Finite Group Databasebeta

← C2×#20256107 #27095954

Subgroups — C2×#20256107 #27095954

Order 12032.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689845C211yesmaximal, characteristic, complemented
2C2×D4×Dic94C211yesmaximal, characteristic, complemented
3#20256107C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689483C211yesmaximal, characteristic, complemented
6C2×#15689472C211yesmaximal, characteristic, complemented
7C2×#15689418C211yesmaximal, characteristic, complemented
8C2×#15689417C211yesmaximal, characteristic, complemented
9C2×#15689402C211yesmaximal, characteristic, complemented
10C2×#15689340C211yesmaximal, characteristic
11C2×#15689338C211yesmaximal, characteristic
12C2×#15689326C211yesmaximal, characteristic, complemented
13C2×#15689251C211yesmaximal, characteristic, complemented
14C2×#15689220C211yesmaximal, characteristic, complemented
15C2×#15689203C211yesmaximal, characteristic
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C23×Dic94—21no—
18C22×#10625335C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689845—24no—
21#15689845C2218yescomplemented
22D4×Dic94—24no—
23D4×Dic94C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094022C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094018—21no—
30C2×#13094013C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094003—21no—
33C2×#13094002—21no—
34C2×#13094001—21no—
35C2×#13094001—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×#13093981—21no—
42#15689484C2218yescomplemented
43#15689483C2218yescomplemented
44#15689472C2218yescomplemented
45#15689418C2218yescomplemented
46#15689417C2218yescomplemented
47#15689402C2218yescomplemented
48#15689340C2218yes—
49#15689338C2218yes—
50#15689326C2218yescomplemented
51#15689251C2218yescomplemented
52#15689220C2218yescomplemented
53#15689203C2218yes—
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#440C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94—21no—
80C22×Dic94—28no—
81C22×Dic94—48no—
82C22×Dic94D411yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C2×#10625335—24no—
89C2×#10625335C2314yes—
90C2×#10625334—24no—
91C2×#10625334C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094024—22no—
95#13094024C2314yes—
96#13094023—22no—
97#13094023—22no—
98#13094023C2314yes—
99#13094023C2314yes—
100#13094022—22no—
101#13094022C2314yes—
102#13094019—28no—
103#13094018—28no—
104#13094013—22no—
105#13094013C2314yes—
106#13094012—22no—
107#13094012C2314yes—
108#13094003—28no—
109#13094002—28no—
110#13094001—28no—
111#13094001—28no—
112C4×Dic94D414yes—
113C4×Dic94C2314yes—
114#13093989—22no—
115#13093989C2314yes—
116D4×Dic47—22no—
117D4×Dic47—22no—
118D4×Dic47C2314yes—
119D4×Dic47C2314yes—
120#13093986—22no—
121#13093986C2314yes—
122#13093981—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47D411yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C2×Dic47⋊C4D411yescharacteristic
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47C2311yescharacteristic
143C2×C4×Dic47C2311yescharacteristic
144#13093957C2314yes—
145#13093957C2314yes—
146C4⋊(C47⋊C8)C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149#13093949C2314yes—
150#13093949C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093944C2314yes—
157#13093934C2314yes—
158C8×Dic47C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47—21no—
162C2×SD16×C47—24no—
163C2×SD16×C47C2314yes—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C4×Q8×C47—22no—
167C4×Q8×C47C2314yes—
168C4×D4×C47—22no—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C42×C47—21no—
175C2×C42×C47C2311yescharacteristic
176#107×C47C2314yes—
177#103×C47C2314yes—
178#102×C47C2314yes—
179#97×C47C2314yes—
180C24×C47—21no—
181C23×D47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47#4114yes—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—24no—
194C22×C4×C47—44no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—24no—
202C22×Dic47—24no—
203C22×Dic47—44no—
204C22×Dic47—44no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C2×D188—22no—
210C2×D188—22no—
211C2×D188—21no—
212C2×D188C2412yes—
213C2×C4×D47—24no—
214C2×C4×D47—44no—
215C2×Dic94—24no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—21no—
219C2×Dic94—24no—
220C2×Dic94—24no—
221C2×Dic94—24no—
222C2×Dic94—432no—
223C2×Dic94—44no—
224C2×Dic94—44no—
225C2×Dic94—44no—
226C2×Dic94C2×D414yes—
227C2×Dic94C2412yes—
