Finite Group Databasebeta

← C2×#20257475 #27124498

Subgroups — C2×#20257475 #27124498

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257475C2132yesmaximal, direct product factor
2C2×#15689849C211yesmaximal, characteristic, complemented
3C2×#15689848C213yesmaximal, complemented
4C2×#15689844C213yesmaximal, complemented
5C2×#15689815C213yesmaximal, complemented
6C2×#15689813C213yesmaximal, complemented
7C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
9C2×#15689734C213yesmaximal, complemented
10C2×#15689733C213yesmaximal, complemented
11C2×#15689675C213yesmaximal, complemented
12C2×#15689653C213yesmaximal
13C2×#15689601C211yesmaximal, characteristic, complemented
14C2×#15689599C211yesmaximal, characteristic, complemented
15C22×Q8×Dic47C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18#15689849C22116yescomplemented
19#15689848C22148yescomplemented
20#15689844C22148yescomplemented
21#15689815C22148yescomplemented
22#15689813C22148yescomplemented
23Q8×C22⋊D47C22116yescomplemented
24Q8×C22⋊D47C22116yescomplemented
25#15689734C22148yescomplemented
26#15689733C22148yescomplemented
27#15689675C22148yescomplemented
28C2×#13094023C2213yes—
29C2×#13094022C2213yes—
30C2×#13094022C2213yes—
31#15689653C22148yes—
32C2×#13094019C2216yes—
33C2×#13094019C2213yes—
34C2×#13094017C2216yes—
35C2×#13094017C2213yes—
36C2×#13094016C2213yes—
37C2×#13094015C2216yes—
38C2×#13094015C2213yes—
39C2×#13094014C2216yes—
40C2×#13094014C2213yes—
41C2×#13094014C2216yes—
42C2×#13094010C2213yes—
43C2×#13094008C2213yes—
44C2×#13094005C2213yes—
45C2×#13094003C2213yes—
46C2×#13094003C2213yes—
47C2×#13094001C2213yes—
48C2×#13094000C2213yes—
49C2×#13094000C2213yes—
50C2×#13093996C2211yescharacteristic
51#15689601C22116yescomplemented
52#15689599C22116yescomplemented
53C2×Q8×Dic47C2211yescharacteristic
54C2×Q8×Dic47C2211yescharacteristic
55C2×Q8×Dic47C2213yes—
56C2×Q8×Dic47C2213yes—
57C2×Q8×Dic47C2211yescharacteristic
58C2×Q8×Dic47C2213yes—
59C2×Q8×Dic47C2213yes—
60C2×Q8×Dic47C22116yescomplemented
61C2×C4×Dic94C2213yes—
62C2×C4×Dic94C2213yes—
63C2×#13093989C2213yes—
64C2×#13093989C2216yes—
65C2×C4×C22⋊D47C2213yes—
66C2×C4×C22⋊D47C2213yes—
67C2×#13093983C2213yes—
68C2×#13093983C2213yes—
69C2×#13093982C2213yes—
70C2×#13093981C2213yes—
71C2×#13093980C2216yes—
72C22×C4⋊Dic47C2213yes—
73C22×C4×Dic47C2213yes—
74C23×Q8×C47C2211yescharacteristic
75C23×Q8×C47C2211yescharacteristic
76D4×Q8×C47C22116yescomplemented
77C2×C4⋊Q8×C47C2213yes—
78C2×C22⋊Q8×C47C2213yes—
79C2×C22⋊Q8×C47C2213yes—
80C2×C4×Q8×C47C2211yescharacteristic
81C2×C4×D4×C47C2213yes—
82C22×Dic94C2313yes—
83C22×Dic94C2313yes—
84C2×Q8×D47—28no—
85C2×Q8×D47C2318yes—
86C22×C22⋊D47C2311yescharacteristic
87C22×C22⋊D47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2313yes—
