Finite Group Databasebeta

← C2×#20255873 #27094857

Subgroups — C2×#20255873 #27094857

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689830C211yesmaximal, characteristic, complemented
2#20255873C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689458C211yesmaximal, characteristic, complemented
5C2×#15689439C211yesmaximal, characteristic, complemented
6C2×#15689464C211yesmaximal, characteristic, complemented
7C2×#15689434C211yesmaximal, characteristic, complemented
8C2×#15689427C211yesmaximal, characteristic, complemented
9C2×#15689403C211yesmaximal, characteristic, complemented
10C2×#15689367C211yesmaximal, characteristic, complemented
11C2×#15689350C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689166C211yesmaximal, characteristic, complemented
15C22×#13093957C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic
17C22×#10625335C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20#15689830—24no—
21#15689830C2218yescomplemented
22C2×#13094024C2211yescharacteristic
23C2×#13094015—21no—
24C2×#13094003C2211yescharacteristic
25C2×#13094003C2211yescharacteristic
26C2×#13094001—21no—
27C2×#13094001—21no—
28C2×C4×Dic94C2211yescharacteristic
29C2×D4×Dic47—21no—
30C22×C4⋊Dic47C2211yescharacteristic
31C22×C4⋊Dic47C2211yescharacteristic
32#15689533C2218yescomplemented
33#15689464C2218yescomplemented
34#15689458C2218yescomplemented
35#15689439C2218yescomplemented
36#15689434C2218yescomplemented
37#15689427C2218yescomplemented
38#15689403C2218yescomplemented
39#15689367C2218yescomplemented
40#15689350C2218yescomplemented
41#15689223C2218yescomplemented
42#15689195C2218yescomplemented
43#15689166C2218yescomplemented
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093957C2211yescharacteristic
50C2×#13093957C2218yescomplemented
51C2×#13093955C2211yescharacteristic
52C2×#13093955C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
64C47×#553—24no—
65C47×#553C2218yes—
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic
68C2×#123×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×C4×D4×C47—21no—
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C23×Dic47—21no—
80C23×Dic47—21no—
81C2×#10625335—24no—
82C2×#10625335C2314yes—
83C2×#10625329—24no—
84C2×#10625329C2314yes—
85C22×C47⋊C8—24no—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91#13094024—22no—
92#13094024C2314yes—
93#13094015—28no—
94#13094003—22no—
95#13094003—22no—
96#13094003C2314yes—
97#13094003C2314yes—
98#13094001—28no—
99#13094001—28no—
100C4×Dic94—22no—
101C4×Dic94C2314yes—
102D4×Dic47—28no—
103C2×C4⋊Dic47—22no—
104C2×C4⋊Dic47—22no—
105C2×C4⋊Dic47—21no—
106C2×C4⋊Dic47—21no—
107C2×C4⋊Dic47—21no—
108C2×C4⋊Dic47C2311yescharacteristic
109C2×C4⋊Dic47C2314yes—
110C2×C4⋊Dic47C2314yes—
111C2×C4⋊Dic47C2311yescharacteristic
112C2×C4⋊Dic47C2311yescharacteristic
113C2×Dic47⋊C4—21no—
114C2×Dic47⋊C4—21no—
115C2×Dic47⋊C4—21no—
116C2×C22⋊Dic47—21no—
117C2×C22⋊Dic47—21no—
118C2×C4×Dic47—21no—
119#13093957C2314yes—
120#13093957C2314yes—
121#13093957C2314yes—
122#13093957C2314yes—
123#13093957C2314yes—
124#13093957C2314yes—
125#13093955C2314yes—
126#13093955C2314yes—
127#13093955C2314yes—
128C4⋊(C47⋊C8)C2314yes—
129#13093947C2314yes—
130#13093947C2314yes—
131#13093947C2314yes—
132#13093945C2314yes—
133#13093945C2314yes—
134#13093945C2314yes—
135C22⋊(C47⋊C8)C2314yes—
136C22⋊(C47⋊C8)C2314yes—
137#13093935C2314yes—
138C22×D4×C47—21no—
139C22×D4×C47—21no—
140C22×D4×C47D411yescharacteristic
141C22×D4×C47C2311yescharacteristic
142C23×C4×C47—21no—
143C23×C4×C47—21no—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146#126×C47—28no—
147#125×C47—22no—
148#125×C47C2314yes—
149#123×C47—28no—
150#121×C47—28no—
151#121×C47—22no—
152#121×C47—22no—
153#121×C47C2314yes—
154#121×C47C2314yes—
155C4×D4×C47—28no—
156C4×D4×C47—22no—
157C4×D4×C47D414yes—
158C4×D4×C47C2314yes—
159C4×D4×C47C2314yes—
160#117×C47—22no—
161#117×C47C2314yes—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—22no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47D411yescharacteristic
167C2×C4⋊C4×C47C2311yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47D411yescharacteristic
176C2×C22⋊C4×C47D411yescharacteristic
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C24×C47—21no—
180C24×C47C2×D411yescharacteristic
181C24×C47C2×D411yescharacteristic
182C2×D4×C47—24no—
183C2×D4×C47—24no—
184C2×D4×C47—24no—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—44no—
