Finite Group Databasebeta

← C2×#20254389 #27087532

Subgroups — C2×#20254389 #27087532

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689677C211yesmaximal, characteristic, complemented
2C2×#124×D47C211yesmaximal, characteristic
3#20254389C2116yesmaximal, direct product factor
4C2×#15689516C211yesmaximal, characteristic, complemented
5C2×#15689514C211yesmaximal, characteristic, complemented
6C2×#15689484C211yesmaximal, characteristic, complemented
7C2×#15689481C211yesmaximal, characteristic, complemented
8C2×#15689346C211yesmaximal, characteristic, complemented
9C2×#15689345C211yesmaximal, characteristic, complemented
10C2×#15689342C211yesmaximal, characteristic, complemented
11C2×#15689280C211yesmaximal, characteristic, complemented
12C2×#15689277C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic
14C2×#15689272C211yesmaximal, characteristic
15C2×#15689179C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×Dic188C2211yescharacteristic, complemented
20C22×#10625337C2211yescharacteristic, complemented
21C22×#10625337C2211yescharacteristic, complemented
22C22×#10625325C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25#15689677—24no—
26#15689677C2218yescomplemented
27C2×#13094023C2211yescharacteristic, complemented
28C2×#13094022C2211yescharacteristic, complemented
29C2×#13094014—21no—
30C2×#13094013C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094011C2211yescharacteristic
33C2×#13094010—21no—
34C2×#13094010—21no—
35#124×D47—24no—
36#124×D47C2218yes—
37C2×#13094004C2211yescharacteristic
38C2×#13094002—21no—
39C2×#13094000C2211yescharacteristic
40C2×C4×Dic94—21no—
41C2×C4×Dic94C2211yescharacteristic, complemented
42C2×#13093981—21no—
43C2×C22⋊C4×D47—21no—
44C2×C22⋊C4×D47—21no—
45C2×C42×D47C2211yescharacteristic
46#15689516C2218yescomplemented
47#15689514C2218yescomplemented
48#15689484C2218yescomplemented
49#15689481C2218yescomplemented
50#15689346C2218yescomplemented
51#15689345C2218yescomplemented
52#15689342C2218yescomplemented
53#15689280C2218yescomplemented
54#15689277C2218yescomplemented
55#15689275C2218yes—
56#15689272C2218yes—
57#15689179C2218yescomplemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×#13093934C2211yescharacteristic, complemented
69C22×Q16×C47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94—21no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C22×Dic94C2311yescharacteristic
82C2×Q8×D47—22no—
83C2×Q8×D47—42no—
84C2×Q8×D47—42no—
85C2×Q8×D47C2314yes—
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C2×D4×D47—22no—
89C2×D4×D47—42no—
90C2×D4×D47—42no—
91C2×D4×D47C2314yes—
92C22×C4×D47—21no—
93C22×C4×D47D411yescharacteristic
94C22×C4×D47D411yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C2×Dic188—42no—
97C2×Dic188C2314yescomplemented
98C2×#10625337—42no—
99C2×#10625337—42no—
100C2×#10625337C2314yescomplemented
101C2×#10625337C2314yescomplemented
102C2×#10625325—42no—
103C2×#10625325C2314yes—
104C2×#10625335—42no—
105C2×#10625335C2314yes—
106C2×#10625336—42no—
107C2×#10625336C2314yes—
108C22×C47⋊C8C2311yescharacteristic
109C22×C47⋊C8C2311yescharacteristic
110#13094023—22no—
111#13094023C2314yescomplemented
112#13094022—22no—
113#13094022C2314yescomplemented
114#13094014—28no—
115#13094013—22no—
116#13094013C2314yes—
117#13094012—22no—
118#13094012C2314yes—
119#13094011—22no—
120#13094011C2314yes—
121#13094010—28no—
122#13094010—28no—
123#13094004—22no—
124#13094004C2314yes—
125#13094002—28no—
126#13094000—22no—
127#13094000C2314yes—
