Finite Group Databasebeta

← C2×#20253604 #27084543

Subgroups — C2×#20253604 #27084543

Order 12032.

2070 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×#15689735C211yesmaximal, characteristic, complemented
2C2×#15689603C211yesmaximal, characteristic
3#20253604C2116yesmaximal, direct product factor
4C2×#15689459C211yesmaximal, characteristic, complemented
5C2×#15689454C211yesmaximal, characteristic, complemented
6C2×#15689431C211yesmaximal, characteristic, complemented
7C2×#15689424C211yesmaximal, characteristic, complemented
8C2×#15689334C211yesmaximal, characteristic, complemented
9C2×#15689329C211yesmaximal, characteristic, complemented
10C2×#15689287C211yesmaximal, characteristic
11C2×#15689287C211yesmaximal, characteristic
12C2×#15689231C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×C4×Dic188C211yesmaximal, characteristic, complemented
15C2×C4×#10625325C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22#15689735—24no—
23#15689735C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094017—21no—
26C2×#13094017—21no—
27C2×#13094016C2211yescharacteristic
28C2×#13094014—21no—
29C2×#13094014—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094003C2211yescharacteristic
32#15689603—24no—
33#15689603C2218yes—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093982—21no—
43C22×C4⋊Dic47C2211yescharacteristic
44C2×C4⋊C4×D47—21no—
45#15689459C2218yescomplemented
46#15689454C2218yescomplemented
47#15689431C2218yescomplemented
48#15689424C2218yescomplemented
49#15689334C2218yescomplemented
50#15689329C2218yescomplemented
51#15689287C2218yes—
52#15689287C2218yes—
53#15689231C2218yescomplemented
54#15689225C2218yescomplemented
55C4×Dic188C2218yescomplemented
56C4×#10625325C2218yescomplemented
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093949C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C2×Dic188—24no—
91C2×Dic188—24no—
92C2×Dic188C2314yes—
93C2×Dic188C2314yes—
94C2×#10625325—24no—
95C2×#10625325—24no—
96C2×#10625325C2314yes—
97C2×#10625325C2314yes—
98#13094024—22no—
99#13094024C2314yes—
100#13094017—28no—
101#13094017—28no—
102#13094016—22no—
103#13094016C2314yes—
104#13094014—28no—
105#13094014—28no—
106#13094003—22no—
107#13094003—22no—
108#13094003C2314yes—
109#13094003C2314yes—
110C4×Dic94—22no—
111C4×Dic94—22no—
112C4×Dic94—22no—
113C4×Dic94—22no—
114C4×Dic94C2314yes—
115C4×Dic94C2314yes—
116C4×Dic94C2314yes—
117C4×Dic94C2314yes—
118C4×D188—22no—
119C4×D188—22no—
120C4×D188C2314yes—
121C4×D188C2314yes—
122(C22⋊D47)⋊C4—28no—
123(C22⋊D47)⋊C4—28no—
124#13093982—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—22no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2314yes—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C4⋊C4×D47—28no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093958C2314yes—
153#13093956C2314yes—
154#13093956C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093949C2314yes—
160#13093949C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#117×C47D414yes—
169#117×C47C2314yes—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yes—
177C4⋊C8×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yes—
180#97×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2411yescharacteristic
194C2×C22⋊D47—28no—
195C2×C22⋊D47—24no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—24no—
204C22×Dic47—82no—
205#10625350—216no—
206#10625350—28no—
207#10625350—28no—
208C2×D188—21no—
209C2×D188—22no—
210C2×D188#4114yes—
211C2×D188C2412yes—
212C2×C4×D47—28no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—82no—
217C2×C4×D47—82no—
218C2×Dic94—21no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—21no—
225C2×Dic94—21no—
226C2×Dic94#4114yes—
227C2×Dic94C2412yes—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47C2×D414yes—
239C4⋊C4×C47C2×D414yes—
240C22⋊C4×C47C2×D414yes—
241C22⋊C4×C47C2×D414yes—
242C42×C47C2×D412yes—
243C42×C47C2×D412yes—
244C42×C47C2412yes—
245C42×C47C2412yes—
246C22⋊Dic47—24no—
247C22⋊Dic47—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47—24no—
273Dic188—28no—
274Dic188—28no—
275#10625325—28no—
276#10625325—28no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47C22×D412yes—
