Finite Group Databasebeta

← C2×#20243373 #26215670

Subgroups — C2×#20243373 #26215670

Order 12032.

2066 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×#13093938C212yesmaximal
3C2×#15688983C211yesmaximal, characteristic, complemented
4#20243373C218yesmaximal, direct product factor
5C2×#15688889C212yesmaximal, complemented
6C2×C47×#380C211yesmaximal, 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×C4⋊Dic47—21no—
18C22×Dic47⋊C4C411yescharacteristic, complemented
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2211yescharacteristic
21C22×(C2×D47)⋊C4C411yescharacteristic, complemented
22C22×C4×Dic47C411yescharacteristic, complemented
23C2×#13093938—28no—
24C2×#13093938C2218yes—
25#15688983—22no—
26#15688983C2214yescomplemented
27C2×C47⋊#95—21no—
28#15688889C2218yescomplemented
29C24×C4×C47C2211yescharacteristic
30C22×C4⋊C4×C47—21no—
31C22×C22⋊C4×C47C2212yes—
32C47×#380—22no—
33C47×#380C2214yescomplemented
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—22no—
41C22×C22⋊D47—22no—
42C22×C22⋊D47C2×C412yes—
43C22×C22⋊D47D414yes—
44C22×C22⋊D47Q814yes—
45C22×C22⋊D47C2312yes—
46C23×Dic47—22no—
47C23×Dic47C2×C411yescharacteristic
48C23×Dic47C2×C411yescharacteristic
49C23×Dic47C2×C411yescharacteristic
50C22×C4×D47—21no—
51C22×C4×D47—22no—
52C22×C4×D47—21no—
53C22×C4×D47—44no—
54C22×C4×D47C2×C414yescomplemented
55C4×C22⋊D47—24no—
56C4×C22⋊D47—24no—
57C4×C22⋊D47—24no—
58C4×C22⋊D47—24no—
59C4×C22⋊D47—24no—
60C4×C22⋊D47—24no—
61C4×C22⋊D47—24no—
62C4×C22⋊D47—24no—
63C2×C4⋊Dic47—24no—
64C2×C4⋊Dic47—44no—
65C2×Dic47⋊C4—21no—
66C2×Dic47⋊C4—21no—
67C2×Dic47⋊C4—22no—
68C2×Dic47⋊C4C2×C414yescomplemented
69C2×C22⋊Dic47—21no—
70C2×C22⋊Dic47—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—22no—
76C2×C22⋊Dic47C2×C412yes—
77C2×C22⋊Dic47C2314yes—
78C2×C22⋊Dic47C2312yes—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4C2×C414yescomplemented
83C2×C4×Dic47—21no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47C2×C414yescomplemented
87#13093938—216no—
88C47⋊#95—24no—
89C25×C47C2311yescharacteristic
90C23×C4×C47—22no—
91C23×C4×C47—44no—
92C23×C4×C47C2×C411yescharacteristic
93C23×C4×C47C2×C411yescharacteristic
94C23×C4×C47C2×C412yes—
95C23×C4×C47D411yescharacteristic
96C23×C4×C47D411yescharacteristic
97C23×C4×C47D411yescharacteristic
98C23×C4×C47D412yes—
99C23×C4×C47D411yescharacteristic
100C23×C4×C47D412yes—
101C23×C4×C47C2312yes—
102C2×C4⋊C4×C47—24no—
103C2×C4⋊C4×C47—44no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47C2314yes—
108#95×C47—24no—
109C24×C47—42no—
110C24×C47—42no—
111C24×C47C22×C411yescharacteristic
112C24×C47C22×C411yescharacteristic
113C24×C47C2×D411yescharacteristic
114C24×C47C2×D411yescharacteristic
115C24×C47C2×D411yescharacteristic
116C24×C47C2×D411yescharacteristic
117C24×C47C2×D412yes—
118C24×C47C2×Q812yes—
119C24×C47#4112yes—
120C24×C47#4112yes—
121C24×C47C2411yescharacteristic
122C23×D47—21no—
123C23×D47—21no—
124C23×D47—22no—
125C23×D47—42no—
126C23×D47—42no—
127C23×D47C4⋊C414yescomplemented
128C23×D47C22×C412yes—
129C22×C4×C47—24no—
130C22×C4×C47—24no—
131C22×C4×C47—24no—
132C22×C4×C47—24no—
