Finite Group Databasebeta

← C2×#20256327 #27096799

Subgroups — C2×#20256327 #27096799

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689833C211yesmaximal, characteristic
2#20256327C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689529C211yesmaximal, characteristic, complemented
5C2×#15689522C211yesmaximal, characteristic, complemented
6C2×#15689430C211yesmaximal, characteristic, complemented
7C2×#15689430C211yesmaximal, characteristic, complemented
8C2×#15689408C211yesmaximal, characteristic, complemented
9C2×#15689420C211yesmaximal, characteristic
10C2×#15689420C211yesmaximal, characteristic
11C2×#15689410C211yesmaximal, characteristic
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689221C211yesmaximal, characteristic
14C2×#15689221C211yesmaximal, characteristic
15C2×C4×#10625336C211yesmaximal, characteristic
16C2×C47×#557C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18#15689833—24no—
19#15689833C2218yes—
20C2×#13094024C2211yescharacteristic
21C2×#13094016C2211yescharacteristic
22C2×#13094016C2211yescharacteristic
23C2×#13094002—21no—
24C2×#13094002—21no—
25C2×#13094000—21no—
26C2×C4×D188C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×C4⋊C4×D47—21no—
30#15689533C2218yescomplemented
31#15689529C2218yescomplemented
32#15689522C2218yescomplemented
33#15689430C2218yescomplemented
34#15689430C2218yescomplemented
35#15689420C2218yes—
36#15689420C2218yes—
37#15689410C2218yes—
38#15689408C2218yescomplemented
39#15689254C2218yescomplemented
40#15689221C2218yes—
41#15689221C2218yes—
42C4×#10625336C2218yes—
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093955C2211yescharacteristic
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#557—24no—
65C47×#557C2218yescomplemented
66C2×C4⋊Q8×C47—21no—
67C2×C4⋊Q8×C47C2211yescharacteristic
68C2×#125×C47—21no—
69C2×#125×C47—21no—
70C2×#125×C47C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×C4×Q8×C47—21no—
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C4×D47—21no—
80C22×C4×D47—21no—
81C22×C4×D47—21no—
82C2×#10625336Q818yescomplemented
83C2×#10625336C2314yes—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88#13094024—22no—
89#13094024C2314yes—
90#13094016—22no—
91#13094016—22no—
92#13094016C2314yes—
93#13094016C2314yes—
94#13094002—28no—
95#13094002—28no—
96#13094000—28no—
97C4×D188—22no—
98C4×D188—22no—
99C4×D188—22no—
100C4×D188C2314yes—
101C4×D188C2314yes—
102C4×D188C2314yes—
103C2×C4⋊Dic47—21no—
104C2×C4⋊Dic47C2311yescharacteristic
105C2×C4⋊Dic47C2311yescharacteristic
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4—21no—
108C2×Dic47⋊C4—21no—
109C2×Dic47⋊C4—21no—
110C2×Dic47⋊C4—21no—
111C4⋊C4×D47—28no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093957C2314yes—
118#13093957C2314yes—
119#13093955C2314yes—
120#13093955C2314yes—
121#13093955C2314yes—
122#13093955C2314yes—
123#13093955C2314yes—
124C4⋊(C47⋊C8)C2314yes—
125C4⋊(C47⋊C8)C2314yes—
126C4⋊(C47⋊C8)C2314yes—
127#13093948C2314yes—
128#13093948C2314yes—
129#13093948C2314yes—
130#13093944C2314yes—
131#13093944C2314yes—
132#13093944C2314yes—
133#13093935C2314yes—
134#13093935C2314yes—
135C4×C47⋊C8C2314yes—
136C22×Q8×C47—21no—
137C22×Q8×C47D411yescharacteristic
138C22×Q8×C47C2311yescharacteristic
139C4⋊Q8×C47—28no—
140C4⋊Q8×C47—22no—
141C4⋊Q8×C47C2314yes—
142#125×C47—28no—
143#125×C47—28no—
144#125×C47—22no—
