Finite Group Databasebeta

← C2×#20255677 #27093170

Subgroups — C2×#20255677 #27093170

Order 12032.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689837C211yesmaximal, characteristic
2C2×#15689786C211yesmaximal, characteristic, complemented
3#20255677C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689466C211yesmaximal, characteristic, complemented
6C2×#15689461C211yesmaximal, characteristic, complemented
7C2×#15689417C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689326C211yesmaximal, characteristic, complemented
10C2×#15689261C211yesmaximal, characteristic, complemented
11C2×#15689260C211yesmaximal, characteristic, complemented
12C2×#15689214C211yesmaximal, characteristic, complemented
13C2×#15689199C211yesmaximal, characteristic, complemented
14C2×#15689133C211yesmaximal, characteristic, complemented
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689837—24no—
23#15689837C2218yes—
24#15689786—24no—
25#15689786C2218yescomplemented
26C2×#13094023—21no—
27C2×#13094023C2211yescharacteristic
28C2×#13094022C2211yescharacteristic
29C2×#13094011—21no—
30C2×#13094010—21no—
31C2×#13094004C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13094001—21no—
34C2×#13093996—21no—
35C2×#13093995C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093983C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093980—21no—
43#15689472C2218yescomplemented
44#15689466C2218yescomplemented
45#15689461C2218yescomplemented
46#15689417C2218yescomplemented
47#15689368C2218yescomplemented
48#15689326C2218yescomplemented
49#15689261C2218yescomplemented
50#15689260C2218yescomplemented
51#15689214C2218yescomplemented
52#15689199C2218yescomplemented
53C2×#13093957C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56#15689133C2218yescomplemented
57#15689130C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—24no—
78C22×Dic94—22no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94—21no—
82C22×Dic94—42no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2314yes—
85C22×Dic94C2311yescharacteristic
86C2×Q8×D47—22no—
87C2×Q8×D47—24no—
88C2×Q8×D47—42no—
89C2×Q8×D47C2314yes—
90C22×C22⋊D47—21no—
91C22×C22⋊D47D411yescharacteristic
92C23×Dic47—21no—
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96C2×#10625335—24no—
97C2×#10625335—42no—
98C2×#10625335C2314yes—
99C2×#10625335C2314yes—
100C2×#10625324—42no—
101C2×#10625324C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104#13094023—28no—
105#13094023—22no—
106#13094023C2314yes—
107#13094022—22no—
108#13094022C2314yes—
109#13094011—28no—
110#13094010—28no—
111#13094004—22no—
112#13094004C2314yes—
113#13094002—28no—
114#13094001—28no—
115#13093996—28no—
116#13093995—22no—
117#13093995C2314yes—
118#13093989—22no—
119#13093989C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124(C22⋊D47)⋊C4—28no—
125#13093983—22no—
126#13093983C2314yes—
127#13093982—22no—
128#13093982C2314yes—
129#13093980—28no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162C8×Dic47C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47—21no—
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×SD16×C47—42no—
168C2×SD16×C47C2314yes—
169C2×M16×C47—42no—
170C2×M16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175#121×C47—22no—
176#121×C47C2314yes—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#107×C47C2314yes—
183#103×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47C2412yes—
192C2×D4×C47—24no—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—82no—
197C2×D4×C47C2412yes—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—82no—
210C2×C22⋊D47C2×D414yes—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—24no—
216C22×Dic47—24no—
217C22×Dic47—44no—
218C22×Dic47—44no—
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222Q8×D47—28no—
223Q8×D47—44no—
224Q8×D47—48no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—24no—
228C2×C4×D47—44no—
229C2×C4×D47C2×D412yes—
230C2×C4×D47C2412yes—
231C2×Dic94—21no—
232C2×Dic94—22no—
233C2×Dic94—22no—
234C2×Dic94—22no—
235C2×Dic94—28no—
236C2×Dic94—24no—
237C2×Dic94—21no—
238C2×Dic94—24no—
239C2×Dic94—24no—
240C2×Dic94—44no—
241C2×Dic94—48no—
242C2×Dic94—44no—
243C2×Dic94—44no—
244C2×Dic94—82no—
245C2×Dic94#4114yes—
246C2×Dic94C2412yes—
247C2×Dic94C2412yes—
248SD16×C47—44no—
249M16×C47—44no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47C2412yes—
258C4⋊C4×C47C2412yes—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C22⋊Dic47—24no—
262C22⋊Dic47—24no—
263C22⋊Dic47—24no—
264C22⋊Dic47C2×D414yes—
265#10625335—28no—
