Finite Group Databasebeta

← C2×#19146028 #25969530

Subgroups — C2×#19146028 #25969530

Order 11008.

1818 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×#14583523C211yesmaximal, characteristic
2C2×#14583507C211yesmaximal, characteristic, complemented
3#19146028C2116yesmaximal, direct product factor
4C2×#14583209C211yesmaximal, characteristic, complemented
5C2×#14583191C211yesmaximal, characteristic, complemented
6C2×#14583198C211yesmaximal, characteristic, complemented
7C2×#14583158C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic
9C2×#14583139C211yesmaximal, characteristic, complemented
10C2×#14583129C211yesmaximal, characteristic
11C2×#14583122C211yesmaximal, characteristic, complemented
12C2×#14583121C211yesmaximal, characteristic, complemented
13C2×#14583108C211yesmaximal, characteristic, complemented
14C2×#14583103C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#475C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583523—24no—
24#14583523C2218yes—
25#14583507—24no—
26#14583507C2218yescomplemented
27C2×#13063323C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063320—21no—
30C2×#13063319—21no—
31C2×#13063317—21no—
32C2×#13063316C2211yescharacteristic
33C2×#13063315—21no—
34C2×#13063314—21no—
35C2×#13063313C2211yescharacteristic
36C2×#13063310—21no—
37C2×#13063305C2211yescharacteristic
38C2×#13063305C2211yescharacteristic
39C2×#13063301—21no—
40C2×#13063301C2211yescharacteristic
41C2×#13063300C2211yescharacteristic
42C2×C4×Dic86C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583209C2218yescomplemented
47#14583198C2218yescomplemented
48#14583191C2218yescomplemented
49#14583158C2218yescomplemented
50#14583148C2218yes—
51#14583139C2218yescomplemented
52#14583129C2218yes—
53#14583122C2218yescomplemented
54#14583121C2218yescomplemented
55#14583108C2218yescomplemented
56#14583103C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#475C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×Dic172—42no—
84C2×Dic172C2314yes—
85C2×#10621885—42no—
86C2×#10621885C2314yes—
87C2×#10621873—42no—
88C2×#10621873C2314yes—
89C2×#10621884—42no—
90C2×#10621884C2314yes—
91C2×#10621872—42no—
92C2×#10621872C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—42no—
96C2×C8×D43C2314yes—
97#13063323—22no—
98#13063323C2314yes—
99#13063320—28no—
100#13063320—28no—
101#13063319—28no—
102#13063317—28no—
103#13063316—22no—
104#13063316C2314yes—
105#13063315—28no—
106#13063314—28no—
107#13063313—22no—
108#13063313C2314yes—
109#13063310—28no—
110#13063305—22no—
111#13063305—22no—
112#13063305C2314yes—
113#13063305C2314yes—
114#13063301—22no—
115#13063301—28no—
116#13063301C2314yes—
117#13063300—22no—
118#13063300C2314yes—
119C4×Dic86—22no—
120C4×Dic86C2314yes—
121#13063290—22no—
122#13063290C2314yes—
123#13063287—22no—
124#13063287C2314yes—
125#13063282D414yes—
126#13063282C2314yes—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×Dic43⋊C4D411yescharacteristic
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43C2311yescharacteristic
151#13063258C2314yes—
152#13063258C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063247C2314yes—
161#13063245C2314yes—
162C22×Q8×C43—21no—
163C22×Q8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C4⋊Q8×C43—22no—
167C4⋊Q8×C43C2314yes—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#106×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—24no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—82no—
189C2×Q8×C43C2412yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C2×D172—21no—
204C2×D172—24no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—82no—
208C2×D172C2412yes—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×C4×D43—82no—
213C2×C4×D43C2×D412yes—
214C2×C4×D43C2412yes—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86C2412yes—
222C2×Dic86C2412yes—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43C2412yes—
226C2×C8×C43C2412yes—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C2412yes—
233C4⋊C4×C43C2412yes—
234C4⋊C4×C43C2412yes—
235C42×C43—24no—
236C42×C43C2×D412yes—
237C42×C43C2412yes—
238#10621885—44no—
239#10621884—44no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4C2×D414yes—
248(C2×D43)⋊C4C2×D414yes—
249C4⋊Dic43—21no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261Dic43⋊C4C2×D414yes—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270Dic172—44no—
271#10621873—44no—
272#10621872—44no—
273C8×D43—44no—
274C23×C43C22×D411yescharacteristic
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43C22×D412yes—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—42no—
286Q8×C43—84no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43H(5,𝔽2)12yes—
301C2×C4×C432−1+412yes—
302C2×C4×C43C2511yescharacteristic
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315D172—22no—
316D172—22no—
317D172—42no—
318D172—84no—
319C4×D43—24no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—84no—
323Dic86—22no—
324Dic86—22no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—42no—
329C8×C43—22no—
330C8×C43—22no—
331C43⋊C8—22no—
332C43⋊C8—22no—
333C2×#3258—431nomaximal, Sylow
334C22×C43#53712yes—
335C22×C43#57712yes—
336C22×C43#57812yes—
337C22×C43C23×D411yescharacteristic
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—44no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—84no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#53712yes—
353C4×C43C2×H(5,𝔽2)11yescharacteristic
354C4×C43C2×2−1+411yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541—431no—
363#3258—4316no—
364C2×#479—431no—
365C2×#477—431no—
366C2×#475D4311yescharacteristic, complemented
367C2×#478—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#464—431no—
373C2×#464—431no—
374C2×#462—431no—
375C2×#461—431no—
