dic43⋊C4C24116yes—
270Dic43⋊C4C24116yes—
271Dic43⋊C4C24116yes—
272Dic43⋊C4C24116yes—
273Dic43⋊C4C24116yes—
274C4×Dic43C2418yes—
275C4×Dic43C2414yes—
276C4×Dic43C24116yes—
277C4×Dic43C2418yes—
278C4×Dic43C24116yes—
279C4×Dic43C24116yes—
280C23×C43—24no—
281C23×C43—28no—
282C23×C43C2514yes—
283C23×C43C2511yescharacteristic
284C22×D43—24no—
285C22×D43—22no—
286C22×D43—24no—
287C22×D43—28no—
288C22×D43C2514yes—
289C22×D43C2512yes—
290Q8×C43—48no—
291Q8×C43—44no—
292D4×C43—44no—
293C2×C4×C43—28no—
294C2×C4×C43—22no—
295C2×C4×C43—24no—
296C2×C4×C43—28no—
297C2×C4×C43—24no—
298C2×C4×C43—48no—
299C2×C4×C43C2518yes—
300C2×C4×C43C2514yes—
301C2×C4×C43C2512yes—
302C2×C4×C43C2514yes—
303C2×C4×C43C2518yes—
304C22⋊D43—232no—
305C22⋊D43—48no—
306C2×Dic43—28no—
307C2×Dic43—24no—
308C2×Dic43—28no—
309C2×Dic43—216no—
310C2×Dic43—48no—
311C2×Dic43H(5,𝔽2)14yes—
312C2×Dic432−1+418yes—
313C2×Dic43C2518yes—
314C2×Dic43C2514yes—
315C2×Dic43C2518yes—
316C2×Dic43C2512yes—
317C2×Dic43C2514yes—
318D172—44no—
319D172—48no—
320C4×D43—28no—
321C4×D43—216no—
322C4×D43—216no—
323C4×D43—416no—
324Dic86—232no—
325Dic86—232no—
326Dic86—416no—
327Dic86—44no—
328Dic86—48no—
329C2×#3550—431nomaximal, Sylow
330C22×C43—24no—
331C22×C43—28no—
332C22×C43—48no—
333C22×C43C2×H(5,𝔽2)12yes—
334C22×C43C2×2−1+414yes—
335C22×C43C2611yescharacteristic
336C2×D43—24no—
337C2×D43—22no—
338C2×D43—24no—
339C2×D43—28no—
340C2×D43—48no—
341C2×D43—44no—
342C4×C43—28no—
343C4×C43—22no—
344C4×C43—24no—
345C4×C43—28no—
346C4×C43—24no—
347Dic43—28no—
348Dic43—24no—
349Dic43—28no—
350Dic43C2×H(5,𝔽2)14yes—
351Dic43C2×2−1+418yes—
352#3550—4332no—
353C2×#563—432no—
354C2×#563—431no—
355C2×#563D4311yescharacteristic, complemented
356C2×#559—432no—
357C2×Q82—432no—
358C2×#556—434no—
359C2×D4×Q8—434no—
360C2×#542—434no—
361C2×#542—434no—
362C2×#536—432no—
363C2×#536—432no—
364C2×#533—432no—
365C2×#532—431no—
366C2×C43—44no—
367C2×C43#355014yescomplemented
368C2×C43C22×H(5,𝔽2)11yescharacteristic
369C2×C43C22×2−1+412yes—
370D43—44no—
371D43—42no—
372C22×#41—431no—
373C22×#41—431no—
374C23×Q8—432no—
375C23×Q8—432no—
376#563—4332no—
377#563—4316no—
378#563C2×D43116yescomplemented
379#559—4332no—
380Q82—4332no—
381#556—4364no—
382D4×Q8—4364no—
383#542—4364no—
384#542—4364no—
385#536—4332no—
386#536—4332no—
387#533—4332no—
388#532—4316no—
389C2×C4⋊Q8—431no—
390C2×C4⋊Q8—432no—
391C2×C4⋊Q8—434no—
392C2×C4⋊Q8—432no—
393C2×C4⋊Q8—432no—
394C2×C4⋊Q8—434no—
395C2×C4⋊Q8—434no—
396C2×C4⋊Q8C2×D4312yes—
397C2×#127—431no—
398C2×#126—434no—
399C2×#126—434no—
400C2×#126—434no—
401C2×#126C2×D4314yes—
402C2×#125—432no—
403C2×#125C2×D4312yes—
404C2×#124—432no—
405C2×#124—434no—
406C2×#124—434no—
407C2×#124—434no—
408C2×#124—431no—
409C2×#124—432no—
410C2×#124C2×D4311yescharacteristic
411C2×#123—432no—
412C2×#123—432no—
413C2×#123—434no—
414C2×#123—434no—
415C2×#123—432no—
416C2×#123C2×D4312yes—
417C2×C22⋊Q8—434no—
418C2×C22⋊Q8—434no—
419C2×C22⋊Q8—434no—
420C2×C22⋊Q8—434no—
421C2×C22⋊Q8—434no—
422C2×C22⋊Q8—434no—
423C2×C22⋊Q8—434no—
424C2×C22⋊Q8C2×D4314yes—
425C2×#121—434no—
426C2×C4×Q8—434no—
427C2×C4×Q8—434no—
428C2×C4×Q8—434no—
429C2×C4×Q8—434no—
430C2×C4×D4—434no—
431C2×C4×D4—434no—