189C2×D4×C47—82no—
190C2×D4×C47C2×D414yes—
191C2×D4×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—24no—
201C22×C4×C47—82no—
202C22×C4×C47—82no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D412yes—
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—24no—
218C22×Dic47—82no—
219C22×Dic47—82no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—21no—
223C2×Dic94—24no—
224C2×Dic94—82no—
225C2×Dic94C2412yes—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47C2×D414yes—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47C2×D414yes—
241C22⋊C4×C47C2×D414yes—
242C42×C47—24no—
243C42×C47C2×D412yes—
244C42×C47C2412yes—
245C22⋊Dic47—24no—
246C22⋊Dic47—24no—
247#10625335—28no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260C4×Dic47—24no—
261#10625329—28no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—28no—
266C2×C47⋊C8#4114yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270C2×C47⋊C8C2412yes—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47#13714yes—
281C23×C47C22×D412yes—
282C23×C47C22×D412yes—
283C23×C47C22×D411yescharacteristic
284D4×C47—28no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—48no—
288D4×C47—42no—
289D4×C47—84no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—84no—
307C2×C4×C47—84no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4112yes—
314C2×C4×C472−1+412yes—
315C2×C4×C47C2511yescharacteristic
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—84no—
325C2×Dic47—84no—
326Dic94—22no—
327Dic94—22no—
328Dic94—42no—
329Dic94—84no—
330C47⋊C8—22no—
331C47⋊C8—22no—
332C47⋊C8—22no—
333C47⋊C8C2×#4114yes—
334C2×#3346—471nomaximal, Sylow
335C22×C47—28no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—44no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—84no—
346C22×C47#54712yes—
347C22×C47C2×#13714yes—
348C22×C47C2×#13712yes—
349C22×C47#57612yes—
350C22×C47C23×D411yescharacteristic
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47#54712yes—
359C4×C47C22×#4111yescharacteristic
360C4×C47C2×2−1+411yescharacteristic
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#554—471no—
366C2×#553D4711yescharacteristic
367#3346—4716no—
368C2×#501—471no—
369C2×#484—471no—
370C2×#481—471no—
371C2×#485—471no—
372C2×#480—471no—
373C2×#479—471no—
374C2×#474—471no—
375C2×#468—471no—
376C2×#465—471no—
377C2×#440—471no—
378C2×#435—471no—
379C2×#428—471no—
380C22×#107—471no—
381C2×C47—24no—
382C2×C47—42no—
383C2×C47—82no—
384C2×C47#334614yescomplemented
385C2×C47C2×#54711yescharacteristic
386C2×C47C22×#13711yescharacteristic
387C2×C47C2×#57611yescharacteristic
388C22×SD16—471no—
389C22×M16—471no—
390C23×C8—471no—
391#554—478no—
392#554—944no—
393#553—24no—
394#553C2×D4718yes—
395C2×C4⋊Q8—471no—
396C2×#126—21no—
397C2×#125—941no—
398C2×#125C2×D4711yescharacteristic
399C2×#123—21no—
400C2×C22⋊Q8—471no—
401C2×C22⋊Q8—471no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8—941no—
404C2×#121—21no—
405C2×#121C2×D4711yescharacteristic
406C2×#121C2×D4711yescharacteristic
407C2×C4×Q8—471no—
408C2×C4×D4—21no—
409C2×C4×D4—941no—
410C2×C4×D4C2×D4711yescharacteristic
411C2×C4×D4C2×D4711yescharacteristic
412C2×#117C2×D4711yescharacteristic
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4C2×D4711yescharacteristic
416#501—478no—
417#485—478no—
418#484—478no—
419#481—478no—
420#480—478no—
421#479—478no—
422#474—478no—
423#468—478no—
424#465—478no—
425#440—478no—
426#435—478no—
427#428—478no—
428C2×#107—471no—
429C2×#107—471no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—478no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×#102—471no—
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×#97—471no—
448C47C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—471no—
450C22×Q8—941no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C22⋊D4711yescharacteristic
454C22×D4C22×D4711yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—941no—
458C23×C4—941no—
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C2×SD16—474no—
462C2×SD16—944no—
463C2×M16—474no—
464C2×M16—944no—
465C22×C8—471no—
466C22×C8—471no—
467C22×C8—474no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—944no—
471C4⋊Q8—474no—
472C4⋊Q8—942no—
473#126—28no—
474#125—22no—
475#125—948no—
476#125C22×D4714yes—
477#123—28no—
478C22⋊Q8—474no—
479C22⋊Q8—474no—
480C22⋊Q8—942no—
481C22⋊Q8—942no—
482C22⋊Q8—948no—
