Finite Group Databasebeta

← C2×#20254844 #27089238

Subgroups — C2×#20254844 #27089238

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2#20254844C2116yesmaximal, direct product factor
3C2×#15689418C211yesmaximal, characteristic, complemented
4C2×#15689415C211yesmaximal, characteristic, complemented
5C2×#15689403C211yesmaximal, characteristic, complemented
6C2×#15689400C211yesmaximal, characteristic, complemented
7C2×#15689371C211yesmaximal, characteristic, complemented
8C2×#15689367C211yesmaximal, characteristic, complemented
9C2×#15689362C211yesmaximal, characteristic, complemented
10C2×#15689357C211yesmaximal, characteristic
11C2×#15689345C211yesmaximal, characteristic, complemented
12C2×#15689342C211yesmaximal, characteristic, complemented
13C2×#15689338C211yesmaximal, characteristic, complemented
14C2×#15689335C211yesmaximal, characteristic, complemented
15C2×#15689150C211yesmaximal, characteristic, complemented
16C2×C47×#542C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625329C2211yescharacteristic
22C23×C47⋊C8C2211yescharacteristic
23#15689744—24no—
24#15689744C2218yescomplemented
25C2×#13094024C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094012C2211yescharacteristic
28C2×#13094010—21no—
29C2×#13094006—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094002—21no—
32C2×#13093998C2211yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×C4×D188C2211yescharacteristic
35#15689418C2218yescomplemented
36#15689415C2218yescomplemented
37#15689403C2218yescomplemented
38#15689400C2218yescomplemented
39#15689371C2218yescomplemented
40#15689367C2218yescomplemented
41#15689362C2218yescomplemented
42#15689357C2218yes—
43#15689345C2218yescomplemented
44#15689342C2218yescomplemented
45#15689338C2218yescomplemented
46#15689335C2218yescomplemented
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093957C2211yescharacteristic
50C2×#13093957C2211yescharacteristic
51#15689150C2218yescomplemented
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×C4⋊(C47⋊C8)C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C47×#542—24no—
65C47×#542C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic
67C2×#126×C47—21no—
68C2×#124×C47—21no—
69C2×#124×C47C2211yescharacteristic
70C2×#123×C47—21no—
71C2×C22⋊Q8×C47—21no—
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×#121×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C2×#117×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625337—42no—
83C2×#10625337C2314yes—
84C2×#10625335—42no—
85C2×#10625335C2314yes—
86C2×#10625336—42no—
87C2×#10625336C2314yes—
88C2×#10625334—42no—
89C2×#10625334C2314yes—
90C2×#10625329—42no—
91C2×#10625329C2314yes—
92C22×C47⋊C8—42no—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2314yes—
98#13094024—22no—
99#13094024C2314yes—
100#13094019—28no—
101#13094012—22no—
102#13094012C2314yes—
103#13094010—28no—
104#13094006—28no—
105#13094003—22no—
106#13094003C2314yes—
107#13094002—28no—
108#13093998—22no—
109#13093998C2314yes—
110C4×Dic94—22no—
111C4×Dic94C2314yes—
112C4×D188—22no—
113C4×D188C2314yes—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47C2311yescharacteristic
116C2×C4⋊Dic47C2311yescharacteristic
117C2×Dic47⋊C4—21no—
118C2×Dic47⋊C4—21no—
119C2×C22⋊Dic47—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×(C2×D47)⋊C4—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×C4×Dic47—21no—
125#13093957C2314yes—
126#13093957C2314yes—
127#13093957C2314yes—
128#13093957C2314yes—
129C4⋊(C47⋊C8)C2314yes—
130C4⋊(C47⋊C8)C2314yes—
131C4⋊(C47⋊C8)C2314yes—
132C4⋊(C47⋊C8)C2314yes—
133#13093948C2314yes—
134#13093948C2314yes—
135#13093947C2314yes—
136#13093947C2314yes—
137#13093945C2314yes—
138#13093945C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22×Q8×C47—21no—
142C22×Q8×C47C2311yescharacteristic
143C22×D4×C47—21no—
144C22×D4×C47C2311yescharacteristic
145C23×C4×C47—21no—
146C23×C4×C47C2311yescharacteristic
147C4⋊Q8×C47—22no—
148C4⋊Q8×C47C2314yes—
149#126×C47—28no—
150#124×C47—28no—
151#124×C47—22no—
152#124×C47C2314yes—
153#123×C47—28no—
154C22⋊Q8×C47—22no—
155C22⋊Q8×C47—28no—
156C22⋊Q8×C47C2314yes—
157#121×C47—22no—
158#121×C47C2314yes—
159C4×Q8×C47—22no—
160C4×Q8×C47C2314yes—
161C4×D4×C47—22no—
162C4×D4×C47C2314yes—
163#117×C47D414yes—
164#117×C47C2314yes—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2311yescharacteristic
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—24no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—82no—
190C2×Q8×C47C2412yes—
191C2×D4×C47—24no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—82no—
196C2×D4×C47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—24no—
