Finite Group Databasebeta

← C2×#20255875 #27094859

Subgroups — C2×#20255875 #27094859

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×#15689830C211yesmaximal, characteristic, complemented
2C2×#15689819C211yesmaximal, characteristic
3#20255875C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689442C211yesmaximal, characteristic, complemented
7C2×#15689465C211yesmaximal, characteristic, complemented
8C2×#15689437C211yesmaximal, characteristic, complemented
9C2×#15689431C211yesmaximal, characteristic, complemented
10C2×#15689404C211yesmaximal, characteristic, complemented
11C2×#15689369C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C22×#13093958C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18#15689830—24no—
19#15689830C2218yescomplemented
20#15689819—24no—
21#15689819C2218yes—
22C2×#13094024C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094016C2211yescharacteristic
25C2×#13094015—21no—
26C2×#13094006—21no—
27C2×#13094003C2211yescharacteristic
28C2×#13094003C2211yescharacteristic
29C2×#13094001—21no—
30C2×#13094001—21no—
31C2×#13093998C2211yescharacteristic
32C2×#13093998C2211yescharacteristic
33C2×#13093996—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×D4×Dic47—21no—
37C2×(C22⋊D47)⋊C4—21no—
38C2×#13093983C2211yescharacteristic
39C22×C4⋊Dic47C2211yescharacteristic
40C22×C4⋊Dic47C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689465C2218yescomplemented
44#15689459C2218yescomplemented
45#15689442C2218yescomplemented
46#15689437C2218yescomplemented
47#15689431C2218yescomplemented
48#15689404C2218yescomplemented
49#15689369C2218yescomplemented
50#15689352C2218yescomplemented
51#15689225C2218yescomplemented
52#15689165C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093958C2218yescomplemented
60C2×#13093956C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093956C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C23×Dic47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C2×#10625325—24no—
87C2×#10625325C2314yes—
88#13094024—22no—
89#13094024C2314yes—
90#13094019—28no—
91#13094016—22no—
92#13094016C2314yes—
93#13094015—28no—
94#13094006—28no—
95#13094003—22no—
96#13094003—22no—
97#13094003C2314yes—
98#13094003C2314yes—
99#13094001—28no—
100#13094001—28no—
101#13093998—22no—
102#13093998—22no—
103#13093998C2314yes—
104#13093998C2314yes—
105#13093996—28no—
106C4×Dic94—22no—
107C4×Dic94C2314yes—
108C4×D188—22no—
109C4×D188C2314yes—
110D4×Dic47—28no—
111(C22⋊D47)⋊C4—28no—
112#13093983—22no—
113#13093983C2314yes—
114C2×C4⋊Dic47—22no—
115C2×C4⋊Dic47—22no—
116C2×C4⋊Dic47—22no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2314yes—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2314yes—
124C2×C4⋊Dic47C2314yes—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093958C2314yes—
147#13093958C2314yes—
148#13093958C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158C22×D4×C47D411yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×M16×C47—24no—
162C2×M16×C47C2314yes—
163C22×C8×C47—24no—
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C4⋊C8×C47C2314yes—
176C22⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178#97×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C2×D4×C47—24no—
183C2×D4×C47C2×D414yes—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—82no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—24no—
210C22×Dic47—24no—
211C22×Dic47—82no—
212C22×Dic47—82no—
213C22×Dic47—82no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188C2412yes—
218C2×C4×D47—24no—
219C2×C4×D47—82no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—21no—
223C2×Dic94—24no—
224C2×Dic94—82no—
225C2×Dic94C2412yes—
226M16×C47—28no—
227C2×C8×C47—22no—
228C2×C8×C47—22no—
229C2×C8×C47—22no—
230C2×C8×C47—28no—
231C2×C8×C47#4114yes—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C4⋊C4×C47C2×D414yes—
237C22⋊C4×C47C2×D414yes—
238C22⋊C4×C47C2×D414yes—
239C42×C47C2×D412yes—
240C42×C47C2412yes—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47—21no—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270#10625325—28no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47#13714yes—