145#125×C47—22no—
146#125×C47C2314yes—
147#125×C47C2314yes—
148C4×Q8×C47—28no—
149C4×Q8×C47—22no—
150C4×Q8×C47—22no—
151C4×Q8×C47—22no—
152C4×Q8×C47D414yes—
153C4×Q8×C47C2314yes—
154C4×Q8×C47C2314yes—
155C4×Q8×C47C2314yes—
156C4×Q8×C47C2314yes—
157C2×C4⋊C4×C47—21no—
158C2×C4⋊C4×C47—21no—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47D411yescharacteristic
166C2×C4⋊C4×C47D411yescharacteristic
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C42×C47—21no—
172C2×C42×C47—21no—
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177C23×D47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—24no—
180C2×Q8×C47—22no—
181C2×Q8×C47—42no—
182C2×Q8×C47—44no—
183C2×Q8×C47C2×D414yes—
184C2×Q8×C47C2×Q814yes—
185C2×Q8×C47C2412yes—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C2×D188—21no—
201C2×D188—22no—
202C2×D188C2×Q814yes—
203C2×D188C2412yes—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—24no—
207C2×C4×D47—44no—
208C2×C4×D47—82no—
209C2×C4×D47—82no—
210C2×Dic94—24no—
211C2×Dic94—82no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—24no—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—24no—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47C2×D414yes—
224C4⋊C4×C47C2×D414yes—
225C4⋊C4×C47C2×D414yes—
226C4⋊C4×C47C2412yes—
227C4⋊C4×C47C2412yes—
228C4⋊C4×C47C2412yes—
229C42×C47—24no—
230C42×C47—24no—
231C42×C47—24no—
232C42×C47C2×D412yes—
233C42×C47C2×D412yes—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C42×C47C2412yes—
237C42×C47C2412yes—
238#10625336C2×Q8116yescomplemented
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253C2×C47⋊C8—22no—
254C2×C47⋊C8—22no—
255C2×C47⋊C8—22no—
256C2×C47⋊C8C2×Q814yes—
257C2×C47⋊C8C2412yes—
258C2×C47⋊C8C2412yes—
259C2×C47⋊C8C2412yes—
260C2×C47⋊C8C2412yes—
261C23×C47C22×D411yescharacteristic
262C22×D47—24no—
263C22×D47—22no—
264C22×D47—42no—
265C22×D47—42no—
266Q8×C47—24no—
267Q8×C47—22no—
268Q8×C47—44no—
269Q8×C47—48no—
270Q8×C47C22×Q814yes—
271C2×C4×C47—24no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C22×Q812yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301D188—24no—
302D188—22no—
303D188C22×Q814yes—
304C4×D47—48no—
305C4×D47—84no—
306C4×D47—84no—
307Dic94—84no—
308C47⋊C8—22no—
309C47⋊C8—22no—
310C47⋊C8—22no—
311C47⋊C8C22×Q814yes—
312C2×#3388—471nomaximal, Sylow
313C22×C47D4×Q812yes—
314C22×C47#57512yes—
315C22×C47#57712yes—
316C22×C47C23×D411yescharacteristic
317C2×D47—24no—
318C2×D47—48no—
319C2×D47—42no—
320C2×D47—42no—
321C4×C47—24no—
322C4×C47—22no—
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—22no—
327C4×C47—22no—
328C4×C47—42no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47D4×Q812yes—
332C4×C47C23×Q811yescharacteristic
333C4×C47C2×2−1+411yescharacteristic
334Dic47—42no—
335Dic47—42no—
336Dic47—42no—
337C2×#557D4711yescharacteristic, complemented
338C2×#554—471no—
339#3388—4716no—
340C2×#501—471no—
341C2×#501—471no—
342C2×#499—471no—
343C2×#479—471no—
344C2×#479—471no—
345C2×#475—471no—
346C2×#478—471no—
347C2×#478—471no—
348C2×#476—471no—
349C2×#446—471no—
350C2×#440—471no—
351C2×#440—471no—
352C2×C4×SD16—471no—
353C2×C47#338814yescomplemented
354C2×C47C2×D4×Q811yescharacteristic
355C2×C47C2×#57511yescharacteristic
356C2×C47C2×#57711yescharacteristic
357D47—44no—
358C22×SD16—471no—
359#557—24no—
360#557C2×D4718yescomplemented
361#554—478no—
