Finite Group Databasebeta

← C2×#20257370 #27124464

Subgroups — C2×#20257370 #27124464

Order 12032.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257370C2132yesmaximal, direct product factor
2C2×#15689852C211yesmaximal, characteristic, complemented
3C2×#15689842C213yesmaximal, complemented
4C2×#15689830C213yesmaximal, complemented
5C2×#15689825C213yesmaximal, complemented
6C2×#15689815C213yesmaximal, complemented
7C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
8C2×#15689780C211yesmaximal, characteristic, complemented
9C2×#15689742C213yesmaximal, complemented
10C2×#15689733C213yesmaximal, complemented
11C2×#15689654C213yesmaximal, complemented
12C2×#15689653C213yesmaximal, complemented
13C2×#15689606C211yesmaximal, characteristic, complemented
14C2×#15689599C211yesmaximal, characteristic, complemented
15C22×Q8×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18#15689852C22116yescomplemented
19#15689842C22148yescomplemented
20#15689830C22148yescomplemented
21#15689825C22148yescomplemented
22#15689815C22148yescomplemented
23Q8×C22⋊D47C22116yescomplemented
24#15689780C22116yescomplemented
25#15689742C22148yescomplemented
26#15689733C22148yescomplemented
27C2×#13094024C2213yes—
28C2×#13094022C2213yes—
29#15689654C22148yescomplemented
30#15689653C22148yescomplemented
31C2×#13094019C2213yes—
32C2×#13094017C2213yes—
33C2×#13094017C2216yes—
34C2×#13094017C2216yes—
35C2×#13094015C2213yes—
36C2×#13094015C2216yes—
37C2×#13094015C2213yes—
38C2×#13094014C2213yes—
39C2×#13094011C2213yes—
40C2×#13094010C2213yes—
41C2×#13094008C2216yes—
42C2×#13094008C2211yescharacteristic
43C2×#13094005C2213yes—
44C2×#13094003C2213yes—
45C2×#13094003C2213yes—
46C2×#13094001C2213yes—
47C2×#13094001C2216yes—
48C2×#13094000C2213yes—
49C2×#13093996C2213yes—
50C2×#13093995C2213yes—
51#15689606C22116yescomplemented
52#15689599C22116yescomplemented
53C2×Q8×Dic47C2211yescharacteristic
54C2×Q8×Dic47C2211yescharacteristic
55C2×Q8×Dic47C2213yes—
56C2×Q8×Dic47C2213yes—
57C2×Q8×Dic47C2211yescharacteristic
58C2×Q8×Dic47C22116yescomplemented
59C2×C4×Dic94C2213yes—
60C2×C4×Dic94C2213yes—
61C2×#13093989C2213yes—
62C2×D4×Dic47C2213yes—
63C2×D4×Dic47C2213yes—
64C2×D4×Dic47C2216yes—
65C2×C4×C22⋊D47C2213yes—
66C2×C4×C22⋊D47C2213yes—
67C2×#13093983C2213yes—
68C2×#13093982C2213yes—
69C2×#13093981C2213yes—
70C2×#13093980C2216yes—
71C22×C4⋊Dic47C2213yes—
72C22×C4⋊Dic47C2213yes—
73C22×C4×Dic47C2213yes—
74C22×#41×C47C2211yescharacteristic
75C23×Q8×C47C2211yescharacteristic
76C47×#548C22116yescomplemented
77C2×#124×C47C2213yes—
78C2×C22⋊Q8×C47C2213yes—
79C2×#121×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⋊D47C2313yes—
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2313yes—
90C23×Dic47C2316yes—
91C22×C4×D47C2313yes—
92#13094024C23124yes—