203C22×C4×C47—82no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47—82no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188—21no—
220C2×D188C2412yes—
221C2×C4×D47—24no—
222C2×C4×D47—82no—
223C2×Dic94—22no—
224C2×Dic94—22no—
225C2×Dic94—21no—
226C2×Dic94—24no—
227C2×Dic94—82no—
228C2×Dic94C2412yes—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2×D414yes—
235C4⋊C4×C47C2×D414yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—24no—
243C22⋊C4×C47C2×D414yes—
244C22⋊C4×C47C2×D414yes—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2×D412yes—
248C42×C47C2412yes—
249C42×C47C2412yes—
250C22⋊Dic47—24no—
251#10625337—44no—
252#10625336—44no—
253#10625335—44no—
254#10625334—44no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266C4×Dic47—24no—
267#10625329—44no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—44no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D412yes—
285C23×C47C22×D411yescharacteristic
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293Q8×C47—84no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—42no—
297D4×C47—84no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—84no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47H(5,𝔽2)12yes—
320C2×C4×C472−1+412yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—84no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329D188—22no—
330D188—22no—
331D188—42no—
332C4×D47—84no—
333Dic94—22no—
334Dic94—22no—
335Dic94—42no—
336Dic94—84no—
337C47⋊C8—22no—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C2×#3262—471nomaximal, Sylow
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—84no—
350C22×C47#53712yes—
351C22×C47#57612yes—
352C22×C47#57812yes—
353C22×C47C23×D411yescharacteristic
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—84no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47#53712yes—
367C4×C47C2×H(5,𝔽2)11yescharacteristic
368C4×C47C2×2−1+411yescharacteristic
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#542—471no—
373C2×#542D4711yescharacteristic, complemented
374#3262—4716no—
375C2×#477—471no—
376C2×#477—471no—
377C2×#474—471no—
378C2×#474—471no—
379C2×#468—471no—
380C2×#468—471no—
381C2×#467—471no—
382C2×#466—471no—
383C2×#464—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#463—471no—
387C2×#424—471no—
388C2×C47—42no—
389C2×C47—82no—
390C2×C47#326214yescomplemented
391C2×C47C2×#53711yescharacteristic
392C2×C47C2×#57611yescharacteristic
393C2×C47C2×#57811yescharacteristic
394D47—82no—
395C22×Q16—471no—
396C22×SD16—471no—
397C22×SD16—471no—
398C22×D8—471no—
399C22×M16—471no—
400C23×C8—471no—
401#542—24no—
402#542—478no—
403#542—944no—
404#542C2×D4718yescomplemented
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8C2×D4711yescharacteristic
407C2×#126—21no—
408C2×#126—941no—
409C2×#124—21no—
410C2×#124—471no—
411C2×#124—941no—
412C2×#124C2×D4711yescharacteristic
413C2×#123—21no—
414C2×#123—941no—
415C2×C22⋊Q8—21no—
416C2×C22⋊Q8—471no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8C2×D4711yescharacteristic
419C2×#121—471no—
420C2×#121C2×D4711yescharacteristic
421C2×C4×Q8—471no—
422C2×C4×Q8C2×D4711yescharacteristic
423C2×C4×D4—471no—
424C2×C4×D4C2×D4711yescharacteristic
425C2×#117C2×D4711yescharacteristic
426#477—478no—
427#477—478no—
428#474—478no—
429#474—478no—
430#468—478no—
431#468—478no—
432#467—478no—
433#466—478no—
434#464—478no—
435#464—478no—
436#463—478no—
437#463—478no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#107—471no—
441C2×#107—471no—
442#424—478no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×C4⋊C8—471no—
446C2×C4⋊C8—471no—
447C2×#103—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C47C2×#326211yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—471no—
458C22×Q8—941no—
459C22×Q8C22×D4711yescharacteristic
460C22×D4—21no—
461C22×D4—471no—
462C22×D4—941no—
463C22×D4C22×D4711yescharacteristic
464C23×C4—21no—
465C23×C4—941no—
466C23×C4C22×D4711yescharacteristic
467C2×Q16—474no—
468C2×Q16—1882no—
469C2×SD16—474no—
470C2×SD16—474no—
471C2×SD16—1882no—
472C2×SD16—1882no—
473C2×D8—474no—
474C2×D8—1882no—
475C2×M16—474no—
476C2×M16—1882no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—471no—
480C22×C8—471no—
481C22×C8—474no—
482C22×C8—1882no—
483C4⋊Q8—22no—
484C4⋊Q8—474no—
485C4⋊Q8—942no—
486C4⋊Q8C22×D4714yes—
487#126—28no—
488#126—948no—
489#124—28no—
490#124—22no—
491#124—474no—
492#124—948no—
493#124—942no—
494#124C22×D4714yes—
495#123—28no—
496#123—948no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—474no—
500C22⋊Q8—942no—
501C22⋊Q8—948no—
502C22⋊Q8C22×D4714yes—
503#121—22no—
504#121—474no—
505#121—942no—
506#121C22×D4714yes—
507C4×Q8—22no—
508C4×Q8—474no—
509C4×Q8—942no—
510C4×Q8C22×D4714yes—
511C4×D4—22no—
512C4×D4—474no—
