Finite Group Databasebeta

← C2×#19145197 #25966370

Subgroups — C2×#19145197 #25966370

Order 11008.

1986 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×#14583453C211yesmaximal, characteristic, complemented
2C2×#14583431C211yesmaximal, characteristic
3#19145197C2116yesmaximal, direct product factor
4C2×#14583306C211yesmaximal, characteristic, complemented
5C2×#14583290C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583257C211yesmaximal, characteristic, complemented
8C2×#14583158C211yesmaximal, characteristic, complemented
9C2×#14583156C211yesmaximal, characteristic, complemented
10C2×#14583144C211yesmaximal, characteristic
11C2×#14583142C211yesmaximal, characteristic
12C2×C4×Dic172C211yesmaximal, characteristic, complemented
13C2×C4×#10621885C211yesmaximal, characteristic, complemented
14C2×C4×#10621883C211yesmaximal, characteristic, complemented
15C2×C4×#10621872C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22#14583453—24no—
23#14583453C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063323C2211yescharacteristic
26#14583431—24no—
27#14583431C2218yes—
28C2×#13063318—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063315—21no—
31C2×#13063312C2211yescharacteristic
32C2×#13063307—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063303—21no—
36C2×#13063301C2211yescharacteristic
37C2×#13063296C2211yescharacteristic
38C2×C4×Dic86—21no—
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×Dic86C2211yescharacteristic
41C2×C4×C22⋊D43—21no—
42C2×#13063284—21no—
43C2×#13063282—21no—
44C2×C42×D43C2211yescharacteristic
45#14583306C2218yescomplemented
46#14583290C2218yescomplemented
47#14583266C2218yescomplemented
48#14583257C2218yescomplemented
49#14583158C2218yescomplemented
50#14583156C2218yescomplemented
51#14583144C2218yes—
52#14583142C2218yes—
53C4×Dic172C2218yescomplemented
54C4×#10621885C2218yescomplemented
55C4×#10621883C2218yescomplemented
56C2×#13063259C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C4×#10621872C2218yescomplemented
66C2×#13063235C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×SD16×C43C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×Dic172—24no—
85C2×Dic172C2314yes—
86C2×#10621885—24no—
87C2×#10621885C2314yes—
88C2×#10621883—24no—
89C2×#10621883C2314yes—
90C2×#10621872—24no—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C2×#10621872C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96#13063324—22no—
97#13063324C2314yes—
98#13063323—22no—
99#13063323C2314yes—
100#13063318—28no—
101#13063316—22no—
102#13063316C2314yes—
103#13063315—28no—
104#13063312—22no—
105#13063312C2314yes—
106#13063307—28no—
107#13063305—22no—
108#13063305—22no—
109#13063305C2314yes—
110#13063305C2314yes—
111#13063303—28no—
112#13063301—22no—
113#13063301C2314yes—
114#13063296—22no—
115#13063296C2314yes—
116C4×Dic86—22no—
117C4×Dic86—22no—
118C4×Dic86—28no—
119C4×Dic86C2314yes—
120C4×Dic86C2314yes—
121C4×C22⋊D43—28no—
122#13063284—28no—
123#13063282—28no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
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×Dic43⋊C4—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—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×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147C42×D43D414yes—
148C42×D43C2314yes—
149#13063259C2314yes—
150#13063258C2314yes—
151#13063256C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063246C2314yes—
158#13063235C2314yes—
159#13063235C2314yes—
160C4×C43⋊C8C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—24no—
165C2×SD16×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yes—
179#103×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43C2412yes—
192C22×C4×C43—24no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—44no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—24no—
201C2×C22⋊D43—44no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C2×C4×D43—24no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—42no—
213C2×C4×D43C2×D412yes—
214C2×C4×D43C2×D414yes—
215C2×C4×D43C2×D414yes—
216C2×C4×D43C2412yes—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—22no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—24no—