93#13094022C23124yes—
94#13094019C23124yes—
95#13094017C23148yes—
96#13094017C23148yes—
97#13094017C23124yes—
98#13094015C23148yes—
99#13094015C23124yes—
100#13094015C23124yes—
101#13094014C23124yes—
102#13094011C23124yes—
103#13094010C23124yes—
104#13094008C23148yes—
105#13094008C2318yes—
106#13094005C23124yes—
107#13094003C23124yes—
108#13094003C23124yes—
109#13094001C23148yes—
110#13094001C23124yes—
111#13094000C23124yes—
112#13093996C23124yes—
113#13093995C23124yes—
114Q8×Dic47C23124yes—
115Q8×Dic47C2318yes—
116Q8×Dic47C2318yes—
117Q8×Dic47C23124yes—
118Q8×Dic47C2318yes—
119C4×Dic94C23124yes—
120C4×Dic94C23124yes—
121#13093989C23124yes—
122D4×Dic47C23124yes—
123D4×Dic47C23148yes—
124D4×Dic47C23124yes—
125C4×C22⋊D47C23124yes—
126C4×C22⋊D47C23124yes—
127#13093983C23124yes—
128#13093982C23124yes—
129#13093981C23124yes—
130#13093980C23148yes—
131C2×C4⋊Dic47C23124yes—
132C2×C4⋊Dic47C23124yes—
133C2×C4⋊Dic47C2313yes—
134C2×C4⋊Dic47C2313yes—
135C2×C4⋊Dic47C2313yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2316yes—
138C2×C4⋊Dic47C2311yescharacteristic
139C2×C4⋊Dic47C2316yes—
140C2×C4⋊Dic47C2311yescharacteristic
141C2×Dic47⋊C4C2313yes—
142C2×Dic47⋊C4C2316yes—
143C2×Dic47⋊C4C2313yes—
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2313yes—
147C2×Dic47⋊C4C2313yes—
148C2×C22⋊Dic47C2313yes—
149C2×C22⋊Dic47C2313yes—
150C2×C22⋊Dic47C2313yes—
151C2×C22⋊Dic47C2313yes—
152C2×C22⋊Dic47C2316yes—
153C2×(C2×D47)⋊C4C2311yescharacteristic
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2311yescharacteristic
156C2×(C2×D47)⋊C4C2313yes—
157C2×C4×Dic47C2313yes—
158C2×C4×Dic47C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C23124yes—
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C2×#41×C47—28no—
165C2×#41×C47C2318yes—
166C22×Q8×C47—28no—
167C22×Q8×C47C2318yes—
168C22×Q8×C47C2313yes—
169C22×Q8×C47C2311yescharacteristic
170C22×D4×C47C2313yes—
171C22×D4×C47C2313yes—
172C23×C4×C47C2313yes—
173C23×C4×C47C2313yes—
174#124×C47C23124yes—
175C22⋊Q8×C47C23124yes—
176#121×C47C23124yes—
177C4×Q8×C47C2318yes—
178C4×D4×C47C23124yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C4⋊C4×C47C2313yes—
181C2×C22⋊C4×C47C2311yescharacteristic
182C2×C22⋊C4×C47C2313yes—
183C2×C22⋊C4×C47C2316yes—
184C2×C42×C47C2313yes—
185C24×C47C2413yes—
186C24×C47C2411yescharacteristic
187C23×D47C2411yescharacteristic
188#41×C47—232no—
189C2×Q8×C47—232no—
190C2×Q8×C47—212no—
191C2×Q8×C47#4118yes—
192C2×Q8×C47C24112yes—
193C2×Q8×C47C2414yes—
194C2×D4×C47—212no—
195C2×D4×C47—212no—
196C2×D4×C47C24112yes—
197C2×D4×C47C24112yes—
198C22×C4×C47—212no—
199C22×C4×C47—212no—
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2413yes—
202C22×C4×C47C2413yes—
203C22×C4×C47C2411yescharacteristic
204C22×C4×C47C24112yes—
205C22×C4×C47C24112yes—
