Finite Group Databasebeta

← C2×#20244283 #26220249

Subgroups — C2×#20244283 #26220249

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094044C211yesmaximal, characteristic
2C2×#15689159C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689140C211yesmaximal, characteristic, complemented
5C2×#15689096C211yesmaximal, characteristic, complemented
6C2×#15689079C211yesmaximal, characteristic, complemented
7#20244283C218yesmaximal, direct product factor
8C2×C47×#410C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C2×#13094044—21no—
11C2×#13094044—21no—
12C2×#13094044—22no—
13C2×#13094044—21no—
14C2×#13094044—21no—
15C2×#13094044—22no—
16C2×#13094044C414yescomplemented
17C2×#13094044C2214yes—
18C22×#10625337C411yescharacteristic, complemented
19C22×#10625335C411yescharacteristic, complemented
20C22×#10625336C411yescharacteristic, complemented
21C22×#10625334C411yescharacteristic, complemented
22C22×#10625329C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic
24C2×#13093983C2211yescharacteristic
25#15689159—22no—
26#15689159C2214yescomplemented
27C2×#13093957—21no—
28C2×#13093955—21no—
29#15689141—22no—
30#15689141C2214yescomplemented
31#15689140—22no—
32#15689140C2214yescomplemented
33C2×#13093952—22no—
34C2×#13093951—22no—
35#15689096—22no—
36#15689096C2214yescomplemented
37C2×#13093938—22no—
38#15689079—22no—
39#15689079C2214yescomplemented
40C2×#13093935—21no—
41C2×C4×C47⋊C8—21no—
42C22×#41×C47C2211yescharacteristic
43C2×#117×C47C2211yescharacteristic
44C2×#117×C47C2211yescharacteristic
45C47×#410—22no—
46C47×#410C2214yescomplemented
47C2×#99×C47—22no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350—21no—
55C2×#10625350—21no—
56C2×#10625350—21no—
57C2×#10625350—21no—
58C2×#10625350C2×C412yes—
59C2×#10625350C2312yes—
60C22×Dic94C2×C411yescharacteristic
61C22×D188C2×C411yescharacteristic
62C22×C22⋊D47—21no—
63C22×C4×D47—21no—
64#13094044—24no—
65#13094044—24no—
66#13094044—24no—
67#13094044—24no—
68#13094044—24no—
69#13094044—24no—
70#13094044—24no—
71#13094044—24no—
72C2×#10625337—21no—
73C2×#10625337—21no—
74C2×#10625337—22no—
75C2×#10625337C2×C414yescomplemented
76C2×#10625335—21no—
77C2×#10625335—21no—
78C2×#10625335—22no—
79C2×#10625335C2×C414yescomplemented
80C2×#10625336—21no—
81C2×#10625336—21no—
82C2×#10625336—22no—
83C2×#10625336C2×C414yescomplemented
84C2×#10625334—21no—
85C2×#10625334—21no—
86C2×#10625334—22no—
87C2×#10625334C2×C414yescomplemented
88C2×#10625329—21no—
89C2×#10625329—21no—
90C2×#10625329—21no—
91C2×#10625329D412yes—
92C2×#10625329D412yes—
93C2×#10625329C2312yes—
94C22×C47⋊C8—21no—
95C22×C47⋊C8C2×C411yescharacteristic
96C22×C47⋊C8C2×C411yescharacteristic
97C22×C47⋊C8C2×C412yes—
98C22×C47⋊C8D411yescharacteristic
99C22×C47⋊C8D411yescharacteristic
100C22×C47⋊C8D412yes—
101C22×C47⋊C8D411yescharacteristic
102C22×C47⋊C8D411yescharacteristic
103C22×C47⋊C8D412yes—
104C22×C47⋊C8C2312yes—
105#13093983—21no—
106#13093983—21no—
107#13093983—21no—
108#13093983C2312yes—
109C2×C4⋊Dic47—21no—
110C2×C22⋊Dic47—21no—
111C2×C4×Dic47—21no—
112#13093957—24no—
113#13093955—24no—
114#13093952—28no—
115#13093951—28no—
116#13093938—28no—
