Finite Group Databasebeta

← C2×C4×#13093938 #26213925

Subgroups — C2×C4×#13093938 #26213925

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×#13093938C212yesmaximal
3C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
4C4×#13093938C218yesmaximal, direct product factor
5C2×#15688889C212yesmaximal, complemented
6C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C23×C22⋊D47C2211yescharacteristic
8C23×C4×D47C411yescharacteristic, complemented
9C2×C4×C22⋊D47—21no—
10C2×C4×C22⋊D47—21no—
11C2×C4×C22⋊D47—22no—
12C2×C4×C22⋊D47—21no—
13C2×C4×C22⋊D47—21no—
14C2×C4×C22⋊D47—22no—
15C2×C4×C22⋊D47C414yescomplemented
16C2×C4×C22⋊D47C2214yes—
17C22×Dic47⋊C4C411yescharacteristic, complemented
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2212yes—
20C22×(C2×D47)⋊C4C411yescharacteristic, complemented
21C22×C4×Dic47—21no—
22C22×C4×Dic47C411yescharacteristic, complemented
23C2×#13093938C4116yesdirect product factor
24C2×#13093938C2218yes—
25C4×C22⋊Dic47—22no—
26C4×C22⋊Dic47C2214yescomplemented
27C2×C47⋊#95—21no—
28#15688889C2218yescomplemented
29C24×C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2212yes—
31C22×C42×C47—21no—
32C4×C22⋊C4×C47—22no—
33C4×C22⋊C4×C47C2214yescomplemented
34C2×#95×C47—21no—
35C24×D47C2×C411yescharacteristic
36C22×C22⋊D47—21no—
37C22×C22⋊D47—21no—
38C22×C22⋊D47—21no—
39C22×C22⋊D47—21no—
40C22×C22⋊D47—24no—
41C22×C22⋊D47C2×C418yes—
42C22×C22⋊D47C2×C412yes—
43C22×C22⋊D47C2312yes—
44C23×Dic47—22no—
45C23×Dic47C2×C411yescharacteristic
46C23×Dic47C2×C411yescharacteristic
47C23×Dic47C2×C411yescharacteristic
48C22×C4×D47—21no—
49C22×C4×D47—22no—
50C22×C4×D47—21no—
51C22×C4×D47—44no—
52C22×C4×D47C2×C414yescomplemented
53C4×C22⋊D47—24no—
54C4×C22⋊D47—24no—
55C4×C22⋊D47—24no—
56C4×C22⋊D47—24no—
57C4×C22⋊D47—24no—
58C4×C22⋊D47—24no—
59C4×C22⋊D47—24no—
60C4×C22⋊D47—24no—
61C2×Dic47⋊C4—21no—
62C2×Dic47⋊C4—21no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4C2×C414yescomplemented
65C2×C22⋊Dic47—22no—
66C2×C22⋊Dic47—21no—
67C2×C22⋊Dic47—21no—
68C2×C22⋊Dic47—21no—
69C2×C22⋊Dic47—21no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47C2×C412yes—
72C2×C22⋊Dic47C2×C418yescomplemented
73C2×C22⋊Dic47C2312yes—
74C2×C22⋊Dic47C2314yes—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4C2×C414yescomplemented
79C2×C4×Dic47—21no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—44no—
84C2×C4×Dic47C2×C414yescomplemented
85#13093938C2×C4132yesdirect product factor
86C47⋊#95—24no—
87C25×C47C2311yescharacteristic
88C23×C4×C47—22no—
89C23×C4×C47—44no—
90C23×C4×C47C2×C411yescharacteristic
91C23×C4×C47C2×C411yescharacteristic
92C23×C4×C47C2×C412yes—
93C23×C4×C47D411yescharacteristic
94C23×C4×C47D411yescharacteristic
95C23×C4×C47D411yescharacteristic
96C23×C4×C47D412yes—
97C23×C4×C47D411yescharacteristic
98C23×C4×C47D412yes—
99C23×C4×C47C2312yes—
100C2×C22⋊C4×C47—22no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47C2×C418yescomplemented
103C2×C22⋊C4×C47C2314yes—
104C2×C42×C47—24no—
105C2×C42×C47—44no—
106#95×C47—24no—
107C24×C47—42no—
108C24×C47—42no—
109C24×C47C22×C411yescharacteristic
110C24×C47C22×C411yescharacteristic
111C24×C47C22×C414yes—
