Finite Group Databasebeta

← C2×#19145603 #25967888

Subgroups — C2×#19145603 #25967888

Order 11008.

2166 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×#14583451C211yesmaximal, characteristic, complemented
2C2×#14583445C211yesmaximal, characteristic
3#19145603C2116yesmaximal, direct product factor
4C2×#14583292C211yesmaximal, characteristic, complemented
5C2×#14583290C211yesmaximal, characteristic, complemented
6C2×#14583260C211yesmaximal, characteristic, complemented
7C2×#14583257C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583098C211yesmaximal, characteristic, complemented
11C2×#14583097C211yesmaximal, characteristic, complemented
12C2×#14583063C211yesmaximal, characteristic, complemented
13C2×#14583061C211yesmaximal, characteristic, complemented
14C2×#14583059C211yesmaximal, characteristic, complemented
15C2×#14582953C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24#14583451—24no—
25#14583451C2218yescomplemented
26#14583445—24no—
27#14583445C2218yes—
28C2×#13063324C2211yescharacteristic
29C2×#13063323C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063321C2211yescharacteristic
32C2×#13063315—21no—
33C2×#13063314C2211yescharacteristic
34C2×#13063312C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063302—21no—
37C2×#13063297—21no—
38C2×#13063297—21no—
39C2×Q8×Dic43C2211yescharacteristic
40C2×#13063290—21no—
41C2×#13063290C2211yescharacteristic
42C2×C4×C22⋊D43—21no—
43C2×C4×C22⋊D43—21no—
44C2×#13063281—21no—
45C22×C4×Dic43C2211yescharacteristic
46#14583292C2218yescomplemented
47#14583290C2218yescomplemented
48#14583260C2218yescomplemented
49#14583257C2218yescomplemented
50#14583108C2218yescomplemented
51#14583107C2218yescomplemented
52#14583098C2218yescomplemented
53#14583097C2218yescomplemented
54#14583063C2218yescomplemented
55#14583061C2218yescomplemented
56#14583059C2218yescomplemented
57#14582953C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C23×Dic43D411yescharacteristic
89C23×Dic43D411yescharacteristic
90C22×C4×D43—21no—
91C2×Dic172—42no—
92C2×Dic172C2314yes—
93C2×#10621885—42no—
94C2×#10621885—42no—
95C2×#10621885C2314yes—
96C2×#10621885C2314yes—
97C2×#10621873—42no—
98C2×#10621873C2314yes—
99C2×#10621883—42no—
100C2×#10621883C2314yes—
101C2×#10621884—42no—
102C2×#10621884C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063324—22no—
106#13063324C2314yes—
107#13063323—22no—
108#13063323—22no—
109#13063323C2314yes—
110#13063323C2314yes—
111#13063321—22no—
112#13063321C2314yes—
113#13063315—28no—
114#13063314—22no—
115#13063314C2314yes—
116#13063312—22no—
117#13063312C2314yes—
118#13063304—22no—
119#13063304C2314yes—
120#13063302—28no—
121#13063297—28no—
122#13063297—28no—
123Q8×Dic43—22no—
124Q8×Dic43C2314yes—
125#13063290—28no—
126#13063290—22no—
127#13063290C2314yes—
128C4×C22⋊D43—28no—
129C4×C22⋊D43—28no—
130#13063281—28no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D414yes—
150C2×C4×Dic43C2311yescharacteristic
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2314yes—
153Dic43⋊C8C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063248C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063245C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yes—
163#13063235C2314yes—
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C23×C4×C43—21no—
173C23×C4×C43C2311yescharacteristic
174C2×Q16×C43—42no—
175C2×Q16×C43C2314yes—
176C2×SD16×C43—42no—
177C2×SD16×C43C2314yes—
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191#41×C43—44no—
192#41×C43—44no—
193#41×C43—48no—
194C2×Q8×C43—21no—
195C2×Q8×C43—21no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43C2412yes—
201C2×Q8×C43C2412yes—
202C2×D4×C43—21no—
203C2×D4×C43—24no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—44no—
207C2×D4×C43C2412yes—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—44no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C22×Dic43—24no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—42no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D414yes—
