Finite Group Databasebeta

← C2×#20243937 #26218304

Subgroups — C2×#20243937 #26218304

Order 12032.

1670 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689697C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic
4C22×#13093943C211yesmaximal, characteristic, complemented
5#20243937C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688894C211yesmaximal, characteristic, complemented
8C22×#101×C47C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yes—
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19#15689697—22no—
20#15689697—22no—
21#15689697C414yes—
22#15689697C2214yes—
23C2×#13094022—21no—
24C2×#13094013—21no—
25C2×#13094007C414yes—
26C2×#13094000—22no—
27C2×#13093983C2211yescharacteristic
28#15689105—22no—
29#15689105C2214yes—
30C2×#13093943—22no—
31C2×#13093943—22no—
32C2×#13093943C2214yescomplemented
33C2×#13093942—21no—
34C2×#13093940—21no—
35#15688895C2214yescomplemented
36#15688894C2214yescomplemented
37C23×Q8×C47C2211yescharacteristic
38C22×M16×C47C2211yescharacteristic
39C22×M16×C47C2211yescharacteristic
40C2×#101×C47—22no—
41C2×#101×C47—22no—
42C2×#101×C47C2214yescomplemented
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350C2×C412yes—
52C2×#10625350D412yes—
53C2×#10625350D412yes—
54C2×#10625350C2312yes—
55C22×Dic94D411yescharacteristic
56C22×D188D411yescharacteristic
57C22×C22⋊D47C2×C412yes—
58C22×C4×D47D412yes—
59#13094032—28no—
60#13094032—28no—
61#13094030—28no—
62#13094030—28no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329D412yes—
72C2×#10625329D412yes—
73C2×#10625329C2312yes—
74C2×#10625329C2312yes—
75C2×#10625324—24no—
76M16×D47—28no—
77M16×D47—28no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C2×C8×D47—24no—
81#13094022—24no—
82#13094022—24no—
83#13094013—24no—
84#13094013—24no—
85#13094007—28no—
86#13094007C2×C4116yes—
87#13094000—28no—
88#13094000—28no—
89#13093983—21no—
90#13093983—21no—
91#13093983C2×C412yes—
92#13093983C2312yes—
93C2×C4⋊Dic47—21no—
94C2×Dic47⋊C4—24no—
95C2×C22⋊Dic47C2×C412yes—
96C2×(C2×D47)⋊C4—24no—
97C2×C4×Dic47—21no—
98#13093943—28no—
99#13093942—24no—
100#13093940—24no—
101C22×Q8×C47—21no—
102C22×Q8×C47—21no—
103C22×Q8×C47—21no—
104C22×Q8×C47—21no—
105C22×Q8×C47—21no—
106C22×Q8×C47—21no—
107C22×Q8×C47—21no—
108C22×Q8×C47—21no—
109C22×Q8×C47—21no—
110C22×Q8×C47—21no—
111C22×Q8×C47—21no—
112C22×Q8×C47—21no—
113C22×Q8×C47C2×C412yes—
114C22×Q8×C47C2312yes—
115C23×C4×C47C2×C412yes—
116C23×C4×C47C2311yescharacteristic
117C2×M16×C47—21no—
118C2×M16×C47—21no—
119C2×M16×C47—21no—
120C2×M16×C47—21no—
121C2×M16×C47—21no—
122C2×M16×C47—21no—
123C2×M16×C47—21no—
124C2×M16×C47—21no—
125C2×M16×C47D412yes—
126C2×M16×C47D412yes—
127C2×M16×C47C2312yes—
128C2×M16×C47C2312yes—
129C22×C8×C47—21no—
130C22×C8×C47—21no—
131#101×C47—28no—
132C24×C47C22×C411yescharacteristic
133C23×D47C22⋊C412yes—
134C2×Q8×C47—22no—
135C2×Q8×C47—22no—
136C2×Q8×C47—22no—
137C2×Q8×C47—22no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—41no—
147C2×Q8×C47—41no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47—41no—
151C2×Q8×C47—41no—
152C2×Q8×C47—41no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×Q8×C47—41no—
156C2×Q8×C47—41no—
157C2×Q8×C47—41no—
158C2×Q8×C47—41no—
159C2×Q8×C47—41no—
160C2×Q8×C47—41no—
161C2×Q8×C47—41no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47#4111yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47#4111yescharacteristic
181C22×C4×C47#4111yescharacteristic
182C22×C4×C47C2411yescharacteristic
183C2×C22⋊D47—22no—
184C2×C22⋊D47—22no—
185C2×C22⋊D47—22no—
186C2×C22⋊D47—22no—
187C2×C22⋊D47C22⋊C414yes—
188C2×C22⋊D47C22×C414yes—
189C22×Dic47—22no—
190C22×Dic47C22⋊C412yes—
191#10625350—22no—