112C24×C47C2×D411yescharacteristic
113C24×C47C2×D411yescharacteristic
114C24×C47C2×D411yescharacteristic
115C24×C47C2×D411yescharacteristic
116C24×C47#4114yes—
117C24×C47C2411yescharacteristic
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—22no—
121C23×D47—42no—
122C23×D47—42no—
123C23×D47C4214yescomplemented
124C23×D47C22×C412yes—
125C22×C4×C47—24no—
126C22×C4×C47—24no—
127C22×C4×C47—24no—
128C22×C4×C47—28no—
129C22×C4×C47—24no—
130C22×C4×C47—44no—
131C22×C4×C47—44no—
132C22×C4×C47—44no—
133C22×C4×C47—44no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—44no—
138C22×C4×C47—44no—
139C22×C4×C47C22⋊C411yescharacteristic
140C22×C4×C47C22⋊C412yes—
141C22×C4×C47C22⋊C411yescharacteristic
142C22×C4×C47C22⋊C411yescharacteristic
143C22×C4×C47C22⋊C412yes—
144C22×C4×C47C22⋊C412yes—
145C22×C4×C47C22⋊C412yes—
146C22×C4×C47C22⋊C412yes—
147C22×C4×C47C22⋊C412yes—
148C22×C4×C47C22⋊C411yescharacteristic
149C22×C4×C47C22×C412yes—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D412yes—
155C2×C22⋊D47—22no—
156C2×C22⋊D47—22no—
157C2×C22⋊D47—24no—
158C2×C22⋊D47—28no—
159C2×C22⋊D47—28no—
160C2×C22⋊D47—28no—
161C2×C22⋊D47—28no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—22no—
164C2×C22⋊D47—24no—
165C2×C22⋊D47C4218yescomplemented
166C2×C22⋊D47C22×C418yes—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—28no—
175C22×Dic47—24no—
176C22×Dic47—44no—
177C22×Dic47—44no—
178C22×Dic47—42no—
179C22×Dic47—42no—
180C22×Dic47C4214yescomplemented
181C22×Dic47C22×C412yes—
182C22×Dic47C22×C412yes—
183C22×Dic47C22×C412yes—
184C2×C4×D47—24no—
185C2×C4×D47—24no—
186C2×C4×D47—44no—
187C2×C4×D47—48no—
188C2×C4×D47—44no—
189C2×C4×D47—48no—
190C22⋊C4×C47—28no—
191C22⋊C4×C47—24no—
192C22⋊C4×C47C22×C418yescomplemented
193C42×C47—48no—
194C22⋊Dic47—22no—
195C22⋊Dic47—22no—
196C22⋊Dic47—28no—
197C22⋊Dic47—22no—
198C22⋊Dic47—22no—
199C22⋊Dic47—24no—
200C22⋊Dic47C22×C418yescomplemented
201(C2×D47)⋊C4—24no—
202(C2×D47)⋊C4—24no—
203Dic47⋊C4—24no—
204Dic47⋊C4—24no—
205C4×Dic47—24no—
206C4×Dic47—24no—
207C4×Dic47—48no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—41no—
215C23×C47—41no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—41no—
219C23×C47—48no—
220C23×C47—41no—
221C23×C47—41no—
222C23×C47—48no—
223C23×C47—41no—
224C23×C47C2×C4212yes—
225C23×C47C2×C4212yes—
226C23×C47C2×C22⋊C411yescharacteristic
227C23×C47C2×C22⋊C411yescharacteristic
228C23×C47C2×C22⋊C411yescharacteristic
229C23×C47C2×C22⋊C411yescharacteristic
230C23×C47#11712yes—
231C23×C47#11712yes—
232C23×C47C4×D414yes—
233C23×C47C4×D414yes—
234C23×C47C4×D414yes—
235C23×C47C4×D414yes—
236C23×C47C23×C411yescharacteristic
237C23×C47C23×C412yes—
238C23×C47C22×D411yescharacteristic
239C23×C47C22×D411yescharacteristic
240C23×C47C2×#4112yes—
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—48no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—48no—
252C22×D47—42no—
253C22×D47C2×C4214yescomplemented
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—24no—
260C2×C4×C47—24no—
261C2×C4×C47—24no—
262C2×C4×C47—24no—
263C2×C4×C47—28no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—42no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—44no—