90C22×C4×D47C2313yes—
91#13094023C23124yes—
92#13094022C23124yes—
93#13094022C23124yes—
94#13094019C23124yes—
95#13094019C23148yes—
96#13094017C23124yes—
97#13094017C23148yes—
98#13094016C23124yes—
99#13094015C23148yes—
100#13094015C23124yes—
101#13094014C23148yes—
102#13094014C23148yes—
103#13094014C23124yes—
104#13094010C23124yes—
105#13094008C23124yes—
106#13094005C23124yes—
107#13094003C23124yes—
108#13094003C23124yes—
109#13094001C23124yes—
110#13094000C23124yes—
111#13094000C23124yes—
112#13093996C2318yes—
113Q8×Dic47C23124yes—
114Q8×Dic47C23124yes—
115Q8×Dic47C2318yes—
116Q8×Dic47C2318yes—
117Q8×Dic47C23124yes—
118Q8×Dic47C23124yes—
119Q8×Dic47C2318yes—
120C4×Dic94C23124yes—
121C4×Dic94C23124yes—
122#13093989C23124yes—
123#13093989C23148yes—
124C4×C22⋊D47C23124yes—
125C4×C22⋊D47C23124yes—
126#13093983C23124yes—
127#13093983C23124yes—
128#13093982C23124yes—
129#13093981C23124yes—
130#13093980C23148yes—
131C2×C4⋊Dic47C23124yes—
132C2×C4⋊Dic47C2313yes—
133C2×C4⋊Dic47C2313yes—
134C2×C4⋊Dic47C2316yes—
135C2×C4⋊Dic47C2313yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2313yes—
139C2×Dic47⋊C4C2316yes—
140C2×Dic47⋊C4C2316yes—
141C2×Dic47⋊C4C2313yes—
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2313yes—
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2316yes—
146C2×Dic47⋊C4C2311yescharacteristic
147C2×Dic47⋊C4C2313yes—
148C2×C22⋊Dic47C2313yes—
149C2×C22⋊Dic47C2311yescharacteristic
150C2×C22⋊Dic47C2313yes—
151C2×C22⋊Dic47C2313yes—
152C2×(C2×D47)⋊C4C2311yescharacteristic
153C2×(C2×D47)⋊C4C2313yes—
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×C4×Dic47C2313yes—
157C2×C4×Dic47C2313yes—
158C2×C4×Dic47C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C23124yes—
161C2×C4×Dic47C2316yes—
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C22×Q8×C47—28no—
165C22×Q8×C47—28no—
166C22×Q8×C47C2318yes—
167C22×Q8×C47C2318yes—
168C22×Q8×C47C2313yes—
169C22×Q8×C47C2313yes—
170C22×Q8×C47C2311yescharacteristic
171C22×D4×C47C2311yescharacteristic
172C23×C4×C47C2313yes—
173C23×C4×C47C2313yes—
174C4⋊Q8×C47C23124yes—
175C22⋊Q8×C47C23124yes—
176C22⋊Q8×C47C23124yes—
177C4×Q8×C47C2318yes—
178C4×D4×C47C23124yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C4⋊C4×C47C2313yes—
181C2×C4⋊C4×C47C2316yes—
182C2×C22⋊C4×C47C2313yes—
183C2×C22⋊C4×C47C2313yes—
184C2×C42×C47C2313yes—
185C24×C47C2411yescharacteristic
186C24×C47C2411yescharacteristic
187C23×D47C2411yescharacteristic
188C2×Q8×C47—232no—
189C2×Q8×C47—232no—
190C2×Q8×C47—212no—
191C2×Q8×C47—212no—
192C2×Q8×C47#4118yes—
193C2×Q8×C47C24112yes—
194C2×Q8×C47C24112yes—
195C2×Q8×C47C2414yes—
196C2×D4×C47—24no—
197C2×D4×C47C2414yes—
198C22×C4×C47—212no—
199C22×C4×C47—212no—
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2413yes—
202C22×C4×C47C2413yes—
203C22×C4×C47C2413yes—
