Finite Group Databasebeta

← C2×#19145264 #25966466

Subgroups — C2×#19145264 #25966466

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583522C211yesmaximal, characteristic
2C2×#14583509C211yesmaximal, characteristic, complemented
3#19145264C2116yesmaximal, direct product factor
4C2×#14583306C211yesmaximal, characteristic, complemented
5C2×#14583292C211yesmaximal, characteristic, complemented
6C2×#14583255C211yesmaximal, characteristic, complemented
7C2×#14583248C211yesmaximal, characteristic, complemented
8C2×#14583145C211yesmaximal, characteristic
9C2×#14583138C211yesmaximal, characteristic, complemented
10C2×#14583130C211yesmaximal, characteristic
11C2×#14583003C211yesmaximal, characteristic, complemented
12C2×#14583002C211yesmaximal, characteristic, complemented
13C2×Q16×Dic43C211yesmaximal, characteristic, complemented
14C2×#14582986C211yesmaximal, characteristic, complemented
15C2×#14582857C211yesmaximal, characteristic, complemented
16C2×C43×#470C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583522—24no—
22#14583522C2218yes—
23#14583509—24no—
24#14583509C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063323C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063318—21no—
29C2×#13063318—21no—
30C2×#13063316—21no—
31C2×#13063316C2211yescharacteristic
32C2×#13063315—21no—
33C2×#13063314C2211yescharacteristic
34C2×#13063311—21no—
35C2×#13063307—21no—
36C2×#13063305—21no—
37C2×#13063304C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×Q8×Dic43C2211yescharacteristic
40C2×Q8×Dic43C2211yescharacteristic
41C2×#13063290C2211yescharacteristic
42C2×#13063287C2211yescharacteristic
43C2×#13063284C2211yescharacteristic
44#14583306C2218yescomplemented
45#14583292C2218yescomplemented
46#14583255C2218yescomplemented
47#14583248C2218yescomplemented
48#14583145C2218yes—
49#14583138C2218yescomplemented
50#14583130C2218yes—
51#14583003C2218yescomplemented
52#14583002C2218yescomplemented
53Q16×Dic43C2218yescomplemented
54#14582986C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64#14582857C2218yescomplemented
65C2×#13063235C2211yescharacteristic
66C2×#13063235C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#470C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C2×#10621885—24no—
83C2×#10621885C2314yes—
84C2×#10621873—24no—
85C2×#10621873C2314yes—
86C2×#10621884—24no—
87C2×#10621884C2314yes—
88C22×C43⋊C8—24no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92#13063324—22no—
93#13063324C2314yes—
94#13063323—22no—
95#13063323C2314yes—
96#13063320—28no—
97#13063318—28no—
98#13063318—28no—
99#13063316—28no—
100#13063316—22no—
101#13063316C2314yes—
102#13063315—28no—
103#13063314—22no—
104#13063314C2314yes—
105#13063311—28no—
106#13063307—28no—
107#13063305—28no—
108#13063304—22no—
109#13063304C2314yes—
110#13063299—22no—
111#13063299C2314yes—
112Q8×Dic43—22no—
113Q8×Dic43—22no—
114Q8×Dic43C2314yes—
115Q8×Dic43C2314yes—
116#13063290—22no—
117#13063290C2314yes—
118#13063287—22no—
119#13063287C2314yes—
120#13063284D414yes—
121#13063284C2314yes—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43D411yescharacteristic
126C2×C4⋊Dic43D411yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43D411yescharacteristic
137C2×C22⋊Dic43D411yescharacteristic
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43C2311yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063256C2314yes—
150#13063250C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063248C2314yes—
154#13063247C2314yes—
155#13063245C2314yes—
156#13063235C2314yes—
157#13063235C2314yes—
158C8×Dic43C2314yes—
159C8×Dic43C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C2×M16×C43—24no—
166C2×M16×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22⋊Q8×C43—22no—
170C22⋊Q8×C43—22no—
171C22⋊Q8×C43C2314yes—
172C22⋊Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179#106×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—82no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C2×D172—21no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172C2412yes—
