Finite Group Databasebeta

← C2×#20255763 #27094721

Subgroups — C2×#20255763 #27094721

Order 12032.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689821C211yesmaximal, characteristic
2C2×#15689808C211yesmaximal, characteristic, complemented
3#20255763C2116yesmaximal, direct product factor
4C2×#15689523C211yesmaximal, characteristic, complemented
5C2×#15689458C211yesmaximal, characteristic, complemented
6C2×#15689467C211yesmaximal, characteristic, complemented
7C2×#15689449C211yesmaximal, characteristic, complemented
8C2×#15689436C211yesmaximal, characteristic, complemented
9C2×#15689433C211yesmaximal, characteristic, complemented
10C2×#15689422C211yesmaximal, characteristic, complemented
11C2×#15689353C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C2×#15689158C211yesmaximal, characteristic, complemented
16C22×#106×C47C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689821—24no—
20#15689821C2218yes—
21#15689808—24no—
22#15689808C2218yescomplemented
23C2×#13094019—21no—
24C2×#13094019—21no—
25C2×#13094015C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094009—21no—
29C2×#13094007—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094003C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093998—21no—
34C2×#13093998C2211yescharacteristic
35C2×#13093989C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093983—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42#15689523C2218yescomplemented
43#15689467C2218yescomplemented
44#15689458C2218yescomplemented
45#15689449C2218yescomplemented
46#15689436C2218yescomplemented
47#15689433C2218yescomplemented
48#15689422C2218yescomplemented
49#15689353C2218yescomplemented
50#15689352C2218yescomplemented
51#15689210C2218yescomplemented
52C8×C22⋊D47C2218yescomplemented
53#15689158C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×C8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#106×C47C2218yescomplemented
77C22×Dic94C2311yescharacteristic
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47D411yescharacteristic
82C22×C4×D47—21no—
83C22×C4×D47C2311yescharacteristic
84C2×#10625325—24no—
85C2×#10625325C2314yes—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C2×C8×D47—24no—
89C2×C8×D47C2314yes—
90#13094019—28no—
91#13094019—28no—
92#13094015—22no—
93#13094015—22no—
94#13094015C2314yes—
95#13094015C2314yes—
96#13094014—28no—
97#13094009—28no—
98#13094007—28no—
99#13094004—22no—
100#13094004C2314yes—
101#13094003—22no—
102#13094003C2314yes—
103#13093999—22no—
104#13093999C2314yes—
105#13093998—22no—
106#13093998—28no—
107#13093998C2314yes—
108#13093989—22no—
109#13093989C2314yes—
110#13093986—22no—
111#13093986C2314yes—
112C4×C22⋊D47—28no—
113C4×C22⋊D47D414yes—
114C4×C22⋊D47C2314yes—
115#13093983—28no—
116#13093982—22no—
117#13093982—22no—
118#13093982C2314yes—
119#13093982C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4D411yescharacteristic
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47D411yescharacteristic
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4D411yescharacteristic
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47C2311yescharacteristic
143#13093957C2314yes—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148Dic47⋊C8C2314yes—
149#13093949C2314yes—
150#13093947C2314yes—
151#13093947C2314yes—
152#13093946C2314yes—
153#13093944C2314yes—
154#13093944C2314yes—
155C22⋊(C47⋊C8)C2314yes—
156(C2×D47)⋊C8C2314yes—
157C8×Dic47C2314yes—
158C23×C4×C47—21no—
159C23×C4×C47—21no—
160C23×C4×C47C2311yescharacteristic
161C22×C8×C47—24no—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2314yes—
164C22×C8×C47C2311yescharacteristic
165C2×C4⋊C4×C47—22no—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2314yes—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175#106×C47C2314yes—
176#106×C47C2314yes—
177#106×C47C2314yes—
178#106×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47—21no—
181C23×D47C2×D411yescharacteristic
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—24no—
189C22×C4×C47—24no—
190C22×C4×C47—44no—
191C22×C4×C47—82no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—44no—
199C2×C22⋊D47C2×D414yes—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—21no—
209C2×D188—24no—
210C2×D188—82no—
211C2×D188C2412yes—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—24no—
215C2×C4×D47—82no—
216C2×C4×D47C2×D412yes—
217C2×C4×D47C2412yes—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—21no—
221C2×Dic94C2412yes—
