Finite Group Databasebeta

← C2×#20254809 #27089199

Subgroups — C2×#20254809 #27089199

Order 12032.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689746C211yesmaximal, characteristic
2C2×#15689733C211yesmaximal, characteristic, complemented
3#20254809C2116yesmaximal, direct product factor
4C2×#15689432C211yesmaximal, characteristic, complemented
5C2×#15689416C211yesmaximal, characteristic, complemented
6C2×#15689407C211yesmaximal, characteristic, complemented
7C2×#15689422C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic
9C2×#15689362C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic
11C2×#15689348C211yesmaximal, characteristic, complemented
12C2×#15689347C211yesmaximal, characteristic, complemented
13C2×#15689331C211yesmaximal, characteristic, complemented
14C2×#15689327C211yesmaximal, characteristic, complemented
15C2×#15689151C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21#15689746—24no—
22#15689746C2218yes—
23#15689733—24no—
24#15689733C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094022C2211yescharacteristic
27C2×#13094019—21no—
28C2×#13094017—21no—
29C2×#13094017—21no—
30C2×#13094015—21no—
31C2×#13094015C2211yescharacteristic
32C2×#13094014—21no—
33C2×#13094013C2211yescharacteristic
34C2×#13094010—21no—
35C2×#13094006—21no—
36C2×#13094004—21no—
37C2×#13094003C2211yescharacteristic
38C2×#13093998C2211yescharacteristic
39C2×Q8×Dic47C2211yescharacteristic
40C2×Q8×Dic47C2211yescharacteristic
41C2×#13093989C2211yescharacteristic
42C2×#13093986C2211yescharacteristic
43C2×#13093983C2211yescharacteristic
44#15689432C2218yescomplemented
45#15689422C2218yescomplemented
46#15689416C2218yescomplemented
47#15689407C2218yescomplemented
48#15689369C2218yes—
49#15689362C2218yescomplemented
50#15689354C2218yes—
51#15689348C2218yescomplemented
52#15689347C2218yescomplemented
53#15689331C2218yescomplemented
54#15689327C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689151C2218yescomplemented
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093944C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#470C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625337—42no—
83C2×#10625337C2314yes—
84C2×#10625325—42no—
85C2×#10625325C2314yes—
86C2×#10625336—42no—
87C2×#10625336C2314yes—
88C22×C47⋊C8—42no—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2314yes—
92#13094023—22no—
93#13094023C2314yes—
94#13094022—22no—
95#13094022C2314yes—
96#13094019—28no—
97#13094017—28no—
98#13094017—28no—
99#13094015—28no—
100#13094015—22no—
101#13094015C2314yes—
102#13094014—28no—
103#13094013—22no—
104#13094013C2314yes—
105#13094010—28no—
106#13094006—28no—
107#13094004—28no—
108#13094003—22no—
109#13094003C2314yes—
110#13093998—22no—
111#13093998C2314yes—
112Q8×Dic47—22no—
113Q8×Dic47—22no—
114Q8×Dic47C2314yes—
115Q8×Dic47C2314yes—
116#13093989—22no—
117#13093989C2314yes—
118#13093986—22no—
119#13093986C2314yes—
120#13093983D414yes—
121#13093983C2314yes—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47D411yescharacteristic
126C2×C4⋊Dic47D411yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
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⋊Dic47D411yescharacteristic
137C2×C22⋊Dic47D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093957C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C2×Q16×C47—42no—
164C2×Q16×C47C2314yes—
165C2×M16×C47—42no—
166C2×M16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22⋊Q8×C47—22no—
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172C22⋊Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#106×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—82no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—21no—
214C2×D188C2412yes—
215C2×C4×D47—24no—
216C2×C4×D47—82no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—21no—
220C2×Dic94—24no—
221C2×Dic94—82no—
222C2×Dic94C2412yes—
223Q16×C47—44no—
224M16×C47—44no—
225C2×C8×C47—22no—
226C2×C8×C47—22no—
227C2×C8×C47C2412yes—
228C2×C8×C47C2412yes—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47C2×D414yes—