277C23×C47C22×D412yes—
278C23×C47C22×D412yes—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—42no—
284D4×C47—28no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—24no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4112yes—
301C2×C4×C472−1+412yes—
302C2×C4×C47C2511yescharacteristic
303C22⋊D47—48no—
304C22⋊D47—84no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—84no—
320C2×Dic47—84no—
321C2×Dic47—84no—
322D188—22no—
323D188—22no—
324D188—42no—
325C4×D47—84no—
326Dic94—22no—
327Dic94—22no—
328Dic94—42no—
329Dic94—84no—
330C8×C47—22no—
331C8×C47—22no—
332C8×C47—22no—
333C8×C47C2×#4114yes—
334C2×#3346—471nomaximal, Sylow
335C22×C47—28no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—44no—
342C22×C47#54712yes—
343C22×C47C2×#13714yes—
344C22×C47C2×#13712yes—
345C22×C47#57612yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—84no—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47#54712yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C2×2−1+411yescharacteristic
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#554—471no—
366C2×#553—471no—
367#3346—4716no—
368C2×#501—471no—
369C2×#484—471no—
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×#435D4711yescharacteristic, complemented
379C2×#428—471no—
380C22×#107—471no—
381C2×C47—24no—
382C2×C47—42no—
383C2×C47#334614yescomplemented
384C2×C47C2×#54711yescharacteristic
385C2×C47C22×#13711yescharacteristic
386C2×C47C2×#57611yescharacteristic
387D47—82no—
388C22×SD16—471no—
389C22×M16C2×D4711yescharacteristic
390C23×C8C2×D4711yescharacteristic
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—471no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8—941no—
404C2×#121—471no—
405C2×#121—471no—
406C2×#121—941no—
407C2×C4×Q8—471no—
408C2×C4×D4—471no—
409C2×C4×D4—941no—
410C2×C4×D4—941no—
411C2×C4×D4C2×D4711yescharacteristic
412C2×#117—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—471no—
416#501—478no—
417#485—478no—
418#484—478no—
419#481—478no—
420#480—478no—
421#479—478no—
422#474—478no—
423#468—478no—
424#465—478no—
425#440—478no—
426#435C2×D4718yescomplemented
427#428—478no—
428C2×#107—471no—
429C2×#107—471no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—478no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8C2×D4711yescharacteristic
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×#102—471no—
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×C22⋊C8C2×D4711yescharacteristic
447C2×#97C2×D4711yescharacteristic
448C47C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—471no—
450C22×Q8—941no—
451C22×D4—471no—
452C22×D4—941no—
453C22×D4—941no—
454C22×D4D18811yescharacteristic
455C23×C4—941no—
456C23×C4—941no—
457C23×C4—941no—
458C23×C4—941no—
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C2×SD16—474no—
462C2×SD16—944no—
463C2×M16—24no—
464C2×M16C22×D4714yes—
465C22×C8—24no—
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4714yes—
468C22×C8C22×D4711yescharacteristic
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C4⋊Q8—474no—
472C4⋊Q8—942no—
473#126—948no—
474#125—474no—
475#125—948no—
476#125—942no—
477#123—948no—
478C22⋊Q8—474no—
479C22⋊Q8—474no—
480C22⋊Q8—942no—
481C22⋊Q8—942no—
482C22⋊Q8—948no—
483C22⋊Q8—948no—
484#121—474no—
485#121—474no—
486#121—948no—
487#121—942no—
488#121—942no—
489C4×Q8—474no—
490C4×Q8—942no—
491C4×D4—474no—
492C4×D4—948no—
493C4×D4—948no—
494C4×D4—942no—
495C4×D4D18814yes—
496C4×D4C22×D4714yes—
497#117—474no—
498#117—942no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4D18811yescharacteristic
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4D18811yescharacteristic
528C2×C22⋊C4D18811yescharacteristic
529C2×C42—941no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532#107—474no—
533#107—474no—
534#107—474no—
535#107—474no—
536#107—474no—
537#107—474no—
538#106—474no—
539#106—474no—
540#106—474no—
541C4⋊C8C22×D4714yes—
542#103—474no—
543#103—474no—
544#103—474no—
545#102—474no—
546#102—474no—
547#102—474no—