362#554—944no—
363C2×C4⋊Q8—21no—
364C2×C4⋊Q8—471no—
365C2×C4⋊Q8C2×D4711yescharacteristic
366C2×#125—21no—
367C2×#125—21no—
368C2×#125—471no—
369C2×#125—471no—
370C2×#125C2×D4711yescharacteristic
371C2×#125C2×D4711yescharacteristic
372C2×C22⋊Q8—941no—
373C2×C22⋊Q8—941no—
374C2×C22⋊Q8—941no—
375C2×C4×Q8—21no—
376C2×C4×Q8C2×D4711yescharacteristic
377C2×C4×Q8C2×D4711yescharacteristic
378C2×C4×Q8C2×D4711yescharacteristic
379C2×C4×Q8C2×D4711yescharacteristic
380C2×C4×D4—471no—
381C2×C4×D4—471no—
382C2×C4×D4—471no—
383C22×C4⋊C4—941no—
384#501—478no—
385#501—478no—
386#499—478no—
387#479—478no—
388#479—478no—
389#478—478no—
390#478—478no—
391#476—478no—
392#475—478no—
393#446—478no—
394#440—478no—
395#440—478no—
396C4×SD16—478no—
397C2×#107—471no—
398C2×#107—471no—
399C2×#107—471no—
400C2×#107—471no—
401C2×#106—471no—
402C2×#106—471no—
403C2×#106—471no—
404C2×#106—471no—
405C2×#106—471no—
406C2×C4⋊C8—471no—
407C2×C4⋊C8—471no—
408C2×C4⋊C8—471no—
409C2×#103—471no—
410C2×#103—471no—
411C2×#103—471no—
412C2×#102—471no—
413C2×#102—471no—
414C2×#102—471no—
415C2×#97—471no—
416C2×#97—471no—
417C2×C4×C8—471no—
418C47C2×#338811yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8—941no—
421C22×Q8C22⋊D4711yescharacteristic
422C22×Q8C22×D4711yescharacteristic
423C22×D4—471no—
424C23×C4—941no—
425C23×C4—941no—
426C23×C4—941no—
427C2×SD16—478no—
428C2×SD16—474no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—471no—
432C22×C8—471no—
433C4⋊Q8—28no—
434C4⋊Q8—22no—
435C4⋊Q8—474no—
436C4⋊Q8—942no—
437C4⋊Q8C22×D4714yes—
438#125—28no—
439#125—28no—
440#125—22no—
441#125—22no—
442#125—474no—
443#125—474no—
444#125—942no—
445#125—942no—
446#125C22×D4714yes—
447#125C22×D4714yes—
448C22⋊Q8—948no—
449C22⋊Q8—948no—
450C22⋊Q8—948no—
451C4×Q8—28no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8C22⋊D4714yes—
456C4×Q8C22×D4714yes—
457C4×Q8C22×D4714yes—
458C4×Q8C22×D4714yes—
459C4×Q8C22×D4714yes—
460C4×D4—474no—
461C4×D4—474no—
462C4×D4—474no—
463C4×D4—942no—
464C4×D4—942no—
465C4×D4—942no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—471no—
475C2×C4⋊C4—471no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—941no—
478C2×C4⋊C4—941no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—941no—
482C2×C4⋊C4—948no—
483C2×C4⋊C4C22⋊D4711yescharacteristic
484C2×C4⋊C4C22⋊D4711yescharacteristic
485C2×C4⋊C4C22⋊D4711yescharacteristic
486C2×C4⋊C4C22×D4711yescharacteristic
487C2×C4⋊C4C22×D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C22⋊C4—941no—
490C2×C22⋊C4—941no—
491C2×C22⋊C4—941no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C22×D4711yescharacteristic
496C2×C42C22×D4711yescharacteristic
497C2×C42C22×D4711yescharacteristic
498#107—474no—
499#107—474no—
500#107—474no—
501#107—474no—
502#106—474no—
503#106—474no—
504#106—474no—
505#106—474no—
506#106—474no—
507C4⋊C8—474no—
508C4⋊C8—474no—
509C4⋊C8—474no—
510#103—474no—
511#103—474no—
512#103—474no—
513#102—474no—
514#102—474no—
515#102—474no—
516#97—474no—
517#97—474no—
518C4×C8—474no—
519C24—941no—
520C2×Q8—21no—
521C2×Q8—24no—
522C2×Q8—22no—
523C2×Q8—42no—
524C2×Q8—44no—
525C2×Q8—944no—
526C2×Q8—3762no—
527C2×Q8Q8×D4714yes—
528C2×Q8C2×C22⋊D4714yes—
529C2×Q8C23×D4712yes—
530C2×D4—474no—
531C2×D4—472no—
532C2×D4—941no—
533C2×D4—942no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—944no—
542C22×C4—944no—
543C22×C4—944no—