239C22⋊Dic47C2×D414yes—
240#10625337—44no—
241#10625336—44no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47C2×D414yes—
252C4⋊Dic47C2×D414yes—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2×D412yes—
266C4×Dic47C2412yes—
267C4×Dic47C2412yes—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—44no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273#10625325—44no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47C22×D412yes—
278C23×C47C22×D411yescharacteristic
279C22×D47—22no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283Q8×C47—22no—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—42no—
288Q8×C47—42no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47H(5,𝔽2)12yes—
304C2×C4×C472−1+412yes—
305C2×C4×C47C2511yescharacteristic
306C22⋊D47—84no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321D188—22no—
322D188—22no—
323D188—42no—
324C4×D47—84no—
325Dic94—22no—
326Dic94—22no—
327Dic94—42no—
328Dic94—84no—
329C8×C47—22no—
330C8×C47—22no—
331C47⋊C8—22no—
332C47⋊C8—22no—
333C2×#3258—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—44no—
338C22×C47#53712yes—
339C22×C47#57712yes—
340C22×C47#57812yes—
341C22×C47C23×D411yescharacteristic
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—84no—
346C4×C47—22no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47#53712yes—
352C4×C47C2×H(5,𝔽2)11yescharacteristic
353C4×C47C2×2−1+411yescharacteristic
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#542—471no—
362C2×#541—471no—
363#3258—4716no—
364C2×#479—471no—
365C2×#477—471no—
366C2×#475—471no—
367C2×#478—471no—
368C2×#470D4711yescharacteristic, complemented
369C2×#468—471no—
370C2×#467—471no—
371C2×#465—471no—
372C2×#464—471no—
373C2×#464—471no—
374C2×#462—471no—
375C2×#461—471no—
376C2×#424—471no—
377C2×C47—42no—
378C2×C47#325814yescomplemented
379C2×C47C2×#53711yescharacteristic
380C2×C47C2×#57711yescharacteristic
381C2×C47C2×#57811yescharacteristic
382D47—82no—
383C22×Q16—471no—
384C22×Q16C2×D4711yescharacteristic
385C22×SD16—471no—
386C22×SD16—471no—
387C22×M16C2×D4711yescharacteristic
388C23×C8—471no—
389#542—478no—
390#542—944no—
391#541—478no—
392#541—944no—
393C2×C4⋊Q8—471no—
394C2×C4⋊Q8—471no—
395C2×#126—941no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#125—471no—
399C2×#125—941no—
400C2×#125—941no—
401C2×#124—471no—
402C2×#124—941no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—941no—
406C2×C22⋊Q8C2×D4711yescharacteristic
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×D4—471no—
413C2×#117—471no—
414#479—478no—
415#478—478no—
416#477—478no—
417#475—478no—
418#470C2×D4718yescomplemented
419#468—478no—
420#467—478no—
421#465—478no—
422#464—478no—
423#464—478no—
424#462—478no—
425#461—478no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#106—471no—
429C2×#106C2×D4711yescharacteristic
430#424—478no—
431C2×C4⋊C8—471no—
432C2×C4⋊C8—471no—
433C2×C4⋊C8—471no—
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103C2×D4711yescharacteristic
440C2×#103C2×D4711yescharacteristic
441C2×#102—471no—
442C2×#102—471no—
443C47C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—471no—
445C22×Q8—941no—
446C22×Q8C22×D4711yescharacteristic
447C22×Q8C22×D4711yescharacteristic
448C22×D4—471no—
449C22×D4—941no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C2×Q16—42no—
453C2×Q16—474no—
454C2×Q16—1882no—
455C2×Q16C22×D4714yes—
456C2×SD16—474no—
457C2×SD16—474no—
458C2×SD16—1882no—
459C2×SD16—1882no—
460C2×M16—42no—
461C2×M16C22×D4714yes—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—474no—
465C22×C8—1882no—
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4⋊Q8—474no—
469C4⋊Q8—474no—
470C4⋊Q8—942no—
471C4⋊Q8—942no—
472#126—948no—
473#126—948no—
474#126—948no—
475#125—474no—
476#125—942no—
477#125—948no—
478#125—948no—
479#124—474no—
480#124—942no—
481#124—948no—
482#123—948no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—474no—
486C22⋊Q8—948no—
487C22⋊Q8—942no—
488C22⋊Q8C22×D4714yes—
489C22⋊Q8C22×D4714yes—
490#121—474no—
491#121—942no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×D4—474no—