548C22⋊C8C22×D4714yes—
549C22⋊C8C22×D4714yes—
550#97C22×D4714yes—
551C24—941no—
552C24C2×D18811yescharacteristic
553C24C2×D18811yescharacteristic
554C2×Q8—472no—
555C2×Q8—944no—
556C2×Q8—941no—
557C2×Q8—942no—
558C2×Q8—942no—
559C2×Q8—3762no—
560C2×D4—24no—
561C2×D4—472no—
562C2×D4—944no—
563C2×D4—944no—
564C2×D4—941no—
565C2×D4—942no—
566C2×D4—942no—
567C2×D4—3762no—
568C2×D4—1884no—
569C2×D4C2×D18814yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—944no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—944no—
585C22×C4—3762no—
586C22×C4—3762no—
587C22×C4—3762no—
588C22×C4—3762no—
589C22×C4C2×D18812yes—
590C22×C4C2×D18812yes—
591C22×C4C2×D18811yescharacteristic
592C22×C4C2×D18811yescharacteristic
593C22×C4C2×D18811yescharacteristic
594C22×C4C2×D18811yescharacteristic
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598SD16—948no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1062535214yes—
605C2×C8C23×D4712yes—
606C2×C8C23×D4712yes—
607C2×C8C23×D4712yes—
608C2×C8C23×D4712yes—
609C4⋊C4—472no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—472no—
613C4⋊C4—472no—
614C4⋊C4—472no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4—944no—
628C4⋊C4—941no—
629C4⋊C4—944no—
630C4⋊C4C2×D18814yes—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4C2×D18814yes—
638C22⋊C4C2×D18814yes—
639C42—944no—
640C42—944no—
641C42C2×D18812yes—
642C42C23×D4712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—942no—
649C23—1882no—
650C23—1882no—
651C23—1882no—
652C23#1309405714yes—
653C23C22×D18812yes—
654C23C22×D18812yes—
655C23C22×D18811yescharacteristic
656Q8—942no—
657Q8—942no—
658Q8—3764no—
659Q8—1882no—
660D4—28no—
661D4—942no—
662D4—942no—
663D4—3764no—
664D4—1888no—
665D4—1882no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—3764no—
684C2×C4—3764no—
685C2×C4—3764no—
686C2×C4—3764no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4C22×D18812yes—
695C2×C4C22×D18812yes—
696C2×C4C22×D18812yes—
697C2×C4C22×D18812yes—
698C2×C4C22×D18811yescharacteristic
699C2×C4C2×#1062535212yes—
700C2×C4#1309407112yes—
701C2×C4C24×D4711yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1062535214yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—3764no—
714C22—1882no—
715C22—1882no—
716C22—1882no—
717C22#1568977712yes—
718C22C2×#1309405714yes—
719C22C2×#1309405712yes—
720C22#1568992812yes—
721C22C23×D18811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—1882no—
727C4—1882no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4#1568977712yes—
734C4C22×#1062535211yescharacteristic
735C4C2×#1309407111yescharacteristic
736C2—24no—
737C2—42no—
738C2—3762no—
739C2#2025587514yesdirect product factor
740C2C2×#1568977711yescharacteristic
741C2C22×#1309405711yescharacteristic
742C2C2×#1568992811yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
hypercenterC2×#435D47
hypocenterC47C2×#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#15689830C2semidirect
3. #20255875C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689442C2semidirect
7. C2×#15689465C2semidirect
8. C2×#15689437C2semidirect
9. C2×#15689431C2semidirect
10. C2×#15689404C2semidirect
11. C2×#15689369C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689165C2semidirect
15. C22×#13093958C2semidirect
16. C2×C47×#435C2semidirect
19. #15689830C22semidirect
42. #15689532C22semidirect
43. #15689465C22semidirect
44. #15689459C22semidirect
45. #15689442C22semidirect
46. #15689437C22semidirect
47. #15689431C22semidirect
48. #15689404C22semidirect
49. #15689369C22semidirect
50. #15689352C22semidirect
51. #15689225C22semidirect
52. #15689165C22semidirect
59. C2×#13093958C22semidirect
72. C47×#435C22semidirect
378. C2×#435D47semidirect
383. C2×C47#3346semidirect
426. #435C2×D47semidirect
448. C47C2×#3346semidirect
739. C2#20255875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898302
C2×#156898192
#202558752
C2×#156895322
C2×#156894592
C2×#156894422
C2×#156894652
C2×#156894372
C2×#156894312
C2×#156894042
C2×#156893692
C2×#156893522
C2×#156892252
C2×#156891652
C22×#130939582
C2×C47×#4352
C2×#334647