Finite Group Databasebeta

← C2×#20256986 #27123336

Subgroups — C2×#20256986 #27123336

Order 12032.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256986C2132yesmaximal, direct product factor
2C2×#15689856C213yesmaximal, complemented
3C2×#15689849C211yesmaximal, characteristic, complemented
4C2×#15689841C213yesmaximal, complemented
5C2×#15689823C213yesmaximal, complemented
6C2×#15689817C213yesmaximal, complemented
7C2×#15689792C211yesmaximal, characteristic, complemented
8C2×#15689785C211yesmaximal, characteristic, complemented
9C2×#15689780C211yesmaximal, characteristic, complemented
10C2×#15689670C213yesmaximal, complemented
11C2×#15689657C213yesmaximal, complemented
12C2×#15689655C213yesmaximal, complemented
13C2×C4×#10625354C211yesmaximal, characteristic, complemented
14C2×C4×#10625350C213yesmaximal, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C2×C4×#41×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2213yes—
19C22×Q8×D47C2211yescharacteristic
20#15689856C22148yescomplemented
21#15689849C22116yescomplemented
22#15689841C22148yescomplemented
23#15689823C22148yescomplemented
24#15689817C22148yescomplemented
25#15689792C22116yescomplemented
26#15689785C22116yescomplemented
27#15689780C22116yescomplemented
28#15689670C22148yescomplemented
29C2×#13094023C2213yes—
30C2×#13094020C2213yes—
31#15689657C22148yescomplemented
32#15689655C22148yescomplemented
33C2×#13094018C2216yes—
34C2×#13094017C2216yes—
35C2×#13094016C2213yes—
36C2×#13094015C2213yes—
37C2×#13094012C2213yes—
38C2×#13094011C2213yes—
39C2×#13094010C2216yes—
40C2×#13094007C2216yes—
41C2×#13094006C2216yes—
42C2×#13094004C2213yes—
43C2×#13094003C2213yes—
44C2×#13093999C2213yes—
45C2×#13093998C2213yes—
46C2×#13093997C2216yes—
47C2×#13093995C2213yes—
48C2×#13093995C2213yes—
49C4×#10625354C22116yescomplemented
50C4×#10625350C22148yescomplemented
51C2×Q8×Dic47C2211yescharacteristic
52C2×Q8×Dic47C2211yescharacteristic
53C2×C4×Dic94C2213yes—
54C2×C4×Dic94C2213yes—
55C2×C4×Dic94C2213yes—
56C2×#13093989C2213yes—
57C4×Q8×D47C22116yescomplemented
58C2×C4×D188C2213yes—
59C2×C4×D188C2213yes—
60C2×C4×D188C2213yes—
61C2×#13093986C2213yes—
62C2×C4×C22⋊D47C2213yes—
63C2×C4×C22⋊D47C2213yes—
64C2×C4×C22⋊D47C2213yes—
65C2×C4×C22⋊D47C2213yes—
66C2×C4×C22⋊D47C2216yes—
67C2×#13093983C2213yes—
68C2×#13093982C2213yes—
69C2×#13093981C2211yescharacteristic
70C2×#13093981C2213yes—
71C2×C4⋊C4×D47C2213yes—
72C2×C42×D47C2213yes—
73C2×C42×D47C2213yes—
74C22×#41×C47C2211yescharacteristic
75C4×#41×C47C22116yescomplemented
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2211yescharacteristic
78C2×C4×D4×C47C2213yes—
79C2×C4×D4×C47C2213yes—
80C2×#117×C47C2213yes—
81C22×C42×C47C2213yes—
82C2×#10625354—28no—
83C2×#10625354C2318yes—
84C2×#10625350—224no—
85C2×#10625350C23124yes—
86C22×Dic94C2313yes—
87C22×Dic94C2313yes—
88C2×Q8×D47—28no—
89C2×Q8×D47C2318yes—
90C22×D188C2313yes—
91C22×D188C2313yes—