432C2×C4×D4—434no—
433C2×#117—432no—
434C2×#117—432no—
435C2×#117—432no—
436C2×#117—432no—
437C22×C42—431no—
438C43C2×#355011yescharacteristic, complemented, Sylow
439C2×#41—438no—
440C2×#41—438no—
441C2×#41—1724no—
442C2×#41—1724no—
443C22×Q8—4316no—
444C22×Q8—434no—
445C22×Q8—434no—
446C22×Q8—434no—
447C22×Q8—432no—
448C22×Q8—431no—
449C22×Q8—4316no—
450C22×Q8—1728no—
451C22×Q8—1728no—
452C22×Q8C22×D4312yes—
453C22×Q8C22×D4311yescharacteristic
454C22×D4—434no—
455C22×D4—432no—
456C22×D4—432no—
457C22×D4—431no—
458C22×D4C22×D4311yescharacteristic
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—432no—
462C23×C4—432no—
463C23×C4—431no—
464C23×C4—434no—
465C23×C4C22×D4312yes—
466C4⋊Q8—438no—
467C4⋊Q8—4316no—
468C4⋊Q8—4332no—
469C4⋊Q8—4316no—
470C4⋊Q8—4316no—
471C4⋊Q8—4332no—
472C4⋊Q8—4332no—
473C4⋊Q8C22×D43116yes—
474#127—438no—
475#126—4332no—
476#126—4332no—
477#126—4332no—
478#126C22×D43132yes—
479#125—4316no—
480#125C22×D43116yes—
481#124—4316no—
482#124—4332no—
483#124—4332no—
484#124—4332no—
485#124—438no—
486#124—4316no—
487#124C22×D4318yes—
488#123—4316no—
489#123—4316no—
490#123—4332no—
491#123—4332no—
492#123—4316no—
493#123C22×D43116yes—
494C22⋊Q8—4332no—
495C22⋊Q8—4332no—
496C22⋊Q8—4332no—
497C22⋊Q8—4332no—
498C22⋊Q8—4332no—
499C22⋊Q8—4332no—
500C22⋊Q8—4332no—
501C22⋊Q8C22×D43132yes—
502#121—4332no—
503C4×Q8—4332no—
504C4×Q8—4332no—
505C4×Q8—4332no—
506C4×Q8—4332no—
507C4×D4—4332no—
508C4×D4—4332no—
509C4×D4—4332no—
510#117—4316no—
511#117—4316no—
512#117—4316no—
513#117—4316no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—432no—
516C2×C4⋊C4—432no—
517C2×C4⋊C4—434no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4C22×D4312yes—
525C2×C4⋊C4C22×D4312yes—
526C2×C4⋊C4C22×D4314yes—
527C2×C4⋊C4C22×D4314yes—
528C2×C4⋊C4C22×D4314yes—
529C2×C22⋊C4—432no—
530C2×C22⋊C4—434no—
531C2×C22⋊C4—434no—
532C2×C22⋊C4—434no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—434no—
537C2×C22⋊C4C22×D4312yes—
538C2×C22⋊C4C22×D4314yes—
539C2×C22⋊C4C22×D4314yes—
540C2×C42—434no—
541C2×C42—434no—
542C2×C42—432no—
543C2×C42—434no—
544C2×C42—432no—
545C2×C42—431no—
546C2×C42—438no—
547C2×C42C22×D4312yes—
548C2×C42C22×D4311yescharacteristic
549C24—432no—
550C24—431no—
551C24C23×D4312yes—
552#41—17216no—
553#41—17216no—
554C2×Q8—44no—
555C2×Q8—42no—
556C2×Q8—4316no—
557C2×Q8—4316no—
558C2×Q8—4316no—
559C2×Q8—438no—
560C2×Q8—434no—
561C2×Q8—8616no—
562C2×Q8—8616no—
563C2×Q8—1728no—
564C2×Q8—1724no—
565C2×Q8—1722no—
566C2×Q8—17232no—
567C2×Q8—17232no—
568C2×Q8C23×D4318yes—
569C2×Q8C23×D4314yes—
570C2×D4—42no—
571C2×D4—4316no—
572C2×D4—438no—
573C2×D4—438no—
574C2×D4—434no—
575C2×D4—8616no—
576C2×D4—1722no—
577C2×D4—1724no—
578C2×D4—1724no—
579C2×D4C23×D4314yes—
580C22×C4—44no—
581C22×C4—432no—
582C22×C4—431no—
583C22×C4—438no—
584C22×C4—434no—
585C22×C4—432no—
586C22×C4—434no—
587C22×C4—438no—
588C22×C4—438no—
589C22×C4—434no—
590C22×C4—438no—
591C22×C4—4316no—
592C22×C4—868no—
593C22×C4—864no—
594C22×C4—868no—
595C22×C4—868no—
596C22×C4—1728no—
597C22×C4—1724no—
598C22×C4C23×D4314yes—
599C22×C4C23×D4312yes—
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602C22×C4C23×D4314yes—
603C22×C4C23×D4318yes—
