Finite Group Databasebeta

← C2×#20255721 #27093218

Subgroups — C2×#20255721 #27093218

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic, complemented
2C2×#15689791C211yesmaximal, characteristic
3#20255721C2116yesmaximal, direct product factor
4C2×#15689468C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic, complemented
6C2×#15689434C211yesmaximal, characteristic, complemented
7C2×#15689417C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689321C211yesmaximal, characteristic, complemented
10C2×#15689283C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×#15689199C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C2×#15689121C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689831—24no—
23#15689831C2218yescomplemented
24#15689791—24no—
25#15689791C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094020—21no—
28C2×#13094020C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094004—21no—
31C2×#13094001—21no—
32C2×#13094000C2211yescharacteristic
33C2×#13093999C2211yescharacteristic
34C2×#13093997—21no—
35C2×#13093996—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C2×(C22⋊D47)⋊C4—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689468C2218yescomplemented
44#15689438C2218yescomplemented
45#15689434C2218yescomplemented
46#15689417C2218yescomplemented
47#15689372C2218yescomplemented
48#15689321C2218yescomplemented
49#15689283C2218yescomplemented
50#15689282C2218yescomplemented
51#15689215C2218yescomplemented
52#15689199C2218yescomplemented
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56#15689125C2218yescomplemented
57#15689121C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C2×#10625352—22no—
82C2×#10625352—24no—
83C2×#10625352—42no—
84C2×#10625352C2314yes—
85C22×Dic94—21no—
86C22×Dic94C2311yescharacteristic
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47D411yescharacteristic
94C23×Dic47—21no—
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99C2×#10625337—24no—
100C2×#10625337C2314yes—
101C2×#10625336—42no—
102C2×#10625336C2314yes—
103C2×#10625324—42no—
104C2×#10625324C2314yes—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107#13094023—22no—
108#13094023C2314yes—
109#13094020—28no—
110#13094020—22no—
111#13094020C2314yes—
112#13094014—28no—
113#13094004—28no—
114#13094001—28no—
115#13094000—22no—
116#13094000C2314yes—
117#13093999—22no—
118#13093999C2314yes—
119#13093997—28no—
120#13093996—28no—
121Q8×Dic47—22no—
122Q8×Dic47C2314yes—
123#13093989—22no—
124#13093989C2314yes—
125C4×C22⋊D47D414yes—
126C4×C22⋊D47C2314yes—
127(C22⋊D47)⋊C4—28no—
128(C22⋊D47)⋊C4—28no—
129C2×C4⋊Dic47—22no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2314yes—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4D411yescharacteristic
140C4⋊C4×D47—22no—
141C4⋊C4×D47C2314yes—
142C2×C22⋊Dic47D411yescharacteristic
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093957C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162C8×Dic47C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47—21no—
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×SD16×C47—42no—
168C2×SD16×C47C2314yes—
169C2×M16×C47—42no—
170C2×M16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175#121×C47—22no—
176#121×C47C2314yes—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#107×C47C2314yes—
183#103×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C2×D4×C47—24no—
194C2×D4×C47—21no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—82no—
198C2×D4×C47C2412yes—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2411yescharacteristic
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—44no—
215C2×C22⋊D47—44no—
216C2×C22⋊D47—82no—
217C2×C22⋊D47C2×D414yes—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—24no—
222C22×Dic47—24no—
223C22×Dic47—44no—
224C22×Dic47—82no—
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228#10625352—28no—
229#10625352—44no—
230#10625352—48no—
231#10625350—28no—
232#10625350—44no—
233#10625350—48no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—21no—
237C2×D188—24no—
238C2×D188—82no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—44no—
245C2×C4×D47—82no—
246C2×C4×D47C2×D412yes—
247C2×C4×D47C2412yes—
248C2×Dic94—21no—
249C2×Dic94—22no—
250C2×Dic94—24no—
251C2×Dic94—82no—
252C2×Dic94#4114yes—
253C2×Dic94C2412yes—
254SD16×C47—44no—
255M16×C47—44no—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47C2412yes—
259C2×C8×C47C2412yes—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—24no—
267C22⋊Dic47C2×D414yes—
268#10625337—28no—
269#10625336—44no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4C2×D414yes—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47—24no—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4C2×D414yes—
284C4×Dic47—24no—
285C4×Dic47—24no—
286C4×Dic47C2×D412yes—