224C2×Dic86—44no—
225C2×Dic86C2412yes—
226C2×Dic86C2412yes—
227SD16×C43—28no—
228C2×C8×C43—22no—
229C2×C8×C43#4114yes—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C42×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244#10621885—28no—
245#10621883—28no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43—24no—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43C2×D412yes—
266C4×Dic43C2×D414yes—
267C4×Dic43C2×D414yes—
268C4×Dic43C2412yes—
269C2×C43⋊C8—22no—
270C2×C43⋊C8#4114yes—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273Dic172—28no—
274#10621872—28no—
275#10621872—28no—
276C23×C43—22no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43C22×D412yes—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—42no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—48no—
299C2×C4×C43#13714yes—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D412yes—
303C2×C4×C43C2×#4112yes—
304C2×C4×C43C2×#4112yes—
305C2×C4×C43C2511yescharacteristic
306C22⋊D43—48no—
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×Dic43—42no—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C4×D43—24no—
322C4×D43—28no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—44no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—48no—
331Dic86—42no—
332Dic86—42no—
333C8×C43—22no—
334C8×C43C2×#4114yes—
335C43⋊C8—22no—
336C43⋊C8C2×#4114yes—
337C2×#3172—431nomaximal, Sylow
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—84no—
342C22×C43#53212yes—
343C22×C43C2×#13712yes—
344C22×C43#57512yes—
345C22×C43C23×D411yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—44no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43#53212yes—
355C4×C43C2×#13714yes—
356C4×C43C22×#4111yescharacteristic
357C4×C43C22×#4111yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C2×#533—431no—
366C2×#529—431no—
367#3172—4316no—
368C2×#501—431no—
369C2×#497—431no—
370C2×#491—431no—
371C2×#489—431no—
372C2×#470—431no—
373C2×#470—431no—
374C2×#468—431no—
375C2×#468—431no—
376C2×C4×Q16—431no—
377C2×C4×Q16—431no—
378C2×C4×SD16—431no—
379C2×C4×SD16D4311yescharacteristic, complemented
380C2×C4×M16—431no—
381C2×C43—82no—
382C2×C43#317214yescomplemented
383C2×C43C2×#53211yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57511yescharacteristic
386D43—42no—
387C22×Q16—431no—
388C22×Q16—431no—
389C22×SD16—431no—
390C22×SD16C2×D4311yescharacteristic
391C22×M16—431no—
392C22×M16—431no—
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—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—861no—
412C2×C4×Q8C2×D4311yescharacteristic
413C2×C4×D4—861no—
414C2×C4×D4C2×D4311yescharacteristic
415C2×#117—861no—
416C2×#117—861no—
417C22×C42—431no—
418#501—438no—
419#497—438no—
420#491—438no—
421#489—438no—
422#470—438no—
423#470—438no—
424#468—438no—
425#468—438no—
426C4×Q16—438no—
427C4×Q16—438no—
428C4×SD16—438no—
429C4×SD16C2×D4318yescomplemented
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106C2×D4311yescharacteristic
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103C2×D4311yescharacteristic
440C2×#102—431no—
441C2×#102C2×D4311yescharacteristic
442C4×M16—438no—
443C2×#97—431no—
444C2×#97—431no—
445C2×C4×C8—431no—
446C2×C4×C8C2×D4311yescharacteristic
447C43C2×#317211yescharacteristic, complemented, Sylow
448C22×Q8—431no—
449C22×Q8—431no—
450C22×Q8—861no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—861no—
453C22×D4C22×D4311yescharacteristic
454C23×C4—21no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C2×Q16—434no—
459C2×Q16—434no—
460C2×Q16—864no—
461C2×Q16—864no—
462C2×SD16—24no—
463C2×SD16—434no—
464C2×SD16—864no—
465C2×SD16C22×D4314yes—
466C2×M16—434no—
467C2×M16—434no—
468C2×M16—864no—
469C2×M16—864no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
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—434no—
486C22⋊Q8—434no—
487C22⋊Q8—434no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490C22⋊Q8—868no—
491C22⋊Q8—862no—
492#121—434no—
493#121—862no—
494C4×Q8—22no—
495C4×Q8—434no—
496C4×Q8—434no—
497C4×Q8—868no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8C22×D4314yes—
501C4×D4—22no—
502C4×D4—868no—
503C4×D4C22×D4314yes—
504#117—868no—
