Finite Group Databasebeta

← C2×#19135146 #25098625

Subgroups — C2×#19135146 #25098625

Order 11008.

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×#14583665C211yesmaximal, characteristic
2C2×#14583475C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C22×#13063243C211yesmaximal, characteristic, complemented
5C22×#13063243C211yesmaximal, characteristic, complemented
6#19135146C218yesmaximal, direct product factor
7C2×#14582669C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×Dic86C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yes—
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583475—22no—
21#14583475—22no—
22#14583475C414yes—
23#14583475C2214yes—
24C2×#13063325—21no—
25C2×#13063313—21no—
26C2×#13063309C414yes—
27C2×#13063305—22no—
28#14582881—22no—
29#14582881C2214yes—
30C2×#13063243—21no—
31C2×#13063243—22no—
32C2×#13063243—22no—
33C2×#13063243—22no—
34C2×#13063243—22no—
35C2×#13063243C2214yescomplemented
36C2×#13063243C2214yescomplemented
37C2×#13063241—21no—
38#14582669C2214yescomplemented
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C43×#344C2214yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86—21no—
56C22×Dic86—21no—
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86—21no—
60C22×Dic86—21no—
61C22×Dic86—21no—
62C22×Dic86—21no—
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86—21no—
66C22×Dic86—21no—
67C22×Dic86C2×C412yes—
68C22×Dic86D411yescharacteristic
69C22×Dic86C2312yes—
70C22×D172D411yescharacteristic
71C22×C22⋊D43C2×C412yes—
72C23×Dic43C2×C412yes—
73C22×C4×D43D412yes—
74#13063333—28no—
75#13063333—28no—
76#13063331—28no—
77#13063331—28no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877D412yes—
87C2×#10621877D412yes—
88C2×#10621877C2312yes—
89C2×#10621877C2312yes—
90C2×#10621872—24no—
91M16×D43—28no—
92M16×D43—28no—
93C22×C43⋊C8—21no—
94C22×C43⋊C8—21no—
95C2×C8×D43—24no—
96#13063325—24no—
97#13063325—24no—
98#13063313—24no—
99#13063313—24no—
100#13063309—28no—
101#13063309C2×C4116yes—
102#13063305—28no—
103#13063305—28no—
104C2×C4⋊Dic43—24no—
105C2×(C2×D43)⋊C4—24no—
106#13063243—24no—
107#13063243—28no—
108#13063243—28no—
109#13063241—24no—
110C23×C4×C43C2311yescharacteristic
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D412yes—
120C2×M16×C43D412yes—
121C2×M16×C43C2312yes—
122C2×M16×C43C2312yes—
123C22×C8×C43—21no—
124C22×C8×C43—21no—
125#117×C43—21no—
126#117×C43—21no—
127#117×C43C2×C412yes—
128#117×C43C2312yes—
129C2×C4⋊C4×C43—21no—
130C2×C22⋊C4×C43C2×C412yes—
131C2×C42×C43—21no—
132C24×C43C22×C411yescharacteristic
133C23×D43C22⋊C412yes—
134C22×C4×C43—22no—
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43#4111yescharacteristic
145C22×C4×C43#4111yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C22×C4×C43#4111yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43C22⋊C414yes—
154C2×C22⋊D43C22×C414yes—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43C22⋊C412yes—
162C22×Dic43C22×C414yes—
163#10621898—22no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
178#10621898—22no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C22⋊C412yes—
184C2×D172C2×D412yes—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43C22⋊C414yes—
190C2×C4×D43C2×D414yes—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—22no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—22no—
203C2×Dic86—22no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86—22no—
207C2×Dic86—41no—
208C2×Dic86—41no—
209C2×Dic86—41no—
210C2×Dic86—41no—
211C2×Dic86—41no—
212C2×Dic86—41no—
213C2×Dic86—41no—
214C2×Dic86—41no—
215C2×Dic86—41no—
216C2×Dic86—41no—
217C2×Dic86—41no—
218C2×Dic86—41no—
219C2×Dic86—41no—
220C2×Dic86—41no—
221C2×Dic86—41no—
222C2×Dic86—41no—
223C2×Dic86C22⋊C412yes—
224C2×Dic86C2×D412yes—
225M16×C43—22no—
226M16×C43—22no—
227M16×C43—22no—
228M16×C43—22no—
229M16×C43—22no—
230M16×C43—41no—
231M16×C43—41no—
232M16×C43C2×D414yes—
233C2×C8×C43—22no—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43—41no—
238C2×C8×C43—41no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43C22×C414yes—
243C42×C43—22no—
244C42×C43—22no—
245(C2×D43)⋊C4—216no—
246C4⋊Dic43—216no—