133C22×C4×C47—44no—
134C22×C4×C47—44no—
135C22×C4×C47—44no—
136C22×C4×C47—44no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—44no—
141C22×C4×C47—44no—
142C22×C4×C47—44no—
143C22×C4×C47C22⋊C411yescharacteristic
144C22×C4×C47C22⋊C412yes—
145C22×C4×C47C22⋊C411yescharacteristic
146C22×C4×C47C22⋊C411yescharacteristic
147C22×C4×C47C22⋊C412yes—
148C22×C4×C47C22⋊C412yes—
149C22×C4×C47C22⋊C412yes—
150C22×C4×C47C22⋊C412yes—
151C22×C4×C47C22⋊C412yes—
152C22×C4×C47C22⋊C411yescharacteristic
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—24no—
162C2×C22⋊D47—24no—
163C2×C22⋊D47—24no—
164C2×C22⋊D47—24no—
165C2×C22⋊D47—24no—
166C2×C22⋊D47—24no—
167C2×C22⋊D47—24no—
168C2×C22⋊D47—24no—
169C2×C22⋊D47—24no—
170C2×C22⋊D47—22no—
171C2×C22⋊D47—22no—
172C2×C22⋊D47—22no—
173C2×C22⋊D47—22no—
174C2×C22⋊D47C4⋊C418yescomplemented
175C2×C22⋊D47C2×D414yes—
176C2×C22⋊D47C2×Q814yes—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—22no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—24no—
185C22×Dic47—42no—
186C22×Dic47—42no—
187C22×Dic47—44no—
188C22×Dic47—44no—
189C22×Dic47—44no—
190C22×Dic47C4⋊C414yescomplemented
191C22×Dic47C22×C412yes—
192C22×Dic47C22×C412yes—
193C22×Dic47C22×C412yes—
194C2×C4×D47—24no—
195C2×C4×D47—24no—
196C2×C4×D47—44no—
197C2×C4×D47—48no—
198C2×C4×D47—44no—
199C2×C4×D47—48no—
200C4⋊C4×C47—48no—
201C22⋊C4×C47—24no—
202C22⋊C4×C47—24no—
203C22⋊C4×C47—44no—
204C22⋊Dic47—22no—
205C22⋊Dic47—22no—
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208C22⋊Dic47—24no—
209C22⋊Dic47—24no—
210C22⋊Dic47—44no—
211(C2×D47)⋊C4—24no—
212(C2×D47)⋊C4—24no—
213C4⋊Dic47—48no—
214Dic47⋊C4—24no—
215Dic47⋊C4—24no—
216C4×Dic47—24no—
217C4×Dic47—24no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—44no—
231C23×C47—41no—
232C23×C47—44no—
233C23×C47—44no—
234C23×C47—44no—
235C23×C47—41no—
236C23×C47C2×C22⋊C411yescharacteristic
237C23×C47C2×C22⋊C411yescharacteristic
238C23×C47C2×C22⋊C411yescharacteristic
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C4⋊C412yes—
241C23×C47C2×C4⋊C412yes—
242C23×C47#11712yes—
243C23×C47#11712yes—
244C23×C47#12112yes—
245C23×C47#12112yes—
246C23×C47#12112yes—
247C23×C47#12112yes—
248C23×C47C22⋊Q812yes—
249C23×C47C22⋊Q812yes—
250C23×C47C22⋊Q812yes—
251C23×C47C22⋊Q812yes—
252C23×C47C23×C411yescharacteristic
253C23×C47C22×D411yescharacteristic
254C23×C47C22×D411yescharacteristic
255C23×C47C22×D411yescharacteristic
256C23×C47C22×Q811yescharacteristic
257C23×C47C2×#4111yescharacteristic
258C23×C47C2×#4111yescharacteristic
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—24no—
262C22×D47—24no—
263C22×D47—42no—
264C22×D47—48no—
265C22×D47—42no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—48no—
270C22×D47—42no—
271C22×D47C2×C4⋊C414yescomplemented
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—24no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—44no—
288C2×C4×C47—44no—
289C2×C4×C47—44no—
290C2×C4×C47—88no—
291C2×C4×C47#9914yescomplemented
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C2×C22⋊C412yes—
295C2×C4×C47C2×C22⋊C412yes—
296C22⋊D47—24no—
297C22⋊D47—24no—
298C22⋊D47—24no—