287C4×Dic47C2412yes—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292#10625324—44no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47C22×D412yes—
301C23×C47C22×D411yescharacteristic
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47C22×D412yes—
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—42no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—42no—
316D4×C47—84no—
317C2×C4×C47—22no—
318C2×C4×C47—24no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C47H(5,𝔽2)12yes—
331C2×C4×C47C2511yescharacteristic
332C22⋊D47—28no—
333C22⋊D47—48no—
334C22⋊D47—48no—
335C22⋊D47—48no—
336C22⋊D47—84no—
337C2×Dic47—24no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—48no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—84no—
347C2×Dic47#13714yes—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351D188—22no—
352D188—22no—
353D188—42no—
354D188—84no—
355C4×D47—24no—
356C4×D47—22no—
357C4×D47—22no—
358C4×D47—48no—
359C4×D47—84no—
360Dic94—24no—
361Dic94—22no—
362Dic94—84no—
363Dic94C2×#4114yes—
364C8×C47—22no—
365C8×C47—22no—
366C47⋊C8—22no—
367C47⋊C8—22no—
368C2×#3333—471nomaximal, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—44no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#54612yes—
378C22×C47C2×#13712yes—
379C22×C47#57612yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—44no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—84no—
389C4×C47—22no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47#54612yes—
394C4×C47C22×#4111yescharacteristic
395C4×C47C2×H(5,𝔽2)11yescharacteristic
396Dic47—24no—
397Dic47—22no—
398Dic47—22no—
399Dic47—42no—
400Dic47—42no—
401Dic47C2×#13714yes—
402C2×#554—471no—
403C2×#550—471no—
404#3333—4716no—
405C2×#486—471no—
406C2×#480—471no—
407C2×#480—471no—
408C2×#477—471no—
409C2×#468—471no—
410C2×#468D4711yescharacteristic, complemented
411C2×#460—471no—
412C2×#452—471no—
413C2×#452—471no—
414C2×C4×Q16—471no—
415C2×#436—471no—
416C2×#417—471no—
417C2×#417—471no—
418C2×C47—42no—
419C2×C47—82no—
420C2×C47#333314yescomplemented
421C2×C47C2×#54611yescharacteristic
422C2×C47C22×#13711yescharacteristic
423C2×C47C2×#57611yescharacteristic
424D47—42no—
425D47—82no—
426C22×#41—471no—
427C22×#41—471no—
428C22×Q16—471no—
429C22×SD16—471no—
430C22×SD16C2×D4711yescharacteristic
431C22×M16—471no—
432C22×M16C2×D4711yescharacteristic
433#554—478no—
434#554—944no—
435#550—478no—
436#550—944no—
437C2×C4⋊Q8—471no—
438C2×#127—471no—
439C2×#127—941no—
440C2×#125—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—941no—
443C2×C22⋊Q8—941no—
444C2×C22⋊Q8C2×D4711yescharacteristic
445C2×#121—471no—
446C2×#121—941no—
447C2×#121—941no—
448C2×#121C2×D4711yescharacteristic
449C2×C4×Q8—471no—
450C2×C4×Q8—471no—
451C2×C4×D4—471no—
452C2×C4×D4—941no—
453C2×C4×D4—941no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4—471no—
456#486—478no—
457#480—478no—
458#480—478no—
459#477—478no—
460#468—478no—
461#468C2×D4718yescomplemented
462#460—478no—
463#452—478no—
464#452—478no—
465C4×Q16—478no—
466#436—478no—
467C2×#107—471no—
468C2×#107—471no—
469C2×#107C2×D4711yescharacteristic
470C2×C4⋊C8—471no—
471#417—478no—
472#417—478no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103C2×D4711yescharacteristic
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102—471no—
482C2×#102C2×D4711yescharacteristic
483C2×C22⋊C8—471no—
484C2×C22⋊C8—471no—
485C2×C4×C8—471no—
486C47C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—474no—
488C2×#41—474no—
489C2×#41—944no—
490C2×#41—942no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1882no—
494C2×#41—1882no—
495C22×Q8—471no—
496C22×Q8—941no—
497C22×Q8C22×D4711yescharacteristic
498C22×D4—21no—
499C22×D4—471no—
500C22×D4—471no—
501C22×D4—941no—
502C22×D4—941no—
503C22×D4—941no—
504C22×D4—941no—
505C22×D4—941no—
506C22×D4C22×D4711yescharacteristic
507C23×C4—471no—
508C23×C4—941no—
509C23×C4—941no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4C22×D4711yescharacteristic
513C2×Q16—474no—
514C2×Q16—944no—
515C2×SD16—42no—
516C2×SD16—474no—
517C2×SD16—1882no—
518C2×SD16C22×D4714yes—
519C2×M16—42no—
520C2×M16—474no—
521C2×M16—1882no—
522C2×M16C22×D4714yes—
523C22×C8—471no—
524C22×C8—471no—
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4711yescharacteristic
527C4⋊Q8—474no—
528C4⋊Q8—942no—
529#127—474no—
530#127—942no—
531#127—948no—
532#125—948no—
533C22⋊Q8—22no—
534C22⋊Q8—474no—
535C22⋊Q8—948no—
536C22⋊Q8—948no—
537C22⋊Q8—942no—
538C22⋊Q8C22×D4714yes—
539#121—22no—
540#121—474no—
541#121—948no—
542#121—948no—
543#121—942no—
544#121C22×D4714yes—
545C4×Q8—474no—
546C4×Q8—474no—
547C4×Q8—942no—
548C4×Q8—942no—
549C4×D4—474no—
550C4×D4—474no—
551C4×D4—948no—
552C4×D4—948no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—474no—
558C2×C4⋊C4—474no—
559C2×C4⋊C4—942no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—942no—
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—471no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C42—471no—