128C4×Dic94—22no—
129C4×Dic94—28no—
130C4×Dic94C2314yescomplemented
131#13093981—28no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C22⋊C4×D47—28no—
148C22⋊C4×D47—28no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47D411yescharacteristic
151C2×C4×Dic47D411yescharacteristic
152C2×C4×Dic47C2311yescharacteristic
153C42×D47D414yes—
154C42×D47C2314yes—
155C4⋊(C47⋊C8)C2314yescomplemented
156#13093949C2314yescomplemented
157#13093948C2314yescomplemented
158#13093947C2314yescomplemented
159#13093946C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164#13093934C2314yescomplemented
165#13093934C2314yescomplemented
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C2×Q16×C47—42no—
170C2×Q16×C47C2314yescomplemented
171C2×SD16×C47—42no—
172C2×SD16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175#124×C47—22no—
176#124×C47C2314yes—
177C4×Q8×C47—22no—
178C4×Q8×C47C2314yescomplemented
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C4⋊C8×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187#102×C47C2314yes—
188C24×C47—21no—
189C23×D47—21no—
190C23×D47—24no—
191C23×D47—44no—
192C23×D47—44no—
193C23×D47—44no—
194C23×D47C2×D411yescharacteristic
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47C2412yes—
202C2×Q8×C47C2412yes—
203C2×D4×C47—21no—
204C2×D4×C47—22no—
205C2×D4×C47—22no—
206C2×D4×C47C2412yes—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—44no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221Q8×D47—44no—
222Q8×D47—44no—
223Q8×D47—48no—
224D4×D47—44no—
225D4×D47—44no—
226D4×D47—48no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—21no—
230C2×D188C2412yes—
231C2×C4×D47—24no—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—24no—
235C2×C4×D47—42no—
236C2×C4×D47—44no—
237C2×C4×D47C2×D412yes—
238C2×C4×D47C2×D414yes—
239C2×C4×D47C2×D414yes—
240C2×C4×D47C2412yes—
241C2×Dic94—22no—
242C2×Dic94—22no—
243C2×Dic94—22no—
244C2×Dic94—22no—
245C2×Dic94—21no—
246C2×Dic94—21no—
247C2×Dic94—24no—
248C2×Dic94—24no—
249C2×Dic94—44no—
250C2×Dic94—44no—
251C2×Dic94C2412yes—
252C2×Dic94C2412yes—
253Q16×C47—44no—
254SD16×C47—44no—
255C2×C8×C47—22no—
256C2×C8×C47—22no—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—24no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47C2412yes—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C42×C47—24no—
265C42×C47C2×D412yes—
266C42×C47C2412yes—
267C22⋊Dic47—24no—
268C22⋊Dic47—24no—
269#10625337—44no—
270#10625337—44no—
271#10625336—44no—
272#10625335—44no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279C4⋊Dic47—21no—
280C4⋊Dic47—24no—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285Dic47⋊C4—24no—
286Dic47⋊C4—24no—
287C4×Dic47—24no—
288C4×Dic47C2×D412yes—
289C4×Dic47C2×D414yes—
290C4×Dic47C2×D414yes—
291C4×Dic47C2412yes—
292C2×C47⋊C8—22no—
293C2×C47⋊C8—22no—
294C2×C47⋊C8C2412yes—
295C2×C47⋊C8C2412yes—
296Dic188—44no—
297#10625325—44no—
298C23×C47—22no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—48no—
307C22×D47—48no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—48no—
312C22×D47—816no—
313C22×D47#13714yes—
314C22×D47C22×D412yes—
315Q8×C47—22no—
316Q8×C47—22no—
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47—42no—
320Q8×C47—42no—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—42no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47H(5,𝔽2)12yes—
336C2×C4×C47H(5,𝔽2)12yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—48no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351D188—22no—