299C22⋊D47—24no—
300C22⋊D47—28no—
301C22⋊D47—28no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—44no—
315C2×Dic47—44no—
316C2×Dic47—44no—
317C2×Dic47—88no—
318C2×Dic47C2×C4⋊C414yescomplemented
319C4×D47—48no—
320C4×D47—48no—
321C2×#1799—471nomaximal, Sylow
322C22×C47—24no—
323C22×C47—24no—
324C22×C47—24no—
325C22×C47—24no—
326C22×C47—24no—
327C22×C47—24no—
328C22×C47—21no—
329C22×C47—21no—
330C22×C47—21no—
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47#38012yes—
351C22×C47#38012yes—
352C22×C47#38012yes—
353C22×C47#38012yes—
354C22×C47C2×#9912yes—
355C22×C47#41012yes—
356C22×C47C22×C22⋊C411yescharacteristic
357C22×C47C22×C4⋊C411yescharacteristic
358C22×C47C2×#11711yescharacteristic
359C22×C47C2×#12111yescharacteristic
360C22×C47C2×#12111yescharacteristic
361C22×C47C2×C22⋊Q811yescharacteristic
362C22×C47C2×C22⋊Q811yescharacteristic
363C2×D47—24no—
364C2×D47—44no—
365C2×D47—48no—
366C2×D47—48no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—44no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—84no—
374C4×C47C2×#9914yescomplemented
375Dic47—24no—
376Dic47—42no—
377Dic47—42no—
378Dic47—84no—
379C22×C4×D4—471no—
380C22×#99—472no—
381C2×#380—471no—
382C2×#380D4711yescharacteristic, complemented
383#1799—478no—
384C2×#342—472no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47—21no—
389C2×C47—22no—
390C2×C47—21no—
391C2×C47—21no—
392C2×C47—22no—
393C2×C47—22no—
394C2×C47#179914yescomplemented
395C2×C47C2×#38011yescharacteristic
396C2×C47C22×#9911yescharacteristic
397C2×C47C2×#41011yescharacteristic
398D47—44no—
399C23×D4—471no—
400C24×C4—471no—
401C24×C4C2×D4711yescharacteristic
402C2×C4×D4—474no—
403C2×C4×D4—474no—
404C2×C4×D4—941no—
405C2×C4×D4—941no—
406C2×C4×D4—942no—
407C2×C4×D4—941no—
408C2×C4×D4—941no—
409C2×C4×D4—942no—
410C22×C4⋊C4—21no—
411C22×C4⋊C4—471no—
412C22×C4⋊C4—941no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C22⋊C4—472no—
416C22×C22⋊C4C2×D4712yes—
417C22×C42—471no—
418C2×#99—478no—
419C2×#99—948no—
420#380—22no—
421#380—474no—
422#380—942no—
423#380C2×D4714yescomplemented
424C2×#95—21no—
425C2×#95—941no—
426#342—478no—
427C47C2×#179911yescharacteristic, complemented, Sylow
428C25—471no—
429C25C22×D4711yescharacteristic
430C22×D4—472no—
431C22×D4—474no—
432C22×D4—474no—
433C22×D4—472no—
434C22×D4—941no—
435C22×D4—941no—
436C22×D4—942no—
437C22×D4—942no—
438C22×D4—941no—
439C22×D4—941no—
440C23×C4—22no—
441C23×C4—44no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—474no—
446C23×C4—942no—
447C23×C4—941no—
448C23×C4—941no—
449C23×C4—942no—
450C23×C4—1884no—
451C23×C4C4×D4711yescharacteristic
452C23×C4C4×D4711yescharacteristic
453C23×C4C4×D4712yes—
454C23×C4D18811yescharacteristic
455C23×C4D18811yescharacteristic
456C23×C4D18812yes—
457C23×C4C22⋊D4711yescharacteristic
458C23×C4C22⋊D4711yescharacteristic
459C23×C4C22⋊D4712yes—
460C23×C4C22×D4712yes—
461C4×D4—944no—
462C4×D4—944no—
463C4×D4—944no—
464C4×D4—944no—
465C4×D4—944no—
466C4×D4—944no—
467C4×D4—944no—
468C4×D4—944no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—44no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—942no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4—944no—