505#117—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
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⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
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—431no—
531C2×C42—431no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—861no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#107—434no—
538#107—434no—
539#106—434no—
540#106C22×D4314yes—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103C22×D4314yes—
547#102—434no—
548#102C22×D4314yes—
549#97—434no—
550#97—434no—
551C4×C8—434no—
552C4×C8C22×D4314yes—
553C24—21no—
554C24—431no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—864no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—862no—
564C2×Q8—862no—
565C2×Q8—862no—
566C2×Q8—862no—
567C2×Q8—1724no—
568C2×Q8C23×D4312yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—864no—
573C2×D4—1724no—
574C2×D4C23×D4312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—434no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—434no—
587C22×C4—864no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—1722no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598Q16—868no—
599Q16—868no—
600SD16—28no—
601SD16—868no—
602M16—868no—
603M16—868no—
604C2×C8—22no—
605C2×C8—434no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—862no—
609C2×C8#1062189814yes—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—24no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—24no—
639C42—434no—
640C42—432no—
641C42—434no—
642C42—432no—
643C42—864no—
644C42—864no—
645C42D4×D4312yes—
646C42C23×D4312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—432no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—862no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—1728no—
664Q8—1722no—
665Q8—1722no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—1728no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—48no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—868no—
685C2×C4—864no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—1724no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4#1306335414yes—
698C2×C4C2×D4×D4312yes—
699C2×C4C2×D4×D4312yes—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4#41×D4312yes—
702C2×C4C2×#1062189812yes—
703C2×C4C24×D4311yescharacteristic
704C8—22no—
705C8—434no—
706C8—862no—
707C8C2×#1062189814yes—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—1724no—
716C22#1458344612yes—
717C22C2×#1306335412yes—
718C22#1458369612yes—
719C22C22×D4×D4311yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—862no—
725C4—862no—
726C4—862no—
727C4—1722no—
728C4—1722no—
729C4—1722no—
730C4—1722no—
731C4#1458344612yes—
732C4C2×#1306335414yes—
733C4C2×#41×D4311yescharacteristic
734C4C22×#1062189811yescharacteristic
735C2—82no—
736C2—1722no—
737C2#1914519714yesdirect product factor
738C2C2×#1458344611yescharacteristic
739C2C22×#1306335411yescharacteristic
740C2C2×#1458369611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×C4×SD16D43
hypocenterC43C2×#3172
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
3. #19145197C2direct (N × H)
4. C2×#14583306C2semidirect
5. C2×#14583290C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583257C2semidirect
8. C2×#14583158C2semidirect
9. C2×#14583156C2semidirect
12. C2×C4×Dic172C2semidirect
13. C2×C4×#10621885C2semidirect
14. C2×C4×#10621883C2semidirect
15. C2×C4×#10621872C2semidirect
16. C2×C4×SD16×C43C2semidirect
23. #14583453C22semidirect
45. #14583306C22semidirect
46. #14583290C22semidirect
47. #14583266C22semidirect
48. #14583257C22semidirect
49. #14583158C22semidirect
50. #14583156C22semidirect
53. C4×Dic172C22semidirect
54. C4×#10621885C22semidirect
55. C4×#10621883C22semidirect
65. C4×#10621872C22semidirect
72. C4×SD16×C43C22semidirect
379. C2×C4×SD16D43semidirect
382. C2×C43#3172semidirect
429. C4×SD16C2×D43semidirect
447. C43C2×#3172semidirect
737. C2#19145197direct (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×#145834312
#191451972
C2×#145833062
C2×#145832902
C2×#145832662
C2×#145832572
C2×#145831582
C2×#145831562
C2×#145831442
C2×#145831422
C2×C4×Dic1722
C2×C4×#106218852
C2×C4×#106218832
C2×C4×#106218722
C2×C4×SD16×C432
C2×#317243