228SD16×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C42×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244#10625335—28no—
245#10625334—28no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47C2×D414yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4C2×D414yes—
263Dic47⋊C4C2×D414yes—
264C4×Dic47—24no—
265C4×Dic47C2×D412yes—
266C4×Dic47C2×D412yes—
267C4×Dic47C2412yes—
268C4×Dic47C2412yes—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273C23×C47—24no—
274C23×C47—22no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—42no—
285D4×C47—24no—
286D4×C47—22no—
287D4×C47C2×#4114yes—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—48no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4112yes—
301C2×C4×C472−1+412yes—
302C2×C4×C47C2511yescharacteristic
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—48no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—48no—
314C2×Dic47AGL(1,ℤ/8)14yes—
315C2×Dic47C22×D412yes—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319D188—22no—
320D188—22no—
321D188—42no—
322C4×D47—48no—
323Dic94—28no—
324Dic94—22no—
325Dic94—22no—
326Dic94—48no—
327Dic94—48no—
328Dic94—42no—
329Dic94—48no—
330C8×C47—22no—
331C8×C47—22no—
332C47⋊C8—22no—
333C47⋊C8—22no—
334C2×#3367—471nomaximal, Sylow
335C22×C47—24no—
336C22×C47—48no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47#54812yes—
340C22×C47C2×AGL(1,ℤ/8)12yes—
341C22×C47#57812yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—84no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47#54812yes—
353C4×C47C22×#4111yescharacteristic
354C4×C47C2×2−1+411yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361Dic47C2×AGL(1,ℤ/8)14yes—
362C2×#556—471no—
363C2×D4×Q8—471no—
364#3367—4716no—
365C2×#489—471no—
366C2×#489—471no—
367C2×#487—471no—
368C2×#477—471no—
369C2×#477—471no—
370C2×#474—471no—
371C2×#463—471no—
372C2×#463—471no—
373C2×#461—471no—
374C2×#446—471no—
375C2×#440—471no—
376C2×#440D4711yescharacteristic, complemented
377C2×C4×D8—471no—
378C2×C47—44no—
379C2×C47#336714yescomplemented
380C2×C47C2×#54811yescharacteristic
381C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C47C2×#57811yescharacteristic
383D47—82no—
384C23×Q8—941no—
385C22×SD16—471no—
386C22×SD16C2×D4711yescharacteristic
387C22×D8—471no—
388#556—478no—
389#556—944no—
390D4×Q8—478no—
391D4×Q8—944no—
392C2×C4⋊Q8—471no—
393C2×C4⋊Q8—471no—
394C2×C4⋊Q8—471no—
395C2×C4⋊Q8—471no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#124—471no—
399C2×#124—471no—
400C2×C22⋊Q8—941no—
401C2×C22⋊Q8—941no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8—941no—
404C2×C4×Q8—471no—
405C2×C4×Q8—471no—
406C2×C4×Q8C2×D4711yescharacteristic
407C2×C4×D4—471no—
408C2×C4×D4—471no—
409C2×C4×D4—471no—
410C2×C4×D4C2×D4711yescharacteristic
411C2×#117—941no—
412#489—478no—
413#489—478no—
414#487—478no—
415#477—478no—
416#477—478no—
417#474—478no—
418#463—478no—
419#463—478no—
420#461—478no—
421#446—478no—
422#440—478no—
423#440C2×D4718yescomplemented
424C4×D8—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107C2×D4711yescharacteristic
428C2×C4⋊C8—471no—
429C2×C4⋊C8—471no—
430C2×C4⋊C8—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#103C2×D4711yescharacteristic
437C2×#102—471no—
438C2×#102—471no—
439C2×#102—471no—
440C2×#102C2×D4711yescharacteristic
441C2×#97—471no—
442C2×#97C2×D4711yescharacteristic
443C2×C4×C8—471no—
444C47C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—471no—
446C22×Q8—471no—
447C22×Q8—941no—
448C22×Q8—941no—
449C22×Q8—948no—
450C22×Q8—941no—
451C22×Q8—1888no—
452C22×Q8C22×D4711yescharacteristic
453C22×D4—471no—
454C22×D4C22×D4711yescharacteristic
455C23×C4—21no—
456C23×C4—941no—
457C23×C4—941no—
458C23×C4—941no—
459C2×SD16—24no—
460C2×SD16—474no—
461C2×SD16—944no—
462C2×SD16C22×D4714yes—
463C2×D8—474no—
464C2×D8—944no—
465C22×C8—471no—
466C22×C8—471no—
467C22×C8C22×D4711yescharacteristic
468C22×C8C22×D4711yescharacteristic
469C4⋊Q8—474no—
470C4⋊Q8—474no—
471C4⋊Q8—474no—
472C4⋊Q8—474no—
473C4⋊Q8—942no—
474C4⋊Q8—942no—
475C4⋊Q8—942no—
476C4⋊Q8—942no—
477#126—948no—
478#126—948no—
479#124—474no—
480#124—474no—
481#124—942no—
482#124—942no—
483C22⋊Q8—948no—
484C22⋊Q8—948no—
485C22⋊Q8—948no—
486C22⋊Q8—948no—
487C4×Q8—22no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—942no—
492C4×Q8C22×D4714yes—
493C4×D4—22no—
494C4×D4—474no—
495C4×D4—474no—
496C4×D4—474no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4C22×D4714yes—
501#117—948no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4C22×D4711yescharacteristic