544C22×C4—3762no—
545C22×C4—3762no—
546C22×C4—1884no—
547C22×C4C2×C22⋊D4711yescharacteristic
548C22×C4C2×C22⋊D4711yescharacteristic
549C22×C4C2×C22⋊D4711yescharacteristic
550C22×C4C2×C22⋊D4711yescharacteristic
551C22×C4C2×C22⋊D4711yescharacteristic
552C22×C4C2×C22⋊D4711yescharacteristic
553C22×C4C23×D4711yescharacteristic
554SD16—4716no—
555C2×C8—474no—
556C2×C8—472no—
557C2×C8—472no—
558C2×C8—472no—
559C2×C8—472no—
560C2×C8—942no—
561C2×C8—942no—
562C2×C8—942no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—472no—
575C4⋊C4—472no—
576C4⋊C4—472no—
577C4⋊C4—944no—
578C4⋊C4—944no—
579C4⋊C4—944no—
580C4⋊C4—944no—
581C4⋊C4—941no—
582C4⋊C4—941no—
583C4⋊C4—941no—
584C4⋊C4—944no—
585C4⋊C4C2×C22⋊D4714yes—
586C4⋊C4C2×C22⋊D4714yes—
587C4⋊C4C2×C22⋊D4714yes—
588C4⋊C4C23×D4712yes—
589C4⋊C4C23×D4712yes—
590C4⋊C4C23×D4712yes—
591C22⋊C4—944no—
592C22⋊C4—944no—
593C22⋊C4—944no—
594C42—24no—
595C42—24no—
596C42—24no—
597C42C2×C22⋊D4712yes—
598C42C2×C22⋊D4712yes—
599C42C2×C22⋊D4712yes—
600C42C23×D4712yes—
601C42C23×D4712yes—
602C42C23×D4712yes—
603C23—944no—
604C23—942no—
605C23—1882no—
606C23—1882no—
607C23C22×C22⋊D4711yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—3764no—
613Q8C2×Q8×D4714yes—
614D4—474no—
615D4—944no—
616D4—942no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—3764no—
635C2×C4—3764no—
636C2×C4—1888no—
637C2×C4—1882no—
638C2×C4—1882no—
639C2×C4—1882no—
640C2×C4C22×C22⋊D4712yes—
641C2×C4C22×C22⋊D4712yes—
642C2×C4C22×C22⋊D4712yes—
643C2×C4C22×C22⋊D4712yes—
644C2×C4C22×C22⋊D4712yes—
645C2×C4C22×C22⋊D4712yes—
646C2×C4C22×C22⋊D4711yescharacteristic
647C2×C4C2×Q8×D4712yes—
648C2×C4#1309407212yes—
649C2×C4C24×D4711yescharacteristic
650C8—474no—
651C8—942no—
652C8—942no—
653C8—942no—
654C22—944no—
655C22—1888no—
656C22—1882no—
657C22—1882no—
658C22Q8×C22⋊D4712yes—
659C22#1568992112yes—
660C22#1568993112yes—
661C22C23×C22⋊D4711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—24no—
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—1882no—
673C4—1882no—
674C4—1882no—
675C4Q8×C22⋊D4712yes—
676C4C22×Q8×D4711yescharacteristic
677C4C2×#1309407211yescharacteristic
678C2—1884no—
679C2#2025632714yesdirect product factor
680C2C2×Q8×C22⋊D4711yescharacteristic
681C2C2×#1568992111yescharacteristic
682C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#557C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC2×#557D47
hypocenterC47C2×#3388
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #20256327C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689529C2semidirect
5. C2×#15689522C2semidirect
6. C2×#15689430C2semidirect
7. C2×#15689430C2semidirect
8. C2×#15689408C2semidirect
12. C2×#15689254C2semidirect
16. C2×C47×#557C2semidirect
30. #15689533C22semidirect
31. #15689529C22semidirect
32. #15689522C22semidirect
33. #15689430C22semidirect
34. #15689430C22semidirect
38. #15689408C22semidirect
39. #15689254C22semidirect
65. C47×#557C22semidirect
82. C2×#10625336Q8semidirect
238. #10625336C2×Q8semidirect
337. C2×#557D47semidirect
353. C2×C47#3388semidirect
360. #557C2×D47semidirect
418. C47C2×#3388semidirect
679. C2#20256327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898332
#202563272
C2×#156895332
C2×#156895292
C2×#156895222
C2×#156894302
C2×#156894082
C2×#156894202
C2×#156894102
C2×#156892542
C2×#156892212
C2×C4×#106253362
C2×C47×#5572
C2×#338847