281C23×C47C22×D411yescharacteristic
282C22×D47—24no—
283C22×D47—22no—
284C22×D47—42no—
285C22×D47—42no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47C22×D412yes—
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×C47C2×#4112yes—
302C2×C4×C47C2511yescharacteristic
303C22⋊D47—216no—
304C2×Dic47—24no—
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—84no—
319D188—24no—
320D188—22no—
321D188C2×#4114yes—
322C4×D47—216no—
323C4×D47—84no—
324C4×D47—84no—
325Dic94—24no—
326Dic94—22no—
327Dic94—22no—
328Dic94—22no—
329Dic94—22no—
330Dic94—22no—
331Dic94—42no—
332Dic94—42no—
333Dic94C2×#4114yes—
334C8×C47—22no—
335C8×C47—22no—
336C8×C47—22no—
337C8×C47—22no—
338C2×#3120—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—44no—
343C22×C47#52512yes—
344C22×C47#57712yes—
345C22×C47#57812yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—24no—
348C2×D47—48no—
349C2×D47—42no—
350C2×D47—42no—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47#52512yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C22×#4111yescharacteristic
359Dic47—24no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366C2×#541—471no—
367C2×#520—471no—
368#3120—4716no—
369C2×#484—471no—
370C2×#483—471no—
371C2×#479—471no—
372C2×#478—471no—
373C2×#462—471no—
374C2×#461—471no—
375C2×#452—471no—
376C2×#452—471no—
377C2×#441—471no—
378C2×#440—471no—
379C2×C4×Q16—471no—
380C2×C4×SD16—471no—
381C2×#433D4711yescharacteristic, complemented
382C2×C47—42no—
383C2×C47#312014yescomplemented
384C2×C47C2×#52511yescharacteristic
385C2×C47C2×#57711yescharacteristic
386C2×C47C2×#57811yescharacteristic
387D47—44no—
388C22×#41—471no—
389C22×Q16—471no—
390C22×Q16—471no—
391C22×SD16—471no—
392C22×SD16—471no—
393#541—478no—
394#541—944no—
395C2×C4⋊Q8—471no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#125—471no—
399C2×#125—941no—
400C2×#125—941no—
401C2×C22⋊Q8—471no—
402C2×C22⋊Q8—471no—
403#520—478no—
404#520—944no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×D4—471no—
410C2×C4×D4—471no—
411C2×C4×D4—941no—
412C2×C4×D4—941no—
413C2×#117—941no—
414C2×#117C2×D4711yescharacteristic
415C22×C4⋊C4—471no—
416C22×C4⋊C4—941no—
417#484—478no—
418#483—478no—
419#479—478no—
420#478—478no—
421#462—478no—
422#461—478no—
423#452—478no—
424#452—478no—
425#441—478no—
426#440—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429#433C2×D4718yescomplemented
430C2×#107—471no—
431C2×#107—471no—
432C2×#106—471no—
433C2×#106—471no—
434C2×C4⋊C8C2×D4711yescharacteristic
435C2×C4⋊C8C2×D4711yescharacteristic
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×C22⋊C8C2×D4711yescharacteristic
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×#97C2×D4711yescharacteristic
447C2×C4×C8C2×D4711yescharacteristic
448C47C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—474no—
450C2×#41—944no—
451C2×#41—944no—
452C2×#41—942no—
453C22×Q8—471no—
454C22×Q8—471no—
455C22×Q8—471no—
456C22×D4—471no—
457C22×D4—941no—
458C23×C4—941no—
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×Q16—474no—
464C2×Q16—474no—
465C2×Q16—944no—
466C2×Q16—944no—
467C2×SD16—474no—
468C2×SD16—474no—
469C2×SD16—944no—
470C2×SD16—944no—
471C22×C8C22×D4711yescharacteristic
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#126—948no—
479#125—474no—
480#125—948no—
481#125—948no—
482#125—942no—
483C22⋊Q8—474no—
484C22⋊Q8—474no—
485C22⋊Q8—942no—
486C22⋊Q8—942no—
487C4×Q8—474no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—942no—
492C4×Q8—942no—
493C4×Q8—942no—
494C4×Q8—942no—
495C4×D4—474no—
496C4×D4—474no—
497C4×D4—948no—
498C4×D4—948no—
499C4×D4—942no—
500C4×D4—942no—
501#117—948no—
502#117D18814yes—
503#117C22×D4714yes—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—942no—
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⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—948no—
522C2×C4⋊C4D18811yescharacteristic
523C2×C4⋊C4D18811yescharacteristic
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4D18811yescharacteristic
529C2×C22⋊C4D18811yescharacteristic
530C2×C42—941no—
531C2×C42—941no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42C22×D4711yescharacteristic
535C2×C42C22×D4711yescharacteristic
536#107—474no—
537#107—474no—