513C4×D4—942no—
514C4×D4C22×D4714yes—
515#117C22⋊D4714yes—
516#117C22×D4714yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4C22⋊D4711yescharacteristic
526C2×C4⋊C4C22⋊D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4C22⋊D4711yescharacteristic
540C2×C22⋊C4C22⋊D4711yescharacteristic
541C2×C42—21no—
542C2×C42—941no—
543C2×C42C22×D4711yescharacteristic
544C2×C42C22×D4711yescharacteristic
545#107—474no—
546#107—474no—
547#107—474no—
548#107—474no—
549C4⋊C8—474no—
550C4⋊C8—474no—
551C4⋊C8—474no—
552C4⋊C8—474no—
553#103—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#102—474no—
558#102—474no—
559#102—474no—
560#102—474no—
561C24—21no—
562C24—941no—
563C24C2×C22⋊D4711yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—472no—
570C2×Q8—944no—
571C2×Q8—941no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—3762no—
575C2×Q8C23×D4712yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—472no—
582C2×D4—944no—
583C2×D4—941no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—3762no—
587C2×D4C23×D4712yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—944no—
599C22×C4—3762no—
600C22×C4C2×C22⋊D4712yes—
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C2×C22⋊D4711yescharacteristic
603C22×C4C2×C22⋊D4711yescharacteristic
604C22×C4C2×C22⋊D4711yescharacteristic
605C22×C4C2×C22⋊D4711yescharacteristic
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608Q16—1884no—
609SD16—1884no—
610SD16—1884no—
611D8—1884no—
612M16—1884no—
613C2×C8—472no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—472no—
617C2×C8—942no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8—942no—
621C2×C8—1884no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—472no—
628C4⋊C4—472no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—941no—
632C4⋊C4—941no—
633C4⋊C4—944no—
634C4⋊C4C2×C22⋊D4714yes—
635C4⋊C4C2×C22⋊D4714yes—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4C2×C22⋊D4714yes—
649C22⋊C4C2×C22⋊D4714yes—
650C42—24no—
651C42—944no—
652C42C2×C22⋊D4712yes—
653C42C2×C22⋊D4712yes—
654C42C23×D4712yes—
655C42C23×D4712yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—942no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23C22×C22⋊D4712yes—
668C23C22×C22⋊D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—942no—
674Q8—942no—
675Q8—3764no—
676Q8—1882no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—942no—
682D4—942no—
683D4—3764no—
684D4—1882no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—3764no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4C22×C22⋊D4712yes—
708C2×C4C22×C22⋊D4712yes—
709C2×C4C22×C22⋊D4712yes—
710C2×C4C22×C22⋊D4712yes—
711C2×C4C22×C22⋊D4712yes—
712C2×C4C22×C22⋊D4711yescharacteristic
713C2×C4#1309407012yes—
714C2×C4#1309407112yes—
715C2×C4C24×D4711yescharacteristic
716C8—942no—
717C8—942no—
718C8—942no—
719C8—942no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3764no—
729C22—1882no—
730C22—1882no—
731C22—1882no—
732C22#1568970112yes—
733C22#1568992612yes—
734C22#1568993812yes—
735C22C23×C22⋊D4711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4#1568970112yes—
748C4C2×#1309407011yescharacteristic
749C4C2×#1309407111yescharacteristic
750C2—42no—
751C2—82no—
752C2—3762no—
753C2#2025484414yesdirect product factor
754C2C2×#1568970111yescharacteristic
755C2C2×#1568992611yescharacteristic
756C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
prime radicalC2×#15689357C2
hypercenterC2×#542D47
hypocenterC47C2×#3262
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. #20254844C2direct (N × H)
3. C2×#15689418C2semidirect
4. C2×#15689415C2semidirect
5. C2×#15689403C2semidirect
6. C2×#15689400C2semidirect
7. C2×#15689371C2semidirect
8. C2×#15689367C2semidirect
9. C2×#15689362C2semidirect
11. C2×#15689345C2semidirect
12. C2×#15689342C2semidirect
13. C2×#15689338C2semidirect
14. C2×#15689335C2semidirect
15. C2×#15689150C2semidirect
16. C2×C47×#542C2semidirect
24. #15689744C22semidirect
35. #15689418C22semidirect
36. #15689415C22semidirect
37. #15689403C22semidirect
38. #15689400C22semidirect
39. #15689371C22semidirect
40. #15689367C22semidirect
41. #15689362C22semidirect
43. #15689345C22semidirect
44. #15689342C22semidirect
45. #15689338C22semidirect
46. #15689335C22semidirect
51. #15689150C22semidirect
65. C47×#542C22semidirect
373. C2×#542D47semidirect
390. C2×C47#3262semidirect
404. #542C2×D47semidirect
455. C47C2×#3262semidirect
753. C2#20254844direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
#202548442
C2×#156894182
C2×#156894152
C2×#156894032
C2×#156894002
C2×#156893712
C2×#156893672
C2×#156893622
C2×#156893572
C2×#156893452
C2×#156893422
C2×#156893382
C2×#156893352
C2×#156891502
C2×C47×#5422
C2×#326247