206C22×C4×C47C2413yes—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—46no—
209C2×C22⋊D47C2414yes—
210C2×C22⋊D47C24112yes—
211C22×Dic47—24no—
212C22×Dic47—412no—
213C22×Dic47—46no—
214C22×Dic47C2411yescharacteristic
215C22×Dic47C2411yescharacteristic
216C22×Dic47C2414yes—
217C22×Dic47C2413yes—
218C22×Dic47C2411yescharacteristic
219C22×Dic47C2413yes—
220C22×Dic47C2413yes—
221C22×Dic47C2413yes—
222C22×Dic47C24112yes—
223C22×Dic47C24124yes—
224Q8×D47—232no—
225C2×C4×D47—212no—
226C2×C4×D47C24112yes—
227C2×Dic94—212no—
228C2×Dic94—46no—
229C2×Dic94C24112yes—
230C2×Dic94C24112yes—
231C4⋊C4×C47C24112yes—
232C4⋊C4×C47C24112yes—
233C22⋊C4×C47C2414yes—
234C22⋊C4×C47C24112yes—
235C22⋊C4×C47C24124yes—
236C42×C47C24112yes—
237C22⋊Dic47C24112yes—
238C22⋊Dic47C24112yes—
239C22⋊Dic47C24112yes—
240C22⋊Dic47C24112yes—
241C22⋊Dic47C24124yes—
242(C2×D47)⋊C4C2414yes—
243(C2×D47)⋊C4C24112yes—
244(C2×D47)⋊C4C2414yes—
245(C2×D47)⋊C4C24112yes—
246C4⋊Dic47C24112yes—
247C4⋊Dic47C24112yes—
248C4⋊Dic47C24112yes—
249C4⋊Dic47C24112yes—
250C4⋊Dic47C24124yes—
251C4⋊Dic47C2414yes—
252C4⋊Dic47C24124yes—
253C4⋊Dic47C2414yes—
254Dic47⋊C4C24112yes—
255Dic47⋊C4C24124yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C24112yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C24112yes—
260Dic47⋊C4C24112yes—
261C4×Dic47C24112yes—
262C4×Dic47C24112yes—
263C4×Dic47C24112yes—
264C4×Dic47C24112yes—
265C4×Dic47C24124yes—
266C4×Dic47C24112yes—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—26no—
270C23×C47—26no—
271C23×C47—26no—
272C23×C472−1+414yes—
273C23×C47C2516yes—
274C23×C47C2512yes—
275C23×C47C2511yescharacteristic
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47C2512yes—
280Q8×C47—224no—
281Q8×C47C2×#41116yes—
282D4×C47—224no—
283D4×C47—224no—
284C2×C4×C47—22no—
285C2×C4×C47—26no—
286C2×C4×C47—26no—
287C2×C4×C47—22no—
288C2×C4×C47—224no—
289C2×C4×C47—224no—
290C2×C4×C47C2×#41112yes—
291C2×C4×C47C2516yes—
292C2×C4×C47C2516yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2512yes—
295C2×C4×C47C2516yes—
296C22⋊D47—28no—
297C22⋊D47—412no—
298C2×Dic47—26no—
299C2×Dic47—28no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—26no—
304C2×Dic47—26no—
305C2×Dic47—26no—
306C2×Dic47—424no—
307C2×Dic47—412no—
308C2×Dic47C2512yes—
309C2×Dic47C2512yes—
310C2×Dic47C2516yes—
311C2×Dic47C2512yes—
312C2×Dic47C2516yes—
313C2×Dic47C2516yes—
314C2×Dic47C2516yes—
315C4×D47—224no—
316Dic94—224no—
317Dic94—412no—
318C2×#3516—471nomaximal, Sylow
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—28no—
322C22×C47—26no—
323C22×C47—26no—
324C22×C47—26no—
325C22×C47—412no—
326C22×C47C22×#4112yes—
327C22×C47C2×2−1+414yes—
328C22×C47C2×2−1+412yes—
329C22×C47#58512yes—
330C22×C47C2611yescharacteristic
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—44no—
335C4×C47—22no—