266#10625335—44no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4C2×D414yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4C2×D414yes—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625324—44no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—42no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C22×D412yes—
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47C22×D412yes—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—42no—
309D4×C47—84no—
310C2×C4×C47—22no—
311C2×C4×C47—24no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47C22×D412yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C2×#4112yes—
323C2×C4×C47H(5,𝔽2)12yes—
324C2×C4×C47C2511yescharacteristic
325C22⋊D47—28no—
326C22⋊D47—84no—
327C2×Dic47—24no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—48no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—48no—
339C2×Dic47#13714yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342C2×Dic47C22×D412yes—
343C4×D47—24no—
344C4×D47—22no—
345C4×D47—22no—
346C4×D47—48no—
347Dic94—24no—
348Dic94—22no—
349Dic94—22no—
350Dic94—22no—
351Dic94—48no—
352Dic94—48no—
353Dic94—42no—
354Dic94—84no—
355Dic94C2×#4114yes—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3329—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—44no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—84no—
369C22×C47#54612yes—
370C22×C47C2×#13712yes—
371C22×C47#57712yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—44no—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47#54612yes—
382C4×C47C22×#4111yescharacteristic
383C4×C47C2×H(5,𝔽2)11yescharacteristic
384Dic47—24no—
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47C2×#13714yes—
391C2×#555—471no—
392C2×D4×Q8—471no—
393#3329—4716no—
394C2×#487—471no—
395C2×#485—471no—
396C2×#485—471no—
397C2×#477—471no—
398C2×#468—471no—
399C2×#468D4711yescharacteristic, complemented
400C2×#461—471no—
401C2×#448—471no—
402C2×#448—471no—
403C2×C4×SD16—471no—
404C2×#436—471no—
405C2×#419—471no—
406C2×#419—471no—
407C2×C47—42no—
408C2×C47—82no—
409C2×C47#332914yescomplemented
410C2×C47C2×#54611yescharacteristic
411C2×C47C22×#13711yescharacteristic
412C2×C47C2×#57711yescharacteristic
413D47—42no—
414C23×Q8—471no—
415C23×Q8—471no—
416C22×SD16—471no—
417C22×SD16—471no—
418C22×SD16C2×D4711yescharacteristic
419C22×M16—471no—
420C22×M16C2×D4711yescharacteristic
421#555—478no—
422#555—944no—
423D4×Q8—478no—
424D4×Q8—944no—
425C2×C4⋊Q8—471no—
426C2×C4⋊Q8—471no—
427C2×C4⋊Q8—941no—
428C2×#124—941no—
429C2×#124—941no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—941no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8C2×D4711yescharacteristic
434C2×#121—471no—
435C2×#121—941no—
436C2×#121C2×D4711yescharacteristic
437C2×C4×Q8—471no—
438C2×C4×D4—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C2×#117—471no—
442C2×#117—471no—
443C2×#117—941no—
444#487—478no—
445#485—478no—
446#485—478no—
447#477—478no—
448#468—478no—
449#468C2×D4718yescomplemented
450#461—478no—
451#448—478no—
452#448—478no—
453C4×SD16—478no—
454#436—478no—
455C2×#107—471no—
456C2×#107C2×D4711yescharacteristic
457C2×#106—471no—
458C2×C4⋊C8—471no—
459#419—478no—
460#419—478no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#103—471no—
469C2×#103C2×D4711yescharacteristic
470C2×#102C2×D4711yescharacteristic
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×C4×C8—471no—
474C47C2×#332911yescharacteristic, complemented, Sylow
475C22×Q8—474no—
476C22×Q8—471no—
477C22×Q8—471no—
478C22×Q8—474no—
479C22×Q8—941no—
480C22×Q8—941no—
481C22×Q8—944no—
482C22×Q8—942no—
483C22×Q8—941no—
484C22×Q8—942no—
485C22×Q8—944no—
486C22×Q8—1882no—
487C22×Q8—1882no—
488C22×Q8C22×D4711yescharacteristic
489C22×D4—21no—
490C22×D4—471no—
491C22×D4—941no—
492C22×D4C22×D4711yescharacteristic
493C23×C4—471no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4C22×D4711yescharacteristic
498C2×SD16—42no—
499C2×SD16—474no—
500C2×SD16—474no—
501C2×SD16—944no—
502C2×SD16—1882no—
503C2×SD16C22×D4714yes—
504C2×M16—42no—
505C2×M16—474no—
506C2×M16—1882no—
507C2×M16C22×D4714yes—
508C22×C8—471no—
509C22×C8—471no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—474no—
514C4⋊Q8—942no—
515C4⋊Q8—942no—
516C4⋊Q8—948no—
517#124—948no—
518#124—948no—
519C22⋊Q8—22no—
520C22⋊Q8—474no—
521C22⋊Q8—948no—
522C22⋊Q8—948no—
523C22⋊Q8—942no—
524C22⋊Q8C22×D4714yes—
525#121—22no—
526#121—474no—
527#121—942no—
528#121—948no—
529#121C22×D4714yes—
530C4×Q8—474no—
531C4×Q8—942no—
532C4×D4—474no—
533C4×D4—474no—
534C4×D4—474no—
535C4×D4—942no—
536C4×D4—948no—
537#117—474no—
538#117—474no—
539#117—948no—
540#117—942no—
541#117—942no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—471no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4C22×D4711yescharacteristic