92C22×C22⋊D47C2313yes—
93C22×C22⋊D47C2313yes—
94C22×C22⋊D47C2316yes—
95C22×C4×D47C2313yes—
96C22×C4×D47C2313yes—
97C22×C4×D47C2313yes—
98C22×C4×D47C2313yes—
99C22×C4×D47C2313yes—
100C22×C4×D47C2311yescharacteristic
101#13094023C23124yes—
102#13094020C23124yes—
103#13094018C23148yes—
104#13094017C23148yes—
105#13094016C23124yes—
106#13094015C23124yes—
107#13094012C23124yes—
108#13094011C23124yes—
109#13094010C23148yes—
110#13094007C23148yes—
111#13094006C23148yes—
112#13094004C23124yes—
113#13094003C23124yes—
114#13093999C23124yes—
115#13093998C23124yes—
116#13093997C23148yes—
117#13093995C23124yes—
118#13093995C23124yes—
119Q8×Dic47C2318yes—
120Q8×Dic47C2318yes—
121C4×Dic94C23124yes—
122C4×Dic94C23124yes—
123C4×Dic94C23124yes—
124#13093989C23124yes—
125C4×D188C23124yes—
126C4×D188C23124yes—
127C4×D188C23124yes—
128#13093986C23124yes—
129C4×C22⋊D47C23124yes—
130C4×C22⋊D47C23124yes—
131C4×C22⋊D47C23124yes—
132C4×C22⋊D47C23124yes—
133C4×C22⋊D47C23148yes—
134#13093983C23124yes—
135#13093982C23124yes—
136#13093981C2318yes—
137#13093981C23124yes—
138C2×C4⋊Dic47C2313yes—
139C2×C4⋊Dic47C2313yes—
140C2×C4⋊Dic47C2313yes—
141C2×C4⋊Dic47C2313yes—
142C2×Dic47⋊C4C2316yes—
143C2×Dic47⋊C4C2311yescharacteristic
144C2×Dic47⋊C4C2311yescharacteristic
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2313yes—
147C2×Dic47⋊C4C2316yes—
148C4⋊C4×D47C23124yes—
149C2×C22⋊Dic47C2313yes—
150C2×C22⋊Dic47C2313yes—
151C2×C22⋊Dic47C2316yes—
152C2×(C2×D47)⋊C4C2311yescharacteristic
153C2×(C2×D47)⋊C4C2311yescharacteristic
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×(C2×D47)⋊C4C2316yes—
157C2×(C2×D47)⋊C4C2316yes—
158C2×C4×Dic47C2311yescharacteristic
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C2313yes—
163C2×C4×Dic47C2313yes—
164C42×D47C23124yes—
165C42×D47C23124yes—
166C2×#41×C47—28no—
167C2×#41×C47C2318yes—
168C22×Q8×C47C2311yescharacteristic
169C22×D4×C47C2313yes—
170C23×C4×C47C2313yes—
171C23×C4×C47C2313yes—
172C23×C4×C47C2313yes—
173C4×Q8×C47C2318yes—
174C4×Q8×C47C2318yes—
175C4×D4×C47C23124yes—
176C4×D4×C47C23124yes—
177#117×C47C23124yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C22⋊C4×C47C2316yes—
181C2×C42×C47C2311yescharacteristic
182C2×C42×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2313yes—
185C2×C42×C47C23124yes—
186C24×C47C2413yes—
187C23×D47C2413yes—
188C23×D47C2411yescharacteristic
189#41×C47—232no—
190C2×Q8×C47#4118yescomplemented
191C2×Q8×C47C2414yes—
192C2×D4×C47—212no—
193C2×D4×C47C24112yes—
194C22×C4×C47—212no—
195C22×C4×C47—212no—
196C22×C4×C47—46no—
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2413yes—
200C22×C4×C47C2413yes—
201C22×C4×C47C24112yes—
202C22×C4×C47C24112yes—
203C22×C4×C47C24112yes—
204C22×C4×C47C2413yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—212no—
207C2×C22⋊D47—212no—
208C2×C22⋊D47—412no—
209C2×C22⋊D47C24112yes—
210C2×C22⋊D47C24112yes—
211C2×C22⋊D47C24124yes—
212C22×Dic47C2411yescharacteristic
