Finite Group Databasebeta

← C2×#20256416 #27097243

Subgroups — C2×#20256416 #27097243

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689848C211yesmaximal, characteristic, complemented
2C2×#15689842C211yesmaximal, characteristic
3#20256416C2116yesmaximal, direct product factor
4C2×#15689514C211yesmaximal, characteristic
5C2×#15689501C211yesmaximal, characteristic, complemented
6C2×#15689343C211yesmaximal, characteristic
7C2×#15689342C211yesmaximal, characteristic
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689331C211yesmaximal, characteristic, complemented
10C2×#15689330C211yesmaximal, characteristic, complemented
11C2×#15689326C211yesmaximal, characteristic
12C2×#15689251C211yesmaximal, characteristic, complemented
13C2×#15689231C211yesmaximal, characteristic, complemented
14C2×#15689230C211yesmaximal, characteristic, complemented
15C2×SD16×Dic47C211yesmaximal, characteristic
16C2×C47×#497C211yesmaximal, characteristic
17C22×Dic188C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22#15689848—24no—
23#15689848C2218yescomplemented
24#15689842—24no—
25#15689842C2218yes—
26C2×#13094022C2211yescharacteristic
27C2×#13094022C2211yescharacteristic
28C2×#13094022C2211yescharacteristic
29C2×#13094017—21no—
30C2×#13094017—21no—
31C2×#13094015—21no—
32C2×#13094014—21no—
33C2×#13094014—21no—
34C2×#13094011C2211yescharacteristic
35C2×#13094001—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×C4×Dic94C2211yescharacteristic
41C2×C4×Dic94C2211yescharacteristic
42C2×#13093989—21no—
43C2×D4×Dic47C2211yescharacteristic
44C2×#13093980—21no—
45#15689514C2218yes—
46#15689501C2218yescomplemented
47#15689343C2218yes—
48#15689342C2218yes—
49#15689331C2218yescomplemented
50#15689331C2218yescomplemented
51#15689330C2218yescomplemented
52#15689326C2218yes—
53#15689251C2218yescomplemented
54#15689231C2218yescomplemented
55#15689230C2218yescomplemented
56SD16×Dic47C2218yes—
57C2×#13093956C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×C4⋊Q8×C47C2211yescharacteristic
74C2×#124×C47C2211yescharacteristic
75C47×#497C2218yes—
76C2×#97×C47C2211yescharacteristic
77C22×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C23×Dic47—21no—
81C2×Dic188—24no—
82C2×Dic188C2314yes—
83C2×#10625337—42no—
84C2×#10625337—42no—
85C2×#10625337—42no—
86C2×#10625337C2314yes—
87C2×#10625337C2314yes—
88C2×#10625337C2314yes—
89C2×#10625335—42no—
90C2×#10625335C2314yes—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93#13094022—22no—
94#13094022—22no—
95#13094022—22no—
96#13094022C2314yes—
97#13094022C2314yes—
98#13094022C2314yes—
99#13094017—28no—
100#13094017—28no—
101#13094015—28no—
102#13094014—28no—
103#13094014—28no—
104#13094011—22no—
105#13094011C2314yes—
106#13094001—28no—
107Q8×Dic47—22no—
108Q8×Dic47—22no—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111Q8×Dic47C2314yes—
112Q8×Dic47C2314yes—
113C4×Dic94—22no—
114C4×Dic94—22no—
115C4×Dic94D414yes—
116C4×Dic94C2314yes—
117C4×Dic94C2314yes—
118C4×Dic94C2314yes—
119#13093989—28no—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093980—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
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×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×Dic47⋊C4D411yescharacteristic
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093956C2314yes—
150C4⋊(C47⋊C8)C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093945C2314yes—
159#13093934C2314yes—
160C8×Dic47C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47C2311yescharacteristic
165C2×Q16×C47—24no—
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yes—
168C2×Q16×C47C2314yes—
169C2×SD16×C47—24no—
170C2×SD16×C47—42no—
171C2×SD16×C47C2314yes—
172C2×SD16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175C4⋊Q8×C47—22no—
176C4⋊Q8×C47C2314yes—
177#124×C47—22no—
178#124×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#97×C47C2314yes—
185C24×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47C2412yes—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C2×D4×C47—21no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2411yescharacteristic
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—24no—