192#10625350—22no—
193#10625350—22no—
194#10625350—22no—
195#10625350—22no—
196#10625350—22no—
197#10625350—22no—
198#10625350—22no—
199#10625350—22no—
200#10625350—22no—
201#10625350—22no—
202#10625350—22no—
203#10625350—22no—
204#10625350—22no—
205#10625350—22no—
206#10625350—22no—
207C2×D188—21no—
208C2×D188—21no—
209C2×D188—21no—
210C2×D188—21no—
211C2×D188C22⋊C412yes—
212C2×D188C2×D412yes—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47C22⋊C414yes—
218C2×C4×D47C2×D414yes—
219C2×Dic94—21no—
220C2×Dic94—21no—
221C2×Dic94—21no—
222C2×Dic94—21no—
223C2×Dic94C22⋊C412yes—
224C2×Dic94C2×D412yes—
225M16×C47—22no—
226M16×C47—22no—
227M16×C47—22no—
228M16×C47—22no—
229M16×C47—22no—
230M16×C47—41no—
231M16×C47—41no—
232M16×C47C2×D414yes—
233C2×C8×C47—22no—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47—22no—
237C2×C8×C47—41no—
238C2×C8×C47—41no—
239C22⋊Dic47—22no—
240C22⋊Dic47C22×C414yes—
241(C2×D47)⋊C4—216no—
242C4⋊Dic47—22no—
243C4⋊Dic47—22no—
244Dic47⋊C4—216no—
245C4×Dic47—22no—
246C4×Dic47—22no—
247#10625329—22no—
248#10625329—22no—
249#10625329—22no—
250#10625329—22no—
251#10625329—22no—
252#10625329—41no—
253#10625329—41no—
254#10625329C2×D414yes—
255C2×C47⋊C8—22no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—41no—
260C2×C47⋊C8—41no—
261#10625324—216no—
262C8×D47—216no—
263C23×C47—42no—
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47C2×C22⋊C411yescharacteristic
266C23×C47C4×D411yescharacteristic
267C23×C47C4×D411yescharacteristic
268C23×C47C4×D411yescharacteristic
269C23×C47C4×D411yescharacteristic
270C23×C47C23×C411yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—44no—
274C22×D47C2×C22⋊C414yes—
275Q8×C47—42no—
276Q8×C47—42no—
277Q8×C47—42no—
278Q8×C47—42no—
279Q8×C47—42no—
280Q8×C47—42no—
281Q8×C47—42no—
282Q8×C47—42no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47C4×D411yescharacteristic
295C2×C4×C47C4×D411yescharacteristic
296C2×C4×C47#12011yescharacteristic
297C2×C4×C47#12011yescharacteristic
298C2×C4×C47#12011yescharacteristic
299C2×C4×C47#12011yescharacteristic
300C2×C4×C47#12111yescharacteristic
301C2×C4×C47#12111yescharacteristic
302C2×C4×C47#12111yescharacteristic
303C2×C4×C47#12111yescharacteristic
304C2×C4×C47#12111yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12311yescharacteristic
309C2×C4×C47#12311yescharacteristic
310C2×C4×C47#12311yescharacteristic
311C2×C4×C47#12311yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C22⋊D47—24no—
319C22⋊D47—24no—
320C22⋊D47—24no—
321C22⋊D47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—44no—
326C2×Dic47C2×C22⋊C414yes—
327D188—22no—
328D188—22no—
329D188—22no—
330D188—22no—
331C4×D47—24no—
332C4×D47—24no—
333C4×D47—24no—
334C4×D47—24no—
335Dic94—22no—
336Dic94—22no—
337Dic94—22no—
338Dic94—22no—
339C8×C47—24no—
340C8×C47—42no—
341C47⋊C8—24no—
342C47⋊C8—42no—
343C2×#1915—471nomaximal, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47#38611yescharacteristic
352C22×C47#38611yescharacteristic
353C22×C47#38611yescharacteristic
354C22×C47#38611yescharacteristic
355C22×C47C22×C22⋊C411yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47C2×C4×D411yescharacteristic
358C2×D47—24no—
359C2×D47—44no—
360C2×D47—44no—
361C2×D47—82no—
362C4×C47—44no—
363C4×C47#38611yescharacteristic
364C4×C47#38611yescharacteristic
365C4×C47#38611yescharacteristic
366C4×C47#38611yescharacteristic
367C4×C47C2×#12011yescharacteristic
368C4×C47C2×#12111yescharacteristic
369C4×C47C2×#12111yescharacteristic
370C4×C47C2×#12311yescharacteristic
371Dic47—24no—
372Dic47—44no—
373C2×#568—471no—
374C2×#536—471no—
375C2×#413—471no—
376C22×#101—471no—
377C22×#101D4711yescharacteristic, complemented
378#1915—478no—