538#106—474no—
539#106—474no—
540C4⋊C8C22×D4714yes—
541C4⋊C8C22×D4714yes—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103—474no—
547#103—474no—
548#102—474no—
549#102—474no—
550C22⋊C8C22×D4714yes—
551C22⋊C8C22×D4714yes—
552#97C22×D4714yes—
553C4×C8C22×D4714yes—
554C24—941no—
555C24C2×D18811yescharacteristic
556#41—948no—
557#41—948no—
558#41—9416no—
559C2×Q8—474no—
560C2×Q8—472no—
561C2×Q8—472no—
562C2×Q8—472no—
563C2×Q8—941no—
564C2×Q8—941no—
565C2×Q8—941no—
566C2×Q8—942no—
567C2×Q8—942no—
568C2×Q8—942no—
569C2×Q8—942no—
570C2×Q8—942no—
571C2×D4—474no—
572C2×D4—472no—
573C2×D4—948no—
574C2×D4—944no—
575C2×D4—941no—
576C2×D4—942no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—948no—
580C22×C4—941no—
581C22×C4—944no—
582C22×C4—944no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—944no—
590C22×C4—944no—
591C22×C4—3762no—
592C22×C4—3762no—
593C22×C4—3762no—
594C22×C4C2×D18812yes—
595C22×C4C2×D18811yescharacteristic
596C22×C4C2×D18811yescharacteristic
597C22×C4C2×D18811yescharacteristic
598C22×C4C2×D18811yescharacteristic
599C22×C4C2×D18811yescharacteristic
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602Q16—948no—
603Q16—948no—
604SD16—948no—
605SD16—948no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C2×C8C23×D4712yes—
614C4⋊C4—472no—
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—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4C2×D18814yes—
634C4⋊C4C2×D18814yes—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4C2×D18814yes—
640C22⋊C4C2×D18814yes—
641C42—944no—
642C42—944no—
643C42—944no—
644C42—944no—
645C42C2×D18812yes—
646C42C2×D18812yes—
647C42C23×D4712yes—
648C42C23×D4712yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—944no—
653C23—942no—
654C23—1882no—
655C23—1882no—
656C23C22×D18812yes—
657C23C22×D18811yescharacteristic
658Q8—474no—
659Q8—944no—
660Q8—942no—
661Q8—942no—
662Q8—942no—
663Q8—942no—
664Q8—942no—
665Q8—1882no—
666Q8—1882no—
667D4—474no—
668D4—9416no—
669D4—944no—
670D4—942no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—9416no—
680C2×C4—944no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—3764no—
689C2×C4—3764no—
690C2×C4—3764no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4C22×D18812yes—
698C2×C4C22×D18812yes—
699C2×C4C22×D18812yes—
700C2×C4C22×D18812yes—
701C2×C4C22×D18812yes—
702C2×C4C22×D18811yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#41×D4712yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—944no—
715C22—1882no—
716C22—1882no—
717C22—1888no—
718C22#1568963512yes—
719C22#1568993512yes—
720C22#1568994012yes—
721C22C23×D18811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—944no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C4#1568963512yes—
735C4C2×#41×D4711yescharacteristic
736C4C2×#41×D4711yescharacteristic
737C2—42no—
738C2—1884no—
739C2#2025360414yesdirect product factor
740C2C2×#1568963511yescharacteristic
741C2C2×#1568993511yescharacteristic
742C2C2×#1568994011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#433D47
hypocenterC47C2×#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689735C2semidirect
3. #20253604C2direct (N × H)
4. C2×#15689459C2semidirect
5. C2×#15689454C2semidirect
6. C2×#15689431C2semidirect
7. C2×#15689424C2semidirect
8. C2×#15689334C2semidirect
9. C2×#15689329C2semidirect
12. C2×#15689231C2semidirect
13. C2×#15689225C2semidirect
14. C2×C4×Dic188C2semidirect
15. C2×C4×#10625325C2semidirect
16. C2×C47×#433C2semidirect
23. #15689735C22semidirect
45. #15689459C22semidirect
46. #15689454C22semidirect
47. #15689431C22semidirect
48. #15689424C22semidirect
49. #15689334C22semidirect
50. #15689329C22semidirect
53. #15689231C22semidirect
54. #15689225C22semidirect
55. C4×Dic188C22semidirect
56. C4×#10625325C22semidirect
70. C47×#433C22semidirect
381. C2×#433D47semidirect
383. C2×C47#3120semidirect
429. #433C2×D47semidirect
448. C47C2×#3120semidirect
739. C2#20253604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897352
C2×#156896032
#202536042
C2×#156894592
C2×#156894542
C2×#156894312
C2×#156894242
C2×#156893342
C2×#156893292
C2×#156892872
C2×#156892312
C2×#156892252
C2×C4×Dic1882
C2×C4×#106253252
C2×C47×#4332
C2×#312047