Finite Group Databasebeta

← C2×#19145299 #25966515

Subgroups — C2×#19145299 #25966515

Order 11008.

1998 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic, complemented
2C2×#14583435C211yesmaximal, characteristic
3#19145299C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583292C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583260C211yesmaximal, characteristic, complemented
8C2×#14583138C211yesmaximal, characteristic, complemented
9C2×#14583130C211yesmaximal, characteristic
10C2×#14583128C211yesmaximal, characteristic
11C2×#14583006C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14582998C211yesmaximal, characteristic, complemented
15C22×#13063235C211yesmaximal, characteristic, complemented
16C2×C43×#467C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583451—24no—
22#14583451C2218yescomplemented
23C2×#13063324C2211yescharacteristic
24C2×#13063323C2211yescharacteristic
25#14583435—24no—
26#14583435C2218yes—
27C2×#13063320—21no—
28C2×#13063316C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063314C2211yescharacteristic
31C2×#13063309—21no—
32C2×#13063304C2211yescharacteristic
33C2×#13063302—21no—
34C2×#13063299C2211yescharacteristic
35C2×Q8×Dic43C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×#13063290—21no—
38C2×#13063290C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063283—21no—
42C2×#13063281—21no—
43C22×C4×Dic43C2211yescharacteristic
44#14583307C2218yescomplemented
45#14583292C2218yescomplemented
46#14583266C2218yescomplemented
47#14583260C2218yescomplemented
48#14583138C2218yescomplemented
49#14583130C2218yes—
50#14583128C2218yes—
51#14583006C2218yescomplemented
52#14583003C2218yescomplemented
53#14583002C2218yescomplemented
54#14582998C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063235C2211yescharacteristic
65C2×#13063235C2211yescharacteristic
66C2×#13063235C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2218yescomplemented
69C22×Q16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#467C2218yescomplemented
74C2×#107×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C23×Dic43D411yescharacteristic
82C23×Dic43D411yescharacteristic
83C22×C4×D43—21no—
84C2×#10621885—24no—
85C2×#10621885C2314yes—
86C2×#10621873—24no—
87C2×#10621873C2314yes—
88C2×#10621884—24no—
89C2×#10621884C2314yes—
90C22×C43⋊C8—24no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94#13063324—22no—
95#13063324C2314yes—
96#13063323—22no—
97#13063323C2314yes—
98#13063320—28no—
99#13063316—22no—
100#13063316C2314yes—
101#13063315—28no—
102#13063314—22no—
103#13063314C2314yes—
104#13063309—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063302—28no—
108#13063299—22no—
109#13063299C2314yes—
110Q8×Dic43—22no—
111Q8×Dic43—22no—
112Q8×Dic43C2314yes—
113Q8×Dic43C2314yes—
114#13063290—28no—
115#13063290—22no—
116#13063290C2314yes—
117#13063287—22no—
118#13063287C2314yes—
119(C22⋊D43)⋊C4—28no—
120#13063283—28no—
121#13063281—28no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D414yes—
144C2×C4×Dic43C2311yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146C2×C4×Dic43C2314yes—
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150#13063250C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063248C2314yes—
154#13063247C2314yes—
155#13063245C2314yes—
156#13063235C2314yes—
157#13063235C2314yes—
158#13063235C2314yes—
159#13063235C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C22×C8×C43—24no—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2314yes—
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#107×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—44no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—42no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D414yes—
214C22×Dic43C2×D414yes—
215C2×D172—21no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172C2412yes—
219C2×C4×D43—24no—
220C2×C4×D43—44no—
221C2×Dic86—22no—
222C2×Dic86—22no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86—44no—
226C2×Dic86C2412yes—
227Q16×C43—28no—
228C2×C8×C43—22no—
229C2×C8×C43—28no—
230C2×C8×C43#4114yes—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊Dic43—24no—
242#10621885—28no—
243#10621884—28no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
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×D414yes—
265C4×Dic43C2×D412yes—
266C4×Dic43C2×D414yes—
267C4×Dic43C2×D412yes—
268C4×Dic43C2412yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—28no—
272C2×C43⋊C8#4114yes—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275#10621873—28no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43#13714yes—
279C23×C43C22×D412yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—42no—
290Q8×C43—42no—
291C2×C4×C43—22no—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C43C2×#4112yes—
307C2×C4×C43C2511yescharacteristic
308C22⋊D43—48no—
309C2×Dic43—28no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—44no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325D172—22no—
326D172—22no—
327D172—42no—
328C4×D43—48no—
329Dic86—22no—
330Dic86—22no—
331Dic86—48no—
332Dic86—42no—
333C8×C43—22no—
334C8×C43C2×#4114yes—
335C43⋊C8—22no—
336C43⋊C8C2×#4114yes—
337C2×#3181—431nomaximal, Sylow
338C22×C43—28no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43#53212yes—
342C22×C43C2×#13714yes—
343C22×C43C2×#13712yes—
344C22×C43#57512yes—
345C22×C43C23×D411yescharacteristic
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—84no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#53212yes—
356C4×C43C22×#4111yescharacteristic
357C4×C43C22×#4111yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C2×#533—431no—
366C2×#529—431no—
367#3181—4316no—
368C2×#501—431no—
369C2×#497—431no—
370C2×#491—431no—
371C2×#489—431no—
372C2×#467—431no—
373C2×#467D4311yescharacteristic, complemented
374C2×#465—431no—
375C2×#465—431no—
376C2×#441—431no—
377C2×#441—431no—
378C2×#440—431no—
379C2×#440—431no—
380C22×#97—431no—
381C2×C43—24no—
382C2×C43#318114yescomplemented
383C2×C43C2×#53211yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57511yescharacteristic
386D43—82no—
387C22×Q16—431no—
388C22×Q16C2×D4311yescharacteristic
389C22×SD16—431no—
390C22×SD16—431no—
391C23×C8—431no—
392C23×C8C2×D4311yescharacteristic
393#533—438no—
394#533—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397#529—438no—
398#529—864no—
399C2×#126—861no—
400C2×#125—431no—
401C2×#125—861no—
402C2×#124—431no—
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×Q8—861no—
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×#117—861no—
416C2×#117—861no—
417C22×C42—431no—
418#501—438no—
419#497—438no—
420#491—438no—
421#489—438no—
422#467—438no—
423#467C2×D4318yescomplemented
424#465—438no—
425#465—438no—
426#441—438no—
427#441—438no—
428#440—438no—
429#440—438no—
430C2×#107—431no—
431C2×#107C2×D4311yescharacteristic
432C2×#106—431no—
433C2×#106—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103C2×D4311yescharacteristic
439C2×#103C2×D4311yescharacteristic
440C2×#102—431no—
441C2×#102—431no—
442C2×#97—431no—
443C2×#97—431no—
444C2×#97—431no—
445C2×#97—431no—
446C2×#97—438no—
447C43C2×#318111yescharacteristic, complemented, Sylow
448C22×Q8—431no—
449C22×Q8—861no—
450C22×Q8C22×D4311yescharacteristic
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C22×D4—861no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—861no—
457C23×C4C22×D4311yescharacteristic
458C2×Q16—24no—
459C2×Q16—434no—
460C2×Q16—864no—
461C2×Q16C22×D4314yes—
462C2×SD16—434no—
463C2×SD16—434no—
464C2×SD16—864no—
465C2×SD16—864no—
466C22×C8—24no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—434no—
470C22×C8—864no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4314yes—
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477C4⋊Q8—862no—
478#126—868no—
479#125—434no—
480#125—862no—
481#125—868no—
482#124—434no—
483#124—862no—
484#123—868no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—434no—
488C22⋊Q8—868no—
489C22⋊Q8—862no—
490C22⋊Q8C22×D4314yes—
491C22⋊Q8C22×D4314yes—
492#121—434no—
493#121—862no—
494C4×Q8—434no—
495C4×Q8—434no—
496C4×Q8—434no—
497C4×Q8—862no—
498C4×Q8—868no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—868no—
504#117—868no—
505#117—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