499C4×D4—942no—
500#117—474no—
501#117—474no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—941no—
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—941no—
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—941no—
531C2×C42—941no—
532C2×C42—941no—
533#107—474no—
534#107—474no—
535#106—474no—
536#106C22×D4714yes—
537C4⋊C8—474no—
538C4⋊C8—474no—
539C4⋊C8—474no—
540C4⋊C8—474no—
541#103—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103C22×D4714yes—
546#103C22×D4714yes—
547#102—474no—
548#102—474no—
549C24—941no—
550C24D4×D4711yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—472no—
558C2×Q8—944no—
559C2×Q8—941no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—3762no—
563C2×Q8C23×D4712yes—
564C2×Q8C23×D4712yes—
565C2×D4—472no—
566C2×D4—944no—
567C2×D4—941no—
568C2×D4—942no—
569C2×D4—942no—
570C2×D4—3762no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—944no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—3762no—
586C22×C4D4×D4712yes—
587C22×C4D4×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590Q16—44no—
591Q16—1884no—
592SD16—1884no—
593SD16—1884no—
594M16—44no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—472no—
598C2×C8—472no—
599C2×C8—942no—
600C2×C8—942no—
601C2×C8—1884no—
602C2×C8C23×D4712yes—
603C2×C8C23×D4712yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—474no—
609C4⋊C4—474no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4C23×D4712yes—
624C4⋊C4C23×D4712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—474no—
628C22⋊C4—474no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C42—472no—
635C42—472no—
636C42—472no—
637C42—472no—
638C42—944no—
639C42—944no—
640C42—944no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—942no—
645C23—1882no—
646C23—1882no—
647C23—1882no—
648C23C2×D4×D4712yes—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—942no—
657Q8—942no—
658Q8—3764no—
659Q8—1882no—
660D4—942no—
661D4—942no—
662D4—3764no—
663D4—1882no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—3764no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4C2×D4×D4712yes—
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4#1309406912yes—
694C2×C4#1309407112yes—
695C2×C4C24×D4711yescharacteristic
696C8—22no—
697C8—22no—
698C8—942no—
699C8—942no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3764no—
705C22—1882no—
706C22—1882no—
707C22—1882no—
708C22#1568970012yes—
709C22#1568993212yes—
710C22#1568993912yes—
711C22C22×D4×D4711yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—942no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4#1568970012yes—
725C4C2×#1309406911yescharacteristic
726C4C2×#1309407111yescharacteristic
727C2—42no—
728C2—3762no—
729C2#2025480914yesdirect product factor
730C2C2×#1568970011yescharacteristic
731C2C2×#1568993211yescharacteristic
732C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#470D47
hypocenterC47C2×#3258
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#15689733C2semidirect
3. #20254809C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689416C2semidirect
6. C2×#15689407C2semidirect
7. C2×#15689422C2semidirect
9. C2×#15689362C2semidirect
11. C2×#15689348C2semidirect
12. C2×#15689347C2semidirect
13. C2×#15689331C2semidirect
14. C2×#15689327C2semidirect
15. C2×#15689151C2semidirect
16. C2×C47×#470C2semidirect
24. #15689733C22semidirect
44. #15689432C22semidirect
45. #15689422C22semidirect
46. #15689416C22semidirect
47. #15689407C22semidirect
49. #15689362C22semidirect
51. #15689348C22semidirect
52. #15689347C22semidirect
53. #15689331C22semidirect
54. #15689327C22semidirect
58. #15689151C22semidirect
73. C47×#470C22semidirect
368. C2×#470D47semidirect
378. C2×C47#3258semidirect
418. #470C2×D47semidirect
443. C47C2×#3258semidirect
729. C2#20254809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156897332
#202548092
C2×#156894322
C2×#156894162
C2×#156894072
C2×#156894222
C2×#156893692
C2×#156893622
C2×#156893542
C2×#156893482
C2×#156893472
C2×#156893312
C2×#156893272
C2×#156891512
C2×C47×#4702
C2×#325847