117#13093935—24no—
118C4×C47⋊C8—24no—
119C2×#41×C47—21no—
120C2×#41×C47—21no—
121C2×#41×C47—21no—
122C2×#41×C47—21no—
123C2×#41×C47—21no—
124C2×#41×C47—21no—
125C2×#41×C47—21no—
126C2×#41×C47—21no—
127C2×#41×C47—21no—
128C2×#41×C47—21no—
129C2×#41×C47C2×C412yes—
130C2×#41×C47C2312yes—
131C22×Q8×C47C2×C411yescharacteristic
132C22×D4×C47—21no—
133C22×D4×C47C2×C411yescharacteristic
134C23×C4×C47—21no—
135C23×C4×C47C2311yescharacteristic
136#117×C47—21no—
137#117×C47—21no—
138#117×C47—21no—
139#117×C47—21no—
140#117×C47—21no—
141#117×C47D412yes—
142#117×C47C2312yes—
143#117×C47C2312yes—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47D412yes—
148C2×C42×C47—21no—
149C2×C42×C47—21no—
150#99×C47—28no—
151C24×C47—21no—
152C24×C47C2×D411yescharacteristic
153C23×D47—21no—
154#41×C47—22no—
155#41×C47—22no—
156#41×C47—22no—
157#41×C47—22no—
158#41×C47—22no—
159#41×C47—22no—
160#41×C47—22no—
161#41×C47—22no—
162#41×C47—41no—
163#41×C47—41no—
164#41×C47—41no—
165#41×C47—41no—
166#41×C47—41no—
167#41×C47—41no—
168#41×C47—41no—
169#41×C47—41no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47—21no—
175C2×Q8×C47C22×C412yes—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—41no—
184C2×D4×C47—41no—
185C2×D4×C47—41no—
186C2×D4×C47—41no—
187C2×D4×C47C22×C412yes—
188C22×C4×C47—21no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—41no—
193C22×C4×C47—41no—
194C22×C4×C47—41no—
195C22×C4×C47—41no—
196C22×C4×C47—41no—
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47#4111yescharacteristic
207C22×C4×C47#4111yescharacteristic
208C22×C4×C47#4111yescharacteristic
209C22×C4×C47#4111yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—22no—
212C2×C22⋊D47—22no—
213C2×C22⋊D47—41no—
214C2×C22⋊D47—41no—
215C2×C22⋊D47—41no—
216C2×C22⋊D47—41no—
217C22×Dic47—21no—
218C22×Dic47—41no—
219#10625350—22no—
220#10625350—22no—
221#10625350—22no—
222#10625350—22no—
223#10625350—22no—
224#10625350—22no—
225#10625350—22no—
226#10625350—22no—
227#10625350—41no—
228#10625350—41no—
229#10625350—41no—
230#10625350—41no—
231#10625350—41no—
232#10625350—41no—
233#10625350—41no—
234#10625350—41no—
235C2×D188—21no—
236C2×D188—21no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—21no—
240C2×D188C22×C412yes—
241C2×C4×D47—22no—
242C2×C4×D47—22no—
243C2×C4×D47—41no—
244C2×C4×D47—41no—
245C2×C4×D47—41no—
246C2×C4×D47—41no—
247C2×Dic94—21no—
248C2×Dic94—21no—
249C2×Dic94—21no—
250C2×Dic94—21no—
251C2×Dic94—21no—
252C2×Dic94C22×C412yes—
253C4⋊C4×C47—22no—
254C4⋊C4×C47—22no—
255C4⋊C4×C47—22no—
256C4⋊C4×C47—41no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—41no—
260C22⋊C4×C47C2×D414yes—
261C42×C47—22no—
262C42×C47—22no—
263C42×C47—22no—
264C42×C47—41no—
265C22⋊Dic47—22no—
266C22⋊Dic47—41no—
267#10625337—24no—
268#10625337—24no—
269#10625336—24no—
270#10625336—24no—
271#10625335—24no—
272#10625335—24no—
273#10625334—24no—
274#10625334—24no—
275C4⋊Dic47—22no—
276C4⋊Dic47—41no—
277C4×Dic47—22no—
278C4×Dic47—41no—
279#10625329—22no—
280#10625329—22no—
281#10625329—22no—
282#10625329C2×D414yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8C22⋊C411yescharacteristic