352D188—22no—
353D188—42no—
354C4×D47—28no—
355C4×D47—24no—
356C4×D47—22no—
357C4×D47—22no—
358C4×D47—44no—
359C4×D47—48no—
360Dic94—22no—
361Dic94—22no—
362Dic94—22no—
363Dic94—22no—
364Dic94—48no—
365Dic94—48no—
366Dic94—42no—
367Dic94—42no—
368C8×C47—22no—
369C8×C47—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C2×#3215—471nomaximal, Sylow
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#53512yes—
378C22×C47C2×#13712yes—
379C22×C47#57512yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—22no—
382C2×D47—28no—
383C2×D47—22no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—816no—
388C2×D47—84no—
389C2×D47C2×#13714yes—
390C4×C47—22no—
391C4×C47—22no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47#53512yes—
396C4×C47C2×H(5,𝔽2)11yescharacteristic
397C4×C47C2×H(5,𝔽2)11yescharacteristic
398Dic47—22no—
399Dic47—22no—
400Dic47—22no—
401Dic47—42no—
402Dic47—42no—
403Dic47—42no—
404C2×#533—471no—
405C22×#124—471no—
406#3215—4716no—
407C2×#497—471no—
408C2×#497—471no—
409C2×#489—471no—
410C2×#489—471no—
411C2×#464—471no—
412C2×#464—471no—
413C2×#464—471no—
414C2×#464D4711yescharacteristic, complemented
415C2×#451—471no—
416C2×#451—471no—
417C2×#450—471no—
418C2×#450—471no—
419C2×#432—471no—
420C2×C47—82no—
421C2×C47#321514yescomplemented
422C2×C47C2×#53511yescharacteristic
423C2×C47C22×#13711yescharacteristic
424C2×C47C2×#57511yescharacteristic
425D47—24no—
426D47—82no—
427C23×Q8—471no—
428C23×D4—471no—
429C22×Q16—471no—
430C22×Q16—471no—
431C22×Q16—471no—
432C22×Q16C2×D4711yescharacteristic, complemented
433C22×SD16—471no—
434C22×SD16—471no—
435C22×SD16—471no—
436C22×SD16C2×D4711yescharacteristic
437#533—478no—
438#533—944no—
439C2×C4⋊Q8—471no—
440C2×C4⋊Q8—471no—
441C2×#125—941no—
442C2×#124—471no—
443C2×#124—471no—
444C2×#124—478no—
445C2×#124—471no—
446C2×#124—941no—
447C2×#124—941no—
448C2×#124—944no—
449C2×#124C2×D4711yescharacteristic
450C2×C22⋊Q8—471no—
451C2×C22⋊Q8—471no—
452C2×C22⋊Q8—941no—
453C2×C4×Q8—471no—
454C2×C4×Q8—941no—
455C2×C4×Q8C2×D4711yescharacteristic, complemented
456C2×#117—941no—
457C22×C22⋊C4—941no—
458C22×C22⋊C4—941no—
459C22×C42—471no—
460#497—478no—
461#497—478no—
462#489—478no—
463#489—478no—
464#464—478no—
465#464—478no—
466#464—478no—
467#464C2×D4718yescomplemented
468#451—478no—
469#451—478no—
470#450—478no—
471#450—478no—
472#432—478no—
473C2×C4⋊C8—471no—
474C2×C4⋊C8C2×D4711yescharacteristic, complemented
475C2×#103—471no—
476C2×#103—471no—
477C2×#103—471no—
478C2×#103C2×D4711yescharacteristic, complemented
479C2×#102—471no—
480C2×#102—471no—
481C2×#102—471no—
482C2×#102C2×D4711yescharacteristic
483C2×C22⋊C8—471no—
484C2×C22⋊C8—471no—
485C2×#97—471no—
486C2×#97—471no—
487C47C2×#321511yescharacteristic, complemented, Sylow
488C25—941no—
489C22×Q8—474no—
490C22×Q8—471no—
491C22×Q8—471no—
492C22×Q8—941no—
493C22×Q8—941no—
494C22×Q8—942no—
495C22×Q8—1882no—
496C22×Q8—1882no—
497C22×Q8C22×D4711yescharacteristic
498C22×Q8C22×D4711yescharacteristic
499C22×D4—474no—
500C22×D4—471no—
501C22×D4—942no—
502C22×D4—941no—
503C22×D4—1882no—
504C22×D4—1882no—
505C22×D4C22×D4711yescharacteristic
506C23×C4—471no—
507C23×C4—471no—
508C23×C4—471no—
509C23×C4—941no—
510C2×Q16—42no—
511C2×Q16—474no—
512C2×Q16—474no—
513C2×Q16—474no—
514C2×Q16—1882no—
515C2×Q16—1882no—
516C2×Q16—1882no—
517C2×Q16C22×D4714yescomplemented
518C2×SD16—42no—
519C2×SD16—474no—
520C2×SD16—474no—
521C2×SD16—474no—
522C2×SD16—1882no—
523C2×SD16—1882no—
524C2×SD16—1882no—
525C2×SD16C22×D4714yes—
526C22×C8—471no—