204C22×C4×C47C24112yes—
205C22×C4×C47C24112yes—
206C22×C4×C47C2413yes—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47C2414yes—
210C2×C22⋊D47C2414yes—
211C22×Dic47—212no—
212C22×Dic47—24no—
213C22×Dic47C2411yescharacteristic
214C22×Dic47C2413yes—
215C22×Dic47C2414yes—
216C22×Dic47C2413yes—
217C22×Dic47C2411yescharacteristic
218C22×Dic47C2413yes—
219C22×Dic47C2413yes—
220C22×Dic47C24112yes—
221C22×Dic47C2411yescharacteristic
222Q8×D47—232no—
223C2×C4×D47—212no—
224C2×C4×D47C24112yes—
225C2×Dic94—212no—
226C2×Dic94—212no—
227C2×Dic94C24112yes—
228C2×Dic94C24112yes—
229C4⋊C4×C47C24112yes—
230C4⋊C4×C47C24112yes—
231C4⋊C4×C47C24124yes—
232C22⋊C4×C47C24112yes—
233C22⋊C4×C47C24112yes—
234C42×C47C24112yes—
235C22⋊Dic47C24112yes—
236C22⋊Dic47C2414yes—
237C22⋊Dic47C24112yes—
238C22⋊Dic47C24112yes—
239(C2×D47)⋊C4C2414yes—
240(C2×D47)⋊C4C24112yes—
241(C2×D47)⋊C4C24112yes—
242(C2×D47)⋊C4C24112yes—
243C4⋊Dic47C24112yes—
244C4⋊Dic47C24112yes—
245C4⋊Dic47C24124yes—
246C4⋊Dic47C24112yes—
247C4⋊Dic47C24112yes—
248C4⋊Dic47C24112yes—
249C4⋊Dic47C24112yes—
250Dic47⋊C4C24124yes—
251Dic47⋊C4C24124yes—
252Dic47⋊C4C24112yes—
253Dic47⋊C4C24112yes—
254Dic47⋊C4C24112yes—
255Dic47⋊C4C24112yes—
256Dic47⋊C4C24124yes—
257Dic47⋊C4C2414yes—
258Dic47⋊C4C24112yes—
259C4×Dic47C24112yes—
260C4×Dic47C24112yes—
261C4×Dic47C24112yes—
262C4×Dic47C24112yes—
263C4×Dic47C24124yes—
264C4×Dic47C24124yes—
265C4×Dic47C24112yes—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C472−1+414yes—
272C23×C47C2512yes—
273C23×C47C2512yes—
274C23×C47C2511yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47C2512yes—
279Q8×C47—224no—
280Q8×C47—224no—
281Q8×C47C2×#41116yes—
282D4×C47—28no—
283C2×C4×C47—26no—
284C2×C4×C47—26no—
285C2×C4×C47—26no—
286C2×C4×C47—22no—
287C2×C4×C47—224no—
288C2×C4×C47—224no—
289C2×C4×C47C2×#41112yes—
290C2×C4×C47C2516yes—
291C2×C4×C47C2516yes—
292C2×C4×C47C2516yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2516yes—
295C22⋊D47—28no—
296C22⋊D47—28no—
297C2×Dic47—26no—
298C2×Dic47—26no—
299C2×Dic47—22no—
300C2×Dic47—224no—
301C2×Dic47—26no—
302C2×Dic47—26no—
303C2×Dic47—22no—
304C2×Dic47—28no—
305C2×Dic472−1+414yes—
306C2×Dic47C2512yes—
307C2×Dic47C2516yes—
308C2×Dic47C2516yes—
309C2×Dic47C2512yes—
310C2×Dic47C2516yes—
311C2×Dic47C2516yes—
312C2×Dic47C2512yes—
313C4×D47—224no—
314Dic94—224no—
315Dic94—224no—
316C2×#3523—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—28no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—44no—
324C22×C47C22×#4112yes—
325C22×C47C2×2−1+412yes—
326C22×C47C2×2−1+414yes—
327C22×C47C2×2−1+412yes—
328C22×C47C2611yescharacteristic
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—44no—
333C4×C47—26no—
334C4×C47—26no—
335C4×C47—26no—
336C4×C47—22no—
337C4×C47C22×#41112yes—
