Finite Group Databasebeta

← C2×#19145550 #25967806

Subgroups — C2×#19145550 #25967806

Order 11008.

2186 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic, complemented
2C2×#14583448C211yesmaximal, characteristic
3#19145550C2116yesmaximal, direct product factor
4C2×#14583277C211yesmaximal, characteristic, complemented
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583248C211yesmaximal, characteristic, complemented
7C2×#14583244C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583118C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583062C211yesmaximal, characteristic, complemented
13C2×#14583060C211yesmaximal, characteristic, complemented
14C2×#14583058C211yesmaximal, characteristic, complemented
15C2×#14582951C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25#14583453—24no—
26#14583453C2218yescomplemented
27#14583448—24no—
28#14583448C2218yes—
29C2×#13063324C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063323C2211yescharacteristic
32C2×#13063321C2211yescharacteristic
33C2×#13063315—21no—
34C2×#13063313C2211yescharacteristic
35C2×#13063305C2211yescharacteristic
36C2×#13063303—21no—
37C2×#13063301C2211yescharacteristic
38C2×#13063298—21no—
39C2×#13063298—21no—
40C2×C4×Dic86—21no—
41C2×C4×Dic86C2211yescharacteristic
42C2×(C22⋊D43)⋊C4—21no—
43C2×(C22⋊D43)⋊C4—21no—
44C2×#13063282—21no—
45C2×C42×D43C2211yescharacteristic
46#14583277C2218yescomplemented
47#14583270C2218yescomplemented
48#14583248C2218yescomplemented
49#14583244C2218yescomplemented
50#14583122C2218yescomplemented
51#14583121C2218yescomplemented
52#14583118C2218yescomplemented
53#14583064C2218yescomplemented
54#14583062C2218yescomplemented
55#14583060C2218yescomplemented
56#14583058C2218yescomplemented
57#14582951C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—42no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621900—22no—
82C2×#10621900—42no—
83C2×#10621900—42no—
84C2×#10621900C2314yes—
85C22×Dic86—21no—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43D411yescharacteristic
96C22×C4×D43D411yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×Dic172—42no—
99C2×Dic172C2314yes—
100C2×#10621885—42no—
101C2×#10621885—42no—
102C2×#10621885C2314yes—
103C2×#10621885C2314yes—
104C2×#10621873—42no—
105C2×#10621873C2314yes—
106C2×#10621883—42no—
107C2×#10621883C2314yes—
108C2×#10621884—42no—
109C2×#10621884C2314yes—
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112#13063324—22no—
113#13063324C2314yes—
114#13063323—22no—
115#13063323—22no—
116#13063323C2314yes—
117#13063323C2314yes—
118#13063321—22no—
119#13063321C2314yes—
120#13063315—28no—
121#13063313—22no—
122#13063313C2314yes—
123#13063305—22no—
124#13063305C2314yes—
125#13063303—28no—
126#13063301—22no—
127#13063301C2314yes—
128#13063298—28no—
129#13063298—28no—
130C4×Dic86—22no—
131C4×Dic86—28no—
132C4×Dic86C2314yes—
133(C22⋊D43)⋊C4—28no—
134(C22⋊D43)⋊C4—28no—
135#13063282—28no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43D411yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C42×D43D414yes—
154C42×D43C2314yes—
155C4⋊(C43⋊C8)C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C8×Dic43C2314yes—
165C8×Dic43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C2×Q16×C43—42no—
170C2×Q16×C43C2314yes—
171C2×SD16×C43—42no—
172C2×SD16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#124×C43—22no—
176#124×C43C2314yes—
177C4×Q8×C43—22no—
178C4×Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yes—
186#103×C43C2314yes—
187#102×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43C2×D411yescharacteristic
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43C2412yes—
198C2×Q8×C43C2412yes—
199C2×D4×C43—21no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43C2412yes—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—44no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C22×Dic43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—44no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223#10621902—44no—
224#10621902—44no—
225#10621902—48no—
226#10621900—44no—
227#10621900—44no—
228#10621900—48no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—44no—
234C2×D172C2412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2×D414yes—
243C2×C4×D43C2×D414yes—
244C2×C4×D43C2412yes—
245C2×Dic86—22no—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—22no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—24no—
252C2×Dic86—44no—
253C2×Dic86C2412yes—
254C2×Dic86C2412yes—
255Q16×C43—44no—
256SD16×C43—44no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C42×C43—24no—
267C42×C43C2×D412yes—
268C42×C43C2412yes—
269#10621885—44no—
270#10621885—44no—
271#10621884—44no—
