Finite Group Databasebeta

← C2×#20255741 #27094697

Subgroups — C2×#20255741 #27094697

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689828C211yesmaximal, characteristic, complemented
2C2×#15689774C211yesmaximal, characteristic
3#20255741C2116yesmaximal, direct product factor
4C2×#15689520C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689441C211yesmaximal, characteristic, complemented
7C2×#15689455C211yesmaximal, characteristic, complemented
8C2×#15689453C211yesmaximal, characteristic, complemented
9C2×#15689407C211yesmaximal, characteristic, complemented
10C2×#15689412C211yesmaximal, characteristic, complemented
11C2×#15689353C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C2×#106×D47C211yesmaximal, characteristic, complemented
16C22×#106×C47C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625325C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689828—24no—
21#15689828C2218yescomplemented
22#15689774—24no—
23#15689774C2218yes—
24C2×#13094023C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094009—21no—
28C2×#13094007—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094003—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13094002—21no—
34C2×#13093999C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689520C2218yescomplemented
43#15689455C2218yescomplemented
44#15689453C2218yescomplemented
45#15689443C2218yescomplemented
46#15689441C2218yescomplemented
47#15689412C2218yescomplemented
48#15689407C2218yescomplemented
49#15689353C2218yescomplemented
50#15689352C2218yescomplemented
51#15689210C2218yescomplemented
52C8×C22⋊D47C2218yescomplemented
53C2×#13093956C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#106×D47C2218yescomplemented
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×C8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#106×C47C2218yescomplemented
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94C2311yescharacteristic
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47D411yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625325—24no—
91C2×#10625325C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C2×C8×D47—24no—
95C2×C8×D47C2314yes—
96#13094023—22no—
97#13094023—22no—
98#13094023C2314yes—
99#13094023C2314yes—
100#13094014—28no—
101#13094009—28no—
102#13094007—28no—
103#13094004—22no—
104#13094004C2314yes—
105#13094003—22no—
106#13094003—28no—
107#13094003C2314yes—
108#13094002—28no—
109#13094002—28no—
110#13093999—22no—
111#13093999C2314yes—
112#13093998—22no—
113#13093998C2314yes—
114#13093989—22no—
115#13093989C2314yes—
116#13093986—22no—
117#13093986C2314yes—
118C4×C22⋊D47—28no—
119C4×C22⋊D47D414yes—
120C4×C22⋊D47C2314yes—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4D411yescharacteristic
131C4⋊C4×D47—22no—
132C4⋊C4×D47—22no—
133C4⋊C4×D47C2314yes—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47C2311yescharacteristic
144#13093956C2314yes—
145#13093955C2314yes—
146#13093955C2314yes—
147#13093955C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150#13093949C2314yes—
151#13093947C2314yes—
152#13093947C2314yes—
153#13093946C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156C22⋊(C47⋊C8)C2314yes—
157(C2×D47)⋊C8C2314yes—
158C8×Dic47C2314yes—
159C23×C4×C47—21no—
160C23×C4×C47—21no—
161C23×C4×C47C2311yescharacteristic
162C22×C8×C47—24no—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—22no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2314yes—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2314yes—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176#106×C47C2314yes—
177#106×C47C2314yes—
178#106×C47C2314yes—
179#106×C47C2314yes—
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C23×D47C2×D411yescharacteristic
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—24no—
191C22×C4×C47—44no—
192C22×C4×C47—82no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—24no—
198C2×C22⋊D47—44no—
199C2×C22⋊D47SD1618yescomplemented
200C2×C22⋊D47C2×D414yes—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207#10625350—432no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—24no—
211C2×D188—21no—
212C2×D188—44no—
213C2×D188C2412yes—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—24no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C2×C4×D47—82no—
222C2×C4×D47C2×D412yes—
223C2×C4×D47C2412yes—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94—24no—
228C2×Dic94—24no—
229C2×Dic94—44no—
230C2×Dic94—82no—
231C2×Dic94C2412yes—
232C2×C8×C47—22no—
233C2×C8×C47—28no—
234C2×C8×C47#4114yescomplemented
235C2×C8×C47C2412yes—
236C2×C8×C47C2412yes—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C4⋊C4×C47C2412yes—
247C22⋊Dic47—24no—