234C22×Dic43C2×D414yes—
235C22×Dic43C2×D411yescharacteristic
236#10621898—44no—
237#10621898—44no—
238#10621898—48no—
239C2×D172—21no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172C2412yes—
243C2×C4×D43—24no—
244C2×C4×D43—44no—
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⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268#10621885—44no—
269#10621885—44no—
270#10621884—44no—
271#10621883—44no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284C4×Dic43—24no—
285C4×Dic43—24no—
286C4×Dic43C2×D414yes—
287C4×Dic43C2×D414yes—
288C4×Dic43C2×D412yes—
289C4×Dic43C2×D412yes—
290C4×Dic43C2412yes—
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—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43C22×D412yes—
306C23×C43C22×D411yescharacteristic
307C22×D43—22no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
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—48no—
320D4×C43—42no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43H(5,𝔽2)12yes—
336C2×C4×C43C2511yescharacteristic
337C22⋊D43—48no—
338C22⋊D43—48no—
339C22⋊D43—48no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—28no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—44no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43#13714yes—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356D172—22no—
357D172—22no—
358D172—42no—
359C4×D43—48no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—48no—
365Dic86—42no—
366Dic86—42no—
367C8×C43—22no—
368C8×C43—22no—
369C43⋊C8—22no—
370C43⋊C8—22no—
371C2×#3216—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—44no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—84no—
380C22×C43#53512yes—
381C22×C43C2×#13712yes—
382C22×C43#57512yes—
383C22×C43C23×D411yescharacteristic
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—84no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#53512yes—
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—22no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×#13714yes—
402C2×#533—431no—
403C2×#532—431no—
404#3216—4316no—
405C2×#497—431no—
406C2×#497—431no—
407C2×#489—431no—
408C2×#489—431no—
409C2×#462—431no—
410C2×#462—431no—
411C2×#460—431no—
412C2×#460—431no—
413C2×#452—431no—
414C2×#452—431no—
415C2×#452—431no—
416C2×#452D4311yescharacteristic, complemented
417C2×#432—431no—
418C2×C43—42no—
419C2×C43—82no—
420C2×C43#321614yescomplemented
421C2×C43C2×#53511yescharacteristic
422C2×C43C22×#13711yescharacteristic
423C2×C43C2×#57511yescharacteristic
424D43—82no—
425C22×#41—431no—
426C22×#41C2×D4311yescharacteristic
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×#124—431no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—861no—
448C2×C22⋊Q8C2×D4311yescharacteristic
449C2×#121—861no—
450C2×#121—861no—
451C2×C4×Q8—431no—
452C2×C4×Q8—431no—
453C2×C4×Q8—861no—
454C2×C4×D4—861no—
455C2×C4×D4—861no—
456C2×#117—861no—
457C22×C42—431no—
458#497—438no—
459#497—438no—
460#489—438no—
461#489—438no—
462#462—438no—
463#462—438no—
464#460—438no—
465#460—438no—
466#452—438no—
467#452—438no—
468#452—438no—
469#452C2×D4318yescomplemented
470#432—438no—
471C2×C4⋊C8—431no—
472C2×C4⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
483C2×#97—431no—
484C2×#97—431no—
485C43C2×#321611yescharacteristic, complemented, Sylow
486C2×#41—22no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41—434no—
490C2×#41—862no—
491C2×#41—1722no—
492C2×#41—1722no—
493C2×#41C22×D4314yes—
494C22×Q8—431no—
495C22×Q8—431no—
496C22×Q8—861no—
497C22×Q8C22×D4311yescharacteristic
498C22×Q8C22×D4311yescharacteristic
499C22×D4—21no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4C22×D4311yescharacteristic
505C23×C4—21no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—861no—
509C23×C4C22×D4311yescharacteristic
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—434no—
540#124—434no—
541#124—862no—
542#124—862no—
543C22⋊Q8—22no—
544C22⋊Q8—434no—
545C22⋊Q8—868no—
546C22⋊Q8—862no—
547C22⋊Q8C22×D4314yes—
548#121—868no—
549#121—868no—
