Finite Group Databasebeta

← C2×#20255844 #27094826

Subgroups — C2×#20255844 #27094826

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689828C211yesmaximal, characteristic
2C2×#15689812C211yesmaximal, characteristic
3#20255844C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689464C211yesmaximal, characteristic, complemented
7C2×#15689455C211yesmaximal, characteristic, complemented
8C2×#15689453C211yesmaximal, characteristic, complemented
9C2×#15689429C211yesmaximal, characteristic, complemented
10C2×#15689407C211yesmaximal, characteristic, complemented
11C2×#15689381C211yesmaximal, characteristic, complemented
12C2×#15689365C211yesmaximal, characteristic, complemented
13C2×#15689229C211yesmaximal, characteristic, complemented
14C2×#15689192C211yesmaximal, characteristic
15C2×#106×D47C211yesmaximal, characteristic, complemented
16C2×C47×#428C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689828—24no—
20#15689828C2218yes—
21#15689812—24no—
22#15689812C2218yes—
23C2×#13094023C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094016—21no—
26C2×#13094015C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094006—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094004C2211yescharacteristic
31C2×#13094003—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×#13094002—21no—
35C2×#13093989C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093981—21no—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689531C2218yescomplemented
43#15689464C2218yescomplemented
44#15689460C2218yescomplemented
45#15689455C2218yescomplemented
46#15689453C2218yescomplemented
47#15689429C2218yescomplemented
48#15689407C2218yescomplemented
49#15689381C2218yescomplemented
50#15689365C2218yescomplemented
51#15689229C2218yescomplemented
52#15689192C2218yes—
53C2×#13093957C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#106×D47C2218yescomplemented
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C47×#428C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#107×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#106×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×C22⋊D47D411yescharacteristic
81C22×C4×D47—21no—
82C22×C4×D47—21no—
83C22×C4×D47C2311yescharacteristic
84C2×Dic188—24no—
85C2×Dic188C2314yes—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C2×C8×D47—24no—
89C2×C8×D47C2314yes—
90#13094023—22no—
91#13094023C2314yes—
92#13094017—28no—
93#13094016—28no—
94#13094015—22no—
95#13094015C2314yes—
96#13094014—28no—
97#13094006—28no—
98#13094004—22no—
99#13094004—22no—
100#13094004C2314yes—
101#13094004C2314yes—
102#13094003—22no—
103#13094003—22no—
104#13094003—28no—
105#13094003C2314yes—
106#13094003C2314yes—
107#13094002—28no—
108#13093989—22no—
109#13093989—22no—
110#13093989C2314yes—
111#13093989C2314yes—
112C4×C22⋊D47—28no—
113C4×C22⋊D47D414yes—
114C4×C22⋊D47C2314yes—
115#13093981—28no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4D411yescharacteristic
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C4⋊C4×D47C2314yes—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47C2311yescharacteristic
143#13093957C2314yes—
144#13093956C2314yes—
145#13093955C2314yes—
146#13093955C2314yes—
147#13093955C2314yes—
148Dic47⋊C8C2314yes—
149#13093949C2314yes—
150#13093949C2314yes—
151#13093947C2314yes—
152#13093947C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155C22⋊(C47⋊C8)C2314yes—
156(C2×D47)⋊C8C2314yes—
157#13093934C2314yes—
158C23×C4×C47—21no—
159C23×C4×C47C2311yescharacteristic
160C2×M16×C47—24no—
161C2×M16×C47C2314yes—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164#117×C47—22no—
165#117×C47C2314yes—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C42×C47—21no—
175#107×C47C2314yes—
176#107×C47C2314yes—
177#106×C47C2314yes—
178#106×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—24no—
188C22×C4×C47—82no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2411yescharacteristic
193C2×C22⋊D47—24no—
194C2×C22⋊D47C2×D414yes—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C2×C4×D47—22no—
203C2×C4×D47—22no—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—44no—
207C2×C4×D47—82no—
208C2×C4×D47C2×D412yes—
209C2×C4×D47C2412yes—
210C2×Dic94—22no—
211C2×Dic94—22no—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—21no—
215C2×Dic94—21no—
216C2×Dic94—24no—
217C2×Dic94—82no—
218C2×Dic94C2412yes—
219C2×Dic94C2412yes—
220M16×C47—28no—
221C2×C8×C47—22no—