552C2×C4⋊C4C22×D4711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—471no—
556C2×C22⋊C4—471no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C42—471no—
563C2×C42—941no—
564C2×C42—941no—
565C2×C42—941no—
566#107—474no—
567#107C22×D4714yes—
568#106—474no—
569C4⋊C8—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103—474no—
576#103—474no—
577#103—474no—
578#103C22×D4714yes—
579#102C22×D4714yes—
580C22⋊C8—474no—
581C22⋊C8—474no—
582C4×C8—474no—
583C24—21no—
584C24—471no—
585C24D4×D4711yescharacteristic
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—474no—
590C2×Q8—472no—
591C2×Q8—472no—
592C2×Q8—944no—
593C2×Q8—944no—
594C2×Q8—948no—
595C2×Q8—941no—
596C2×Q8—944no—
597C2×Q8—941no—
598C2×Q8—942no—
599C2×Q8—948no—
600C2×Q8—942no—
601C2×Q8—942no—
602C2×Q8—3762no—
603C2×Q8—1884no—
604C2×Q8—1884no—
605C2×Q8—1888no—
606C2×Q8—1884no—
607C2×Q8—1884no—
608C2×Q8—1888no—
609C2×Q8C23×D4712yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—82no—
615C2×D4—474no—
616C2×D4—944no—
617C2×D4—944no—
618C2×D4—3762no—
619C2×D4C23×D4712yes—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—471no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—472no—
629C22×C4—472no—
630C22×C4—944no—
631C22×C4—944no—
632C22×C4—941no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—944no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—1884no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646SD16—44no—
647SD16—948no—
648SD16—1884no—
649M16—44no—
650M16—1884no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—472no—
654C2×C8—472no—
655C2×C8—942no—
656C2×C8—942no—
657C2×C8C23×D4712yes—
658C2×C8C23×D4712yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—474no—
663C4⋊C4—472no—
664C4⋊C4—472no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—941no—
671C4⋊C4—941no—
672C4⋊C4C23×D4712yes—
673C4⋊C4C23×D4712yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—474no—
677C22⋊C4—474no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C42—472no—
684C42—472no—
685C42—944no—
686C42—944no—
687C42—944no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—472no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—474no—
705Q8—944no—
706Q8—942no—
707Q8—942no—
708Q8—942no—
709Q8—3764no—
710Q8—1888no—
711Q8—1888no—
712Q8—1882no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—84no—
717D4—948no—
718D4—3764no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—474no—
730C2×C4—472no—
731C2×C4—472no—
732C2×C4—472no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—1888no—
744C2×C4—1888no—
745C2×C4—1888no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4#41×D4712yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—942no—
767C22—942no—
768C22—942no—
769C22—1884no—
770C22#1568976212yes—
771C22#137×D4712yes—
772C22#1568993312yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—474no—
779C4—942no—
780C4—944no—
781C4—942no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976212yes—
786C4C2×#41×D4711yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—42no—
789C2—82no—
790C2—1882no—
791C2#2025567714yesdirect product factor
792C2C2×#1568976211yescharacteristic
793C2C2×#137×D4711yescharacteristic
794C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689837C2
hypercenterC2×#468D47
hypocenterC47C2×#3329
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#15689786C2semidirect
3. #20255677C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689466C2semidirect
6. C2×#15689461C2semidirect
7. C2×#15689417C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689326C2semidirect
10. C2×#15689261C2semidirect
11. C2×#15689260C2semidirect
12. C2×#15689214C2semidirect
13. C2×#15689199C2semidirect
14. C2×#15689133C2semidirect
15. C2×#15689130C2semidirect
16. C2×C47×#468C2semidirect
25. #15689786C22semidirect
43. #15689472C22semidirect
44. #15689466C22semidirect
45. #15689461C22semidirect
46. #15689417C22semidirect
47. #15689368C22semidirect
48. #15689326C22semidirect
49. #15689261C22semidirect
50. #15689260C22semidirect
51. #15689214C22semidirect
52. #15689199C22semidirect
56. #15689133C22semidirect
57. #15689130C22semidirect
73. C47×#468C22semidirect
399. C2×#468D47semidirect
409. C2×C47#3329semidirect
449. #468C2×D47semidirect
474. C47C2×#3329semidirect
791. C2#20255677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898372
C2×#156897862
#202556772
C2×#156894722
C2×#156894662
C2×#156894612
C2×#156894172
C2×#156893682
C2×#156893262
C2×#156892612
C2×#156892602
C2×#156892142
C2×#156891992
C2×#156891332
C2×#156891302
C2×C47×#4682
C2×#332947