215C2×C4×D43—24no—
216C2×C4×D43—82no—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—82no—
222C2×Dic86C2412yes—
223Q16×C43—28no—
224M16×C43—28no—
225C2×C8×C43—22no—
226C2×C8×C43#4114yes—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C2412yes—
234C4⋊C4×C43C2412yes—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C22⋊Dic43—24no—
238C22⋊Dic43C2×D414yes—
239C22⋊Dic43C2×D414yes—
240#10621885—28no—
241#10621884—28no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2×D414yes—
252C4⋊Dic43C2×D414yes—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2×D412yes—
266C4×Dic43C2412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—28no—
270C2×C43⋊C8#4114yes—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273#10621873—28no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43C22×D412yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288Q8×C43—42no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4112yes—
304C2×C4×C43C2×#4112yes—
305C2×C4×C43C2511yescharacteristic
306C22⋊D43—84no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321D172—22no—
322D172—22no—
323D172—42no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—84no—
329C8×C43—22no—
330C8×C43C2×#4114yes—
331C43⋊C8—22no—
332C43⋊C8C2×#4114yes—
333C2×#3178—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43#53212yes—
339C22×C43#57712yes—
340C22×C43#57812yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—84no—
346C4×C43—22no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43#53212yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C22×#4111yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541—431no—
363#3178—4316no—
364C2×#501—431no—
365C2×#497—431no—
366C2×#488—431no—
367C2×#487—431no—
368C2×#470D4311yescharacteristic, complemented
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#441—431no—
373C2×#440—431no—
374C2×C4×Q16—431no—
375C2×C4×SD16—431no—
376C2×#405—431no—
377C2×C43—42no—
378C2×C43#317814yescomplemented
379C2×C43C2×#53211yescharacteristic
380C2×C43C2×#57711yescharacteristic
381C2×C43C2×#57811yescharacteristic
382D43—82no—
383C22×Q16—431no—
384C22×Q16C2×D4311yescharacteristic
385C22×SD16—431no—
386C22×SD16—431no—
387C22×M16C2×D4311yescharacteristic
388C23×C8—431no—
389#542—438no—
390#542—864no—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8—431no—
395C2×#126—861no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×#124—431no—
402C2×#124—861no—
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—861no—
406C2×C22⋊Q8C2×D4311yescharacteristic
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×D4—431no—
413C2×#117—431no—
414#501—438no—
415#497—438no—
416#488—438no—
417#487—438no—
418#470C2×D4318yescomplemented
419#468—438no—
420#467—438no—
421#465—438no—
422#441—438no—
423#440—438no—
424C4×Q16—438no—
425C4×SD16—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106C2×D4311yescharacteristic
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103C2×D4311yescharacteristic
435C2×#103C2×D4311yescharacteristic
436C2×#102—431no—
437C2×#102—431no—
438#405—438no—
439C2×#97—431no—
440C2×#97—431no—
441C2×C4×C8—431no—
442C2×C4×C8—431no—
443C43C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—431no—
445C22×Q8—861no—
446C22×Q8C22×D4311yescharacteristic
447C22×Q8C22×D4311yescharacteristic
448C22×D4—431no—
449C22×D4—861no—
450C23×C4—861no—
451C23×C4C22×D4311yescharacteristic
452C2×Q16—24no—
453C2×Q16—434no—
454C2×Q16—864no—
455C2×Q16C22×D4314yes—
456C2×SD16—434no—
457C2×SD16—434no—
458C2×SD16—864no—
459C2×SD16—864no—
460C2×M16—24no—
461C2×M16C22×D4314yes—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—434no—
465C22×C8—864no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C4⋊Q8—434no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#126—868no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—862no—
477#125—868no—
478#125—868no—
479#124—434no—
480#124—862no—
481#124—868no—