515C2×C4⋊C4C22×D4711yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C42—21no—
525C2×C42—471no—
526C2×C42—471no—
527C2×C42—941no—
528C2×C42C22×D4711yescharacteristic
529#107—474no—
530#107—474no—
531#107C22×D4714yes—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535#103—474no—
536#103—474no—
537#103—474no—
538#103—474no—
539#103—474no—
540#103C22×D4714yes—
541#102—474no—
542#102—474no—
543#102—474no—
544#102C22×D4714yes—
545#97—474no—
546#97C22×D4714yes—
547C4×C8—474no—
548C24—21no—
549C24—941no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—474no—
554C2×Q8—472no—
555C2×Q8—944no—
556C2×Q8—944no—
557C2×Q8—944no—
558C2×Q8—941no—
559C2×Q8—944no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—1884no—
563C2×Q8—1884no—
564C2×Q8—1884no—
565C2×Q8—18832no—
566C2×Q8C23×D4712yes—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—472no—
570C2×D4—941no—
571C2×D4—942no—
572C2×D4—942no—
573C2×D4#1062535014yes—
574C2×D4C23×D4712yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—1884no—
591C22×C4—1884no—
592C22×C4—1884no—
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4711yescharacteristic
595C22×C4C23×D4711yescharacteristic
596SD16—28no—
597SD16—948no—
598D8—948no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—472no—
602C2×C8—472no—
603C2×C8—942no—
604C2×C8—942no—
605C2×C8C23×D4712yes—
606C2×C8C23×D4712yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—474no—
611C4⋊C4—474no—
612C4⋊C4—474no—
613C4⋊C4—472no—
614C4⋊C4—472no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—944no—
623C4⋊C4C23×D4712yes—
624C4⋊C4C23×D4712yes—
625C22⋊C4—24no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C42—24no—
634C42—472no—
635C42—472no—
636C42—472no—
637C42—472no—
638C42—944no—
639C42D4×D4712yes—
640C42C23×D4712yes—
641C23—24no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—942no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—948no—
654Q8—942no—
655Q8—942no—
656Q8—1888no—
657Q8—1888no—
658Q8—1888no—
659Q8—1882no—
660D4—24no—
661D4—22no—
662D4—942no—
663D4—942no—
664D4—1882no—
665D4C2×#1062535014yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—48no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—474no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—1888no—
687C2×C4—1888no—
688C2×C4—1888no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4C2×D4×D4712yes—
693C2×C4C2×D4×D4712yes—
694C2×C4C2×D4×D4711yescharacteristic
695C2×C4C2×#1062535012yes—
696C2×C4#1309407112yes—
697C2×C4C24×D4711yescharacteristic
698C8—22no—
699C8—22no—
700C8—942no—
701C8—942no—
702C22—24no—
703C22—42no—
704C22—42no—
705C22—48no—
706C22—3764no—
707C22—1882no—
708C22—1882no—
709C22—1882no—
710C22#1568978212yes—
711C22AGL(1,ℤ/8)×D4712yes—
712C22#1568993912yes—
713C22C22×D4×D4711yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—474no—
720C4—942no—
721C4—942no—
722C4—942no—
723C4—1882no—
724C4—1882no—
725C4—1882no—
726C4#1568978212yes—
727C4C22×#1062535011yescharacteristic
728C4C2×#1309407111yescharacteristic
729C2—44no—
730C2—3762no—
731C2#2025610714yesdirect product factor
732C2C2×#1568978211yescharacteristic
733C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
734C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#440D47
hypocenterC47C2×#3367
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#15689845C2semidirect
2. C2×D4×Dic94C2semidirect
3. #20256107C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689483C2semidirect
6. C2×#15689472C2semidirect
7. C2×#15689418C2semidirect
8. C2×#15689417C2semidirect
9. C2×#15689402C2semidirect
12. C2×#15689326C2semidirect
13. C2×#15689251C2semidirect
14. C2×#15689220C2semidirect
16. C2×C47×#440C2semidirect
21. #15689845C22semidirect
23. D4×Dic94C22semidirect
42. #15689484C22semidirect
43. #15689483C22semidirect
44. #15689472C22semidirect
45. #15689418C22semidirect
46. #15689417C22semidirect
47. #15689402C22semidirect
50. #15689326C22semidirect
51. #15689251C22semidirect
52. #15689220C22semidirect
72. C47×#440C22semidirect
376. C2×#440D47semidirect
379. C2×C47#3367semidirect
423. #440C2×D47semidirect
444. C47C2×#3367semidirect
731. C2#20256107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898452
C2×D4×Dic942
#202561072
C2×#156894842
C2×#156894832
C2×#156894722
C2×#156894182
C2×#156894172
C2×#156894022
C2×#156893402
C2×#156893382
C2×#156893262
C2×#156892512
C2×#156892202
C2×#156892032
C2×C47×#4402
C2×#336747