338Dic47—26no—
339Dic47—26no—
340Dic47—22no—
341Dic47—26no—
342Dic47—26no—
343Dic47—22no—
344Dic47C2×2−1+414yes—
345#3523—4732no—
346C2×#557—473no—
347C2×#557—471no—
348C2×#556—473no—
349C2×#552—473no—
350C2×#552—473no—
351C2×D4×Q8—471no—
352C2×D4×Q8—471no—
353C2×D4×Q8D4711yescharacteristic, complemented
354C2×#541—473no—
355C2×#541—473no—
356C2×#533—473no—
357C2×#529—473no—
358C2×#519—471no—
359C2×#519—471no—
360C22×C4×Q8—471no—
361C2×C47—24no—
362C2×C47—42no—
363C2×C47#352314yescomplemented
364C2×C47C23×#4111yescharacteristic
365C2×C47C22×2−1+411yescharacteristic
366C2×C47C22×2−1+411yescharacteristic
367D47—42no—
368C23×Q8—471no—
369C23×Q8C2×D4711yescharacteristic
370C23×Q8C2×D4711yescharacteristic
371#557—4748no—
372#557—4716no—
373#556—4748no—
374#552—4748no—
375#552—4748no—
376D4×Q8—4716no—
377D4×Q8—4716no—
378D4×Q8C2×D47116yescomplemented
379#541—4748no—
380#541—4748no—
381#533—4748no—
382C2×C4⋊Q8—473no—
383C2×C4⋊Q8—473no—
384C2×C4⋊Q8—473no—
385C2×C4⋊Q8C2×D4713yes—
386#529—4748no—
387C2×#126—473no—
388C2×#126—476no—
389C2×#126—473no—
390C2×#126—476no—
391C2×#125—473no—
392C2×#125—476no—
393C2×#125—476no—
394C2×#125—476no—
395C2×#125—473no—
396C2×#125—473no—
397C2×#124—473no—
398C2×#123—473no—
399C2×#123—473no—
400C2×C22⋊Q8—473no—
401C2×C22⋊Q8—473no—
402C2×C22⋊Q8—473no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8C2×D4713yes—
406C2×C22⋊Q8C2×D4713yes—
407C2×#121—471no—
408#519—4716no—
409#519—4716no—
410C2×C4×Q8—471no—
411C2×C4×Q8—473no—
412C2×C4×Q8—471no—
413C2×C4×Q8—473no—
414C2×C4×Q8—4716no—
415C2×C4×Q8—473no—
416C2×C4×Q8—471no—
417C2×C4×Q8—473no—
418C2×C4×Q8—473no—
419C2×C4×Q8—476no—
420C2×C4×Q8—473no—
421C2×C4×Q8—473no—
422C2×C4×Q8C2×D4711yescharacteristic
423C2×C4×D4—473no—
424C2×C4×D4—473no—
425C2×C4×D4C2×D4713yes—
426C2×#117—473no—
427C2×#117—473no—
428C2×#117—473no—
429C2×#117—476no—
430C2×#117—473no—
431C22×C4⋊C4—473no—
432C22×C42—473no—
433C47C2×#352311yescharacteristic, complemented, Sylow
434C22×Q8—28no—
435C22×Q8—28no—
436C22×Q8—478no—
437C22×Q8—473no—
438C22×Q8—473no—
439C22×Q8—948no—
440C22×Q8C22×D4713yes—
441C22×Q8C22×D4713yes—
442C22×Q8C22×D4718yes—
443C22×Q8C22×D4718yes—
444C22×Q8C22×D4711yescharacteristic
445C22×D4—471no—
446C22×D4—471no—
447C22×D4C22×D4711yescharacteristic
448C23×C4—473no—
449C23×C4—471no—
450C23×C4—473no—
451C23×C4C22×D4713yes—
452C23×C4C22×D4713yes—
453C4⋊Q8—4724no—
454C4⋊Q8—4724no—
455C4⋊Q8—4724no—
456C4⋊Q8C22×D47124yes—
457#126—4724no—
458#126—4748no—
459#126—4724no—
460#126—4748no—
461#125—4724no—
462#125—4748no—
463#125—4748no—
464#125—4748no—
465#125—4724no—
466#125—4724no—
467#124—4724no—
468#123—4724no—
469#123—4724no—
470C22⋊Q8—4724no—
471C22⋊Q8—4724no—
472C22⋊Q8—4724no—
473C22⋊Q8—4724no—
474C22⋊Q8—4724no—
475C22⋊Q8C22×D47124yes—
476C22⋊Q8C22×D47124yes—