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⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
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—434no—
531C2×C42—431no—
532C2×C42—431no—
533C2×C42—434no—
534C2×C42—861no—
535C2×C42—861no—
536C2×C42—861no—
537#107—434no—
538#107C22×D4314yes—
539#106—434no—
540#106—434no—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103C22×D4314yes—
546#103C22×D4314yes—
547#102—434no—
548#102—434no—
549#97—434no—
550#97—434no—
551#97—434no—
552#97—434no—
553C24—861no—
554C24D4×D4311yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—432no—
562C2×Q8—864no—
563C2×Q8—861no—
564C2×Q8—862no—
565C2×Q8—862no—
566C2×Q8—1724no—
567C2×Q8C23×D4312yes—
568C2×Q8C23×D4312yes—
569C2×D4—432no—
570C2×D4—864no—
571C2×D4—861no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—1724no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—434no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—434no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—1724no—
593C22×C4—1722no—
594C22×C4D4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4C23×D4312yes—
597C22×C4C23×D4311yescharacteristic
598Q16—28no—
599Q16—868no—
600SD16—868no—
601SD16—868no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8—434no—
605C2×C8—432no—
606C2×C8—432no—
607C2×C8—868no—
608C2×C8—862no—
609C2×C8#1062190014yes—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—864no—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—434no—
639C42—432no—
640C42—434no—
641C42—432no—
642C42—432no—
643C42—432no—
644C42—864no—
645C42—864no—
646C42—864no—
647C23—22no—
648C23—22no—
649C23—862no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23#1306335714yes—
654C23C2×D4×D4312yes—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—862no—
663Q8—862no—
664Q8—1728no—
665Q8—1722no—
666D4—862no—
667D4—862no—
668D4—1728no—
669D4—1722no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—868no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—1728no—
695C2×C4—1724no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4C2×D4×D4312yes—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4#41×D4312yes—
702C2×C4C2×#1062190012yes—
703C2×C4C24×D4311yescharacteristic
704C8—22no—
705C8—434no—
706C8—862no—
707C8C2×#1062190014yes—
708C22—22no—
709C22—28no—
710C22—22no—
711C22—3444no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22#1458344412yes—
716C22C2×#1306335714yes—
717C22C2×#1306335712yes—
718C22#1458369612yes—
719C22C22×D4×D4311yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—862no—
726C4—862no—
727C4—862no—
728C4—862no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4#1458344412yes—
733C4C2×#41×D4311yescharacteristic
734C4C22×#1062190011yescharacteristic
735C2—24no—
736C2—3442no—
737C2#1914529914yesdirect product factor
738C2C2×#1458344411yescharacteristic
739C2C22×#1306335711yescharacteristic
740C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#467D43
hypocenterC43C2×#3181
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
3. #19145299C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583292C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583260C2semidirect
8. C2×#14583138C2semidirect
11. C2×#14583006C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14582998C2semidirect
15. C22×#13063235C2semidirect
16. C2×C43×#467C2semidirect
22. #14583451C22semidirect
44. #14583307C22semidirect
45. #14583292C22semidirect
46. #14583266C22semidirect
47. #14583260C22semidirect
48. #14583138C22semidirect
51. #14583006C22semidirect
52. #14583003C22semidirect
53. #14583002C22semidirect
54. #14582998C22semidirect
68. C2×#13063235C22semidirect
73. C43×#467C22semidirect
373. C2×#467D43semidirect
382. C2×C43#3181semidirect
423. #467C2×D43semidirect
447. C43C2×#3181semidirect
737. C2#19145299direct (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×#145834352
#191452992
C2×#145833072
C2×#145832922
C2×#145832662
C2×#145832602
C2×#145831382
C2×#145831302
C2×#145831282
C2×#145830062
C2×#145830032
C2×#145830022
C2×#145829982
C22×#130632352
C2×C43×#4672
C2×#318143