271C2×C4×C47—44no—
272C2×C4×C47—416no—
273C2×C4×C47#9914yescomplemented
274C2×C4×C47C2×C22⋊C412yes—
275C2×C4×C47C2×C22⋊C412yes—
276C2×C4×C47C2×C22⋊C412yes—
277C2×C4×C47C2×C22⋊C412yes—
278C22⋊D47—28no—
279C22⋊D47—28no—
280C22⋊D47—28no—
281C22⋊D47—28no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—28no—
289C2×Dic47—44no—
290C2×Dic47—42no—
291C2×Dic47—44no—
292C2×Dic47—416no—
293C2×Dic47—42no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47C2×C4214yescomplemented
299C4×D47—48no—
300C4×D47—48no—
301C2×C4×#99—471nomaximal, Sylow
302C22×C47—21no—
303C22×C47—21no—
304C22×C47—21no—
305C22×C47—21no—
306C22×C47—21no—
307C22×C47—21no—
308C22×C47—21no—
309C22×C47—21no—
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—21no—
313C22×C47—21no—
314C22×C47—28no—
315C22×C47—28no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—44no—
321C22×C47—44no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47C4×C22⋊C412yes—
325C22×C47C4×C22⋊C412yes—
326C22×C47C4×C22⋊C412yes—
327C22×C47C4×C22⋊C412yes—
328C22×C47C2×#9912yes—
329C22×C47#41012yes—
330C22×C47C22×C4211yescharacteristic
331C22×C47C22×C22⋊C411yescharacteristic
332C22×C47C2×#11711yescharacteristic
333C22×C47C2×C4×D412yes—
334C22×C47C2×C4×D412yes—
335C2×D47—24no—
336C2×D47—44no—
337C2×D47—48no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—48no—
341C2×D47—44no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—48no—
346C4×C47C2×#9914yescomplemented
347Dic47—24no—
348Dic47—48no—
349Dic47—42no—
350Dic47—42no—
351C22×C4×D4—471no—
352C22×#99—472no—
353C2×C4×C22⋊C4—471no—
354C2×C4×C22⋊C4D4711yescharacteristic, complemented
355C4×#99—478no—
356C2×#342—472no—
357C2×C47—22no—
358C2×C47—22no—
359C2×C47—21no—
360C2×C47—22no—
361C2×C47—21no—
362C2×C47—22no—
363C2×C47—22no—
364C2×C47C4×#9914yescomplemented
365C2×C47C2×C4×C22⋊C411yescharacteristic
366C2×C47C22×#9911yescharacteristic
367C2×C47C2×#41011yescharacteristic
368D47—44no—
369C23×D4—471no—
370C24×C4—471no—
371C24×C4C2×D4711yescharacteristic
372C2×C4×D4—474no—
373C2×C4×D4—474no—
374C2×C4×D4—941no—
375C2×C4×D4—942no—
376C2×C4×D4—941no—
377C2×C4×D4—941no—
378C2×C4×D4—942no—
379C2×C4×D4—941no—
380C22×C4⋊C4—471no—
381C22×C22⋊C4—472no—
382C22×C22⋊C4—471no—
383C22×C22⋊C4—471no—
384C22×C22⋊C4C2×D4712yes—
385C22×C42—21no—
386C22×C42—471no—
387C22×C42—941no—
388C2×#99—4716no—
389C2×#99—478no—
390C4×C22⋊C4—22no—
391C4×C22⋊C4—474no—
392C4×C22⋊C4—942no—
393C4×C22⋊C4C2×D4714yescomplemented
394C2×#95—21no—
395C2×#95—941no—
396#342—478no—
397C47C2×C4×#9911yescharacteristic, complemented, Sylow
398C25—471no—
399C25C22×D4711yescharacteristic
400C22×D4—472no—
401C22×D4—478no—
402C22×D4—472no—
403C22×D4—941no—
404C22×D4—941no—
405C22×D4—944no—
406C22×D4—941no—
407C22×D4—941no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4—471no—
411C23×C4—471no—
412C23×C4—471no—
413C23×C4—474no—
414C23×C4—942no—
415C23×C4—942no—
416C23×C4—941no—
417C23×C4—941no—
418C23×C4—1884no—
419C23×C4C4×D4711yescharacteristic
420C23×C4C4×D4711yescharacteristic
421C23×C4C4×D4712yes—
422C23×C4D18811yescharacteristic
423C23×C4D18811yescharacteristic
424C23×C4D18812yes—
425C23×C4C22⋊D4711yescharacteristic
