Finite Group Databasebeta

← C2×#20255877 #27094861

Subgroups — C2×#20255877 #27094861

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic, complemented
2C2×#15689821C211yesmaximal, characteristic
3#20255877C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic, complemented
6C2×#15689462C211yesmaximal, characteristic, complemented
7C2×#15689438C211yesmaximal, characteristic, complemented
8C2×#15689428C211yesmaximal, characteristic, complemented
9C2×#15689402C211yesmaximal, characteristic, complemented
10C2×#15689372C211yesmaximal, characteristic, complemented
11C2×#15689354C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×#15689191C211yesmaximal, characteristic, complemented
14C2×#15689164C211yesmaximal, characteristic, complemented
15C22×#13093957C211yesmaximal, characteristic, complemented
16C2×C47×#484C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20#15689831—24no—
21#15689831C2218yescomplemented
22#15689821—24no—
23#15689821C2218yes—
24C2×#13094023C2211yescharacteristic
25C2×#13094019—21no—
26C2×#13094015C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094009—21no—
29C2×#13094004—21no—
30C2×#13094001—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093998—21no—
34C2×#13093998C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689531C2218yescomplemented
44#15689462C2218yescomplemented
45#15689442C2218yescomplemented
46#15689438C2218yescomplemented
47#15689428C2218yescomplemented
48#15689402C2218yescomplemented
49#15689372C2218yescomplemented
50#15689354C2218yescomplemented
51#15689226C2218yescomplemented
52#15689191C2218yescomplemented
53#15689164C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#484C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47D411yescharacteristic
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47C2311yescharacteristic
86C2×#10625336—24no—
87C2×#10625336C2314yes—
88C2×#10625324—24no—
89C2×#10625324C2314yes—
90C22×C47⋊C8—24no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94#13094023—22no—
95#13094023C2314yes—
96#13094019—28no—
97#13094015—22no—
98#13094015C2314yes—
99#13094014—28no—
100#13094009—28no—
101#13094004—28no—
102#13094001—28no—
103#13094000—22no—
104#13094000C2314yes—
105#13093999—22no—
106#13093999C2314yes—
107#13093998—22no—
108#13093998—28no—
109#13093998C2314yes—
110Q8×Dic47—22no—
111Q8×Dic47C2314yes—
112#13093986—22no—
113#13093986C2314yes—
114C4×C22⋊D47—28no—
115C4×C22⋊D47D414yes—
116C4×C22⋊D47C2314yes—
117(C22⋊D47)⋊C4—28no—
118#13093982—22no—
119#13093982C2314yes—
120C2×C4⋊Dic47—22no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2314yes—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47D411yescharacteristic
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093957C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093948C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093944C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22⋊Q8×C47—22no—
165C22⋊Q8×C47C2314yes—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174#107×C47C2314yes—
175#107×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47—21no—
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—82no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47C2×D414yes—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—24no—
206C22×Dic47—82no—
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—21no—
213C2×D188—24no—
214C2×D188—82no—
215C2×D188C2412yes—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—82no—
221C2×C4×D47—82no—
222C2×C4×D47C2×D412yes—
223C2×C4×D47C2412yes—
224C2×Dic94—24no—
225C2×Dic94—82no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊Dic47C2×D414yes—
240#10625336—28no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4C2×D414yes—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4C2×D414yes—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47C2×D412yes—
264C4×Dic47C2412yes—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—28no—
267C2×C47⋊C8#4114yes—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270#10625324—28no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47#13714yes—
274C23×C47C22×D412yes—
275C23×C47C22×D411yescharacteristic