222C2×C8×C47—22no—
223C2×C8×C47—28no—
224C2×C8×C47#4114yes—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊Dic47—24no—
238C22⋊Dic47C2×D414yes—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4C2×D414yes—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4C2×D414yes—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D412yes—
262C4×Dic47C2412yes—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267#10625325—28no—
268C8×D47—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47#13514yes—
272C23×C47C22×D412yes—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47C22×D412yes—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—48no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—84no—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D411yescharacteristic
298C2×C4×C47C2×#4112yes—
299C2×C4×C472−1+412yes—
300C2×C4×C47C2511yescharacteristic
301C22⋊D47—28no—
302C22⋊D47—48no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315D188—22no—
316D188—22no—
317D188—42no—
318D188—84no—
319C4×D47—24no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—84no—
323Dic94—22no—
324Dic94—22no—
325Dic94—42no—
326C8×C47—22no—
327C8×C47C2×#4114yes—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3337—471nomaximal, Sylow
331C22×C47—28no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47#54712yes—
335C22×C47C2×#13514yes—
336C22×C47C2×#13512yes—
337C22×C47#57712yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—44no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—84no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47#54712yes—
353C4×C47C22×#4111yescharacteristic
354C4×C47C2×2−1+411yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#553—471no—
362C2×#552—471no—
363#3337—4716no—
364C2×#499—471no—
365C2×#484—471no—
366C2×#485—471no—
367C2×#482—471no—
368C2×#480—471no—
369C2×#479—471no—
370C2×#478—471no—
371C2×#465—471no—
372C2×#465—471no—
373C2×C4×SD16—471no—
374C2×C8×D4—471no—
375C2×#427—471no—
376C22×#106D4711yescharacteristic, complemented
377C2×C47—24no—
378C2×C47#333714yescomplemented
379C2×C47C2×#54711yescharacteristic
380C2×C47C22×#13511yescharacteristic
381C2×C47C2×#57711yescharacteristic
382D47—42no—
383D47—82no—
384C22×SD16—471no—
385C23×C8—471no—
386C23×C8C2×D4711yescharacteristic
387#553—478no—
388#553—944no—
389#552—478no—
390#552—944no—
391C2×#126—941no—
392C2×#126—941no—
393C2×#125—471no—
394C2×#125—471no—
395C2×#125—941no—
396C2×#123—941no—
397C2×#123—941no—
398C2×C22⋊Q8—471no—
399C2×C22⋊Q8—471no—
400C2×#121—471no—
401C2×#121—471no—
402C2×#121—941no—
403C2×C4×Q8—471no—
404C2×C4×D4—471no—
405C2×C4×D4—471no—
406C2×C4×D4—941no—
407C2×#117—471no—
408C2×#117—471no—
409C2×#117—941no—
410C22×C4⋊C4C2×D4711yescharacteristic
411C22×C4⋊C4C2×D4711yescharacteristic
412#499—478no—
413#485—478no—
414#484—478no—
415#482—478no—
416#480—478no—
417#479—478no—
418#478—478no—
419#465—478no—
420#465—478no—
421C4×SD16—478no—
422C8×D4—478no—
423#427—478no—
424C2×#107—471no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#106—471no—
429C2×#106C2×D4711yescharacteristic
430C2×#106C2×D4711yescharacteristic
431C2×#106C2×D4711yescharacteristic
432C2×#106C2×D4711yescharacteristic
433C2×#106C2×D4718yescomplemented
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#102—471no—
439C2×#102—471no—
440C2×#102—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C4×C8—471no—
444C47C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—471no—
446C22×D4—471no—
447C22×D4—471no—
448C22×D4—941no—
449C22×D4—941no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—471no—
453C23×C4—941no—
454C23×C4C22×D4711yescharacteristic
455C2×SD16—474no—
456C2×SD16—944no—
457C22×C8—24no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—474no—
461C22×C8—944no—
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4714yes—
464C22×C8C22×D4711yescharacteristic
465#126—948no—
466#126—948no—
467#125—474no—
468#125—474no—
469#125—942no—
470#125—942no—
471#125—948no—
472#123—948no—
473#123—948no—
474C22⋊Q8—474no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C22⋊Q8—942no—
478#121—474no—
479#121—474no—
480#121—942no—
481#121—948no—
482#121—942no—
483C4×Q8—474no—
484C4×Q8—942no—
485C4×D4—474no—
486C4×D4—474no—
487C4×D4—474no—
488C4×D4—942no—
489C4×D4—948no—
490#117—474no—
491#117—474no—
492#117—948no—
493#117—942no—
494#117—942no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4C22×D4711yescharacteristic
510C2×C4⋊C4C22×D4711yescharacteristic