483C22⋊Q8—948no—
484#121—28no—
485#121—22no—
486#121—22no—
487#121C22×D4714yes—
488#121C22×D4714yes—
489C4×Q8—474no—
490C4×Q8—942no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—948no—
494C4×D4C22⋊D4714yes—
495C4×D4C22×D4714yes—
496C4×D4C22×D4714yes—
497#117—22no—
498#117C22×D4714yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4C22⋊D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4714yes—
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4C22⋊D4711yescharacteristic
528C2×C22⋊C4C22⋊D4711yescharacteristic
529C2×C42—21no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532#107—474no—
533#107—474no—
534#107—474no—
535#107—474no—
536#107—474no—
537#107—474no—
538#106—474no—
539#106—474no—
540#106—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#102—474no—
546#102—474no—
547#102—474no—
548C22⋊C8—474no—
549C22⋊C8—474no—
550#97—474no—
551C24—21no—
552C24C2×C22⋊D4711yescharacteristic
553C24C2×C22⋊D4711yescharacteristic
554C2×Q8—472no—
555C2×Q8—944no—
556C2×Q8—941no—
557C2×Q8—942no—
558C2×Q8—942no—
559C2×Q8—3762no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×C22⋊D4714yes—
569C2×D4C23×D4712yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—944no—
582C22×C4—944no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—3762no—
588C22×C4—3762no—
589C22×C4C2×C22⋊D4712yes—
590C22×C4C2×C22⋊D4712yes—
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593C22×C4C2×C22⋊D4711yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598SD16—948no—
599M16—948no—
600C2×C8—474no—
601C2×C8—472no—
602C2×C8—472no—
603C2×C8—472no—
604C2×C8—472no—
605C2×C8—948no—
606C2×C8—942no—
607C2×C8—942no—
608C2×C8—942no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—472no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—941no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—944no—
627C4⋊C4C2×C22⋊D4714yes—
628C4⋊C4C23×D4712yes—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4C2×C22⋊D4714yes—
638C22⋊C4C2×C22⋊D4714yes—
639C42—24no—
640C42—944no—
641C42C2×C22⋊D4712yes—
642C42C23×D4712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#1309405414yes—
653C23C22×C22⋊D4712yes—
654C23C22×C22⋊D4712yes—
655C23C22×C22⋊D4711yescharacteristic
656Q8—942no—
657Q8—942no—
658Q8—3764no—
659Q8—1882no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—3764no—
689C2×C4—3764no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4C22×C22⋊D4712yes—
695C2×C4C22×C22⋊D4712yes—
696C2×C4C22×C22⋊D4712yes—
697C2×C4C22×C22⋊D4712yes—
698C2×C4C22×C22⋊D4711yescharacteristic
699C2×C4#41×D4712yes—
700C2×C4#1309407112yes—
701C2×C4C24×D4711yescharacteristic
702C8—474no—
703C8—942no—
704C8—942no—
705C8—942no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22#1568977212yes—
718C22C2×#1309405414yes—
719C22C2×#1309405412yes—
720C22#1568992612yes—
721C22C23×C22⋊D4711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4#1568977212yes—
734C4C2×#41×D4711yescharacteristic
735C4C2×#1309407111yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#2025587314yesdirect product factor
740C2C2×#1568977211yescharacteristic
741C2C22×#1309405411yescharacteristic
742C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
Fitting, prime radicalC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#15689830C2semidirect
2. #20255873C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689458C2semidirect
5. C2×#15689439C2semidirect
6. C2×#15689464C2semidirect
7. C2×#15689434C2semidirect
8. C2×#15689427C2semidirect
9. C2×#15689403C2semidirect
10. C2×#15689367C2semidirect
11. C2×#15689350C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689166C2semidirect
15. C22×#13093957C2semidirect
21. #15689830C22semidirect
32. #15689533C22semidirect
33. #15689464C22semidirect
34. #15689458C22semidirect
35. #15689439C22semidirect
36. #15689434C22semidirect
37. #15689427C22semidirect
38. #15689403C22semidirect
39. #15689367C22semidirect
40. #15689350C22semidirect
41. #15689223C22semidirect
42. #15689195C22semidirect
43. #15689166C22semidirect
50. C2×#13093957C22semidirect
384. C2×C47#3346semidirect
448. C47C2×#3346semidirect
739. C2#20255873direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898302
#202558732
C2×#156895332
C2×#156894582
C2×#156894392
C2×#156894642
C2×#156894342
C2×#156894272
C2×#156894032
C2×#156893672
C2×#156893502
C2×#156892232
C2×#156891952
C2×#156891662
C22×#130939572
C2×C47×#5532
C2×#334647