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47C22×D412yes—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—42no—
287C2×C4×C47—22no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—84no—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C2×#4112yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C22⋊D47—28no—
306C22⋊D47—48no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—84no—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320D188—22no—
321D188—22no—
322D188—42no—
323D188—84no—
324C4×D47—24no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—84no—
328C4×D47—84no—
329Dic94—84no—
330C8×C47—22no—
331C8×C47—22no—
332C47⋊C8—22no—
333C47⋊C8C2×#4114yes—
334C2×#3346—471nomaximal, Sylow
335C22×C47—28no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47#54712yes—
339C22×C47C2×#13714yes—
340C22×C47C2×#13712yes—
341C22×C47#57612yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—44no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—84no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47#54712yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C2×2−1+411yescharacteristic
359Dic47—22no—
360Dic47—22no—
361Dic47—22no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#554—471no—
366C2×#553—471no—
367#3346—4716no—
368C2×#501—471no—
369C2×#484D4711yescharacteristic, complemented
370C2×#481—471no—
371C2×#485—471no—
372C2×#480—471no—
373C2×#479—471no—
374C2×#474—471no—
375C2×#468—471no—
376C2×#465—471no—
377C2×#440—471no—
378C2×#435—471no—
379C2×#428—471no—
380C22×#107—471no—
381C2×C47—24no—
382C2×C47#334614yescomplemented
383C2×C47C2×#54711yescharacteristic
384C2×C47C22×#13711yescharacteristic
385C2×C47C2×#57611yescharacteristic
386D47—42no—
387D47—82no—
388C22×SD16—471no—
389C22×M16—471no—
390C23×C8—471no—
391#554—478no—
392#554—944no—
393#553—478no—
394#553—944no—
395C2×C4⋊Q8—471no—
396C2×#126—941no—
397C2×#125—471no—
398C2×#125—941no—
399C2×#123—941no—
400C2×C22⋊Q8—471no—
401C2×C22⋊Q8—941no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8C2×D4711yescharacteristic
404C2×#121—471no—
405C2×#121—471no—
406C2×#121—941no—
407C2×C4×Q8—471no—
408C2×C4×D4—471no—
409C2×C4×D4—471no—
410C2×C4×D4—941no—
411C2×C4×D4—941no—
412C2×#117—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4C2×D4711yescharacteristic
416#501—478no—
417#485—478no—
418#484C2×D4718yescomplemented
419#481—478no—
420#480—478no—
421#479—478no—
422#474—478no—
423#468—478no—
424#465—478no—
425#440—478no—
426#435—478no—
427#428—478no—
428C2×#107—471no—
429C2×#107—471no—
430C2×#107—478no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107C2×D4711yescharacteristic
434C2×#107C2×D4711yescharacteristic
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8—471no—
439C2×#103—471no—
440C2×#103C2×D4711yescharacteristic
441C2×#103C2×D4711yescharacteristic
442C2×#102—471no—
443C2×#102—471no—
444C2×#102—471no—
445C2×C22⋊C8—471no—
446C2×C22⋊C8C2×D4711yescharacteristic
447C2×#97—471no—
448C47C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—941no—
450C22×Q8C22×D4711yescharacteristic
451C22×D4—471no—
452C22×D4—471no—
453C22×D4—941no—
454C22×D4—941no—
455C23×C4—21no—
456C23×C4—471no—
457C23×C4—941no—
458C23×C4—941no—
459C23×C4—941no—
460C23×C4C22×D4711yescharacteristic
461C2×SD16—474no—
462C2×SD16—944no—
463C2×M16—474no—
464C2×M16—944no—
465C22×C8—471no—
466C22×C8—471no—
467C22×C8—474no—
468C22×C8—944no—
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C4⋊Q8—474no—
472C4⋊Q8—942no—
473#126—948no—
474#125—474no—
475#125—942no—
476#125—948no—
477#123—948no—
478C22⋊Q8—22no—
479C22⋊Q8—474no—
480C22⋊Q8—948no—
481C22⋊Q8—948no—
482C22⋊Q8—942no—
483C22⋊Q8C22×D4714yes—
484#121—474no—
485#121—474no—
486#121—942no—
487#121—948no—
488#121—942no—
489C4×Q8—474no—
490C4×Q8—942no—
491C4×D4—474no—
492C4×D4—474no—
493C4×D4—474no—
494C4×D4—942no—
495C4×D4—948no—
496C4×D4—948no—
497#117—474no—
498#117—942no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4714yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C42—471no—
530C2×C42—941no—
531C2×C42—941no—
532#107—474no—
533#107—474no—
534#107—474no—
535#107—474no—
536#107C22×D4714yes—
537#107C22×D4714yes—
538#106—474no—
539#106—474no—
540#106—474no—