336C4×C47—26no—
337C4×C47—26no—
338C4×C47—22no—
339C4×C47C22×#41112yes—
340Dic47—26no—
341Dic47—22no—
342Dic47—22no—
343Dic47—22no—
344Dic47—26no—
345Dic47—26no—
346Dic47—26no—
347#3516—4732no—
348C2×#557—471no—
349C2×#556—473no—
350C2×#554—473no—
351C2×#553—473no—
352C2×#552—473no—
353C2×D4×Q8—471no—
354C2×#548—471no—
355C2×#548D4711yescharacteristic, complemented
356C2×#542—473no—
357C2×#541—473no—
358C2×#529—473no—
359C2×#529—473no—
360C2×#520—471no—
361C2×#519—471no—
362C22×C4×Q8—471no—
363C2×C47—24no—
364C2×C47—46no—
365C2×C47#351614yescomplemented
366C2×C47C23×#4111yescharacteristic
367C2×C47C22×2−1+411yescharacteristic
368C2×C47C2×#58511yescharacteristic
369D47—42no—
370C22×#41C2×D4711yescharacteristic
371C23×Q8—471no—
372C23×Q8C2×D4711yescharacteristic
373#557—4716no—
374#556—4748no—
375#554—4748no—
376#553—4748no—
377#552—4748no—
378D4×Q8—4716no—
379#548—4716no—
380#548C2×D47116yescomplemented
381#542—4748no—
382#541—4748no—
383C2×C4⋊Q8—473no—
384C2×C4⋊Q8—473no—
385#529—4748no—
386#529—4748no—
387C2×#126—473no—
388C2×#126—476no—
389C2×#126—473no—
390C2×#126—476no—
391C2×#125—473no—
392C2×#125—473no—
393C2×#125—476no—
394C2×#125—473no—
395C2×#124—473no—
396C2×#124—473no—
397C2×#124C2×D4713yes—
398C2×#123—473no—
399C2×#123—471no—
400C2×#123—476no—
401C2×C22⋊Q8—473no—
402C2×C22⋊Q8—473no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—476no—
406C2×C22⋊Q8C2×D4713yes—
407C2×#121—473no—
408C2×#121—473no—
409C2×#121C2×D4713yes—
410#520—4716no—
411#519—4716no—
412C2×C4×Q8—471no—
413C2×C4×Q8—473no—
414C2×C4×Q8—471no—
415C2×C4×Q8—473no—
416C2×C4×Q8—4716no—
417C2×C4×Q8—471no—
418C2×C4×Q8—473no—
419C2×C4×Q8—473no—
420C2×C4×Q8—473no—
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×D4—473no—
423C2×C4×D4—473no—
424C2×C4×D4—476no—
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4C2×D4713yes—
428C2×#117—473no—
429C2×#117—473no—
430C2×#117—476no—
431C2×#117—473no—
432C22×C4⋊C4—473no—
433C22×C4⋊C4—473no—
434C22×C42—473no—
435C47C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—28no—
437C2×#41C22×D4718yes—
438C22×Q8—28no—
439C22×Q8—478no—
440C22×Q8—473no—
441C22×Q8—473no—
442C22×Q8—948no—
443C22×Q8C22×D4713yes—
444C22×Q8C22×D4718yes—
445C22×Q8C22×D4711yescharacteristic
446C22×D4—471no—
447C22×D4—473no—
448C22×D4C22×D4713yes—
449C22×D4C22×D4713yes—
450C23×C4—471no—
451C23×C4—473no—
452C23×C4—476no—
453C23×C4—473no—
454C23×C4C22×D4713yes—
455C23×C4C22×D4713yes—
456C4⋊Q8—4724no—
457C4⋊Q8—4724no—
458#126—4724no—
459#126—4748no—
460#126—4724no—
461#126—4748no—
462#125—4724no—
463#125—4724no—
464#125—4748no—
465#125—4724no—
466#124—4724no—
467#124—4724no—
468#124C22×D47124yes—
469#123—4724no—
470#123—478no—
471#123—4748no—
472C22⋊Q8—4724no—
473C22⋊Q8—4724no—
474C22⋊Q8—4724no—
475C22⋊Q8—4724no—
476C22⋊Q8—4748no—
