Finite Group Databasebeta

← C2×#20253589 #27084527

Subgroups — C2×#20253589 #27084527

Order 12032.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689728C211yesmaximal, characteristic, complemented
2C2×#15689603C211yesmaximal, characteristic, complemented
3#20253589C2116yesmaximal, direct product factor
4C2×#15689442C211yesmaximal, characteristic, complemented
5C2×#15689437C211yesmaximal, characteristic, complemented
6C2×#15689431C211yesmaximal, characteristic, complemented
7C2×#15689424C211yesmaximal, characteristic, complemented
8C2×#15689324C211yesmaximal, characteristic, complemented
9C2×#15689319C211yesmaximal, characteristic, complemented
10C2×#15689270C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689236C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×C4×#10625325C211yesmaximal, characteristic, complemented
15C2×C4×D376C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689728—24no—
23#15689728C2218yescomplemented
24C2×#13094021C2211yescharacteristic
25C2×#13094016C2211yescharacteristic
26C2×#13094009—21no—
27C2×#13094009—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093997—21no—
31C2×#13093997—21no—
32#15689603—24no—
33#15689603C2218yescomplemented
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093982—21no—
43C22×C4⋊Dic47C2211yescharacteristic
44C2×C4⋊C4×D47—21no—
45#15689442C2218yescomplemented
46#15689437C2218yescomplemented
47#15689431C2218yescomplemented
48#15689424C2218yescomplemented
49#15689324C2218yescomplemented
50#15689319C2218yescomplemented
51#15689270C2218yescomplemented
52#15689270C2218yescomplemented
53#15689236C2218yescomplemented
54#15689225C2218yescomplemented
55C4×#10625325C2218yescomplemented
56C4×D376C2218yescomplemented
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C23×Dic47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C2×#10625325—24no—
97C2×#10625325—24no—
98C2×#10625325C2314yes—
99C2×#10625325C2314yes—
100C2×D376—24no—
101C2×D376—24no—
102C2×D376C2314yes—
103C2×D376C2314yes—
104#13094021—22no—
105#13094021C2314yes—
106#13094016—22no—
107#13094016C2314yes—
108#13094009—28no—
109#13094009—28no—
110#13093998—22no—
111#13093998—22no—
112#13093998C2314yes—
113#13093998C2314yes—
114#13093997—28no—
115#13093997—28no—
116C4×Dic94—22no—
117C4×Dic94—22no—
118C4×Dic94C2314yes—
119C4×Dic94C2314yes—
120C4×D188—22no—
121C4×D188—22no—
122C4×D188—22no—
123C4×D188—22no—
124C4×D188C2314yes—
125C4×D188C2314yes—
126C4×D188C2314yes—
127C4×D188C2314yes—
128(C22⋊D47)⋊C4—28no—
129(C22⋊D47)⋊C4—28no—
130#13093982—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—22no—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2314yes—
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C4⋊C4×D47—28no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093958C2314yes—
153#13093956C2314yes—
154#13093956C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#117×C47D414yes—
169#117×C47C2314yes—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yes—
177C4⋊C8×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yes—
180#97×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47—21no—
185C23×D47—21no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—28no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—82no—
201C2×C22⋊D47—82no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—24no—
208C22×Dic47—82no—
209#10625350—216no—
210#10625350—28no—
211#10625350—28no—
212C2×D188—21no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188—21no—
220C2×D188—24no—
221C2×D188—24no—
222C2×D188—82no—
223C2×D188—82no—
224C2×D188#4114yes—
225C2×D188C2412yes—
226C2×D188C2412yes—
227C2×D188C2412yes—
228C2×C4×D47—28no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—82no—
235C2×C4×D47—82no—
236C2×C4×D47—82no—
237C2×C4×D47—82no—
238C2×Dic94—21no—
239C2×Dic94—22no—
240C2×Dic94#4114yes—
241C2×Dic94C2412yes—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47C2×D414yes—
251C4⋊C4×C47C2×D414yes—
252C22⋊C4×C47C2×D414yes—
253C22⋊C4×C47C2×D414yes—
254C42×C47C2×D412yes—
255C42×C47C2×D412yes—
256C42×C47C2412yes—
257C42×C47C2412yes—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264C4⋊Dic47—24no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279D376—28no—
280D376—28no—
281#10625325—28no—
282#10625325—28no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47C22×D412yes—
287C23×C47C22×D411yescharacteristic
288C22×D47—24no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4112yes—
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2511yescharacteristic
317C22⋊D47—216no—