482#123—868no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—434no—
486C22⋊Q8—868no—
487C22⋊Q8—862no—
488C22⋊Q8C22×D4314yes—
489C22⋊Q8C22×D4314yes—
490#121—434no—
491#121—862no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×D4—434no—
499C4×D4—862no—
500#117—434no—
501#117—434no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42—861no—
533#107—434no—
534#107—434no—
535#106—434no—
536#106C22×D4314yes—
537#103—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#103C22×D4314yes—
542#103C22×D4314yes—
543#102—434no—
544#102—434no—
545#97—434no—
546#97—434no—
547C4×C8—434no—
548C4×C8—434no—
549C24—861no—
550C24D4×D4311yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—3442no—
563C2×Q8C23×D4312yes—
564C2×Q8C23×D4312yes—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—861no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3442no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—864no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—3442no—
586C22×C4D4×D4312yes—
587C22×C4D4×D4311yescharacteristic
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590Q16—28no—
591Q16—868no—
592SD16—868no—
593SD16—868no—
594M16—28no—
595C2×C8—22no—
596C2×C8—434no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—868no—
600C2×C8—862no—
601C2×C8#1062190014yes—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—864no—
623C4⋊C4C23×D4312yes—
624C4⋊C4C23×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—434no—
628C22⋊C4—434no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C42—432no—
635C42—432no—
636C42—432no—
637C42—432no—
638C42—864no—
639C42—864no—
640C42—864no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—862no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C2×D4×D4312yes—
649C23C2×D4×D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—862no—
657Q8—862no—
658Q8—3444no—
659Q8—1722no—
660D4—862no—
661D4—862no—
662D4—3444no—
663D4—1722no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—3444no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#41×D4312yes—
694C2×C4C2×#1062190012yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—434no—
698C8—862no—
699C8C2×#1062190014yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3444no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22#1458344412yes—
709C22#1458370812yes—
710C22#1458371512yes—
711C22C22×D4×D4311yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—862no—
718C4—862no—
719C4—862no—
720C4—862no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458344412yes—
725C4C2×#41×D4311yescharacteristic
726C4C22×#1062190011yescharacteristic
727C2—42no—
728C2—3442no—
729C2#1914526414yesdirect product factor
730C2C2×#1458344411yescharacteristic
731C2C2×#1458370811yescharacteristic
732C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#470D43
hypocenterC43C2×#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#14583509C2semidirect
3. #19145264C2direct (N × H)
4. C2×#14583306C2semidirect
5. C2×#14583292C2semidirect
6. C2×#14583255C2semidirect
7. C2×#14583248C2semidirect
9. C2×#14583138C2semidirect
11. C2×#14583003C2semidirect
12. C2×#14583002C2semidirect
13. C2×Q16×Dic43C2semidirect
14. C2×#14582986C2semidirect
15. C2×#14582857C2semidirect
16. C2×C43×#470C2semidirect
24. #14583509C22semidirect
44. #14583306C22semidirect
45. #14583292C22semidirect
46. #14583255C22semidirect
47. #14583248C22semidirect
49. #14583138C22semidirect
51. #14583003C22semidirect
52. #14583002C22semidirect
53. Q16×Dic43C22semidirect
54. #14582986C22semidirect
64. #14582857C22semidirect
73. C43×#470C22semidirect
368. C2×#470D43semidirect
378. C2×C43#3178semidirect
418. #470C2×D43semidirect
443. C43C2×#3178semidirect
729. C2#19145264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835222
C2×#145835092
#191452642
C2×#145833062
C2×#145832922
C2×#145832552
C2×#145832482
C2×#145831452
C2×#145831382
C2×#145831302
C2×#145830032
C2×#145830022
C2×Q16×Dic432
C2×#145829862
C2×#145828572
C2×C43×#4702
C2×#317843