550C4×Q8—434no—
551C4×Q8—434no—
552C4×Q8—862no—
553C4×Q8—868no—
554C4×Q8—862no—
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—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—434no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—434no—
581C2×C42—861no—
582C2×C42—861no—
583C4⋊C8—434no—
584C4⋊C8—434no—
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⋊C8C22×D4314yes—
595#97—434no—
596#97—434no—
597C24—21no—
598C24—861no—
599C24D4×D4311yescharacteristic
600#41—44no—
601#41—44no—
602#41—48no—
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—24no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—432no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—861no—
634C2×D4—862no—
635C2×D4—862no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4—1724no—
639C2×D4C23×D4312yes—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—44no—
647C22×C4—431no—
648C22×C4—434no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—434no—
653C22×C4—864no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—864no—
658C22×C4—1724no—
659C22×C4—1722no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
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—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—434no—
700C42—434no—
701C42—432no—
702C42—432no—
703C42—432no—
704C42—432no—
705C42—864no—
706C42—864no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—862no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23C2×D4×D4312yes—
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—48no—
736D4—42no—
737D4—862no—
738D4—862no—
739D4—1728no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—434no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—432no—
758C2×C4—432no—
759C2×C4—868no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1728no—
767C2×C4—1724no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4C2×D4×D4312yes—
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4#1306337012yes—
774C2×C4#1306337012yes—
775C2×C4C24×D4311yescharacteristic
776C8—22no—
777C8—22no—
778C8—862no—
779C8—862no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22—3444no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22#1458346412yes—
793C22#137×D4312yes—
794C22#1458369612yes—
795C22C22×D4×D4311yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—434no—
801C4—862no—
802C4—862no—
803C4—862no—
804C4—1722no—
805C4—1722no—
806C4—1722no—
807C4#1458346412yes—
808C4C2×#1306337011yescharacteristic
809C4C2×#1306337011yescharacteristic
810C2—42no—
811C2—82no—
812C2—3442no—
813C2#1914560314yesdirect product factor
814C2C2×#1458346411yescharacteristic
815C2C2×#137×D4311yescharacteristic
816C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC2×#14583445C2
hypercenterC2×#452D43
hypocenterC43C2×#3216
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
3. #19145603C2direct (N × H)
4. C2×#14583292C2semidirect
5. C2×#14583290C2semidirect
6. C2×#14583260C2semidirect
7. C2×#14583257C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583107C2semidirect
10. C2×#14583098C2semidirect
11. C2×#14583097C2semidirect
12. C2×#14583063C2semidirect
13. C2×#14583061C2semidirect
14. C2×#14583059C2semidirect
15. C2×#14582953C2semidirect
16. C2×C43×#452C2semidirect
25. #14583451C22semidirect
46. #14583292C22semidirect
47. #14583290C22semidirect
48. #14583260C22semidirect
49. #14583257C22semidirect
50. #14583108C22semidirect
51. #14583107C22semidirect
52. #14583098C22semidirect
53. #14583097C22semidirect
54. #14583063C22semidirect
55. #14583061C22semidirect
56. #14583059C22semidirect
57. #14582953C22semidirect
73. C43×#452C22semidirect
416. C2×#452D43semidirect
420. C2×C43#3216semidirect
469. #452C2×D43semidirect
485. C43C2×#3216semidirect
813. C2#19145603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145834452
#191456032
C2×#145832922
C2×#145832902
C2×#145832602
C2×#145832572
C2×#145831082
C2×#145831072
C2×#145830982
C2×#145830972
C2×#145830632
C2×#145830612
C2×#145830592
C2×#145829532
C2×C43×#4522
C2×#321643