318C22⋊D47—84no—
319C22⋊D47—84no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—84no—
331D188—24no—
332D188—22no—
333D188—22no—
334D188—22no—
335D188—22no—
336D188—22no—
337D188—42no—
338D188—42no—
339D188—84no—
340D188—84no—
341D188C2×#4114yes—
342C4×D47—216no—
343C4×D47—84no—
344C4×D47—84no—
345C4×D47—84no—
346C4×D47—84no—
347Dic94—24no—
348Dic94—22no—
349Dic94C2×#4114yes—
350C8×C47—22no—
351C8×C47—22no—
352C8×C47—22no—
353C8×C47—22no—
354C2×#3119—471nomaximal, Sylow
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—44no—
359C22×C47#52512yes—
360C22×C47#57612yes—
361C22×C47#57712yes—
362C22×C47C23×D411yescharacteristic
363C2×D47—24no—
364C2×D47—48no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—84no—
374C2×D47—84no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47#52512yes—
381C4×C47C22×#4111yescharacteristic
382C4×C47C22×#4111yescharacteristic
383Dic47—24no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388C2×#540—471no—
389C2×#520—471no—
390#3119—4716no—
391C2×#481—471no—
392C2×#480—471no—
393C2×#479—471no—
394C2×#478—471no—
395C2×#460—471no—
396C2×#459—471no—
397C2×#449—471no—
398C2×#449—471no—
399C2×#442—471no—
400C2×#440—471no—
401C2×C4×SD16—471no—
402C2×C4×D8—471no—
403C2×#433D4711yescharacteristic, complemented
404C2×C47—42no—
405C2×C47#311914yescomplemented
406C2×C47C2×#52511yescharacteristic
407C2×C47C2×#57611yescharacteristic
408C2×C47C2×#57711yescharacteristic
409D47—44no—
410D47—82no—
411D47—82no—
412C22×#41—471no—
413C22×SD16—471no—
414C22×SD16—471no—
415C22×D8—471no—
416C22×D8—471no—
417#540—478no—
418#540—944no—
419C2×#127—471no—
420C2×#125—471no—
421C2×#123—941no—
422C2×#123—941no—
423C2×#121—471no—
424C2×#121—471no—
425C2×#121—941no—
426C2×#121—941no—
427#520—478no—
428#520—944no—
429C2×C4×Q8—471no—
430C2×C4×Q8—471no—
431C2×C4×D4—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—941no—
436C2×C4×D4—941no—
437C2×#117—941no—
438C2×#117C2×D4711yescharacteristic
439C22×C4⋊C4—471no—
440C22×C4⋊C4—941no—
441#481—478no—
442#480—478no—
443#479—478no—
444#478—478no—
445#460—478no—
446#459—478no—
447#449—478no—
448#449—478no—
449#442—478no—
450#440—478no—
451C4×SD16—478no—
452C4×D8—478no—
453#433C2×D4718yescomplemented
454C2×#107—471no—
455C2×#107—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×C4⋊C8C2×D4711yescharacteristic
459C2×C4⋊C8C2×D4711yescharacteristic
460C2×#103—471no—
461C2×#103—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102—471no—
468C2×C22⋊C8C2×D4711yescharacteristic
469C2×C22⋊C8C2×D4711yescharacteristic
470C2×#97C2×D4711yescharacteristic
471C2×C4×C8C2×D4711yescharacteristic
472C47C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—474no—
474C2×#41—944no—
475C2×#41—944no—
476C2×#41—942no—
477C22×Q8—471no—
478C22×D4—471no—
479C22×D4—471no—
480C22×D4—471no—
481C22×D4—941no—
482C22×D4—941no—
483C22×D4—941no—
484C22×D4—941no—
485C22×D4—941no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4C22×D4711yescharacteristic
493C2×SD16—474no—
494C2×SD16—474no—
495C2×SD16—944no—
496C2×SD16—944no—
497C2×D8—474no—
498C2×D8—474no—
499C2×D8—944no—
500C2×D8—944no—
501C22×C8C22×D4711yescharacteristic
502C22×C8C22×D4711yescharacteristic
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505#127—474no—
506#127—942no—
507#125—474no—
508#125—942no—
509#123—948no—
510#123—948no—
511#121—474no—
512#121—474no—
513#121—942no—
514#121—942no—
515#121—948no—
516#121—948no—
517C4×Q8—474no—
518C4×Q8—474no—
519C4×Q8—942no—
520C4×Q8—942no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—474no—
525C4×D4—948no—
526C4×D4—948no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530C4×D4—942no—
531#117—948no—
532#117D18814yes—
533#117C22×D4714yes—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—474no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—948no—
546C2×C4⋊C4D18811yescharacteristic
547C2×C4⋊C4D18811yescharacteristic
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4D18811yescharacteristic
555C2×C22⋊C4D18811yescharacteristic
556C2×C42—941no—
557C2×C42—941no—
558C2×C42C22×D4711yescharacteristic
559C2×C42C22×D4711yescharacteristic
560#107—474no—
561#107—474no—
562#106—474no—
563#106—474no—
564C4⋊C8C22×D4714yes—
565C4⋊C8C22×D4714yes—
566#103—474no—
567#103—474no—
568#102—474no—
569#102—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574C22⋊C8C22×D4714yes—
575C22⋊C8C22×D4714yes—
576#97C22×D4714yes—
577C4×C8C22×D4714yes—
578C24—941no—
579C24—941no—
580C24—941no—
581C24C2×D18811yescharacteristic
582#41—948no—
583#41—948no—
584#41—9416no—
585C2×Q8—474no—
586C2×Q8—472no—