222C2×C8×C47#4114yes—
223C2×C8×C47C2412yes—
224C2×C8×C47C2412yes—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C4⋊C4×C47C2412yes—
234C22⋊C4×C47—24no—
235C42×C47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47C2×D414yes—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4C2×D414yes—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—24no—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4C2×D414yes—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47C2×D412yes—
261C4×Dic47C2412yes—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8C2412yes—
265C2×C47⋊C8C2412yes—
266Dic188—28no—
267C8×D47—28no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47C22×D412yes—
272C23×C47C22×D411yescharacteristic
273C22×D47—22no—
274C22×D47—22no—
275C22×D47#13714yes—
276C22×D47C22×D412yes—
277C2×C4×C47—22no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—84no—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C2×#4112yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
295C22⋊D47—28no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47C22×D412yes—
308C2×Dic47C22×D412yes—
309C2×Dic47C22×D412yes—
310C4×D47—24no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—48no—
314C4×D47—84no—
315Dic94—22no—
316Dic94—22no—
317Dic94—22no—
318Dic94—22no—
319Dic94—42no—
320Dic94—42no—
321Dic94—84no—
322C8×C47—22no—
323C8×C47C2×#4114yes—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C2×#3344—471nomaximal, Sylow
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—44no—
331C22×C47#54712yes—
332C22×C47C2×#13712yes—
333C22×C47#57712yes—
334C22×C47C23×D411yescharacteristic
335C2×D47—28no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47C2×#13714yes—
339C4×C47—22no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47#54712yes—
345C4×C47C22×#4111yescharacteristic
346C4×C47C2×2−1+411yescharacteristic
347Dic47—22no—
348Dic47—22no—
349Dic47—22no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353Dic47—42no—
354C2×#554—471no—
355C2×#552—471no—
356#3344—4716no—
357C2×#501—471no—
358C2×#484—471no—
359C2×#485—471no—
360C2×#483—471no—
361C2×#483—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#470—471no—
365C2×#467—471no—
366C2×#441—471no—
367C2×#435—471no—
368C2×#428D4711yescharacteristic, complemented
369C22×#106—471no—
370C2×C47—42no—
371C2×C47#334414yescomplemented
372C2×C47C2×#54711yescharacteristic
373C2×C47C22×#13711yescharacteristic
374C2×C47C2×#57711yescharacteristic
375D47—24no—
376C22×Q16—471no—
377C22×M16C2×D4711yescharacteristic
378C23×C8—471no—
379#554—478no—
380#554—944no—
381#552—478no—
382#552—944no—
383C2×C4⋊Q8—471no—
384C2×#126—941no—
385C2×#125—471no—
386C2×#125—941no—
387C2×#125—941no—
388C2×#123—941no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391C2×C22⋊Q8—471no—
392C2×C22⋊Q8—471no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×C4×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×D4—471no—
398C2×C4×D4—941no—
399C2×#117—941no—
400C2×#117C2×D4711yescharacteristic
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4C2×D4711yescharacteristic
404#501—478no—
405#485—478no—
406#484—478no—
407#483—478no—
408#483—478no—
409#479—478no—
410#475—478no—
411#470—478no—
412#467—478no—
413#441—478no—
414#435—478no—
415#428C2×D4718yescomplemented
416C2×#107—471no—
417C2×#107C2×D4711yescharacteristic
418C2×#107C2×D4711yescharacteristic
419C2×#106—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—478no—
424C2×#106C2×D4711yescharacteristic
425C2×#106C2×D4711yescharacteristic
426C2×C4⋊C8—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×C22⋊C8—471no—
434C2×C22⋊C8—471no—
435C2×#97—471no—
436C47C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—471no—
438C22×Q8—471no—
439C22×Q8—941no—
440C22×D4—471no—
441C23×C4—21no—
442C23×C4—471no—
443C23×C4—941no—
444C23×C4—941no—
445C23×C4C22×D4711yescharacteristic
446C2×Q16—474no—
447C2×Q16—944no—
448C2×M16—24no—
449C2×M16C22×D4714yes—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—474no—
453C22×C8—944no—
454C22×C8C22×D4711yescharacteristic
455C22×C8C22×D4711yescharacteristic
456C4⋊Q8—474no—
457C4⋊Q8—942no—
458#126—948no—
459#125—474no—
460#125—948no—
461#125—942no—
462#125—948no—
463#123—948no—
464C22⋊Q8—474no—
465C22⋊Q8—474no—
466C22⋊Q8—474no—
467C22⋊Q8—474no—
468C22⋊Q8—948no—
469C22⋊Q8—948no—
470C22⋊Q8—942no—
471C22⋊Q8—942no—
472C22⋊Q8—942no—
473C22⋊Q8—942no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—942no—