287C2×C47⋊C8C22⋊C411yescharacteristic
288C2×C47⋊C8C22⋊C412yes—
289C2×C47⋊C8C22⋊C411yescharacteristic
290C2×C47⋊C8C22⋊C411yescharacteristic
291C2×C47⋊C8C22⋊C412yes—
292C2×C47⋊C8C22⋊C412yes—
293C2×C47⋊C8C22⋊C412yes—
294C2×C47⋊C8C22⋊C412yes—
295C2×C47⋊C8C22⋊C412yes—
296C2×C47⋊C8C22×C412yes—
297C2×C47⋊C8C22×C412yes—
298C2×C47⋊C8C2×D412yes—
299C2×C47⋊C8C2×D412yes—
300C2×C47⋊C8C2×D412yes—
301C2×C47⋊C8C2×D412yes—
302C23×C47—22no—
303C23×C47—42no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—82no—
307C23×C47C4×D411yescharacteristic
308C23×C47C4×D411yescharacteristic
309C23×C47#12111yescharacteristic
310C23×C47#12111yescharacteristic
311C23×C47#12711yescharacteristic
312C23×C47#12711yescharacteristic
313C23×C47C22×D411yescharacteristic
314C22×D47—22no—
315C22×D47—41no—
316C22×D47—41no—
317C22×D47—82no—
318Q8×C47—22no—
319Q8×C47—22no—
320Q8×C47—41no—
321Q8×C47—41no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—42no—
325D4×C47—42no—
326D4×C47—42no—
327D4×C47—42no—
328D4×C47—41no—
329D4×C47—41no—
330C2×C4×C47—22no—
331C2×C4×C47—24no—
332C2×C4×C47—44no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47—42no—
340C2×C4×C47—82no—
341C2×C4×C47C2×C22⋊C411yescharacteristic
342C2×C4×C47C2×C22⋊C411yescharacteristic
343C2×C4×C47C2×C22⋊C411yescharacteristic
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C4×D411yescharacteristic
346C2×C4×C47C4×D411yescharacteristic
347C2×C4×C47C4×D411yescharacteristic
348C2×C4×C47C4×D411yescharacteristic
349C2×C4×C47C4×D411yescharacteristic
350C2×C4×C47C4×D411yescharacteristic
351C2×C4×C47#12111yescharacteristic
352C2×C4×C47#12111yescharacteristic
353C2×C4×C47#12111yescharacteristic
354C2×C4×C47#12111yescharacteristic
355C2×C4×C47#12111yescharacteristic
356C2×C4×C47#12111yescharacteristic
357C2×C4×C47#12411yescharacteristic
358C2×C4×C47#12411yescharacteristic
359C2×C4×C47#12411yescharacteristic
360C2×C4×C47#12411yescharacteristic
361C2×C4×C47#12711yescharacteristic
362C2×C4×C47#12711yescharacteristic
363C2×C4×C47C23×C411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47C2×#4111yescharacteristic
368C2×C4×C47C2×#4111yescharacteristic
369C22⋊D47—42no—
370C22⋊D47—42no—
371C22⋊D47—42no—
372C22⋊D47—42no—
373C2×Dic47—22no—
374C2×Dic47—41no—
375C2×Dic47—41no—
376C2×Dic47—42no—
377C2×Dic47—82no—
378D188—22no—
379D188—22no—
380D188—41no—
381D188—41no—
382C4×D47—42no—
383C4×D47—42no—
384C4×D47—42no—
385C4×D47—42no—
386Dic94—22no—
387Dic94—22no—
388Dic94—41no—
389Dic94—41no—
390C47⋊C8—24no—
391C47⋊C8C2×C22⋊C412yes—
392C47⋊C8C2×C22⋊C412yes—
393C47⋊C8C2×C22⋊C412yes—
394C47⋊C8C2×C22⋊C412yes—
395C2×#1976—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—42no—
404C22×C47—82no—
405C22×C47—82no—
406C22×C47—82no—
407C22×C47#39011yescharacteristic
408C22×C47#39011yescharacteristic
409C22×C47#39011yescharacteristic
410C22×C47#39011yescharacteristic
411C22×C47C2×C4×D411yescharacteristic
412C22×C47C2×#12111yescharacteristic
413C22×C47C2×#12711yescharacteristic
414C2×D47—42no—
415C2×D47—82no—
416C2×D47—82no—
417C2×D47—82no—
418C4×C47—44no—
419C4×C47—42no—
420C4×C47—82no—
421C4×C47#39011yescharacteristic
422C4×C47#39011yescharacteristic