477#121—478no—
478C4×Q8—478no—
479C4×Q8—4724no—
480C4×Q8—478no—
481C4×Q8—4724no—
482C4×Q8—4724no—
483C4×Q8—478no—
484C4×Q8—4724no—
485C4×Q8—4724no—
486C4×Q8—4748no—
487C4×Q8—4724no—
488C4×Q8—4724no—
489C4×Q8C22×D4718yes—
490C4×D4—4724no—
491C4×D4—4724no—
492C4×D4C22×D47124yes—
493#117—4724no—
494#117—4724no—
495#117—4724no—
496#117—4748no—
497#117—4724no—
498C2×C4⋊C4—473no—
499C2×C4⋊C4—473no—
500C2×C4⋊C4—476no—
501C2×C4⋊C4—4724no—
502C2×C4⋊C4—473no—
503C2×C4⋊C4—473no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—473no—
507C2×C4⋊C4—476no—
508C2×C4⋊C4—476no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—476no—
513C2×C4⋊C4—473no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4C22×D4713yes—
516C2×C4⋊C4C22×D4713yes—
517C2×C4⋊C4C22×D4716yes—
518C2×C22⋊C4—471no—
519C2×C22⋊C4—473no—
520C2×C22⋊C4—473no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—473no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4C22×D4713yes—
527C2×C22⋊C4C22×D4713yes—
528C2×C42—473no—
529C2×C42—476no—
530C2×C42—476no—
531C2×C42—473no—
532C2×C42—473no—
533C2×C42—473no—
534C2×C42—473no—
535C2×C42—4724no—
536C2×C42C22×D4713yes—
537C24—471no—
538C24C23×D4711yescharacteristic
539C24C23×D4711yescharacteristic
540C2×Q8—232no—
541C2×Q8—232no—
542C2×Q8—212no—
543C2×Q8—212no—
544C2×Q8—4712no—
545C2×Q8—4712no—
546C2×Q8—9412no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8#1062535218yes—
550C2×Q8C23×D47112yes—
551C2×Q8C23×D47112yes—
552C2×Q8C23×D4714yes—
553C2×D4—24no—
554C2×D4—474no—
555C2×D4—474no—
556C2×D4—944no—
557C2×D4—944no—
558C2×D4C23×D4714yes—
559C22×C4—212no—
560C22×C4—212no—
561C22×C4—471no—
562C22×C4—474no—
563C22×C4—4712no—
564C22×C4—471no—
565C22×C4—473no—
566C22×C4—473no—
567C22×C4—471no—
568C22×C4—473no—
569C22×C4—473no—
570C22×C4—4712no—
571C22×C4—944no—
572C22×C4—9412no—
573C22×C4—9412no—
574C22×C4C23×D47112yes—
575C22×C4C23×D47112yes—
576C22×C4C23×D4713yes—
577C22×C4C23×D4713yes—
578C22×C4C23×D4713yes—
579C22×C4C23×D4711yescharacteristic
580C22×C4C23×D4713yes—
581C4⋊C4—4712no—
582C4⋊C4—4712no—
583C4⋊C4—4724no—
584C4⋊C4—4724no—
585C4⋊C4—4712no—
586C4⋊C4—4712no—
587C4⋊C4—474no—
588C4⋊C4—4724no—
589C4⋊C4—4712no—
590C4⋊C4—4712no—
591C4⋊C4—4712no—
592C4⋊C4—4724no—
593C4⋊C4—4712no—
594C4⋊C4—4712no—
595C4⋊C4—4712no—
596C4⋊C4—4712no—
597C4⋊C4C23×D47112yes—
598C4⋊C4C23×D47112yes—
599C4⋊C4C23×D47124yes—
600C22⋊C4—474no—
601C22⋊C4—4712no—
602C22⋊C4—4712no—
603C22⋊C4—4712no—
604C22⋊C4—474no—
605C22⋊C4—4712no—
606C22⋊C4—4712no—
607C22⋊C4—4712no—
608C22⋊C4C23×D47112yes—
609C22⋊C4C23×D47112yes—
610C42—4712no—
611C42—4712no—
612C42—4712no—
613C42—4712no—
614C42—4724no—
615C42—4724no—
616C42—4712no—
617C42C23×D47112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—472no—
624C23—942no—
625C23—942no—
626C23—942no—