527C22×C8—471no—
528C22×C8C22×D4711yescharacteristic
529C22×C8C22×D4711yescharacteristic
530C4⋊Q8—474no—
531C4⋊Q8—474no—
532C4⋊Q8—942no—
533C4⋊Q8—942no—
534#125—948no—
535#124—22no—
536#124—474no—
537#124—474no—
538#124—474no—
539#124—948no—
540#124—948no—
541#124—942no—
542#124—942no—
543#124—942no—
544#124C22×D4714yes—
545C22⋊Q8—474no—
546C22⋊Q8—474no—
547C22⋊Q8—942no—
548C22⋊Q8—948no—
549C22⋊Q8—942no—
550C4×Q8—22no—
551C4×Q8—474no—
552C4×Q8—948no—
553C4×Q8—942no—
554C4×Q8C22×D4714yescomplemented
555#117—948no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—471no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4C22×D4711yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—948no—
568C2×C22⋊C4—948no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C42—21no—
578C2×C42—471no—
579C2×C42—471no—
580C2×C42—471no—
581C2×C42—474no—
582C2×C42—474no—
583C2×C42—941no—
584C2×C42C22×D4711yescharacteristic
585C4⋊C8—474no—
586C4⋊C8C22×D4714yescomplemented
587#103—474no—
588#103—474no—
589#103—474no—
590#103C22×D4714yescomplemented
591#102—474no—
592#102—474no—
593#102—474no—
594#102C22×D4714yes—
595C22⋊C8—474no—
596C22⋊C8—474no—
597#97—474no—
598#97—474no—
599C24—21no—
600C24—471no—
601C24—944no—
602C24—941no—
603C24—1884no—
604C24—1884no—
605C24—1884no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—472no—
613C2×Q8—472no—
614C2×Q8—944no—
615C2×Q8—944no—
616C2×Q8—941no—
617C2×Q8—941no—
618C2×Q8—942no—
619C2×Q8—942no—
620C2×Q8—942no—
621C2×Q8—942no—
622C2×Q8—1884no—
623C2×Q8—1884no—
624C2×Q8—1884no—
625C2×Q8—1884no—
626C2×Q8—1888no—
627C2×Q8C23×D4712yes—
628C2×Q8C23×D4712yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—472no—
633C2×D4—944no—
634C2×D4—941no—
635C2×D4—942no—
636C2×D4—942no—
637C2×D4—1884no—
638C2×D4—1884no—
639C2×D4—1888no—
640C2×D4—1884no—
641C2×D4C23×D4712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—471no—
646C22×C4—471no—
647C22×C4—471no—
648C22×C4—474no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—474no—
652C22×C4—944no—
653C22×C4—944no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—1882no—
660C22×C4—1884no—
661C22×C4D4×D4711yescharacteristic
662C22×C4D4×D4711yescharacteristic
663C22×C4C23×D4711yescharacteristic
664Q16—44no—
665Q16—1884no—
666Q16—1884no—
667Q16—1884no—
668SD16—44no—
669SD16—1884no—
670SD16—1884no—
671SD16—1884no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—472no—
675C2×C8—472no—
676C2×C8—942no—
677C2×C8—942no—
678C2×C8C23×D4712yes—
679C2×C8C23×D4712yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—472no—
683C4⋊C4—944no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—941no—
690C4⋊C4C23×D4712yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—944no—
694C22⋊C4—944no—
695C22⋊C4—944no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C42—24no—
702C42—474no—
703C42—474no—
704C42—472no—
705C42—472no—
706C42—944no—
707C42D4×D4712yes—
708C42C23×D4712yes—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—474no—
714C23—472no—
715C23—942no—
716C23—942no—
717C23—942no—
718C23—37616no—
719C23—1888no—
720C23—1888no—
721C23—1888no—
722C23—1882no—
723C23—1882no—
724C23—1882no—
725C23C2×D4×D4711yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—942no—
733Q8—942no—
734Q8—942no—
735Q8—942no—
736Q8—1888no—
737Q8—1888no—
738Q8—1882no—
739Q8—1882no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—942no—
744D4—942no—
745D4—1888no—
746D4—1882no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—472no—
756C2×C4—472no—