376C2×#424—431no—
377C2×C43#325814yescomplemented
378C2×C43C2×#53711yescharacteristic
379C2×C43C2×#57711yescharacteristic
380C2×C43C2×#57811yescharacteristic
381D43—42no—
382D43—82no—
383C22×Q16—431no—
384C22×Q16—431no—
385C22×SD16—431no—
386C22×SD16—431no—
387C22×M16—431no—
388C23×C8—431no—
389#542—438no—
390#542—864no—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8C2×D4311yescharacteristic
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—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117—431no—
414#479—438no—
415#478—438no—
416#477—438no—
417#475C2×D4318yescomplemented
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#464—438no—
423#464—438no—
424#462—438no—
425#461—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106C2×D4311yescharacteristic
429C2×#106C2×D4311yescharacteristic
430#424—438no—
431C2×C4⋊C8—431no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103C2×D4311yescharacteristic
440C2×#103C2×D4311yescharacteristic
441C2×#102—431no—
442C2×#102—431no—
443C43C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—21no—
445C22×Q8—431no—
446C22×Q8—431no—
447C22×Q8C22×D4311yescharacteristic
448C22×D4—431no—
449C22×D4—861no—
450C23×C4—431no—
451C23×C4—861no—
452C2×Q16—434no—
453C2×Q16—434no—
454C2×Q16—1722no—
455C2×Q16—1722no—
456C2×SD16—434no—
457C2×SD16—434no—
458C2×SD16—1722no—
459C2×SD16—1722no—
460C2×M16—434no—
461C2×M16—1722no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—434no—
465C22×C8—1722no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8C22×D4314yes—
472#126—868no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—868no—
477#125—862no—
478#125—868no—
479#124—434no—
480#124—868no—
481#124—862no—
482#123—868no—
483C22⋊Q8—434no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—868no—
489C22⋊Q8—862no—
490#121—434no—
491#121—862no—
492C4×Q8—22no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8C22×D4314yes—
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—861no—
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⋊C4C22×D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106C22×D4314yes—
536#106C22×D4314yes—
537C4⋊C8—434no—
538C4⋊C8—434no—
539C4⋊C8—434no—
540C4⋊C8C22×D4314yes—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103C22×D4314yes—
546#103C22×D4314yes—
547#102—434no—
548#102—434no—
549C24—431no—
550C24—861no—
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—82no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—862no—
564C2×Q8C23×D4312yes—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—861no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3442no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—864no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—3442no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590Q16—1724no—
591Q16—1724no—
592SD16—1724no—
593SD16—1724no—
594M16—1724no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—862no—
600C2×C8—862no—
601C2×C8—1724no—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—434no—
610C4⋊C4—434no—
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—864no—
622C4⋊C4C23×D4312yes—
623C4⋊C4C23×D4312yes—
624C4⋊C4C23×D4312yes—
625C22⋊C4—434no—
626C22⋊C4—434no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C42—24no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42D4×D4312yes—
640C42C23×D4312yes—
641C23—432no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23C2×D4×D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—862no—
655Q8—862no—
656Q8—862no—
657Q8—862no—
658Q8—1722no—
659Q8—1722no—
660D4—862no—
661D4—862no—
662D4—3444no—
663D4—1722no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—864no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—3444no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4C2×D4×D4312yes—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#1306337112yes—
694C2×C4#1306337312yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—862no—
700C22—862no—
701C22—862no—
702C22—862no—
703C22—3444no—
704C22—1722no—
705C22—1722no—
706C22—1722no—
707C22—1724no—
708C22#1458347912yes—
709C22#1458370512yes—
710C22#1458371512yes—
711C22C22×D4×D4311yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—862no—
719C4—862no—
720C4—862no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458347912yes—
725C4C2×#1306337111yescharacteristic
726C4C2×#1306337311yescharacteristic
727C2—3442no—
728C2—1722no—
729C2#1914602814yesdirect product factor
730C2C2×#1458347911yescharacteristic
731C2C2×#1458370511yescharacteristic
732C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×#475D43
hypocenterC43C2×#3258
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#14583507C2semidirect
3. #19146028C2direct (N × H)
4. C2×#14583209C2semidirect
5. C2×#14583191C2semidirect
6. C2×#14583198C2semidirect
7. C2×#14583158C2semidirect
9. C2×#14583139C2semidirect
11. C2×#14583122C2semidirect
12. C2×#14583121C2semidirect
13. C2×#14583108C2semidirect
14. C2×#14583103C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#475C2semidirect
26. #14583507C22semidirect
46. #14583209C22semidirect
47. #14583198C22semidirect
48. #14583191C22semidirect
49. #14583158C22semidirect
51. #14583139C22semidirect
53. #14583122C22semidirect
54. #14583121C22semidirect
55. #14583108C22semidirect
56. #14583103C22semidirect
59. #14582924C22semidirect
71. C43×#475C22semidirect
366. C2×#475D43semidirect
377. C2×C43#3258semidirect
417. #475C2×D43semidirect
443. C43C2×#3258semidirect
729. C2#19146028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835232
C2×#145835072
#191460282
C2×#145832092
C2×#145831912
C2×#145831982
C2×#145831582
C2×#145831482
C2×#145831392
C2×#145831292
C2×#145831222
C2×#145831212
C2×#145831082
C2×#145831032
C2×#145829242
C2×C43×#4752
C2×#325843