423C4×C47#39011yescharacteristic
424C4×C47#39011yescharacteristic
425C4×C47C22×C22⋊C411yescharacteristic
426C4×C47C2×C4×D411yescharacteristic
427C4×C47C2×#12111yescharacteristic
428C4×C47C2×#12411yescharacteristic
429Dic47—42no—
430Dic47—82no—
431C22×#135—471no—
432C2×#427—471no—
433C2×#421—471no—
434C2×#421—471no—
435C2×#410—471no—
436C2×#410D4711yescharacteristic, complemented
437C2×#405—471no—
438#1976—478no—
439C2×C47—21no—
440C2×C47—21no—
441C2×C47—21no—
442C2×C47—21no—
443C2×C47—21no—
444C2×C47—21no—
445C2×C47—82no—
446C2×C47#197612yescomplemented
447C2×C47C2×#39011yescharacteristic
448D47—82no—
449C22×#41—471no—
450C22×#41C2×D4711yescharacteristic
451C2×#135—474no—
452C2×#135—474no—
453C2×#135—941no—
454C2×#135—941no—
455C2×#135—942no—
456C2×#135—941no—
457C2×#135—941no—
458C2×#135—942no—
459C22×Q16—471no—
460C22×SD16—471no—
461C22×SD16—471no—
462C22×D8—471no—
463C22×M16—471no—
464C23×C8—471no—
465C2×#117—471no—
466C2×#117C2×D4711yescharacteristic
467C2×#117C2×D4711yescharacteristic
468#427—474no—
469#427—942no—
470C2×#107—941no—
471C2×#106—941no—
472#421—474no—
473#421—474no—
474#421—942no—
475#421—942no—
476C2×#104—942no—
477C2×#104—942no—
478#410—22no—
479#410—474no—
480#410—942no—
481#410C2×D4714yescomplemented
482C2×#99—22no—
483C2×#99—942no—
484#405—474no—
485#405—942no—
486C2×#97—941no—
487C2×C4×C8—941no—
488C47C2×#197611yescharacteristic, complemented, Sylow
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—472no—
500C2×#41—472no—
501C2×#41—941no—
502C2×#41—941no—
503C2×#41—941no—
504C2×#41—941no—
505C2×#41—941no—
506C2×#41—941no—
507C2×#41—941no—
508C2×#41—941no—
509C2×#41—941no—
510C2×#41—941no—
511C2×#41C4×D4712yes—
512C2×#41C22×D4712yes—
513C22×Q8—471no—
514C22×Q8C4×D4711yescharacteristic
515C22×D4—21no—
516C22×D4—471no—
517C22×D4—941no—
518C22×D4C4×D4711yescharacteristic
519C23×C4—21no—
520C23×C4—941no—
521C23×C4C22×D4711yescharacteristic
522#135—944no—
523#135—944no—
524#135—944no—
525#135—944no—
526#135—944no—
527#135—944no—
528#135—944no—
529#135—944no—
530C2×Q16—474no—
531C2×Q16—941no—
532C2×Q16—941no—
533C2×Q16—942no—
534C2×SD16—474no—
535C2×SD16—474no—
536C2×SD16—941no—
537C2×SD16—941no—
538C2×SD16—942no—
539C2×SD16—941no—
540C2×SD16—941no—
541C2×SD16—942no—
542C2×D8—474no—
543C2×D8—941no—
544C2×D8—941no—
545C2×D8—942no—
546C2×M16—472no—
547C2×M16—472no—
548C2×M16—472no—
549C2×M16—941no—
550C2×M16—941no—
551C2×M16—941no—
552C22×C8—471no—
553C22×C8—471no—
554C22×C8—472no—
555C22×C8—471no—
556C22×C8—471no—
557C22×C8—472no—
558C22×C8—471no—
559C22×C8—471no—
560C22×C8—472no—
561C22×C8—472no—
562C22×C8—941no—
563#117—21no—
564#117—21no—
565#117—21no—
566#117—21no—
567#117—21no—
568#117—472no—
569#117—941no—
570#117—941no—
571#117—941no—
572#117C22⋊D4712yes—
573#117C22×D4712yes—
574#117C22×D4712yes—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—941no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4C22⋊D4712yes—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—941no—
584#107—944no—
585#106—944no—
586#104—948no—
587#104—948no—
588#99—28no—
589#99—948no—
590#97—944no—
591C4×C8—944no—
592C24—21no—
593C24—941no—