477C22⋊Q8C22×D47124yes—
478#121—4724no—
479#121—4724no—
480#121C22×D47124yes—
481C4×Q8—478no—
482C4×Q8—4724no—
483C4×Q8—478no—
484C4×Q8—4724no—
485C4×Q8—478no—
486C4×Q8—4724no—
487C4×Q8—4724no—
488C4×Q8—4724no—
489C4×Q8C22×D4718yes—
490C4×D4—4724no—
491C4×D4—4724no—
492C4×D4—4748no—
493C4×D4—4724no—
494C4×D4—4724no—
495C4×D4C22×D47124yes—
496#117—4724no—
497#117—4724no—
498#117—4748no—
499#117—4724no—
500C2×C4⋊C4—473no—
501C2×C4⋊C4—473no—
502C2×C4⋊C4—473no—
503C2×C4⋊C4—473no—
504C2×C4⋊C4—476no—
505C2×C4⋊C4—4724no—
506C2×C4⋊C4—4724no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—476no—
512C2×C4⋊C4—473no—
513C2×C4⋊C4—476no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—473no—
517C2×C4⋊C4C22×D4713yes—
518C2×C4⋊C4C22×D4713yes—
519C2×C22⋊C4—473no—
520C2×C22⋊C4—473no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—476no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—473no—
528C2×C22⋊C4C22×D4716yes—
529C2×C22⋊C4C22×D4711yescharacteristic
530C2×C22⋊C4C22×D4713yes—
531C2×C42—473no—
532C2×C42—476no—
533C2×C42—473no—
534C2×C42—473no—
535C2×C42—473no—
536C2×C42—473no—
537C2×C42—4724no—
538C2×C42C22×D4713yes—
539C24—471no—
540C24C23×D4713yes—
541C24C23×D4711yescharacteristic
542#41—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—4712no—
546C2×Q8—4712no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8—1886no—
550C2×Q8#1062535218yes—
551C2×Q8C23×D47112yes—
552C2×Q8C23×D4714yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—474no—
556C2×D4—4712no—
557C2×D4—944no—
558C2×D4—1886no—
559C2×D4C23×D47112yes—
560C2×D4C23×D47112yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—474no—
564C22×C4—471no—
565C22×C4—471no—
566C22×C4—473no—
567C22×C4—471no—
568C22×C4—473no—
569C22×C4—473no—
570C22×C4—473no—
571C22×C4—4712no—
572C22×C4—4724no—
573C22×C4—4712no—
574C22×C4—944no—
575C22×C4—9412no—
576C22×C4—18812no—
577C22×C4—1886no—
578C22×C4C23×D47112yes—
579C22×C4C23×D47112yes—
580C22×C4C23×D4713yes—
581C22×C4C23×D4713yes—
582C22×C4C23×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584C22×C4C23×D4713yes—
585C4⋊C4—4712no—
586C4⋊C4—4712no—
587C4⋊C4—4712no—
588C4⋊C4—4724no—
589C4⋊C4—4712no—
590C4⋊C4—4712no—
591C4⋊C4—4712no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4712no—
595C4⋊C4—4712no—
596C4⋊C4—4724no—
597C4⋊C4—474no—
598C4⋊C4—4724no—
599C4⋊C4—474no—
600C4⋊C4C23×D47112yes—
601C4⋊C4C23×D47112yes—
602C22⋊C4—4712no—
603C22⋊C4—4712no—
604C22⋊C4—4712no—
605C22⋊C4—4712no—
606C22⋊C4—4724no—
607C22⋊C4—4712no—
608C22⋊C4—474no—
609C22⋊C4—474no—
610C22⋊C4—4712no—
611C22⋊C4C23×D47124yes—
612C22⋊C4C23×D4714yes—
613C22⋊C4C23×D47112yes—
614C42—4712no—
615C42—4712no—
616C42—4712no—
617C42—4712no—
618C42—4724no—
619C42—4712no—
620C42C23×D47112yes—
621C23—22no—
622C23—22no—
623C23—26no—
624C23—26no—
625C23—26no—