426C23×C4C22⋊D4711yescharacteristic
427C23×C4C22⋊D4712yes—
428C23×C4C22×D4712yes—
429C4×D4—944no—
430C4×D4—944no—
431C4×D4—944no—
432C4×D4—944no—
433C4×D4—944no—
434C4×D4—944no—
435C4×D4—944no—
436C4×D4—944no—
437C2×C4⋊C4—474no—
438C2×C4⋊C4—941no—
439C2×C4⋊C4—941no—
440C2×C4⋊C4—942no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—478no—
444C2×C22⋊C4—474no—
445C2×C22⋊C4—472no—
446C2×C22⋊C4—472no—
447C2×C22⋊C4—474no—
448C2×C22⋊C4—941no—
449C2×C22⋊C4—941no—
450C2×C22⋊C4—942no—
451C2×C22⋊C4—944no—
452C2×C22⋊C4—941no—
453C2×C22⋊C4—941no—
454C2×C22⋊C4—941no—
455C2×C22⋊C4—941no—
456C2×C22⋊C4—942no—
457C2×C22⋊C4C4×D4718yescomplemented
458C2×C22⋊C4C22×D4714yes—
459C2×C42—24no—
460C2×C42—44no—
461C2×C42—474no—
462C2×C42—941no—
463C2×C42—942no—
464C2×C42—941no—
465C2×C42—944no—
466C2×C42—1884no—
467#99—4732no—
468#95—24no—
469#95—944no—
470C24—42no—
471C24—42no—
472C24—474no—
473C24—472no—
474C24—941no—
475C24—941no—
476C24—942no—
477C24—1882no—
478C24—1882no—
479C24C2×C4×D4711yescharacteristic
480C24C2×C4×D4711yescharacteristic
481C24C2×C4×D4714yes—
482C24C2×D18811yescharacteristic
483C24C2×D18811yescharacteristic
484C24#1062535014yes—
485C24C2×C22⋊D4711yescharacteristic
486C24C2×C22⋊D4711yescharacteristic
487C24C23×D4711yescharacteristic
488C2×D4—478no—
489C2×D4—478no—
490C2×D4—942no—
491C2×D4—942no—
492C2×D4—944no—
493C2×D4—948no—
494C2×D4—948no—
495C2×D4—948no—
496C2×D4—948no—
497C2×D4—942no—
498C2×D4—942no—
499C2×D4—944no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—474no—
515C22×C4—472no—
516C22×C4—472no—
517C22×C4—472no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—942no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—948no—
526C22×C4—944no—
527C22×C4—944no—
528C22×C4—944no—
529C22×C4—1884no—
530C22×C4—1888no—
531C22×C4—1888no—
532C22×C4—1884no—
533C22×C4—1884no—
534C22×C4—1884no—
535C22×C4—1882no—
536C22×C4—1882no—
537C22×C4(C2×D47)⋊C411yescharacteristic
538C22×C4(C2×D47)⋊C412yes—
539C22×C4(C2×D47)⋊C411yescharacteristic
540C22×C4(C2×D47)⋊C411yescharacteristic
541C22×C4(C2×D47)⋊C412yes—
542C22×C4(C2×D47)⋊C412yes—
543C22×C4(C2×D47)⋊C412yes—
544C22×C4(C2×D47)⋊C412yes—
545C22×C4(C2×D47)⋊C412yes—
546C22×C4(C2×D47)⋊C411yescharacteristic
547C22×C4C2×C4×D4712yes—
548C22×C4C2×C4×D4712yes—
549C22×C4C2×D18812yes—
550C22×C4C2×D18812yes—
551C22×C4C2×C22⋊D4712yes—
552C22×C4C2×C22⋊D4712yes—
553C4⋊C4—944no—
554C4⋊C4—944no—
555C22⋊C4—28no—
556C22⋊C4—24no—
557C22⋊C4—478no—
558C22⋊C4—942no—
559C22⋊C4—942no—
560C22⋊C4—948no—
561C22⋊C4—942no—
562C22⋊C4—942no—
563C22⋊C4—944no—
564C22⋊C4—944no—
565C22⋊C4—944no—
566C22⋊C4C2×C4×D4718yescomplemented
567C42—48no—
568C42—944no—
569C42—944no—
570C42—1888no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—48no—
583C23—41no—
584C23—48no—
585C23—41no—
586C23—41no—
587C23—474no—
588C23—944no—
589C23—944no—
590C23—942no—
591C23—942no—
592C23—1882no—
593C23—1882no—
594C23—1888no—
595C23—1882no—
596C23—1882no—
597C23—1888no—
598C23—1882no—
599C23—1882no—
600C23C42×D4712yes—
601C23C42×D4712yes—
602C23C2×(C2×D47)⋊C411yescharacteristic
603C23C2×(C2×D47)⋊C411yescharacteristic
604C23C2×(C2×D47)⋊C411yescharacteristic