272#10621883—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277C4⋊Dic43—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43C2412yes—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C4×Dic43—24no—
288C4×Dic43C2×D412yes—
289C4×Dic43C2×D414yes—
290C4×Dic43C2×D414yes—
291C4×Dic43C2412yes—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296Dic172—44no—
297#10621873—44no—
298C23×C43—22no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43C22×D412yes—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—42no—
316Q8×C43—42no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—42no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43H(5,𝔽2)12yes—
332C2×C4×C43H(5,𝔽2)12yes—
333C2×C4×C43C2511yescharacteristic
334C22⋊D43—48no—
335C22⋊D43—48no—
336C22⋊D43—48no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—48no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43#13514yes—
346C2×Dic43#13714yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350D172—22no—
351D172—22no—
352D172—48no—
353D172—42no—
354C4×D43—24no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—28no—
358C4×D43—28no—
359C4×D43—48no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—42no—
365Dic86—42no—
366Dic86—48no—
367C8×C43—22no—
368C8×C43—22no—
369C43⋊C8—22no—
370C43⋊C8—22no—
371C2×#3210—431nomaximal, Sylow
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—84no—
376C22×C43#53512yes—
377C22×C43C2×#13512yes—
378C22×C43C2×#13712yes—
379C22×C43C23×D411yescharacteristic
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—44no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—84no—
388C4×C43—22no—
389C4×C43—22no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#53512yes—
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395C4×C43C2×H(5,𝔽2)11yescharacteristic
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400Dic43C2×#13514yes—
401Dic43C2×#13714yes—
402C2×#533—431no—
403C2×#532—431no—
404#3210—4316no—
405C2×#494—431no—
406C2×#492—431no—
407C2×#487—431no—
408C2×#486—431no—
409C2×#464—431no—
410C2×#464—431no—
411C2×#464—431no—
412C2×#464D4311yescharacteristic, complemented
413C2×#452—431no—
414C2×#452—431no—
415C2×#452—431no—
416C2×#452—431no—
417C2×#431—431no—
418C2×C43—82no—
419C2×C43#321014yescomplemented
420C2×C43C2×#53511yescharacteristic
421C2×C43C22×#13511yescharacteristic
422C2×C43C22×#13711yescharacteristic
423D43—42no—
424D43—82no—
425C22×#41—431no—
426C22×#41—431no—
427C22×Q16—431no—
428C22×Q16—431no—
429C22×Q16—431no—
430C22×Q16C2×D4311yescharacteristic
431C22×SD16—431no—
432C22×SD16—431no—
433C22×SD16—431no—
434C22×SD16C2×D4311yescharacteristic
435#533—438no—
436#533—864no—
437#532—438no—
438#532—864no—
439C2×C4⋊Q8—431no—
440C2×C4⋊Q8—431no—
441C2×C4⋊Q8—431no—
442C2×#127—431no—
443C2×#125—861no—
444C2×#124—431no—
445C2×#124C2×D4311yescharacteristic
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—861no—
449C2×#121—861no—
450C2×#121—861no—
451C2×C4×Q8—431no—
452C2×C4×Q8—861no—
453C2×C4×Q8C2×D4311yescharacteristic
454C2×C4×D4—861no—
455C2×C4×D4—861no—
456C2×#117—861no—
457C22×C42—431no—
458#494—438no—
459#492—438no—
460#487—438no—
461#486—438no—
462#464—438no—
463#464—438no—
464#464—438no—
465#464C2×D4318yescomplemented
466#452—438no—
467#452—438no—
468#452—438no—
469#452—438no—
470#431—438no—
471C2×C4⋊C8—431no—
472C2×C4⋊C8C2×D4311yescharacteristic
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103C2×D4311yescharacteristic
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C4×C8—431no—
484C2×C4×C8—431no—
485C43C2×#321011yescharacteristic, complemented, Sylow
486C2×#41—434no—
487C2×#41—434no—
488C2×#41—862no—
489C2×#41—862no—
490C2×#41—1722no—
491C2×#41—1722no—
492C2×#41—1722no—
493C2×#41—1722no—
494C22×Q8—431no—
495C22×Q8—431no—
496C22×Q8—861no—
497C22×Q8C22×D4311yescharacteristic
498C22×Q8C22×D4311yescharacteristic
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4C22×D4311yescharacteristic
505C23×C4—431no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—861no—
509C23×C4—861no—
510C2×Q16—42no—
511C2×Q16—434no—
512C2×Q16—434no—
513C2×Q16—434no—
514C2×Q16—1722no—
515C2×Q16—1722no—
516C2×Q16—1722no—
517C2×Q16C22×D4314yes—
518C2×SD16—42no—
519C2×SD16—434no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×SD16—1722no—
523C2×SD16—1722no—
524C2×SD16—1722no—
525C2×SD16C22×D4314yes—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C4⋊Q8—434no—
531C4⋊Q8—434no—
532C4⋊Q8—434no—
533C4⋊Q8—862no—
534C4⋊Q8—862no—
535C4⋊Q8—862no—
536#127—434no—
537#127—862no—
538#125—868no—
539#124—22no—
540#124—434no—
541#124—862no—
542#124C22×D4314yes—
543C22⋊Q8—434no—
544C22⋊Q8—434no—
545C22⋊Q8—862no—
546C22⋊Q8—868no—
547C22⋊Q8—862no—