627C23#1309407214yes—
628C23C24×D4712yes—
629C23C24×D4712yes—
630C23C24×D4711yescharacteristic
631Q8—224no—
632Q8—224no—
633Q8—9424no—
634Q8—9424no—
635Q8C2×#10625352116yes—
636D4—28no—
637D4—948no—
638D4—948no—
639C2×C4—26no—
640C2×C4—26no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—474no—
646C2×C4—472no—
647C2×C4—472no—
648C2×C4—476no—
649C2×C4—476no—
650C2×C4—472no—
651C2×C4—476no—
652C2×C4—476no—
653C2×C4—948no—
654C2×C4—946no—
655C2×C4—942no—
656C2×C4—946no—
657C2×C4—9424no—
658C2×C4—946no—
659C2×C4—946no—
660C2×C4—942no—
661C2×C4—9424no—
662C2×C4C2×#10625352112yes—
663C2×C4C24×D4716yes—
664C2×C4C24×D4716yes—
665C2×C4C24×D4716yes—
666C2×C4C24×D4712yes—
667C2×C4C24×D4716yes—
668C22—22no—
669C22—22no—
670C22—28no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—44no—
675C22—942no—
676C22—942no—
677C22—942no—
678C22—1884no—
679C22C22×#1062535212yes—
680C222−1+4×D4712yes—
681C22C2×#1309407214yes—
682C22C2×#1309407212yes—
683C22C25×D4711yescharacteristic
684C4—26no—
685C4—26no—
686C4—26no—
687C4—22no—
688C4—474no—
689C4—946no—
690C4—942no—
691C4—946no—
692C4—946no—
693C4—946no—
694C4—942no—
695C4C22×#10625352112yes—
696C2—24no—
697C2—42no—
698C2—1882no—
699C2#2025747514yesdirect product factor
700C2C23×#1062535211yescharacteristic
701C2C2×2−1+4×D4711yescharacteristic
702C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×D4×Q8×C47C2
socleC23×C47C25
prime radicalC2×#13093996C22
hypercenterC2×D4×Q8D47
hypocenterC47C2×#3523
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257475C2direct (N × H)
2. C2×#15689849C2semidirect
3. C2×#15689848C2semidirect
4. C2×#15689844C2semidirect
5. C2×#15689815C2semidirect
6. C2×#15689813C2semidirect
7. C2×Q8×C22⋊D47C2semidirect
8. C2×Q8×C22⋊D47C2semidirect
9. C2×#15689734C2semidirect
10. C2×#15689733C2semidirect
11. C2×#15689675C2semidirect
13. C2×#15689601C2semidirect
14. C2×#15689599C2semidirect
15. C22×Q8×Dic47C2semidirect
16. C2×D4×Q8×C47C2semidirect
18. #15689849C22semidirect
19. #15689848C22semidirect
20. #15689844C22semidirect
21. #15689815C22semidirect
22. #15689813C22semidirect
23. Q8×C22⋊D47C22semidirect
24. Q8×C22⋊D47C22semidirect
25. #15689734C22semidirect
26. #15689733C22semidirect
27. #15689675C22semidirect
51. #15689601C22semidirect
52. #15689599C22semidirect
60. C2×Q8×Dic47C22semidirect
76. D4×Q8×C47C22semidirect
353. C2×D4×Q8D47semidirect
363. C2×C47#3523semidirect
378. D4×Q8C2×D47semidirect
433. C47C2×#3523semidirect
699. C2#20257475direct (N × H)

Maximal subgroups

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

subgroupindex
#202574752
C2×#156898492
C2×#156898482
C2×#156898442
C2×#156898152
C2×#156898132
C2×Q8×C22⋊D472
C2×#156897342
C2×#156897332
C2×#156896752
C2×#156896532
C2×#156896012
C2×#156895992
C22×Q8×Dic472
C2×D4×Q8×C472
C2×#352347