Finite Group Databasebeta

← C4×#15689285 #26221908

Subgroups — C4×#15689285 #26221908

Order 12032.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689285C211yesmaximal, characteristic
2C2×C4×#10625337C211yesmaximal, characteristic, complemented
3C2×C4×#10625335C211yesmaximal, characteristic, complemented
4C4×#13094003C211yesmaximal, characteristic, complemented
5#20243729C211yesmaximal, characteristic, complemented
6#20243722C211yesmaximal, characteristic, complemented
7#20243700C211yesmaximal, characteristic, complemented
8#20243656C211yesmaximal, characteristic, complemented
9#20243635C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic
12C4×#13093948C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C2×C4×#41×C47C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C2×#13094003C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20#15689285C418yesdirect product factor
21C4×#10625337—24no—
22C4×#10625335—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093947C2211yescharacteristic
29C2×#13093947C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37#15689029C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689007—21no—
40#15688996—21no—
41#15688983C2211yescharacteristic
42C4×Dic47⋊C4—21no—
43C4×C4⋊Dic47C2211yescharacteristic
44C4×C22⋊Dic47—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C4×#41×C47—24no—
53C4×#41×C47—24no—
54C2×C4×Q8×C47C2211yescharacteristic
55C2×C4×Q8×C47C2211yescharacteristic
56C2×C4×D4×C47—21no—
57C2×C4×D4×C47—21no—
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47—21no—
61C2×#117×C47C2211yescharacteristic
62C22×C42×C47—21no—
63C22×C42×C47C2211yescharacteristic
64C22×Dic94C2311yescharacteristic
65C2×#10625337—22no—
66C2×#10625337—22no—
67C2×#10625337C2×C414yescomplemented
68C2×#10625335—22no—
69C2×#10625335—22no—
70C2×#10625335C2×C414yescomplemented
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094003—22no—
76#13094003C2×C414yescomplemented
77C4×Dic94—22no—
78C4×Dic94—22no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89#13093957—22no—
90#13093955—22no—
91#13093948—22no—
92#13093948—22no—
93#13093948C2×C414yescomplemented
94#13093947—22no—
95#13093947—22no—
96#13093945—22no—
97#13093945—22no—
98#13093945C2×C414yescomplemented
99C22⋊(C47⋊C8)—22no—
100C22⋊(C47⋊C8)C2×C414yescomplemented
101C4×C47⋊C8—22no—
102C4×C47⋊C8—22no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C2×#41×C47—22no—
109C2×#41×C47—22no—
110C2×#41×C47—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47C2×C414yes—
114C22×Q8×C47C2311yescharacteristic
115C22×D4×C47—21no—
116C22×D4×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47—21no—
119C23×C4×C47—21no—
120C23×C4×C47D411yescharacteristic
121C23×C4×C47D411yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×Q8×C47—22no—
126C4×Q8×C47D414yes—
127C4×D4×C47—28no—
128C4×D4×C47—28no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47—22no—
132C4×D4×C47D414yes—
133#117×C47—28no—
134#117×C47—22no—
135#117×C47—22no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C42×C47—28no—
144C2×C42×C47—21no—
145C2×C42×C47—21no—
146C2×C42×C47—21no—
147C2×C42×C47—22no—
148C2×C42×C47—22no—
149C2×C42×C47D411yescharacteristic
150C2×C42×C47D411yescharacteristic
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155#41×C47—28no—
156#41×C47—28no—
157#41×C47—28no—
158#41×C47—28no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47C22×C412yes—
163C2×Q8×C47C2×D412yes—
164C2×Q8×C47#4112yes—
165C2×D4×C47—24no—
166C2×D4×C47—24no—
167C2×D4×C47—24no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47C22×C412yes—
172C2×D4×C47C2×D412yes—
173C2×D4×C47#4112yes—
174C22×C4×C47—24no—
175C22×C4×C47—24no—
176C22×C4×C47—21no—
177C22×C4×C47—24no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—24no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—24no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—41no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47—42no—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47#4112yes—
203C22×C4×C47C2411yescharacteristic
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C2×Dic94—21no—
209C2×Dic94—21no—
210C2×Dic94—21no—
211C2×Dic94—21no—
212C2×Dic94—21no—
213C2×Dic94C22×C412yes—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47C2×D412yes—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—24no—
223C42×C47—24no—
224C42×C47—24no—
225C42×C47—22no—
226C42×C47—24no—
227C42×C47—22no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47C2×D412yes—