248C22⋊Dic47C2×D414yes—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4C2×D414yes—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4C2×D414yes—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2412yes—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273#10625325—28no—
274C8×D47—28no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47C2×SD1614yes—
278C23×C47C22×D412yes—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47C2×SD1614yes—
287C22×D47C22×D412yes—
288C2×C4×C47—22no—
289C2×C4×C47—24no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—48no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—84no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4112yes—
305C2×C4×C472−1+412yes—
306C2×C4×C47C2511yescharacteristic
307C22⋊D47—48no—
308C22⋊D47C2×SD16116yescomplemented
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47C2×SD1614yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321D188—22no—
322D188—22no—
323D188—48no—
324D188—42no—
325C4×D47—24no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—48no—
329C4×D47—48no—
330C4×D47—84no—
331Dic94—22no—
332Dic94—22no—
333Dic94—42no—
334Dic94—48no—
335Dic94—84no—
336C8×C47—22no—
337C8×C47C2×#4114yescomplemented
338C47⋊C8—22no—
339C47⋊C8—22no—
340C2×#3335—471nomaximal, Sylow
341C22×C47—28no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47#54712yes—
345C22×C47C22×SD1614yes—
346C22×C47C22×SD1612yes—
347C22×C47#57712yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—28no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—84no—
356C2×D47C22×SD1614yes—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47#54712yes—
363C4×C47C22×#4111yescharacteristic
364C4×C47C2×2−1+411yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47—42no—
370Dic47C22×SD1614yes—
371C2×#554—471no—
372C2×#547—471no—
373#3335—4716no—
374C2×#498—471no—
375C2×#481—471no—
376C2×#481—471no—
377C2×#483—471no—
378C2×#483—471no—
379C2×#475—471no—
380C2×#476—471no—
381C2×#465—471no—
382C2×#465—471no—
383C2×C4×SD16—471no—
384C2×C8×D4—471no—
385C22×#106—471no—
386C22×#106D4711yescharacteristic, complemented
387C2×C47—24no—
388C2×C47#333514yescomplemented
389C2×C47C2×#54711yescharacteristic
390C2×C47C23×SD1611yescharacteristic
391C2×C47C2×#57711yescharacteristic
392D47—24no—
393D47—82no—
394C22×#41—941no—
395C22×SD16—471no—
396C23×C8—471no—
397C23×C8C2×D4711yescharacteristic
398#554—478no—
399#554—944no—
400#547—478no—
401#547—944no—
402C2×C4⋊Q8—471no—
403C2×C4⋊Q8—471no—
404C2×#125—941no—
405C2×#123—941no—
406C2×#123—941no—
407C2×C22⋊Q8—471no—
408C2×C22⋊Q8—471no—
409C2×C22⋊Q8—941no—
410C2×C22⋊Q8—941no—
411C2×C22⋊Q8—941no—
412C2×#121—471no—
413C2×#121—471no—
414C2×C4×Q8—471no—
415C2×C4×D4—471no—
416C2×C4×D4—471no—
417C2×C4×D4—941no—
418C22×C4⋊C4—471no—
419C22×C4⋊C4—471no—
420C22×C4⋊C4C2×D4711yescharacteristic
421C22×C4⋊C4C2×D4711yescharacteristic
422#498—478no—
423#483—478no—
424#483—478no—
425#481—478no—
426#481—478no—
427#476—478no—
428#475—478no—
429#465—478no—
430#465—478no—
431C4×SD16—478no—
432C8×D4—478no—
433C2×#106—471no—
434C2×#106—471no—
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×#106—478no—
439C2×#106C2×D4711yescharacteristic
440C2×#106C2×D4711yescharacteristic
441C2×#106C2×D4711yescharacteristic
442C2×#106C2×D4711yescharacteristic
443C2×#106C2×D4718yescomplemented
444C2×C4⋊C8—471no—
445C2×#103—471no—
446C2×#103—471no—
447C2×#103—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×C22⋊C8—471no—
452C2×C22⋊C8—471no—
453C2×C4×C8—471no—
454C47C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—948no—
456C2×#41—1888no—
457C22×Q8—471no—
458C22×Q8—941no—
459C22×Q8—941no—
460C22×D4—471no—
461C22×D4—471no—
462C22×D4—941no—
463C22×D4—941no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—471no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4—941no—
470C23×C4C22×D4711yescharacteristic
471C2×SD16—474no—
472C2×SD16—944no—
473C22×C8—24no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—944no—
478C22×C8C22×D4711yescharacteristic
479C22×C8C22×D4714yes—
480C22×C8C22×D4711yescharacteristic
481C4⋊Q8—474no—
482C4⋊Q8—474no—
483C4⋊Q8—942no—
484C4⋊Q8—942no—
485#125—948no—
486#123—948no—
487#123—948no—
488C22⋊Q8—474no—
489C22⋊Q8—474no—
490C22⋊Q8—948no—
491C22⋊Q8—948no—
492C22⋊Q8—948no—
493C22⋊Q8—942no—
494C22⋊Q8—942no—
495#121—474no—
496#121—474no—
497#121—942no—
498#121—942no—
499C4×Q8—474no—
500C4×Q8—942no—
501C4×D4—474no—
502C4×D4—474no—
503C4×D4—474no—
504C4×D4—942no—
505C4×D4—948no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—474no—
515C2×C4⋊C4—942no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C4⋊C4C22×D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4714yes—
529C2×C4⋊C4C22×D4714yes—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—471no—