541C4⋊C8—474no—
542#103—474no—
543#103C22×D4714yes—
544#103C22×D4714yes—
545#102—474no—
546#102—474no—
547#102—474no—
548C22⋊C8—474no—
549C22⋊C8C22×D4714yes—
550#97—474no—
551C24—471no—
552C24—941no—
553C24D4×D4711yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—944no—
558C2×Q8—3762no—
559C2×Q8C23×D4712yes—
560C2×D4—474no—
561C2×D4—472no—
562C2×D4—944no—
563C2×D4—944no—
564C2×D4—944no—
565C2×D4—941no—
566C2×D4—942no—
567C2×D4—942no—
568C2×D4—3762no—
569C2×D4—1884no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—944no—
584C22×C4—944no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—944no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—3762no—
592C22×C4—3762no—
593C22×C4—3762no—
594C22×C4D4×D4712yes—
595C22×C4D4×D4711yescharacteristic
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598SD16—948no—
599M16—948no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—474no—
603C2×C8—472no—
604C2×C8—472no—
605C2×C8—948no—
606C2×C8—942no—
607C2×C8C23×D4712yes—
608C2×C8C23×D4712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—474no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—472no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—941no—
625C4⋊C4—944no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4C23×D4712yes—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—474no—
633C22⋊C4—474no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—472no—
640C42—472no—
641C42—944no—
642C42—944no—
643C23—22no—
644C23—22no—
645C23—472no—
646C23—942no—
647C23—942no—
648C23—942no—
649C23—942no—
650C23—1882no—
651C23—1882no—
652C23—1882no—
653C23#1309405614yes—
654C23C2×D4×D4712yes—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—3764no—
660D4—948no—
661D4—942no—
662D4—942no—
663D4—3764no—
664D4—1888no—
665D4—1882no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—944no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—3764no—
692C2×C4—3764no—
693C2×C4—3764no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4C2×D4×D4712yes—
698C2×C4C2×D4×D4711yescharacteristic
699C2×C4#41×D4712yes—
700C2×C4#1309407112yes—
701C2×C4C24×D4711yescharacteristic
702C8—22no—
703C8—22no—
704C8—474no—
705C8—942no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—942no—
710C22—942no—
711C22—942no—
712C22—3764no—
713C22—1882no—
714C22—1882no—
715C22—1882no—
716C22—1884no—
717C22#1568977112yes—
718C22C2×#1309405614yes—
719C22C2×#1309405612yes—
720C22#1568992712yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—942no—
728C4—942no—
729C4—942no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4#1568977112yes—
734C4C2×#41×D4711yescharacteristic
735C4C2×#1309407111yescharacteristic
736C2—24no—
737C2—3762no—
738C2—1882no—
739C2#2025587714yesdirect product factor
740C2C2×#1568977111yescharacteristic
741C2C22×#1309405611yescharacteristic
742C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#484C2
socleC23×C47C22×D4
prime radicalC2×#15689821C2
hypercenterC2×#484D47
hypocenterC47C2×#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255877C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689462C2semidirect
7. C2×#15689438C2semidirect
8. C2×#15689428C2semidirect
9. C2×#15689402C2semidirect
10. C2×#15689372C2semidirect
11. C2×#15689354C2semidirect
12. C2×#15689226C2semidirect
13. C2×#15689191C2semidirect
14. C2×#15689164C2semidirect
15. C22×#13093957C2semidirect
16. C2×C47×#484C2semidirect
21. #15689831C22semidirect
43. #15689531C22semidirect
44. #15689462C22semidirect
45. #15689442C22semidirect
46. #15689438C22semidirect
47. #15689428C22semidirect
48. #15689402C22semidirect
49. #15689372C22semidirect
50. #15689354C22semidirect
51. #15689226C22semidirect
52. #15689191C22semidirect
53. #15689164C22semidirect
58. C2×#13093957C22semidirect
71. C47×#484C22semidirect
369. C2×#484D47semidirect
382. C2×C47#3346semidirect
418. #484C2×D47semidirect
448. C47C2×#3346semidirect
739. C2#20255877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156898212
#202558772
C2×#156895312
C2×#156894422
C2×#156894622
C2×#156894382
C2×#156894282
C2×#156894022
C2×#156893722
C2×#156893542
C2×#156892262
C2×#156891912
C2×#156891642
C22×#130939572
C2×C47×#4842
C2×#334647