213C22×Dic47C2411yescharacteristic
214C22×Dic47C2413yes—
215C22×Dic47C2413yes—
216C22×Dic47C2413yes—
217C22×Dic47C2411yescharacteristic
218#10625354—232no—
219Q8×D47—232no—
220#10625350—296no—
221C2×D188—212no—
222C2×D188—212no—
223C2×D188C24112yes—
224C2×D188C24112yes—
225C2×C4×D47—212no—
226C2×C4×D47—212no—
227C2×C4×D47—212no—
228C2×C4×D47—46no—
229C2×C4×D47—46no—
230C2×C4×D47#4118yescomplemented
231C2×C4×D47C24112yes—
232C2×C4×D47C24112yes—
233C2×C4×D47C24112yes—
234C2×C4×D47C24112yes—
235C2×C4×D47C24112yes—
236C2×C4×D47C2414yes—
237C2×Dic94—212no—
238C2×Dic94—212no—
239C2×Dic94C24112yes—
240C2×Dic94C24112yes—
241C4⋊C4×C47C24112yes—
242C4⋊C4×C47C24112yes—
243C22⋊C4×C47C24124yes—
244C42×C47C2414yes—
245C42×C47C24112yes—
246C42×C47C24112yes—
247C42×C47C24112yes—
248C22⋊Dic47C24112yes—
249C22⋊Dic47C24112yes—
250C22⋊Dic47C24124yes—
251(C2×D47)⋊C4C2414yes—
252(C2×D47)⋊C4C2414yes—
253(C2×D47)⋊C4C24112yes—
254(C2×D47)⋊C4C24112yes—
255(C2×D47)⋊C4C24124yes—
256(C2×D47)⋊C4C24124yes—
257C4⋊Dic47C24112yes—
258C4⋊Dic47C24112yes—
259C4⋊Dic47C24112yes—
260C4⋊Dic47C24112yes—
261Dic47⋊C4C24124yes—
262Dic47⋊C4C2414yes—
263Dic47⋊C4C2414yes—
264Dic47⋊C4C24112yes—
265Dic47⋊C4C24112yes—
266Dic47⋊C4C24124yes—
267C4×Dic47C2414yes—
268C4×Dic47C24112yes—
269C4×Dic47C24112yes—
270C4×Dic47C24112yes—
271C4×Dic47C24112yes—
272C4×Dic47C24112yes—
273C23×C47—26no—
274C23×C47—26no—
275C23×C47—26no—
276C23×C47C2516yes—
277C23×C47C2511yescharacteristic
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—26no—
281C22×D47—26no—
282C22×D47—26no—
283C22×D47C2×#4114yes—
284C22×D47C2516yes—
285C22×D47C2512yes—
286Q8×C47C2×#41116yescomplemented
287D4×C47—224no—
288C2×C4×C47—26no—
289C2×C4×C47—22no—
290C2×C4×C47—26no—
291C2×C4×C47—22no—
292C2×C4×C47—224no—
293C2×C4×C47—224no—
294C2×C4×C47—412no—
295C2×C4×C47C2×#4114yes—
296C2×C4×C47C2×#41112yes—
297C2×C4×C47C2516yes—
298C2×C4×C47C2512yes—
299C2×C4×C47C2512yes—
300C2×C4×C47C2516yes—
301C2×C4×C47C2512yes—
302C2×C4×C47C2516yes—
303C22⋊D47—224no—
304C22⋊D47—224no—
305C22⋊D47—424no—
306C2×Dic47—26no—
307C2×Dic47—26no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—26no—
311C2×Dic47C2×#4114yes—
312C2×Dic47C2512yes—
313C2×Dic47C2512yes—
314C2×Dic47C2516yes—
315C2×Dic47C2516yes—
316C2×Dic47C2516yes—
317C2×Dic47C2512yes—
318D188—224no—
319D188—224no—
320C4×D47—224no—
321C4×D47—224no—
322C4×D47—224no—
323C4×D47—412no—
324C4×D47—412no—
325C4×D47C2×#41116yescomplemented
326Dic94—224no—
327Dic94—224no—
328C2×#3480—471nomaximal, Sylow
329C22×C47—26no—
330C22×C47—26no—
331C22×C47—26no—
332C22×C47—412no—
333C22×C47C22×#4112yes—
334C22×C47C22×#4112yes—
335C22×C47#58512yes—
336C22×C47C2611yescharacteristic
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—28no—
340C2×D47—26no—
341C2×D47—26no—
342C2×D47—26no—
343C2×D47—412no—
344C2×D47C22×#4114yes—
345C4×C47—26no—
346C4×C47—22no—
347C4×C47—26no—
348C4×C47—22no—
349C4×C47C22×#4114yes—