477C4×Q8—942no—
478C4×D4—474no—
479C4×D4—474no—
480C4×D4—948no—
481#117—22no—
482#117—948no—
483#117C22×D4714yes—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—942no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4714yes—
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C42—21no—
517C2×C42—471no—
518C2×C42—941no—
519C2×C42—941no—
520#107—474no—
521#107C22×D4714yes—
522#107C22×D4714yes—
523#106—474no—
524#106—474no—
525#106—474no—
526#106—474no—
527#106C22×D4714yes—
528#106C22×D4714yes—
529C4⋊C8—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103—474no—
535#103—474no—
536C22⋊C8—474no—
537C22⋊C8—474no—
538#97—474no—
539C24—471no—
540C24D4×D4711yescharacteristic
541C2×Q8—472no—
542C2×Q8—472no—
543C2×Q8—944no—
544C2×Q8—941no—
545C2×Q8—941no—
546C2×Q8—942no—
547C2×Q8—942no—
548C2×Q8—942no—
549C2×Q8—942no—
550C2×Q8—3762no—
551C2×D4—474no—
552C2×D4—944no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—82no—
561C22×C4—471no—
562C22×C4—471no—
563C22×C4—471no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—944no—
567C22×C4—944no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—3762no—
575C22×C4—1884no—
576C22×C4D4×D4712yes—
577C22×C4D4×D4711yescharacteristic
578C22×C4C23×D4712yes—
579C22×C4C23×D4711yescharacteristic
580Q16—948no—
581M16—28no—
582C2×C8—22no—
583C2×C8—472no—
584C2×C8—472no—
585C2×C8—942no—
586C2×C8—942no—
587C2×C8—948no—
588C2×C8#1062535014yes—
589C2×C8C23×D4712yes—
590C2×C8C23×D4712yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—474no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4C23×D4712yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C4⋊C4C23×D4712yes—
616C22⋊C4—24no—
617C22⋊C4—474no—
618C22⋊C4—474no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—24no—
624C42—472no—
625C42—472no—
626C42—944no—
627C42—944no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—474no—
632C23—472no—
633C23—942no—
634C23—942no—
635C23C2×D4×D4712yes—
636C23C2×D4×D4711yescharacteristic
637Q8—942no—
638Q8—942no—
639Q8—942no—
640Q8—942no—
641Q8—3764no—
642Q8—1882no—
643Q8—1882no—
644D4—948no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—84no—
658C2×C4—472no—
659C2×C4—472no—
660C2×C4—472no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—944no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—3764no—
672C2×C4—1888no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4C2×D4×D4712yes—
678C2×C4C2×D4×D4711yescharacteristic
679C2×C4C2×#1062535012yes—
680C2×C4#1309407212yes—
681C2×C4C24×D4711yescharacteristic
682C8—22no—
683C8—942no—
684C8—942no—
685C8C2×#1062535014yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—474no—
691C22—942no—
692C22—942no—
693C22—948no—
694C22#1568977412yes—
695C22#137×D4712yes—
696C22#1568993312yes—
697C22C22×D4×D4711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—942no—
704C4—942no—
705C4—942no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4#1568977412yes—
711C4C22×#1062535011yescharacteristic
712C4C2×#1309407211yescharacteristic
713C2—42no—
714C2—944no—
715C2#2025584414yesdirect product factor
716C2C2×#1568977411yescharacteristic
717C2C2×#137×D4711yescharacteristic
718C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#428C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#428D47
hypocenterC47C2×#3344
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #20255844C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689464C2semidirect
7. C2×#15689455C2semidirect
8. C2×#15689453C2semidirect
9. C2×#15689429C2semidirect
10. C2×#15689407C2semidirect
11. C2×#15689381C2semidirect
12. C2×#15689365C2semidirect
13. C2×#15689229C2semidirect
15. C2×#106×D47C2semidirect
16. C2×C47×#428C2semidirect
42. #15689531C22semidirect
43. #15689464C22semidirect
44. #15689460C22semidirect
45. #15689455C22semidirect
46. #15689453C22semidirect
47. #15689429C22semidirect
48. #15689407C22semidirect
49. #15689381C22semidirect
50. #15689365C22semidirect
51. #15689229C22semidirect
58. #106×D47C22semidirect
72. C47×#428C22semidirect
368. C2×#428D47semidirect
371. C2×C47#3344semidirect
415. #428C2×D47semidirect
436. C47C2×#3344semidirect
715. C2#20255844direct (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×#156898122
#202558442
C2×#156895312
C2×#156894602
C2×#156894642
C2×#156894552
C2×#156894532
C2×#156894292
C2×#156894072
C2×#156893812
C2×#156893652
C2×#156892292
C2×#156891922
C2×#106×D472
C2×C47×#4282
C2×#334447