538C2×C42—941no—
539#106—474no—
540#106—474no—
541#106—474no—
542#106—474no—
543#106—474no—
544#106C22×D4714yes—
545#106C22×D4714yes—
546#106C22×D4714yes—
547#106C22×D4714yes—
548C4⋊C8—474no—
549#103—474no—
550#103—474no—
551#103—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555C22⋊C8—474no—
556C22⋊C8—474no—
557C4×C8—474no—
558C24—471no—
559C24—941no—
560C24D4×D4711yescharacteristic
561#41—18832no—
562C2×Q8—472no—
563C2×Q8—944no—
564C2×Q8—944no—
565C2×Q8—941no—
566C2×Q8—942no—
567C2×Q8—942no—
568C2×Q8—3762no—
569C2×Q8—1884no—
570C2×D4—478no—
571C2×D4—474no—
572C2×D4—472no—
573C2×D4—944no—
574C2×D4—944no—
575C2×D4—941no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—1884no—
579C2×D4—1884no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—471no—
591C22×C4—471no—
592C22×C4—471no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—944no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—3762no—
604C22×C4—1884no—
605C22×C4—1884no—
606C22×C4D4×D4712yes—
607C22×C4D4×D4711yescharacteristic
608C22×C4C23×D4712yes—
609C22×C4C23×D4711yescharacteristic
610SD16—948no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—472no—
614C2×C8—472no—
615C2×C8—942no—
616C2×C8—942no—
617C2×C8—948no—
618C2×C8#1062535014yescomplemented
619C2×C8C23×D4712yes—
620C2×C8C23×D4712yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—474no—
628C4⋊C4—472no—
629C4⋊C4—472no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—941no—
638C4⋊C4—941no—
639C4⋊C4C23×D4712yes—
640C4⋊C4C23×D4712yes—
641C4⋊C4C23×D4712yes—
642C4⋊C4C23×D4712yes—
643C22⋊C4—474no—
644C22⋊C4—474no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—472no—
651C42—472no—
652C42—944no—
653C23—22no—
654C23—22no—
655C23—474no—
656C23—472no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23SD16×D4714yes—
664C23C2×D4×D4712yes—
665C23C2×D4×D4711yescharacteristic
666Q8—942no—
667Q8—942no—
668Q8—3764no—
669Q8—1888no—
670Q8—1882no—
671D4—4716no—
672D4—942no—
673D4—942no—
674D4—1888no—
675D4—1888no—
676D4—1882no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—474no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—944no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—3764no—
704C2×C4—1888no—
705C2×C4—1888no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4C2×#1062535012yes—
712C2×C4#1309407212yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—942no—
716C8—942no—
717C8C2×#1062535014yescomplemented
718C22—22no—
719C22—22no—
720C22—28no—
721C22—474no—
722C22—942no—
723C22—942no—
724C22—948no—
725C22—3764no—
726C22—1882no—
727C22—1882no—
728C22—1882no—
729C22#1568977412yes—
730C22C2×SD16×D4714yes—
731C22C2×SD16×D4712yes—
732C22#1568992912yes—
733C22C22×D4×D4711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—474no—
740C4—942no—
741C4—942no—
742C4—1882no—
743C4—1882no—
744C4—1882no—
745C4#1568977412yes—
746C4C22×#1062535011yescharacteristic
747C4C2×#1309407211yescharacteristic
748C2—24no—
749C2—944no—
750C2—3762no—
751C2#2025574114yesdirect product factor
752C2C2×#1568977411yescharacteristic
753C2C22×SD16×D4711yescharacteristic
754C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#106×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689774C2
hypercenterC22×#106D47
hypocenterC47C2×#3335
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#15689828C2semidirect
3. #20255741C2direct (N × H)
4. C2×#15689520C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689441C2semidirect
7. C2×#15689455C2semidirect
8. C2×#15689453C2semidirect
9. C2×#15689407C2semidirect
10. C2×#15689412C2semidirect
11. C2×#15689353C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689210C2semidirect
14. C2×C8×C22⋊D47C2semidirect
15. C2×#106×D47C2semidirect
16. C22×#106×C47C2semidirect
21. #15689828C22semidirect
42. #15689520C22semidirect
43. #15689455C22semidirect
44. #15689453C22semidirect
45. #15689443C22semidirect
46. #15689441C22semidirect
47. #15689412C22semidirect
48. #15689407C22semidirect
49. #15689353C22semidirect
50. #15689352C22semidirect
51. #15689210C22semidirect
52. C8×C22⋊D47C22semidirect
58. #106×D47C22semidirect
76. C2×#106×C47C22semidirect
199. C2×C22⋊D47SD16semidirect
234. C2×C8×C47#41semidirect
308. C22⋊D47C2×SD16semidirect
337. C8×C47C2×#41semidirect
386. C22×#106D47semidirect
388. C2×C47#3335semidirect
443. C2×#106C2×D47semidirect
454. C47C2×#3335semidirect
618. C2×C8#10625350semidirect
717. C8C2×#10625350semidirect
751. C2#20255741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898282
C2×#156897742
#202557412
C2×#156895202
C2×#156894432
C2×#156894412
C2×#156894552
C2×#156894532
C2×#156894072
C2×#156894122
C2×#156893532
C2×#156893522
C2×#156892102
C2×C8×C22⋊D472
C2×#106×D472
C22×#106×C472
C2×#333547