594C24C2×C22⋊D4711yescharacteristic
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—942no—
612#41—942no—
613#41—942no—
614#41—942no—
615#41—942no—
616#41—942no—
617#41—942no—
618#41—942no—
619#41—1881no—
620#41—1881no—
621#41—1881no—
622#41—1881no—
623#41—1881no—
624#41—1881no—
625#41—1881no—
626#41—1881no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—472no—
633C2×Q8—941no—
634C2×Q8—941no—
635C2×Q8—941no—
636C2×Q8—941no—
637C2×Q8—941no—
638C2×Q8C2×C4×D4712yes—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4—472no—
651C2×D4—942no—
652C2×D4—942no—
653C2×D4—941no—
654C2×D4—941no—
655C2×D4—941no—
656C2×D4—941no—
657C2×D4—941no—
658C2×D4—1881no—
659C2×D4—1881no—
660C2×D4—1881no—
661C2×D4—1881no—
662C2×D4C2×C4×D4712yes—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—941no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—1881no—
676C22×C4—1881no—
677C22×C4—1881no—
678C22×C4—1881no—
679C22×C4—1881no—
680C22×C4C2×C4×D4711yescharacteristic
681C22×C4C2×C4×D4711yescharacteristic
682C22×C4#1062535011yescharacteristic
683C22×C4#1062535011yescharacteristic
684C22×C4D4×D4711yescharacteristic
685C22×C4D4×D4711yescharacteristic
686C22×C4D4×D4711yescharacteristic
687C22×C4D4×D4711yescharacteristic
688C22×C4D4×D4711yescharacteristic
689C22×C4D4×D4711yescharacteristic
690C22×C4#1062535211yescharacteristic
691C22×C4#1062535211yescharacteristic
692C22×C4C2×C22⋊D4711yescharacteristic
693C22×C4C23×D4711yescharacteristic
694Q16—944no—
695Q16—944no—
696SD16—944no—
697SD16—944no—
698SD16—944no—
699SD16—944no—
700D8—944no—
701D8—944no—
702M16—474no—
703M16—942no—
704M16—942no—
705M16—942no—
706C2×C8—471no—
707C2×C8—471no—
708C2×C8—472no—
709C2×C8—471no—
710C2×C8—471no—
711C2×C8—472no—
712C2×C8—472no—
713C2×C8—472no—
714C2×C8—472no—
715C2×C8—472no—
716C2×C8—472no—
717C2×C8—472no—
718C2×C8—472no—
719C2×C8—472no—
720C2×C8—472no—
721C2×C8—472no—
722C2×C8—942no—
723C2×C8—942no—
724C2×C8—942no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—41no—
729C4⋊C4—942no—
730C4⋊C4—1881no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—41no—
734C22⋊C4—942no—
735C22⋊C4—1881no—
736C22⋊C4C2×C22⋊D4714yes—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—41no—
741C42—942no—
742C42—1881no—
743C23—22no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—82no—
748C23—942no—
749C23—3762no—
750C23—1881no—
751C23—1881no—
752C23C4×C22⋊D4711yescharacteristic
753C23C4×C22⋊D4711yescharacteristic
754C23#1309399611yescharacteristic
755C23#1309399611yescharacteristic
756C23#1309402011yescharacteristic
757C23#1309402011yescharacteristic
758C23C22×C22⋊D4711yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763Q8—942no—
764Q8—942no—
765Q8—1881no—
766Q8—1881no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—41no—
775D4—942no—
776D4—942no—
777D4—1882no—
778D4—1882no—
779D4—1882no—
780D4—1882no—
781D4—1881no—
782D4—1881no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—82no—
794C2×C4—942no—
795C2×C4—3762no—
796C2×C4—1882no—
797C2×C4—1881no—
798C2×C4—1881no—
799C2×C4—1882no—
800C2×C4—1882no—
801C2×C4—1882no—
802C2×C4—1882no—
803C2×C4C22⋊C4×D4711yescharacteristic