476C2×C4⋊C4—1884no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—472no—
481C2×C22⋊C4—472no—
482C2×C22⋊C4—474no—
483C2×C22⋊C4—474no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C22⋊C4—941no—
487C2×C22⋊C4—941no—
488C2×C22⋊C4—942no—
489C2×C22⋊C4—941no—
490C2×C22⋊C4—941no—
491C2×C22⋊C4—944no—
492C2×C22⋊C4—944no—
493C2×C22⋊C4—942no—
494C2×C22⋊C4C22×D4714yes—
495C2×C42—474no—
496C2×C42—942no—
497C2×C42—941no—
498C2×C42—941no—
499#99—9416no—
500#95—24no—
501#95—944no—
502C24—42no—
503C24—42no—
504C24—474no—
505C24—472no—
506C24—941no—
507C24—941no—
508C24—942no—
509C24—1882no—
510C24—1882no—
511C24C2×C4×D4711yescharacteristic
512C24C2×C4×D4711yescharacteristic
513C24C2×D18811yescharacteristic
514C24C2×D18811yescharacteristic
515C24D4×D4712yes—
516C24#1062535212yes—
517C24Q8×D4712yes—
518C24#1062535412yes—
519C24C2×C22⋊D4711yescharacteristic
520C24C2×C22⋊D4711yescharacteristic
521C24C23×D4711yescharacteristic
522C2×D4—478no—
523C2×D4—474no—
524C2×D4—474no—
525C2×D4—942no—
526C2×D4—942no—
527C2×D4—944no—
528C2×D4—944no—
529C2×D4—944no—
530C2×D4—944no—
531C2×D4—944no—
532C2×D4—944no—
533C2×D4—944no—
534C2×D4—944no—
535C2×D4—944no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—942no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—474no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—942no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—944no—
566C22×C4—944no—
567C22×C4—944no—
568C22×C4—1884no—
569C22×C4—1888no—
570C22×C4—1888no—
571C22×C4—1884no—
572C22×C4—1884no—
573C22×C4—1884no—
574C22×C4—1884no—
575C22×C4—1882no—
576C22×C4—1882no—
577C22×C4(C2×D47)⋊C412yes—
578C22×C4(C2×D47)⋊C412yes—
579C22×C4(C2×D47)⋊C412yes—
580C22×C4(C2×D47)⋊C411yescharacteristic
581C22×C4(C2×D47)⋊C411yescharacteristic
582C22×C4(C2×D47)⋊C411yescharacteristic
583C22×C4(C2×D47)⋊C412yes—
584C22×C4(C2×D47)⋊C412yes—
585C22×C4(C2×D47)⋊C412yes—
586C22×C4(C2×D47)⋊C411yescharacteristic
587C22×C4C2×C4×D4712yes—
588C22×C4C2×C4×D4712yes—
589C22×C4C2×D18812yes—
590C22×C4C2×D18812yes—
591C22×C4C2×C22⋊D4712yes—
592C22×C4C2×C22⋊D4712yes—
593C4⋊C4—48no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—1888no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—44no—
600C22⋊C4—942no—
601C22⋊C4—942no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—944no—
605C22⋊C4—944no—
606C22⋊C4—944no—
607C22⋊C4—944no—
608C22⋊C4—1884no—
609C42—944no—
610C42—944no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—41no—
628C23—41no—
629C23—474no—
630C23—944no—
631C23—944no—
632C23—942no—
633C23—942no—
634C23—1882no—
635C23—1888no—
636C23—1882no—
637C23—1882no—
638C23—1888no—
639C23—1882no—
640C23—1882no—
641C23—1882no—
642C23C2×(C2×D47)⋊C411yescharacteristic
643C23C2×(C2×D47)⋊C411yescharacteristic
644C23C2×(C2×D47)⋊C411yescharacteristic
645C23C2×(C2×D47)⋊C411yescharacteristic
646C23C4⋊C4×D4712yes—
647C23C4⋊C4×D4712yes—
648C23#1309398212yes—
649C23#1309398212yes—
650C23#1309399512yes—
651C23#1309399512yes—
652C23#1309399912yes—
653C23#1309399912yes—
654C23#1309400012yes—