548#121—868no—
549#121—868no—
550C4×Q8—22no—
551C4×Q8—434no—
552C4×Q8—868no—
553C4×Q8—862no—
554C4×Q8C22×D4314yes—
555C4×D4—868no—
556C4×D4—868no—
557#117—868no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—21no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—434no—
580C2×C42—434no—
581C2×C42—861no—
582C2×C42C22×D4311yescharacteristic
583C4⋊C8—434no—
584C4⋊C8C22×D4314yes—
585#103—434no—
586#103—434no—
587#103—434no—
588#103C22×D4314yes—
589#102—434no—
590#102—434no—
591#102—434no—
592#102C22×D4314yes—
593C22⋊C8—434no—
594C22⋊C8—434no—
595C4×C8—434no—
596C4×C8—434no—
597C24—21no—
598C24—431no—
599C24—861no—
600#41—1724no—
601#41—1724no—
602#41—1728no—
603#41—1724no—
604#41—1724no—
605#41—1728no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—432no—
613C2×Q8—432no—
614C2×Q8—864no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—862no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×Q8—1724no—
622C2×Q8C23×D4312yes—
623C2×Q8C23×D4312yes—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—861no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4—1724no—
639C2×D4C23×D4312yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—434no—
647C22×C4—434no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—1724no—
660C22×C4—1724no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—44no—
665Q16—1724no—
666Q16—1724no—
667Q16—1724no—
668SD16—44no—
669SD16—1724no—
670SD16—1724no—
671SD16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—432no—
675C2×C8—432no—
676C2×C8—862no—
677C2×C8—862no—
678C2×C8C23×D4312yes—
679C2×C8C23×D4312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4—864no—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—24no—
700C42—434no—
701C42—434no—
702C42—432no—
703C42—432no—
704C42—864no—
705C42D4×D4312yes—
706C42C23×D4312yes—
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—432no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—1722no—
717C23—1722no—
718C23—1722no—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—862no—
727Q8—862no—
728Q8—862no—
729Q8—862no—
730Q8—1728no—
731Q8—1722no—
732Q8—1722no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—862no—
737D4—862no—
738D4—1728no—
739D4—1728no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—434no—
752C2×C4—434no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—868no—
757C2×C4—868no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—1728no—
766C2×C4—1728no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4C2×D4×D4312yes—
771C2×C4C2×D4×D4312yes—
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4#1306337012yes—
774C2×C4#1306337112yes—
775C2×C4C24×D4311yescharacteristic
776C8—22no—
777C8—22no—
778C8—862no—
779C8—862no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—84no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—3444no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1724no—
792C22#1458346512yes—
793C22#135×D4312yes—
794C22#137×D4312yes—
795C22C22×D4×D4311yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—434no—
802C4—434no—
803C4—862no—
804C4—1722no—
805C4—1722no—
806C4—1722no—
807C4#1458346512yes—
808C4C2×#1306337011yescharacteristic
809C4C2×#1306337111yescharacteristic
810C2—82no—
811C2—3442no—
812C2—1722no—
813C2#1914555014yesdirect product factor
814C2C2×#1458346511yescharacteristic
815C2C2×#135×D4311yescharacteristic
816C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583448C2
hypercenterC2×#464D43
hypocenterC43C2×#3210
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
3. #19145550C2direct (N × H)
4. C2×#14583277C2semidirect
5. C2×#14583270C2semidirect
6. C2×#14583248C2semidirect
7. C2×#14583244C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583118C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583062C2semidirect
13. C2×#14583060C2semidirect
14. C2×#14583058C2semidirect
15. C2×#14582951C2semidirect
16. C2×C43×#464C2semidirect
26. #14583453C22semidirect
46. #14583277C22semidirect
47. #14583270C22semidirect
48. #14583248C22semidirect
49. #14583244C22semidirect
50. #14583122C22semidirect
51. #14583121C22semidirect
52. #14583118C22semidirect
53. #14583064C22semidirect
54. #14583062C22semidirect
55. #14583060C22semidirect
56. #14583058C22semidirect
57. #14582951C22semidirect
73. C43×#464C22semidirect
412. C2×#464D43semidirect
419. C2×C43#3210semidirect
465. #464C2×D43semidirect
485. C43C2×#3210semidirect
813. C2#19145550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#145834482
#191455502
C2×#145832772
C2×#145832702
C2×#145832482
C2×#145832442
C2×#145831222
C2×#145831212
C2×#145831182
C2×#145830642
C2×#145830622
C2×#145830602
C2×#145830582
C2×#145829512
C2×C43×#4642
C2×#321043