350C4×C47C22×#41112yes—
351Dic47—26no—
352Dic47—26no—
353Dic47—22no—
354Dic47—22no—
355Dic47—26no—
356Dic47C22×#4114yes—
357#3480—4732no—
358C2×#559—473no—
359C2×#557—471no—
360C2×#556—473no—
361C2×#553—473no—
362C2×#553—473no—
363C2×#550—471no—
364C2×#548—471no—
365C2×#548—471no—
366C2×#532—473no—
367C2×#529—473no—
368C2×#529—473no—
369C2×C4×#41—473no—
370C2×C4×#41—471no—
371C2×C4×#41D4711yescharacteristic, complemented
372C22×C4×Q8—471no—
373C2×C47—46no—
374C2×C47#348014yescomplemented
375C2×C47C23×#4111yescharacteristic
376C2×C47C23×#4111yescharacteristic
377C2×C47C2×#58511yescharacteristic
378D47—24no—
379D47—46no—
380C22×#41—471no—
381C22×#41—473no—
382C22×#41C2×D4711yescharacteristic
383C23×Q8—471no—
384#559—4748no—
385#557—4716no—
386#556—4748no—
387#553—4748no—
388#553—4748no—
389#550—4716no—
390#548—4716no—
391#548—4716no—
392#532—4748no—
393C2×C4⋊Q8—473no—
394C2×#127—473no—
395#529—4748no—
396#529—4748no—
397C2×#126—476no—
398C2×#126—476no—
399C2×#125—473no—
400C2×#125—473no—
401C2×#124—473no—
402C2×#124—476no—
403C2×#124—473no—
404C2×#123—476no—
405C2×#123—476no—
406C2×C22⋊Q8—473no—
407C2×C22⋊Q8—473no—
408C2×#121—473no—
409C2×#121—473no—
410C2×#121—473no—
411C2×#121—473no—
412C2×#121—476no—
413C4×#41—4716no—
414C4×#41—4748no—
415C4×#41C2×D47116yescomplemented
416C2×C4×Q8—471no—
417C2×C4×Q8—471no—
418C2×C4×Q8—4716no—
419C2×C4×Q8—473no—
420C2×C4×Q8—473no—
421C2×C4×Q8—473no—
422C2×C4×Q8—473no—
423C2×C4×Q8C2×D4711yescharacteristic
424C2×C4×Q8C2×D4711yescharacteristic
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4—473no—
428C2×C4×D4—473no—
429C2×C4×D4—476no—
430C2×C4×D4—473no—
431C2×C4×D4—473no—
432C2×C4×D4—473no—
433C2×C4×D4—473no—
434C2×C4×D4C2×D4713yes—
435C2×C4×D4C2×D4713yes—
436C2×#117—473no—
437C2×#117—473no—
438C2×#117—471no—
439C2×#117—473no—
440C2×#117C2×D4713yes—
441C22×C4⋊C4—473no—
442C22×C42—473no—
443C22×C42—473no—
444C22×C42C2×D4713yes—
445C47C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—478no—
448C2×#41—4724no—
449C2×#41—9424no—
450C2×#41—948no—
451C2×#41C22×D4718yes—
452C22×Q8—478no—
453C22×Q8—473no—
454C22×Q8—473no—
455C22×Q8—948no—
456C22×Q8C22×D4711yescharacteristic
457C22×D4—473no—
458C22×D4—473no—
459C22×D4—476no—
460C22×D4—473no—
461C22×D4—473no—
462C22×D4C22×D4713yes—
463C23×C4—471no—
464C23×C4—473no—
465C23×C4—473no—
466C23×C4—473no—
467C23×C4—473no—
468C23×C4—473no—
469C23×C4C22×D4713yes—
470C23×C4C22×D4713yes—
471C23×C4C22×D4713yes—
472C4⋊Q8—4724no—
473#127—4724no—
474#126—4748no—
475#126—4748no—
476#125—4724no—
477#125—4724no—
478#124—4724no—
479#124—4748no—
480#124—4724no—
481#123—4748no—
482#123—4748no—
483C22⋊Q8—4724no—
484C22⋊Q8—4724no—
485#121—4724no—
486#121—4724no—
487#121—4724no—
488#121—4724no—
489#121—4748no—
490C4×Q8—478no—
491C4×Q8—478no—
492C4×Q8—4724no—
493C4×Q8—4724no—
494C4×Q8—4724no—
495C4×Q8—4724no—
496C4×Q8C22×D4718yes—
497C4×Q8C22×D4718yes—
498C4×D4—4724no—
499C4×D4—4724no—
500C4×D4—4724no—