213C22×Dic47—44no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C2×Dic94—24no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—21no—
225C2×Dic94C2×D414yes—
226C2×Dic94C2412yes—
227C2×Dic94C2412yes—
228Q16×C47—28no—
229Q16×C47—44no—
230SD16×C47—28no—
231SD16×C47—44no—
232C2×C8×C47—22no—
233C2×C8×C47#4114yes—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245#10625337—44no—
246#10625337—44no—
247#10625337—44no—
248#10625335—44no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47C2×D414yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4C2×D414yes—
266Dic47⋊C4C2×D414yes—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C4×Dic47C2412yes—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280Dic188—28no—
281C23×C47—22no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47C22×D411yescharacteristic
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293Q8×C47—42no—
294Q8×C47—42no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—42no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C2×#4112yes—
310C2×C4×C47H(5,𝔽2)12yes—
311C2×C4×C47C2511yescharacteristic
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—48no—
324C2×Dic47#13714yes—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329Dic94—28no—
330Dic94—22no—
331Dic94—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94—42no—
335Dic94—42no—
336C8×C47—22no—
337C8×C47C2×#4114yes—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C2×#3398—471nomaximal, Sylow
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—84no—
345C22×C47#55012yes—
346C22×C47C2×#13712yes—
347C22×C47#57812yes—
348C22×C47C23×D411yescharacteristic
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47#55012yes—
355C4×C47C22×#4111yescharacteristic
356C4×C47C2×H(5,𝔽2)11yescharacteristic
357Dic47—22no—
358Dic47—22no—
359Dic47—22no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#557—471no—
366C2×#556—471no—
367#3398—4716no—
368C2×#497—471no—
369C2×#497D4711yescharacteristic
370C2×#494—471no—
371C2×#464—471no—
372C2×#464—471no—
373C2×#462—471no—
374C2×#462—471no—
375C2×#462—471no—
376C2×#461—471no—
377C2×#446—471no—
378C2×#441—471no—
379C2×#441—471no—
380C2×C4×SD16—471no—
381C2×C47—82no—
382C2×C47#339814yescomplemented
383C2×C47C2×#55011yescharacteristic
384C2×C47C22×#13711yescharacteristic
385C2×C47C2×#57811yescharacteristic
386C22×Q16—471no—
387C22×Q16—471no—
388C22×Q16—471no—
389C22×Q16—471no—
390C22×Q16C2×D4711yescharacteristic
391C22×Q16C2×D4711yescharacteristic
392C22×SD16—471no—
393C22×SD16C2×D4711yescharacteristic
394C22×SD16C2×D4711yescharacteristic
395#557—478no—
396#557—944no—
397#556—478no—
398#556—944no—
399C2×C4⋊Q8—471no—
400C2×C4⋊Q8—471no—
401C2×C4⋊Q8—471no—
402C2×C4⋊Q8C2×D4711yescharacteristic
403C2×#126—941no—
404C2×#126—941no—
405C2×#125—941no—
406C2×#125—941no—
407C2×#125—941no—
408C2×#124—471no—
409C2×#124C2×D4711yescharacteristic
410C2×C22⋊Q8—941no—
411C2×C4×Q8—471no—
412C2×C4×Q8—471no—
413C2×C4×Q8—471no—
414C2×C4×Q8—471no—
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8—941no—
418C2×C4×D4—471no—
419C2×#117—941no—
420#497—478no—
421#497C2×D4718yes—
422#494—478no—
423#464—478no—
424#464—478no—
425#462—478no—
426#462—478no—
427#462—478no—
428#461—478no—
429#446—478no—
430#441—478no—
431#441—478no—
432C4×SD16—478no—
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#97—471no—
444C2×#97C2×D4711yescharacteristic
445C2×C4×C8—471no—
446C47C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—471no—
448C22×Q8—471no—
449C22×Q8—471no—
450C22×Q8C22×D4711yescharacteristic
451C22×Q8C22×D4711yescharacteristic
452C22×Q8C22×D4711yescharacteristic
453C22×D4C22×D4711yescharacteristic
454C23×C4—941no—
455C2×Q16—24no—
456C2×Q16—42no—
457C2×Q16—474no—
458C2×Q16—474no—
459C2×Q16—474no—
460C2×Q16—474no—
461C2×Q16—944no—
462C2×Q16—1882no—
463C2×Q16—1882no—
464C2×Q16—1882no—
465C2×Q16C22×D4714yes—
466C2×Q16C22×D4714yes—
467C2×SD16—24no—
468C2×SD16—42no—
469C2×SD16—474no—
470C2×SD16—1882no—
471C2×SD16C22×D4714yes—
472C2×SD16C22×D4714yes—
473C22×C8—471no—
474C22×C8—471no—
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477C4⋊Q8—22no—
478C4⋊Q8—474no—
479C4⋊Q8—474no—