231C42×C47C2×D412yes—
232C22⋊Dic47—24no—
233C22⋊Dic47—42no—
234#10625337—28no—
235#10625335—28no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47C22×C412yes—
242Dic47⋊C4—24no—
243Dic47⋊C4—42no—
244Dic47⋊C4—42no—
245C4×Dic47—42no—
246C4×Dic47—42no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8C22×C412yes—
258C2×C47⋊C8C22×C412yes—
259C23×C47—22no—
260C23×C47—21no—
261C23×C47—22no—
262C23×C47—21no—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47C4×D412yes—
273C23×C47C22×D411yescharacteristic
274Q8×C47—22no—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47C4×D414yes—
278D4×C47—216no—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—22no—
282D4×C47C4×D414yes—
283C2×C4×C47—216no—
284C2×C4×C47—22no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—22no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—44no—
303C2×C4×C47—48no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—44no—
309C2×C4×C47—48no—
310C2×C4×C47C4×D412yes—
311C2×C4×C47#12012yes—
312C2×C4×C47#12012yes—
313C2×C4×C47#13512yes—
314C2×C4×C47#13512yes—
315C2×C4×C47#13712yes—
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334Dic94—22no—
335Dic94—22no—
336Dic94—41no—
337Dic94—41no—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C47⋊C8—41no—
341C47⋊C8—41no—
342C4×#452—471nomaximal, Sylow
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—24no—
347C22×C47—41no—
348C22×C47—42no—
349C22×C47—41no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—41no—
354C22×C47—42no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47C2×C4×D411yescharacteristic
358C22×C47C2×#12011yescharacteristic
359C22×C47#52511yescharacteristic
360C22×C47C2×#13511yescharacteristic
361C22×C47C2×#13511yescharacteristic
362C22×C47C2×#13711yescharacteristic
363C22×C47#57511yescharacteristic
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—24no—
368C4×C47—41no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47#45214yescomplemented
372C4×C47C2×C4×D411yescharacteristic
373C4×C47C2×C4×D411yescharacteristic
374C4×C47#52511yescharacteristic
375C4×C47#52511yescharacteristic
376Dic47—42no—
377Dic47—42no—
378Dic47—81no—
379Dic47—81no—
380C2×C4×#41D4711yescharacteristic
381C2×#452—471no—
382C2×C4×Q16—471no—
383C2×C4×SD16—471no—
384C4×C22⋊Q8—471no—
385#1878—471no—
386#1877—471no—
387#1873—471no—
388#1865—471no—
389#1862—471no—
390#1854—471no—
391#1788—471no—
392C4×#103—471no—
393C4×#102—471no—
394C4×C22⋊C8—471no—
395C2×C47—42no—
396C2×C47—44no—
397C2×C47C4×#12011yescharacteristic
398C2×C47C4×#13511yescharacteristic
399C2×C47C4×#13711yescharacteristic
400C2×C47C2×#45211yescharacteristic
401C2×C47#300211yescharacteristic
402C2×C47#310211yescharacteristic
403C2×C47#310711yescharacteristic
404C22×#41C2×D4711yescharacteristic
405C22×Q16—471no—
406C22×SD16—471no—
407C2×C22⋊Q8—471no—
408C4×#41—24no—
409C4×#41—24no—
410C2×C4×Q8—471no—
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×Q8C2×D4711yescharacteristic
413C2×C4×D4—21no—
414C2×C4×D4—21no—
415C2×C4×D4C2×D4711yescharacteristic
416C2×C4×D4C2×D4711yescharacteristic
417C2×#117—21no—
418C2×#117C2×D4711yescharacteristic
419C22×C42—21no—
420C22×C42C2×D4711yescharacteristic
421#452—478no—
422C4×Q16—944no—
423C4×SD16—944no—
424C2×#107—471no—
425C2×#106—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×C22⋊C8—471no—
435C2×C22⋊C8—471no—
436C2×C4×C8—471no—
437C2×C4×C8—471no—
438#391—471no—
439#389—471no—
440#387—941no—
441#385—941no—
442#380—471no—
443C4×C4⋊C4—471no—
444C4×C4⋊C4—941no—
445C4×C22⋊C4—941no—
446#340—471no—
447#340—471no—
448#340—471no—
449#340—471no—
450#336—471no—
451#336—471no—
452C47C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41C4×D4714yes—
459C22×Q8—471no—
460C22×Q8C22×D4711yescharacteristic
461C22×D4—21no—
462C22×D4C22×D4711yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C22⋊D4711yescharacteristic
467C23×C4C22⋊D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C2×Q16—474no—
470C2×Q16—942no—
471C2×Q16—942no—
472C2×SD16—474no—
473C2×SD16—942no—
474C2×SD16—942no—
475C22×C8—471no—
476C22×C8—471no—
477C22×C8—471no—
478C22×C8—471no—
479C22⋊Q8—474no—
480C22⋊Q8—942no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—942no—
485C4×Q8—942no—
486C4×Q8C22⋊D4714yes—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4C22⋊D4714yes—
493#117—28no—
494#117—22no—
495#117—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C42—28no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42C22⋊D4711yescharacteristic