655C23#1309400012yes—
656C23#1309400412yes—
657C23#1309400412yes—
658C23C22×C4×D4711yescharacteristic
659C23C2×D4×D4711yescharacteristic
660C23C22×C22⋊D4711yescharacteristic
661C23C22×D18811yescharacteristic
662C23C2×Q8×D4711yescharacteristic
663C23C2×#1062535211yescharacteristic
664C23C2×#1062535411yescharacteristic
665D4—948no—
666D4—948no—
667D4—944no—
668D4—944no—
669D4—944no—
670D4—944no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—88no—
690C2×C4—474no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—3768no—
698C2×C4—1888no—
699C2×C4—1884no—
700C2×C4—1884no—
701C2×C4—1884no—
702C2×C4—1882no—
703C2×C4—1882no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1888no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4#1309393814yescomplemented
710C2×C4C2×(C2×D47)⋊C412yes—
711C2×C4C2×(C2×D47)⋊C412yes—
712C2×C4C2×(C2×D47)⋊C412yes—
713C2×C4C2×(C2×D47)⋊C412yes—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—24no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—944no—
743C22—1884no—
744C22—1888no—
745C22—1884no—
746C22—1888no—
747C22—1882no—
748C22—1882no—
749C22#1568898012yes—
750C22#1568898012yes—
751C22#1568898012yes—
752C22#1568898012yes—
753C22C2×#1309393812yes—
754C22#1568909612yes—
755C22C22×(C2×D47)⋊C411yescharacteristic
756C22C2×C4⋊C4×D4711yescharacteristic
757C22C2×#1309398211yescharacteristic
758C22C2×#1309399511yescharacteristic
759C22C2×#1309399911yescharacteristic
760C22C2×#1309400011yescharacteristic
761C22C2×#1309400411yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—84no—
766C4—944no—
767C4—3764no—
768C4—1882no—
769C4—1882no—
770C4C2×#1309393814yescomplemented
771C2—21no—
772C2—21no—
773C2—22no—
774C2—21no—
775C2—21no—
776C2—22no—
777C2—22no—
778C2—21no—
779C2—21no—
780C2—1884no—
781C2#2024337314yesdirect product factor
782C2C2×#1568898011yescharacteristic
783C2C22×#1309393811yescharacteristic
784C2C2×#1568909611yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C47×#380C2
socleC23×C47C2×C22⋊C4
prime radicalC23×C22⋊D47C22
cosocleC24×C47C24
hypercenterC2×#380D47
hypocenterC47C2×#1799
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#15688983C2semidirect
4. #20243373C2direct (N × H)
5. C2×#15688889C2semidirect
6. C2×C47×#380C2semidirect
8. C23×C4×D47C4semidirect
15. C2×C4×C22⋊D47C4semidirect
18. C22×Dic47⋊C4C4semidirect
21. C22×(C2×D47)⋊C4C4semidirect
22. C22×C4×Dic47C4semidirect
26. #15688983C22semidirect
28. #15688889C22semidirect
33. C47×#380C22semidirect
54. C22×C4×D47C2×C4semidirect
68. C2×Dic47⋊C4C2×C4semidirect
82. C2×(C2×D47)⋊C4C2×C4semidirect
86. C2×C4×Dic47C2×C4semidirect
127. C23×D47C4⋊C4semidirect
174. C2×C22⋊D47C4⋊C4semidirect
190. C22×Dic47C4⋊C4semidirect
271. C22×D47C2×C4⋊C4semidirect
291. C2×C4×C47#99semidirect
318. C2×Dic47C2×C4⋊C4semidirect
374. C4×C47C2×#99semidirect
382. C2×#380D47semidirect
394. C2×C47#1799semidirect
423. #380C2×D47semidirect
427. C47C2×#1799semidirect
709. C2×C4#13093938semidirect
770. C4C2×#13093938semidirect
781. C2#20243373direct (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×#156889832
#202433732
C2×#156888892
C2×C47×#3802
C2×#179947