501C4×D4—4724no—
502C4×D4—4748no—
503C4×D4—4724no—
504C4×D4—4724no—
505C4×D4—4724no—
506C4×D4—4724no—
507C4×D4C22×D47124yes—
508C4×D4C22×D47124yes—
509#117—4724no—
510#117—4724no—
511#117—478no—
512#117—4724no—
513#117C22×D47124yes—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—476no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—473no—
519C2×C4⋊C4—473no—
520C2×C4⋊C4—473no—
521C2×C4⋊C4—473no—
522C2×C4⋊C4—473no—
523C2×C4⋊C4—476no—
524C2×C4⋊C4—4724no—
525C2×C4⋊C4C22×D4713yes—
526C2×C4⋊C4C22×D4713yes—
527C2×C22⋊C4—473no—
528C2×C22⋊C4—473no—
529C2×C22⋊C4—476no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—473no—
533C2×C22⋊C4—476no—
534C2×C22⋊C4—473no—
535C2×C22⋊C4—476no—
536C2×C22⋊C4C22×D4716yes—
537C2×C42—473no—
538C2×C42—473no—
539C2×C42—473no—
540C2×C42—473no—
541C2×C42—471no—
542C2×C42—473no—
543C2×C42—4724no—
544C2×C42—4724no—
545C2×C42C22×D4713yes—
546C2×C42C22×D4713yes—
547C2×C42C22×D47124yes—
548C2×C42C22×D4711yescharacteristic
549C2×C42C22×D4713yes—
550C24—471no—
551C24—473no—
552C24C23×D4713yes—
553#41—232no—
554#41—9496no—
555#41—9432no—
556C2×Q8—4712no—
557C2×Q8—4712no—
558C2×Q8—9412no—
559C2×Q8—9432no—
560C2×Q8—9412no—
561C2×Q8#1062535018yescomplemented
562C2×Q8C23×D4714yes—
563C2×D4—212no—
564C2×D4—4712no—
565C2×D4—4712no—
566C2×D4—4724no—
567C2×D4—4712no—
568C2×D4—4712no—
569C2×D4—9412no—
570C2×D4—9412no—
571C2×D4—9412no—
572C2×D4—9412no—
573C2×D4—18812no—
574C2×D4C23×D47112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—471no—
579C22×C4—478no—
580C22×C4—474no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—473no—
584C22×C4—473no—
585C22×C4—473no—
586C22×C4—4712no—
587C22×C4—4712no—
588C22×C4—4712no—
589C22×C4—4712no—
590C22×C4—4712no—
591C22×C4—9412no—
592C22×C4—9412no—
593C22×C4—9412no—
594C22×C4—1886no—
595C22×C4—1886no—
596C22×C4C23×D4713yes—
597C22×C4C23×D4711yescharacteristic
598C22×C4C23×D4711yescharacteristic
599C22×C4C23×D4713yes—
600C22×C4C23×D47112yes—
601C22×C4C23×D47112yes—
602C22×C4C23×D47112yes—
603C22×C4C23×D4713yes—
604C22×C4C23×D4711yescharacteristic
605C4⋊C4—4724no—
606C4⋊C4—474no—
607C4⋊C4—474no—
608C4⋊C4—4712no—
609C4⋊C4—4712no—
610C4⋊C4—4724no—
611C4⋊C4—4712no—
612C4⋊C4—4712no—
613C4⋊C4—4712no—
614C4⋊C4—4712no—
615C4⋊C4C23×D47112yes—
616C4⋊C4C23×D47112yes—
617C22⋊C4—4712no—
618C22⋊C4—4712no—
619C22⋊C4—4724no—
620C22⋊C4—474no—
621C22⋊C4—474no—
622C22⋊C4—4712no—
623C22⋊C4—4724no—
624C22⋊C4—4712no—
625C22⋊C4—4724no—
626C22⋊C4C23×D47124yes—
627C42—474no—
628C42—4712no—
629C42—4712no—
630C42—4712no—
631C42—4712no—
632C42—4712no—
633C42C23×D47112yes—
634C42C23×D4714yes—
635C42C23×D47112yes—
636C42C23×D47112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—474no—
641C23—472no—
642C23—476no—
643C23—942no—
644C23—942no—
645C23—946no—
646C23—946no—
647C23—946no—
648C23C24×D4716yes—
649C23C24×D4711yescharacteristic
650Q8—9424no—
651Q8—9424no—
652Q8C2×#10625350116yescomplemented