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C4⋊C4C22×D4714yes—
514C2×C4⋊C4C22×D4714yes—
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C42—471no—
525C2×C42—941no—
526C2×C42—941no—
527C2×C42—941no—
528#107—474no—
529#107—474no—
530#107—474no—
531#107—474no—
532#106—474no—
533#106C22×D4714yes—
534#106C22×D4714yes—
535#106C22×D4714yes—
536#106C22×D4714yes—
537C4⋊C8—474no—
538#103—474no—
539#103—474no—
540#103—474no—
541#102—474no—
542#102—474no—
543#102—474no—
544C22⋊C8—474no—
545C22⋊C8—474no—
546C4×C8—474no—
547C24—471no—
548C24—941no—
549C24D4×D4711yescharacteristic
550C2×Q8—472no—
551C2×Q8—941no—
552C2×Q8—942no—
553C2×Q8—942no—
554C2×D4—474no—
555C2×D4—472no—
556C2×D4—944no—
557C2×D4—944no—
558C2×D4—944no—
559C2×D4—941no—
560C2×D4—942no—
561C2×D4—942no—
562C2×D4—3762no—
563C2×D4—1884no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—82no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—944no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—3762no—
586C22×C4D4×D4712yes—
587C22×C4D4×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590SD16—948no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—472no—
594C2×C8—472no—
595C2×C8—942no—
596C2×C8—942no—
597C2×C8—948no—
598C2×C8#1062535014yes—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—474no—
608C4⋊C4—472no—
609C4⋊C4—472no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4C23×D4712yes—
620C4⋊C4C23×D4712yes—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C22⋊C4—474no—
624C22⋊C4—474no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C42—472no—
633C42—472no—
634C42—944no—
635C42—944no—
636C42—944no—
637C23—22no—
638C23—22no—
639C23—472no—
640C23—942no—
641C23—942no—
642C23—942no—
643C23—942no—
644C23—1882no—
645C23—1882no—
646C23—1882no—
647C23#1309404514yes—
648C23C2×D4×D4712yes—
649C23C2×D4×D4711yescharacteristic
650Q8—942no—
651Q8—942no—
652Q8—1882no—
653D4—948no—
654D4—942no—
655D4—942no—
656D4—3764no—
657D4—1888no—
658D4—1882no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—944no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—3764no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4C2×D4×D4712yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C2×#1062535012yes—
692C2×C4#1309407212yes—
693C2×C4C24×D4711yescharacteristic
694C8—22no—
695C8—942no—
696C8—942no—
697C8C2×#1062535014yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—942no—
702C22—942no—
703C22—942no—
704C22—3764no—
705C22—1882no—
706C22—1882no—
707C22—1882no—
708C22—1884no—
709C22#1568977412yes—
710C22C2×#1309404514yes—
711C22C2×#1309404512yes—
712C22#1568992912yes—
713C22C22×D4×D4711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—942no—
720C4—942no—
721C4—942no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977412yes—
726C4C22×#1062535011yescharacteristic
727C4C2×#1309407211yescharacteristic
728C2—24no—
729C2—3762no—
730C2—1882no—
731C2#2025576314yesdirect product factor
732C2C2×#1568977411yescharacteristic
733C2C22×#1309404511yescharacteristic
734C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#106×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689821C2
hypercenterC22×#106D47
hypocenterC47C2×#3337
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#15689808C2semidirect
3. #20255763C2direct (N × H)
4. C2×#15689523C2semidirect
5. C2×#15689458C2semidirect
6. C2×#15689467C2semidirect
7. C2×#15689449C2semidirect
8. C2×#15689436C2semidirect
9. C2×#15689433C2semidirect
10. C2×#15689422C2semidirect
11. C2×#15689353C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689210C2semidirect
14. C2×C8×C22⋊D47C2semidirect
15. C2×#15689158C2semidirect
16. C22×#106×C47C2semidirect
22. #15689808C22semidirect
42. #15689523C22semidirect
43. #15689467C22semidirect
44. #15689458C22semidirect
45. #15689449C22semidirect
46. #15689436C22semidirect
47. #15689433C22semidirect
48. #15689422C22semidirect
49. #15689353C22semidirect
50. #15689352C22semidirect
51. #15689210C22semidirect
52. C8×C22⋊D47C22semidirect
53. #15689158C22semidirect
76. C2×#106×C47C22semidirect
376. C22×#106D47semidirect
378. C2×C47#3337semidirect
433. C2×#106C2×D47semidirect
444. C47C2×#3337semidirect
731. C2#20255763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898212
C2×#156898082
#202557632
C2×#156895232
C2×#156894582
C2×#156894672
C2×#156894492
C2×#156894362
C2×#156894332
C2×#156894222
C2×#156893532
C2×#156893522
C2×#156892102
C2×C8×C22⋊D472
C2×#156891582
C22×#106×C472
C2×#333747