587C2×Q8—941no—
588C2×Q8—942no—
589C2×D4—474no—
590C2×D4—472no—
591C2×D4—472no—
592C2×D4—472no—
593C2×D4—948no—
594C2×D4—944no—
595C2×D4—944no—
596C2×D4—944no—
597C2×D4—941no—
598C2×D4—944no—
599C2×D4—944no—
600C2×D4—941no—
601C2×D4—941no—
602C2×D4—942no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—3762no—
608C2×D4—3762no—
609C2×D4—3762no—
610C2×D4—3762no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—948no—
614C22×C4—941no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—944no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—3762no—
626C22×C4—3762no—
627C22×C4—3762no—
628C22×C4—3762no—
629C22×C4—3762no—
630C22×C4C2×D18812yes—
631C22×C4C2×D18811yescharacteristic
632C22×C4C2×D18811yescharacteristic
633C22×C4C2×D18811yescharacteristic
634C22×C4C2×D18811yescharacteristic
635C22×C4C2×D18811yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638SD16—948no—
639SD16—948no—
640D8—948no—
641D8—948no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D4712yes—
647C2×C8C23×D4712yes—
648C2×C8C23×D4712yes—
649C2×C8C23×D4712yes—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—472no—
653C4⋊C4—472no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—941no—
660C4⋊C4—941no—
661C4⋊C4—941no—
662C4⋊C4—941no—
663C4⋊C4C2×D18814yes—
664C4⋊C4C2×D18814yes—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4C2×D18814yes—
672C22⋊C4C2×D18814yes—
673C42—944no—
674C42—944no—
675C42C2×D18812yes—
676C42C2×D18812yes—
677C42C23×D4712yes—
678C42C23×D4712yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—944no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23—1882no—
687C23—1882no—
688C23—1882no—
689C23—1882no—
690C23—1882no—
691C23—1882no—
692C23—1882no—
693C23—1882no—
694C23C22×D18812yes—
695C23C22×D18811yescharacteristic
696Q8—474no—
697Q8—944no—
698Q8—942no—
699D4—474no—
700D4—9416no—
701D4—944no—
702D4—942no—
703D4—942no—
704D4—942no—
705D4—942no—
706D4—942no—
707D4—3764no—
708D4—3764no—
709D4—3764no—
710D4—3764no—
711D4—1882no—
712D4—1882no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—9416no—
722C2×C4—944no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—3764no—
729C2×C4—3764no—
730C2×C4—3764no—
731C2×C4—3764no—
732C2×C4—3764no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4C22×D18812yes—
738C2×C4C22×D18812yes—
739C2×C4C22×D18812yes—
740C2×C4C22×D18812yes—
741C2×C4C22×D18812yes—
742C2×C4C22×D18811yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4#41×D4712yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—944no—
755C22—3764no—
756C22—3764no—
757C22—1882no—
758C22—1882no—
759C22—1882no—
760C22—1882no—
761C22—1882no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1888no—
766C22#1568963512yes—
767C22#1568992812yes—
768C22#1568993512yes—
769C22C23×D18811yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—944no—
776C4—1882no—
777C4—1882no—
778C4—1882no—
779C4—1882no—
780C4#1568963512yes—
781C4C2×#41×D4711yescharacteristic
782C4C2×#41×D4711yescharacteristic
783C2—42no—
784C2—3762no—
785C2—3762no—
786C2—1884no—
787C2#2025358914yesdirect product factor
788C2C2×#1568963511yescharacteristic
789C2C2×#1568992811yescharacteristic
790C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
hypercenterC2×#433D47
hypocenterC47C2×#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689728C2semidirect
2. C2×#15689603C2semidirect
3. #20253589C2direct (N × H)
4. C2×#15689442C2semidirect
5. C2×#15689437C2semidirect
6. C2×#15689431C2semidirect
7. C2×#15689424C2semidirect
8. C2×#15689324C2semidirect
9. C2×#15689319C2semidirect
10. C2×#15689270C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689236C2semidirect
13. C2×#15689225C2semidirect
14. C2×C4×#10625325C2semidirect
15. C2×C4×D376C2semidirect
16. C2×C47×#433C2semidirect
23. #15689728C22semidirect
33. #15689603C22semidirect
45. #15689442C22semidirect
46. #15689437C22semidirect
47. #15689431C22semidirect
48. #15689424C22semidirect
49. #15689324C22semidirect
50. #15689319C22semidirect
51. #15689270C22semidirect
52. #15689270C22semidirect
53. #15689236C22semidirect
54. #15689225C22semidirect
55. C4×#10625325C22semidirect
56. C4×D376C22semidirect
70. C47×#433C22semidirect
403. C2×#433D47semidirect
405. C2×C47#3119semidirect
453. #433C2×D47semidirect
472. C47C2×#3119semidirect
787. C2#20253589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897282
C2×#156896032
#202535892
C2×#156894422
C2×#156894372
C2×#156894312
C2×#156894242
C2×#156893242
C2×#156893192
C2×#156892702
C2×#156892362
C2×#156892252
C2×C4×#106253252
C2×C4×D3762
C2×C47×#4332
C2×#311947