379C2×#344—471no—
380C2×#344—471no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47#191512yescomplemented
388C2×C47C2×#38611yescharacteristic
389D47—44no—
390C22×#41—471no—
391C23×Q8C2×D4711yescharacteristic
392#568—474no—
393#568—942no—
394#568—942no—
395#568—942no—
396C2×#131—942no—
397C2×#131—942no—
398C22×M16—471no—
399C22×M16—471no—
400C22×M16—942no—
401C22×M16C2×D4711yescharacteristic
402C22×M16C2×D4711yescharacteristic
403#536—474no—
404#536—474no—
405#536—942no—
406#536—942no—
407C2×C4⋊Q8—941no—
408C2×#124—941no—
409C2×#123—474no—
410C2×C22⋊Q8—942no—
411C2×#117—471no—
412#413—474no—
413#413—942no—
414C2×#101—22no—
415C2×#101—22no—
416C2×#101—474no—
417C2×#101—941no—
418C2×#101—942no—
419C2×#101—942no—
420C2×#101C2×D4714yescomplemented
421C2×#100—941no—
422#344—474no—
423#344—474no—
424C47C2×#191511yescharacteristic, complemented, Sylow
425C2×#41—472no—
426C2×#41—472no—
427C2×#41—472no—
428C2×#41—472no—
429C2×#41—941no—
430C2×#41—941no—
431C2×#41—941no—
432C2×#41—941no—
433C2×#41—941no—
434C2×#41—941no—
435C2×#41—941no—
436C2×#41—941no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—471no—
450C22×Q8C4×D4712yes—
451C22×Q8C22×D4712yes—
452C22×D4—472no—
453C22×D4—471no—
454C23×C4—472no—
455C23×C4C4×D4712yes—
456C23×C4C22×D4711yescharacteristic
457#131—948no—
458#131—948no—
459#131—948no—
460#131—948no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—472no—
470C2×M16—472no—
471C2×M16—472no—
472C2×M16—472no—
473C2×M16—944no—
474C2×M16—948no—
475C2×M16—948no—
476C2×M16—941no—
477C2×M16—941no—
478C2×M16—941no—
479C2×M16—941no—
480C2×M16—941no—
481C2×M16—941no—
482C2×M16—941no—
483C2×M16—941no—
484C2×M16C22⋊D4712yes—
485C2×M16C22⋊D4712yes—
486C2×M16C22×D4712yes—
487C2×M16C22×D4712yes—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—944no—
491C22×C8—941no—
492C22×C8—941no—
493C4⋊Q8—944no—
494C4⋊Q8—944no—
495#124—944no—
496#124—944no—
497#123—4716no—
498#123—948no—
499C22⋊Q8—948no—
500C22⋊Q8—948no—
501#117—472no—
502#117—472no—
503#117—941no—
504#117—941no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—941no—
507C2×C22⋊C4—472no—
508C2×C22⋊C4—944no—
509C2×C42—941no—
510#101—28no—
511#101—944no—
512#101—948no—
513#100—944no—
514C24—472no—
515C24C2×C4×D4711yescharacteristic
516#41—942no—
517#41—942no—
518#41—942no—
519#41—942no—
520#41—942no—
521#41—942no—
522#41—942no—
523#41—942no—
524#41—942no—
525#41—942no—
526#41—942no—
527#41—942no—
528#41—942no—
529#41—942no—
530#41—942no—
531#41—942no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—472no—
561C2×Q8—472no—
562C2×Q8—941no—
563C2×Q8—941no—
564C2×Q8—941no—
565C2×Q8—941no—
566C2×D4—474no—
567C2×D4—474no—
568C2×D4—472no—
569C2×D4—472no—
570C2×D4—942no—
571C2×D4—942no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—941no—
575C2×D4—941no—
576C2×D4—941no—
577C2×D4—941no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—472no—
585C22×C4—474no—
586C22×C4—474no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4C2×C4×D4714yes—
593C22×C4C2×C4×D4711yescharacteristic
594C22×C4#1062535011yescharacteristic
595C22×C4#1062535011yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4D4×D4711yescharacteristic
598C22×C4D4×D4711yescharacteristic
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4D4×D4711yescharacteristic
602C22×C4#1062535211yescharacteristic
603C22×C4#1062535211yescharacteristic
604C22×C4C2×C22⋊D4711yescharacteristic
605C22×C4C2×C22⋊D4711yescharacteristic
606C22×C4C23×D4711yescharacteristic
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—474no—
615M16—9416no—
616M16—942no—
617M16—942no—
618M16—942no—
619M16—942no—
620M16—942no—
621M16—1881no—
622M16—1881no—