604C4⋊C4—4316no—
605C4⋊C4—438no—
606C4⋊C4—438no—
607C4⋊C4—4316no—
608C4⋊C4—4316no—
609C4⋊C4—4316no—
610C4⋊C4—4316no—
611C4⋊C4—4316no—
612C4⋊C4—4316no—
613C4⋊C4—4316no—
614C4⋊C4C23×D4318yes—
615C4⋊C4C23×D4318yes—
616C4⋊C4C23×D43116yes—
617C4⋊C4C23×D43116yes—
618C4⋊C4C23×D43116yes—
619C22⋊C4—438no—
620C22⋊C4—4316no—
621C22⋊C4—4316no—
622C22⋊C4—4316no—
623C22⋊C4—4316no—
624C22⋊C4—4316no—
625C22⋊C4—4316no—
626C22⋊C4—4316no—
627C22⋊C4C23×D4318yes—
628C22⋊C4C23×D43116yes—
629C22⋊C4C23×D43116yes—
630C42—438no—
631C42—434no—
632C42—4316no—
633C42—4316no—
634C42—438no—
635C42—4316no—
636C42C23×D4314yes—
637C42C23×D4318yes—
638C23—24no—
639C23—28no—
640C23—434no—
641C23—432no—
642C23—864no—
643C23—862no—
644C23—864no—
645C23—868no—
646C23C24×D4314yes—
647C23C24×D4311yescharacteristic
648Q8—48no—
649Q8—44no—
650Q8—8632no—
651Q8—8632no—
652Q8—17216no—
653Q8—1728no—
654Q8—1724no—
655D4—44no—
656D4—8632no—
657D4—1724no—
658D4—1728no—
659D4—1728no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—48no—
666C2×C4—434no—
667C2×C4—438no—
668C2×C4—434no—
669C2×C4—432no—
670C2×C4—438no—
671C2×C4—434no—
672C2×C4—438no—
673C2×C4—8616no—
674C2×C4—868no—
675C2×C4—8616no—
676C2×C4—8616no—
677C2×C4—864no—
678C2×C4—868no—
679C2×C4—868no—
680C2×C4—17216no—
681C2×C4—1728no—
682C2×C4C24×D4318yes—
683C2×C4C24×D4314yes—
684C2×C4C24×D4314yes—
685C2×C4C24×D4312yes—
686C2×C4C24×D4318yes—
687C22—24no—
688C22—28no—
689C22—48no—
690C22—864no—
691C22—862no—
692C22—864no—
693C22—868no—
694C22—1728no—
695C22—1724no—
696C22H(5,𝔽2)×D4312yes—
697C222−1+4×D4314yes—
698C22C25×D4311yescharacteristic
699C4—28no—
700C4—22no—
701C4—24no—
702C4—24no—
703C4—28no—
704C4—434no—
705C4—438no—
706C4—864no—
707C4—868no—
708C4—868no—
709C2—44no—
710C2—1724no—
711C2—1722no—
712C2#1914900514yesdirect product factor
713C2C2×H(5,𝔽2)×D4311yescharacteristic
714C2C2×2−1+4×D4312yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#563C2
socleC23×C43C25
prime radicalC2×#14583448C2
hypercenterC2×#563D43
hypocenterC43C2×#3550
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #19149005C2direct (N × H)
2. C2×#14583653C2semidirect
3. C2×#14583649C2semidirect
4. C2×#14583633C2semidirect
5. C2×#14583629C2semidirect
6. C2×#14583616C2semidirect
7. C2×#14583562C2semidirect
8. C2×#14583519C2semidirect
9. C2×#14583515C2semidirect
10. C2×#14583474C2semidirect
11. C2×#14583471C2semidirect
12. C2×#14583455C2semidirect
14. C2×C43×#563C2semidirect
19. #14583653C22semidirect
20. #14583649C22semidirect
21. #14583633C22semidirect
22. #14583629C22semidirect
23. #14583616C22semidirect
24. #14583562C22semidirect
25. #14583519C22semidirect
26. #14583515C22semidirect
27. #14583474C22semidirect
28. #14583471C22semidirect
29. #14583455C22semidirect
74. C43×#563C22semidirect
355. C2×#563D43semidirect
367. C2×C43#3550semidirect
378. #563C2×D43semidirect
438. C43C2×#3550semidirect
712. C2#19149005direct (N × H)

Maximal subgroups

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

subgroupindex
#191490052
C2×#145836532
C2×#145836492
C2×#145836332
C2×#145836292
C2×#145836162
C2×#145835622
C2×#145835192
C2×#145835152
C2×#145834742
C2×#145834712
C2×#145834552
C2×#145834482
C2×C43×#5632
C2×#355043