653D4—224no—
654D4—9424no—
655D4—9424no—
656D4—9424no—
657D4—9424no—
658D4—18824no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—474no—
667C2×C4—472no—
668C2×C4—4716no—
669C2×C4—472no—
670C2×C4—472no—
671C2×C4—476no—
672C2×C4—476no—
673C2×C4—476no—
674C2×C4—946no—
675C2×C4—942no—
676C2×C4—946no—
677C2×C4—942no—
678C2×C4—946no—
679C2×C4—9424no—
680C2×C4—9424no—
681C2×C4—9424no—
682C2×C4—18812no—
683C2×C4—18812no—
684C2×C4#41×D4714yes—
685C2×C4C2×#10625350112yes—
686C2×C4C24×D4716yes—
687C2×C4C24×D4712yes—
688C2×C4C24×D4712yes—
689C2×C4C24×D4716yes—
690C2×C4C24×D4712yes—
691C2×C4C24×D4716yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—474no—
697C22—942no—
698C22—942no—
699C22—948no—
700C22—946no—
701C22—946no—
702C22—946no—
703C22—18812no—
704C22C2×#41×D4712yes—
705C22C22×#1062535012yes—
706C22#1568995912yes—
707C22C25×D4711yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—474no—
713C4—946no—
714C4—942no—
715C4—946no—
716C4—942no—
717C4—946no—
718C4C2×#41×D4714yes—
719C4C22×#10625350112yes—
720C2—46no—
721C2—944no—
722C2—1886no—
723C2#2025698614yesdirect product factor
724C2C22×#41×D4711yescharacteristic
725C2C23×#1062535011yescharacteristic
726C2C2×#1568995911yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C4×#41×C47C2
socleC23×C47C25
hypercenterC2×C4×#41D47
hypocenterC47C2×#3480
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20256986C2direct (N × H)
2. C2×#15689856C2semidirect
3. C2×#15689849C2semidirect
4. C2×#15689841C2semidirect
5. C2×#15689823C2semidirect
6. C2×#15689817C2semidirect
7. C2×#15689792C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689780C2semidirect
10. C2×#15689670C2semidirect
11. C2×#15689657C2semidirect
12. C2×#15689655C2semidirect
13. C2×C4×#10625354C2semidirect
14. C2×C4×#10625350C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C2×C4×#41×C47C2semidirect
20. #15689856C22semidirect
21. #15689849C22semidirect
22. #15689841C22semidirect
23. #15689823C22semidirect
24. #15689817C22semidirect
25. #15689792C22semidirect
26. #15689785C22semidirect
27. #15689780C22semidirect
28. #15689670C22semidirect
31. #15689657C22semidirect
32. #15689655C22semidirect
49. C4×#10625354C22semidirect
50. C4×#10625350C22semidirect
57. C4×Q8×D47C22semidirect
75. C4×#41×C47C22semidirect
190. C2×Q8×C47#41semidirect
230. C2×C4×D47#41semidirect
286. Q8×C47C2×#41semidirect
325. C4×D47C2×#41semidirect
371. C2×C4×#41D47semidirect
374. C2×C47#3480semidirect
415. C4×#41C2×D47semidirect
445. C47C2×#3480semidirect
561. C2×Q8#10625350semidirect
652. Q8C2×#10625350semidirect
723. C2#20256986direct (N × H)

Maximal subgroups

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

subgroupindex
#202569862
C2×#156898562
C2×#156898492
C2×#156898412
C2×#156898232
C2×#156898172
C2×#156897922
C2×#156897852
C2×#156897802
C2×#156896702
C2×#156896572
C2×#156896552
C2×C4×#106253542
C2×C4×#106253502
C2×C4×Q8×D472
C2×C4×#41×C472
C2×#348047