623M16C2×C22⋊D4714yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—9416no—
631C2×C8—942no—
632C2×C8—942no—
633C2×C8—942no—
634C2×C8—942no—
635C2×C8—1881no—
636C2×C8—1881no—
637C4⋊C4—9416no—
638C4⋊C4—942no—
639C4⋊C4—942no—
640C22⋊C4—474no—
641C22⋊C4—9416no—
642C22⋊C4—942no—
643C42—942no—
644C42—942no—
645C23—42no—
646C23—474no—
647C23—942no—
648C23—942no—
649C23—1884no—
650C23C22⋊C4×D4711yescharacteristic
651C23C22⋊C4×D4711yescharacteristic
652C23(C22⋊D47)⋊C411yescharacteristic
653C23(C22⋊D47)⋊C411yescharacteristic
654C23C4×C22⋊D4711yescharacteristic
655C23C4×C22⋊D4711yescharacteristic
656C23C22×C4×D4711yescharacteristic
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—942no—
666Q8—942no—
667Q8—942no—
668Q8—942no—
669D4—944no—
670D4—944no—
671D4—944no—
672D4—944no—
673D4—942no—
674D4—942no—
675D4—942no—
676D4—942no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—474no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—944no—
688C2×C4—944no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—944no—
692C2×C4—1884no—
693C2×C4C22⋊C4×D4711yescharacteristic
694C2×C4C22⋊C4×D4711yescharacteristic
695C2×C4(C22⋊D47)⋊C411yescharacteristic
696C2×C4(C22⋊D47)⋊C411yescharacteristic
697C2×C4C4×C22⋊D4711yescharacteristic
698C2×C4C4×C22⋊D4711yescharacteristic
699C2×C4#1309399211yescharacteristic
700C2×C4#1309399211yescharacteristic
701C2×C4#1309399211yescharacteristic
702C2×C4#1309399211yescharacteristic
703C2×C4#1309399511yescharacteristic
704C2×C4#1309399511yescharacteristic
705C2×C4#1309399511yescharacteristic
706C2×C4#1309399511yescharacteristic
707C2×C4#1309399711yescharacteristic
708C2×C4#1309399711yescharacteristic
709C2×C4#1309399711yescharacteristic
710C2×C4#1309399711yescharacteristic
711C2×C4#1309400611yescharacteristic
712C2×C4#1309400611yescharacteristic
713C2×C4#1309400611yescharacteristic
714C2×C4#1309400611yescharacteristic
715C2×C4C2×D4×D4711yescharacteristic
716C2×C4C2×D4×D4711yescharacteristic
717C2×C4C2×D4×D4711yescharacteristic
718C2×C4C22×C22⋊D4711yescharacteristic
719C2×C4C2×#1062535211yescharacteristic
720C2×C4C2×#1062535011yescharacteristic
721C8—24no—
722C8—42no—
723C8—944no—
724C8—1882no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—944no—
733C22—3762no—
734C22—1884no—
735C22—1884no—
736C22#1568899911yescharacteristic
737C22#1568899911yescharacteristic
738C22#1568899911yescharacteristic
739C22#1568899911yescharacteristic
740C22C2×C22⋊C4×D4711yescharacteristic
741C22C2×(C22⋊D47)⋊C411yescharacteristic
742C22C2×C4×C22⋊D4711yescharacteristic
743C4—44no—
744C4—944no—
745C4—1884no—
746C4#1568899911yescharacteristic
747C4#1568899911yescharacteristic
748C4#1568899911yescharacteristic
749C4#1568899911yescharacteristic
750C4C2×#1309399211yescharacteristic
751C4C2×#1309399511yescharacteristic
752C4C2×#1309399711yescharacteristic
753C4C2×#1309400611yescharacteristic
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—1884no—
761C2#2024393712yesdirect product factor
762C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#101×C47C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC22×#101D47
hypocenterC47C2×#1915
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
4. C22×#13093943C2semidirect
5. #20243937C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688894C2semidirect
8. C22×#101×C47C2semidirect
32. C2×#13093943C22semidirect
35. #15688895C22semidirect
36. #15688894C22semidirect
42. C2×#101×C47C22semidirect
377. C22×#101D47semidirect
387. C2×C47#1915semidirect
420. C2×#101C2×D47semidirect
424. C47C2×#1915semidirect
761. C2#20243937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156896972
C2×#156891052
C22×#130939432
#202439372
C2×#156888952
C2×#156888942
C22×#101×C472
C2×#191547