804C2×C4C22⋊C4×D4711yescharacteristic
805C2×C4C22⋊C4×D4711yescharacteristic
806C2×C4C22⋊C4×D4711yescharacteristic
807C2×C4(C22⋊D47)⋊C411yescharacteristic
808C2×C4(C22⋊D47)⋊C411yescharacteristic
809C2×C4(C22⋊D47)⋊C411yescharacteristic
810C2×C4(C22⋊D47)⋊C411yescharacteristic
811C2×C4C4×C22⋊D4711yescharacteristic
812C2×C4C4×C22⋊D4711yescharacteristic
813C2×C4#1309399611yescharacteristic
814C2×C4#1309399611yescharacteristic
815C2×C4#1309399711yescharacteristic
816C2×C4#1309399711yescharacteristic
817C2×C4#1309399711yescharacteristic
818C2×C4#1309399711yescharacteristic
819C2×C4#1309401011yescharacteristic
820C2×C4#1309401011yescharacteristic
821C2×C4#1309401011yescharacteristic
822C2×C4#1309401011yescharacteristic
823C2×C4#1309402011yescharacteristic
824C2×C4#1309402011yescharacteristic
825C2×C4C22×C4×D4711yescharacteristic
826C2×C4C2×D4×D4711yescharacteristic
827C2×C4C2×D4×D4711yescharacteristic
828C2×C4C2×D4×D4711yescharacteristic
829C2×C4C2×#1062535211yescharacteristic
830C2×C4C2×#1062535011yescharacteristic
831C8—472no—
832C8—472no—
833C8—472no—
834C8—472no—
835C8—944no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—3762no—
848C22—3762no—
849C22—3762no—
850C22—1882no—
851C22#1568902311yescharacteristic
852C22#1568902311yescharacteristic
853C22#1568902311yescharacteristic
854C22#1568902311yescharacteristic
855C22C2×C4×C22⋊D4711yescharacteristic
856C22C2×#1309399611yescharacteristic
857C22C2×#1309402011yescharacteristic
858C4—44no—
859C4—42no—
860C4—82no—
861C4—3762no—
862C4—1882no—
863C4#1568902311yescharacteristic
864C4#1568902311yescharacteristic
865C4#1568902311yescharacteristic
866C4#1568902311yescharacteristic
867C4C2×C22⋊C4×D4711yescharacteristic
868C4C2×(C22⋊D47)⋊C411yescharacteristic
869C4C2×#1309399711yescharacteristic
870C4C2×#1309401011yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—82no—
878C2—3762no—
879C2#2024428312yesdirect product factor
880C2C2×#1568902311yescharacteristic
subgroupG/H
centerC2×C4#13093997
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#410C2
socleC22×C47#390
prime radicalC22×#13094044C2
cosocleC22×C4×C47C24
hypercenterC2×#410D47
hypocenterC47C2×#1976
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#15689159C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689140C2semidirect
5. C2×#15689096C2semidirect
6. C2×#15689079C2semidirect
7. #20244283C2direct (N × H)
8. C2×C47×#410C2semidirect
16. C2×#13094044C4semidirect
18. C22×#10625337C4semidirect
19. C22×#10625335C4semidirect
20. C22×#10625336C4semidirect
21. C22×#10625334C4semidirect
26. #15689159C22semidirect
30. #15689141C22semidirect
32. #15689140C22semidirect
36. #15689096C22semidirect
39. #15689079C22semidirect
46. C47×#410C22semidirect
75. C2×#10625337C2×C4semidirect
79. C2×#10625335C2×C4semidirect
83. C2×#10625336C2×C4semidirect
87. C2×#10625334C2×C4semidirect
436. C2×#410D47semidirect
446. C2×C47#1976semidirect
481. #410C2×D47semidirect
488. C47C2×#1976semidirect
879. C2#20244283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940442
C2×#156891592
C2×#156891412
C2×#156891402
C2×#156890962
C2×#156890792
#202442832
C2×C47×#4102
C2×#197647