757C2×C4—472no—
758C2×C4—948no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—944no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—1884no—
769C2×C4—1888no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4C2×D4×D4712yes—
774C2×C4C2×D4×D4712yes—
775C2×C4C2×D4×D4711yescharacteristic
776C2×C4#1309406912yes—
777C2×C4#1309407012yes—
778C2×C4C24×D4711yescharacteristic
779C8—22no—
780C8—22no—
781C8—942no—
782C8—942no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—474no—
788C22—942no—
789C22—948no—
790C22—942no—
791C22—37616no—
792C22—3764no—
793C22—1882no—
794C22—1882no—
795C22—1882no—
796C22#1568968912yes—
797C22#137×D4712yes—
798C22#1568992012yes—
799C22C22×D4×D4711yescharacteristic
800C4—22no—
801C4—22no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—942no—
806C4—942no—
807C4—942no—
808C4—1882no—
809C4—1882no—
810C4—1882no—
811C4#1568968912yes—
812C4C2×#1309406911yescharacteristic
813C4C2×#1309407011yescharacteristic
814C2—82no—
815C2—944no—
816C2—3762no—
817C2#2025438914yesdirect product factor
818C2C2×#1568968911yescharacteristic
819C2C2×#137×D4711yescharacteristic
820C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
hypercenterC2×#464D47
hypocenterC47C2×#3215
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#15689677C2semidirect
3. #20254389C2direct (N × H)
4. C2×#15689516C2semidirect
5. C2×#15689514C2semidirect
6. C2×#15689484C2semidirect
7. C2×#15689481C2semidirect
8. C2×#15689346C2semidirect
9. C2×#15689345C2semidirect
10. C2×#15689342C2semidirect
11. C2×#15689280C2semidirect
12. C2×#15689277C2semidirect
15. C2×#15689179C2semidirect
16. C2×C47×#464C2semidirect
19. C22×Dic188C22semidirect
20. C22×#10625337C22semidirect
21. C22×#10625337C22semidirect
26. #15689677C22semidirect
27. C2×#13094023C22semidirect
28. C2×#13094022C22semidirect
41. C2×C4×Dic94C22semidirect
46. #15689516C22semidirect
47. #15689514C22semidirect
48. #15689484C22semidirect
49. #15689481C22semidirect
50. #15689346C22semidirect
51. #15689345C22semidirect
52. #15689342C22semidirect
53. #15689280C22semidirect
54. #15689277C22semidirect
57. #15689179C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093948C22semidirect
61. C2×#13093947C22semidirect
67. C2×#13093934C22semidirect
68. C2×#13093934C22semidirect
69. C22×Q16×C47C22semidirect
72. C2×C4×Q8×C47C22semidirect
73. C47×#464C22semidirect
74. C2×C4⋊C8×C47C22semidirect
75. C2×#103×C47C22semidirect
97. C2×Dic188C23semidirect
100. C2×#10625337C23semidirect
101. C2×#10625337C23semidirect
111. #13094023C23semidirect
113. #13094022C23semidirect
130. C4×Dic94C23semidirect
155. C4⋊(C47⋊C8)C23semidirect
156. #13093949C23semidirect
157. #13093948C23semidirect
158. #13093947C23semidirect
164. #13093934C23semidirect
165. #13093934C23semidirect
170. C2×Q16×C47C23semidirect
178. C4×Q8×C47C23semidirect
185. C4⋊C8×C47C23semidirect
186. #103×C47C23semidirect
414. C2×#464D47semidirect
421. C2×C47#3215semidirect
432. C22×Q16C2×D47semidirect
455. C2×C4×Q8C2×D47semidirect
467. #464C2×D47semidirect
474. C2×C4⋊C8C2×D47semidirect
478. C2×#103C2×D47semidirect
487. C47C2×#3215semidirect
517. C2×Q16C22×D47semidirect
554. C4×Q8C22×D47semidirect
586. C4⋊C8C22×D47semidirect
590. #103C22×D47semidirect
817. C2#20254389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896772
C2×#124×D472
#202543892
C2×#156895162
C2×#156895142
C2×#156894842
C2×#156894812
C2×#156893462
C2×#156893452
C2×#156893422
C2×#156892802
C2×#156892772
C2×#156892752
C2×#156892722
C2×#156891792
C2×C47×#4642
C2×#321547