605C23C2×(C2×D47)⋊C411yescharacteristic
606C23#1309398112yes—
607C23#1309398112yes—
608C23C4×C22⋊D4714yes—
609C23C4×C22⋊D4714yes—
610C23C4×D18814yes—
611C23C4×D18814yes—
612C23C22×C4×D4711yescharacteristic
613C23C22×C4×D4712yes—
614C23C22×C22⋊D4711yescharacteristic
615C23C22×D18811yescharacteristic
616C23C2×#1062535012yes—
617D4—948no—
618D4—948no—
619D4—948no—
620D4—948no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—416no—
640C2×C4—474no—
641C2×C4—944no—
642C2×C4—944no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—948no—
648C2×C4—1888no—
649C2×C4—1884no—
650C2×C4—1884no—
651C2×C4—18816no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4—1888no—
657C2×C4—1882no—
658C2×C4—1882no—
659C2×C4#1309393814yesdirect product factor
660C2×C4C2×(C2×D47)⋊C412yes—
661C2×C4C2×(C2×D47)⋊C412yes—
662C2×C4C2×(C2×D47)⋊C412yes—
663C2×C4C2×(C2×D47)⋊C412yes—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—944no—
687C22—1884no—
688C22—1888no—
689C22—1884no—
690C22—1882no—
691C22—1882no—
692C22—1888no—
693C22C4×(C2×D47)⋊C412yes—
694C22C4×(C2×D47)⋊C412yes—
695C22C4×(C2×D47)⋊C412yes—
696C22C4×(C2×D47)⋊C412yes—
697C22C2×#1309393812yes—
698C22#1568909612yes—
699C22C2×C42×D4711yescharacteristic
700C22C22×(C2×D47)⋊C411yescharacteristic
701C22C2×#1309398111yescharacteristic
702C22C2×C4×C22⋊D4712yes—
703C22C2×C4×D18812yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—944no—
709C4—1888no—
710C4—1882no—
711C4—1882no—
712C4C2×#1309393814yesdirect product factor
713C2—22no—
714C2—22no—
715C2—22no—
716C2—21no—
717C2—21no—
718C2—22no—
719C2—22no—
720C2—1884no—
721C2C4×#1309393814yesdirect product factor
722C2C2×C4×(C2×D47)⋊C411yescharacteristic
723C2C22×#1309393811yescharacteristic
724C2C2×#1568909611yescharacteristic
subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×C22⋊D47C22
cosocleC24×C47C24
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic47C2semidirect
4. C4×#13093938C2direct (N × H)
5. C2×#15688889C2semidirect
6. C2×C4×C22⋊C4×C47C2semidirect
8. C23×C4×D47C4semidirect
15. C2×C4×C22⋊D47C4semidirect
17. C22×Dic47⋊C4C4semidirect
20. C22×(C2×D47)⋊C4C4semidirect
22. C22×C4×Dic47C4semidirect
23. C2×#13093938C4direct (N × H)
26. C4×C22⋊Dic47C22semidirect
28. #15688889C22semidirect
33. C4×C22⋊C4×C47C22semidirect
52. C22×C4×D47C2×C4semidirect
64. C2×Dic47⋊C4C2×C4semidirect
72. C2×C22⋊Dic47C2×C4semidirect
78. C2×(C2×D47)⋊C4C2×C4semidirect
84. C2×C4×Dic47C2×C4semidirect
85. #13093938C2×C4direct (N × H)
102. C2×C22⋊C4×C47C2×C4semidirect
123. C23×D47C42semidirect
165. C2×C22⋊D47C42semidirect
180. C22×Dic47C42semidirect
192. C22⋊C4×C47C22×C4semidirect
200. C22⋊Dic47C22×C4semidirect
253. C22×D47C2×C42semidirect
273. C2×C4×C47#99semidirect
298. C2×Dic47C2×C42semidirect
346. C4×C47C2×#99semidirect
354. C2×C4×C22⋊C4D47semidirect
364. C2×C47C4×#99semidirect
393. C4×C22⋊C4C2×D47semidirect
397. C47C2×C4×#99semidirect
457. C2×C22⋊C4C4×D47semidirect
566. C22⋊C4C2×C4×D47semidirect
659. C2×C4#13093938direct (N × H)
712. C4C2×#13093938direct (N × H)
721. C2C4×#13093938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C22×#130939382
C2×C4×C22⋊Dic472
C4×#130939382
C2×#156888892
C2×C4×C22⋊C4×C472
C2×C4×#9947