576C2×C42—941no—
577C2×C42—941no—
578#107—474no—
579#107—474no—
580#107C22×D4714yes—
581C4⋊C8—474no—
582#103—474no—
583#103—474no—
584#103—474no—
585#103C22×D4714yes—
586#102—474no—
587#102—474no—
588#102—474no—
589#102—474no—
590#102—474no—
591#102C22×D4714yes—
592C22⋊C8—474no—
593C22⋊C8—474no—
594C4×C8—474no—
595C24—21no—
596C24—471no—
597C24—941no—
598C24D4×D4711yescharacteristic
599#41—948no—
600#41—948no—
601#41—1884no—
602#41—1888no—
603#41—1884no—
604#41—1888no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—474no—
609C2×Q8—472no—
610C2×Q8—944no—
611C2×Q8—941no—
612C2×Q8—942no—
613C2×Q8—3762no—
614C2×Q8C23×D4712yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—82no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—941no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—3762no—
632C2×D4—3762no—
633C2×D4—1884no—
634C2×D4—1884no—
635C2×D4—1884no—
636C2×D4C23×D4712yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—471no—
643C22×C4—471no—
644C22×C4—471no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—944no—
648C22×C4—944no—
649C22×C4—941no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—944no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—944no—
656C22×C4—3762no—
657C22×C4—3762no—
658C22×C4—1884no—
659C22×C4—1884no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664Q16—948no—
665SD16—44no—
666SD16—1884no—
667M16—44no—
668M16—1884no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—472no—
672C2×C8—472no—
673C2×C8—942no—
674C2×C8—942no—
675C2×C8C23×D4712yes—
676C2×C8C23×D4712yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—474no—
681C4⋊C4—472no—
682C4⋊C4—472no—
683C4⋊C4—944no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—941no—
689C4⋊C4—944no—
690C4⋊C4—941no—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—474no—
696C22⋊C4—474no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C42—472no—
700C42—472no—
701C42—944no—
702C42—944no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—472no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23C2×D4×D4712yes—
719C23C2×D4×D4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—474no—
724Q8—944no—
725Q8—942no—
726Q8—3764no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—948no—
732D4—942no—
733D4—942no—
734D4—3764no—
735D4—3764no—
736D4—1888no—
737D4—1888no—
738D4—1888no—
739D4—1882no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—474no—
751C2×C4—472no—
752C2×C4—472no—
753C2×C4—472no—
754C2×C4—942no—
755C2×C4—944no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—3764no—
764C2×C4—3764no—
765C2×C4—1888no—
766C2×C4—1888no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4C2×D4×D4712yes—
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4#41×D4712yes—
772C2×C4#1309406912yes—
773C2×C4C24×D4711yescharacteristic
774C8—22no—
775C8—22no—
776C8—942no—
777C8—942no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—942no—
787C22—942no—
788C22—942no—
789C22—3764no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22—1884no—
794C22#1568976212yes—
795C22#137×D4712yes—
796C22#1568992712yes—
797C22C22×D4×D4711yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—474no—
803C4—942no—
804C4—944no—
805C4—942no—
806C4—1882no—
807C4—1882no—
808C4#1568976212yes—
809C4C2×#41×D4711yescharacteristic
810C4C2×#1309406911yescharacteristic
811C2—42no—
812C2—82no—
813C2—3762no—
814C2—1882no—
815C2#2025572114yesdirect product factor
816C2C2×#1568976211yescharacteristic
817C2C2×#137×D4711yescharacteristic
818C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689791C2
hypercenterC2×#468D47
hypocenterC47C2×#3333
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255721C2direct (N × H)
4. C2×#15689468C2semidirect
5. C2×#15689438C2semidirect
6. C2×#15689434C2semidirect
7. C2×#15689417C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689321C2semidirect
10. C2×#15689283C2semidirect
11. C2×#15689282C2semidirect
12. C2×#15689215C2semidirect
13. C2×#15689199C2semidirect
14. C2×#15689125C2semidirect
15. C2×#15689121C2semidirect
16. C2×C47×#468C2semidirect
23. #15689831C22semidirect
43. #15689468C22semidirect
44. #15689438C22semidirect
45. #15689434C22semidirect
46. #15689417C22semidirect
47. #15689372C22semidirect
48. #15689321C22semidirect
49. #15689283C22semidirect
50. #15689282C22semidirect
51. #15689215C22semidirect
52. #15689199C22semidirect
56. #15689125C22semidirect
57. #15689121C22semidirect
73. C47×#468C22semidirect
410. C2×#468D47semidirect
420. C2×C47#3333semidirect
461. #468C2×D47semidirect
486. C47C2×#3333semidirect
815. C2#20255721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156897912
#202557212
C2×#156894682
C2×#156894382
C2×#156894342
C2×#156894172
C2×#156893722
C2×#156893212
C2×#156892832
C2×#156892822
C2×#156892152
C2×#156891992
C2×#156891252
C2×#156891212
C2×C47×#4682
C2×#333347