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482C4⋊Q8—942no—
483C4⋊Q8—942no—
484C4⋊Q8C22×D4714yes—
485#126—948no—
486#126—948no—
487#125—948no—
488#125—948no—
489#125—948no—
490#124—22no—
491#124—474no—
492#124—942no—
493#124C22×D4714yes—
494C22⋊Q8—948no—
495C4×Q8—474no—
496C4×Q8—474no—
497C4×Q8—474no—
498C4×Q8—474no—
499C4×Q8—474no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—942no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8—948no—
506C4×Q8—942no—
507C4×Q8—942no—
508C4×D4—474no—
509C4×D4—942no—
510#117—948no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C42—471no—
535C2×C42—471no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42—941no—
540C2×C42—941no—
541C2×C42C22×D4711yescharacteristic
542#106—474no—
543C4⋊C8—474no—
544C4⋊C8—474no—
545C4⋊C8—474no—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103—474no—
551#102—474no—
552#97—474no—
553#97C22×D4714yes—
554C4×C8—474no—
555C24—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—474no—
566C2×Q8—472no—
567C2×Q8—472no—
568C2×Q8—944no—
569C2×Q8—941no—
570C2×Q8—941no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—942no—
575C2×Q8C23×D4712yes—
576C2×Q8C23×D4712yes—
577C2×Q8C23×D4712yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4C23×D4712yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—1884no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598Q16—28no—
599Q16—44no—
600Q16—948no—
601Q16—1884no—
602Q16—1884no—
603Q16—1884no—
604SD16—28no—
605SD16—44no—
606SD16—1884no—
607C2×C8—22no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8#1062535214yes—
613C2×C8C23×D4712yes—
614C2×C8C23×D4712yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—474no—
618C4⋊C4—474no—
619C4⋊C4—474no—
620C4⋊C4—472no—
621C4⋊C4—472no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—941no—
634C4⋊C4—941no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C42—472no—
641C42—472no—
642C42—472no—
643C42—472no—
644C42—944no—
645C42—944no—
646C42—944no—
647C42—944no—
648C42—944no—
649C42D4×D4712yes—
650C42C23×D4712yes—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—948no—
666Q8—942no—
667Q8—942no—
668Q8—942no—
669Q8—942no—
670Q8—1882no—
671Q8—1882no—
672D4—22no—
673D4—22no—
674D4—42no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—474no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—472no—
687C2×C4—472no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—1888no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4C2×#1062535212yes—
704C2×C4#1309406912yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—942no—
708C8—942no—
709C8C2×#1062535214yes—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22#1568979312yes—
715C22#137×D4712yes—
716C22#1568993912yes—
717C22C22×D4×D4711yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—474no—
724C4—942no—
725C4—942no—
726C4—942no—
727C4—1882no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4#1568979312yes—
732C4C22×#1062535211yescharacteristic
733C4C2×#1309406911yescharacteristic
734C2—82no—
735C2#2025641614yesdirect product factor
736C2C2×#1568979311yescharacteristic
737C2C2×#137×D4711yescharacteristic
738C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#497C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenterC2×#497D47
hypocenterC47C2×#3398
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#15689848C2semidirect
3. #20256416C2direct (N × H)
5. C2×#15689501C2semidirect
8. C2×#15689331C2semidirect
9. C2×#15689331C2semidirect
10. C2×#15689330C2semidirect
12. C2×#15689251C2semidirect
13. C2×#15689231C2semidirect
14. C2×#15689230C2semidirect
23. #15689848C22semidirect
46. #15689501C22semidirect
49. #15689331C22semidirect
50. #15689331C22semidirect
51. #15689330C22semidirect
53. #15689251C22semidirect
54. #15689231C22semidirect
55. #15689230C22semidirect
382. C2×C47#3398semidirect
446. C47C2×#3398semidirect
735. C2#20256416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898482
C2×#156898422
#202564162
C2×#156895142
C2×#156895012
C2×#156893432
C2×#156893422
C2×#156893312
C2×#156893302
C2×#156893262
C2×#156892512
C2×#156892312
C2×#156892302
C2×SD16×Dic472
C2×C47×#4972
C2×#339847