626C23—472no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23#1309407114yes—
631C23C24×D4716yes—
632C23C24×D4712yes—
633C23C24×D4711yescharacteristic
634Q8—224no—
635Q8—9424no—
636Q8—18812no—
637Q8C2×#10625352116yes—
638D4—224no—
639D4—224no—
640D4—948no—
641D4—18812no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—22no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—472no—
649C2×C4—472no—
650C2×C4—476no—
651C2×C4—472no—
652C2×C4—476no—
653C2×C4—476no—
654C2×C4—476no—
655C2×C4—946no—
656C2×C4—948no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—946no—
661C2×C4—946no—
662C2×C4—946no—
663C2×C4—9424no—
664C2×C4—18824no—
665C2×C4—18812no—
666C2×C4C2×#10625352112yes—
667C2×C4C24×D4716yes—
668C2×C4C24×D4716yes—
669C2×C4C24×D4712yes—
670C2×C4C24×D4712yes—
671C2×C4C24×D4716yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—26no—
676C22—26no—
677C22—26no—
678C22—412no—
679C22—942no—
680C22—942no—
681C22—942no—
682C22—1884no—
683C22C22×#1062535212yes—
684C22C2×#1309407114yes—
685C22C2×#1309407112yes—
686C22#1568996012yes—
687C22C25×D4711yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—946no—
693C4—942no—
694C4—942no—
695C4—942no—
696C4—946no—
697C4—946no—
698C4—946no—
699C4C22×#10625352112yes—
700C2—24no—
701C2—46no—
702C2—1882no—
703C2#2025737014yesdirect product factor
704C2C23×#1062535211yescharacteristic
705C2C22×#1309407111yescharacteristic
706C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #20257370C2direct (N × H)
2. C2×#15689852C2semidirect
3. C2×#15689842C2semidirect
4. C2×#15689830C2semidirect
5. C2×#15689825C2semidirect
6. C2×#15689815C2semidirect
7. C2×Q8×C22⋊D47C2semidirect
8. C2×#15689780C2semidirect
9. C2×#15689742C2semidirect
10. C2×#15689733C2semidirect
11. C2×#15689654C2semidirect
12. C2×#15689653C2semidirect
13. C2×#15689606C2semidirect
14. C2×#15689599C2semidirect
15. C22×Q8×Dic47C2semidirect
16. C2×C47×#548C2semidirect
18. #15689852C22semidirect
19. #15689842C22semidirect
20. #15689830C22semidirect
21. #15689825C22semidirect
22. #15689815C22semidirect
23. Q8×C22⋊D47C22semidirect
24. #15689780C22semidirect
25. #15689742C22semidirect
26. #15689733C22semidirect
29. #15689654C22semidirect
30. #15689653C22semidirect
51. #15689606C22semidirect
52. #15689599C22semidirect
58. C2×Q8×Dic47C22semidirect
76. C47×#548C22semidirect
355. C2×#548D47semidirect
365. C2×C47#3516semidirect
380. #548C2×D47semidirect
435. C47C2×#3516semidirect
703. C2#20257370direct (N × H)

Maximal subgroups

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

subgroupindex
#202573702
C2×#156898522
C2×#156898422
C2×#156898302
C2×#156898252
C2×#156898152
C2×Q8×C22⋊D472
C2×#156897802
C2×#156897422
C2×#156897332
C2×#156896542
C2×#156896532
C2×#156896062
C2×#156895992
C22×Q8×Dic472
C2×C47×#5482
C2×#351647