520C2×C42C22⋊D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522C2×C42C22×D4711yescharacteristic
523#107—942no—
524#106—942no—
525#103—474no—
526#103—942no—
527#103—942no—
528#103—942no—
529#103—942no—
530#102—474no—
531#102—942no—
532#102—942no—
533C22⋊C8—474no—
534C22⋊C8—942no—
535C4×C8—942no—
536C4×C8—942no—
537#95—941no—
538#95—941no—
539#95—941no—
540#95—941no—
541#95—941no—
542C24—21no—
543C24C2×C22⋊D4711yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—472no—
552C2×Q8—941no—
553C2×Q8—941no—
554C2×Q8—941no—
555C2×Q8—941no—
556C2×Q8—941no—
557C2×Q8C2×C4×D4712yes—
558C2×Q8#1062535012yes—
559C2×Q8C2×C22⋊D4712yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×C4×D4712yes—
567C2×D4#1062535012yes—
568C2×D4C2×C22⋊D4712yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4C2×C4×D4712yes—
596C22×C4#1062535012yes—
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C2×C22⋊D4711yescharacteristic
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C2×C22⋊D4711yescharacteristic
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C23×D4711yescharacteristic
603Q16—948no—
604SD16—948no—
605C2×C8—472no—
606C2×C8—472no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C2×C8—941no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—472no—
622C4⋊C4—944no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4—1882no—
629C4⋊C4—1882no—
630C4⋊C4C2×C22⋊D4712yes—
631C4⋊C4C2×C22⋊D4712yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—944no—
636C22⋊C4—1882no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—24no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—1882no—
645C42—1882no—
646C42C2×C22⋊D4712yes—
647C42C2×C22⋊D4712yes—
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C4×C22⋊D4712yes—
662C23C22×C22⋊D4711yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—942no—
667Q8—942no—
668Q8—1881no—
669Q8—1881no—
670Q8C4×C22⋊D4714yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4C4×C22⋊D4714yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—44no—
702C2×C4—48no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4C4×C22⋊D4712yes—
716C2×C4#1309399312yes—
717C2×C4#1309399312yes—
718C2×C4#1309404412yes—
719C2×C4#1309404412yes—
720C2×C4#1309405412yes—
721C2×C4C22×C4×D4711yescharacteristic
722C2×C4C22×C22⋊D4711yescharacteristic
723C2×C4C22×C22⋊D4711yescharacteristic
724C2×C4C2×#1062535011yescharacteristic
725C2×C4C2×#1062535011yescharacteristic
726C2×C4C2×#1062535011yescharacteristic
727C8—942no—
728C8—942no—
729C8—1881no—
730C8—1881no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—22no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22C2×C4×C22⋊D4711yescharacteristic
746C22C2×#1309399311yescharacteristic
747C22#1568963411yescharacteristic
748C22C2×#1309404411yescharacteristic
749C22C2×#1309404411yescharacteristic
750C22C2×#1309405411yescharacteristic
751C22#1568992111yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—3761no—
760C4—3761no—
761C4—1882no—
762C4—1882no—
763C4#1568928514yesdirect product factor
764C4C2×C4×C22⋊D4711yescharacteristic
765C4C2×C4×C22⋊D4711yescharacteristic
766C4#1568963411yescharacteristic
767C4#1568963411yescharacteristic
768C2—42no—
769C2—44no—
770C2C4×#1309399311yescharacteristic
771C2C4×#1309404411yescharacteristic
772C2C4×#1309405411yescharacteristic
773C2C2×#1568928511yescharacteristic
774C2#2025260611yescharacteristic
775C2#2025340611yescharacteristic
776C2#2025345911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×#41×C47C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×C4×#41D47
hypocenterC47C4×#452
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625337C2semidirect
3. C2×C4×#10625335C2semidirect
4. C4×#13094003C2semidirect
5. #20243729C2semidirect
6. #20243722C2semidirect
7. #20243700C2semidirect
8. #20243656C2semidirect
9. #20243635C2semidirect
10. #20243587C2semidirect
12. C4×#13093948C2semidirect
13. C4×#13093945C2semidirect
14. C4×C22⋊(C47⋊C8)C2semidirect
20. #15689285C4direct (N × H)
67. C2×#10625337C2×C4semidirect
70. C2×#10625335C2×C4semidirect
76. #13094003C2×C4semidirect
93. #13093948C2×C4semidirect
98. #13093945C2×C4semidirect
100. C22⋊(C47⋊C8)C2×C4semidirect
371. C4×C47#452semidirect
452. C47C4×#452semidirect
763. C4#15689285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156892852
C2×C4×#106253372
C2×C4×#106253352
C4×#130940032
#202437292
#202437222
#202437002
#202436562
#202436352
#202435872
#202433282
C4×#130939482
C4×#130939452
C4×C22⋊(C47⋊C8)2
C2×C4×#41×C472
C4×#45247