247#10621877—22no—
248#10621877—22no—
249#10621877—22no—
250#10621877—22no—
251#10621877—22no—
252#10621877—41no—
253#10621877—41no—
254#10621877C2×D414yes—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—41no—
260C2×C43⋊C8—41no—
261#10621872—216no—
262C8×D43—216no—
263C23×C43—42no—
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C4×D411yescharacteristic
267C23×C43C4×D411yescharacteristic
268C23×C43C4×D411yescharacteristic
269C23×C43C4×D411yescharacteristic
270C23×C43C23×C411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—44no—
274C22×D43C2×C22⋊C414yes—
275C2×C4×C43—24no—
276C2×C4×C43—44no—
277C2×C4×C43C2×C22⋊C411yescharacteristic
278C2×C4×C43C2×C22⋊C411yescharacteristic
279C2×C4×C43C4×D411yescharacteristic
280C2×C4×C43C4×D411yescharacteristic
281C2×C4×C43C4×D411yescharacteristic
282C2×C4×C43C4×D411yescharacteristic
283C2×C4×C43#12011yescharacteristic
284C2×C4×C43#12011yescharacteristic
285C2×C4×C43#12011yescharacteristic
286C2×C4×C43#12011yescharacteristic
287C2×C4×C43#12111yescharacteristic
288C2×C4×C43#12111yescharacteristic
289C2×C4×C43#12111yescharacteristic
290C2×C4×C43#12111yescharacteristic
291C2×C4×C43#12111yescharacteristic
292C2×C4×C43#12111yescharacteristic
293C2×C4×C43#12111yescharacteristic
294C2×C4×C43#12111yescharacteristic
295C2×C4×C43#12311yescharacteristic
296C2×C4×C43#12311yescharacteristic
297C2×C4×C43#12311yescharacteristic
298C2×C4×C43#12311yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C22⋊D43—24no—
306C22⋊D43—24no—
307C22⋊D43—24no—
308C22⋊D43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43C2×C22⋊C414yes—
319D172—22no—
320D172—22no—
321D172—22no—
322D172—22no—
323C4×D43—24no—
324C4×D43—24no—
325C4×D43—24no—
326C4×D43—24no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—42no—
332Dic86—42no—
333Dic86—42no—
334Dic86—42no—
335Dic86—42no—
336Dic86—42no—
337Dic86—42no—
338Dic86—42no—
339C8×C43—24no—
340C8×C43—42no—
341C43⋊C8—24no—
342C43⋊C8—42no—
343C2×#1915—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43#38611yescharacteristic
352C22×C43#38611yescharacteristic
353C22×C43#38611yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43C22×C22⋊C411yescharacteristic
356C22×C43C2×C4×D411yescharacteristic
357C22×C43C2×C4×D411yescharacteristic
358C2×D43—24no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—82no—
362C4×C43—44no—
363C4×C43#38611yescharacteristic
364C4×C43#38611yescharacteristic
365C4×C43#38611yescharacteristic
366C4×C43#38611yescharacteristic
367C4×C43C2×#12011yescharacteristic
368C4×C43C2×#12111yescharacteristic
369C4×C43C2×#12111yescharacteristic
370C4×C43C2×#12311yescharacteristic
371Dic43—24no—
372Dic43—44no—
373C2×#568—431no—
374C2×#536—431no—
375C2×#413—431no—
376C22×#101—431no—
377C22×#101—431no—
378#1915—438no—
379C2×#344—431no—
380C2×#344D4311yescharacteristic, complemented
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43#191512yescomplemented
388C2×C43C2×#38611yescharacteristic
389D43—44no—
390C22×#41—431no—
391C23×Q8—431no—
392#568—434no—
393#568—862no—
394#568—862no—
395#568—862no—
396C2×#131—862no—
397C2×#131—862no—
398C22×M16—431no—
399C22×M16—431no—
400C22×M16—862no—
401C22×M16C2×D4311yescharacteristic
402C22×M16C2×D4311yescharacteristic
403#536—434no—
404#536—434no—
405#536—862no—
406#536—862no—
407C2×C4⋊Q8—861no—
408C2×#124—861no—
409C2×#123—434no—
410C2×C22⋊Q8—862no—
411C2×#117C2×D4311yescharacteristic
412#413—434no—
413#413—862no—
414C2×#101—434no—
415C2×#101—434no—
416C2×#101—862no—
417C2×#101—862no—
418C2×#101—861no—
419C2×#101—862no—
420C2×#101—862no—
421C2×#100—861no—
422#344—434no—
423#344C2×D4314yescomplemented
424C43C2×#191511yescharacteristic, complemented, Sylow
425C2×#41—432no—
426C2×#41—432no—
427C2×#41—432no—
428C2×#41—432no—
429C2×#41—861no—
430C2×#41—861no—
431C2×#41—861no—
432C2×#41—861no—
433C2×#41—861no—
434C2×#41—861no—
435C2×#41—861no—
436C2×#41—861no—
437C22×Q8—432no—
438C22×Q8—431no—
439C22×Q8—432no—
440C22×Q8—861no—
441C22×Q8—861no—
442C22×Q8—861no—
443C22×Q8—861no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8—861no—
447C22×Q8—861no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—861no—
451C22×Q8—861no—
452C22×D4—432no—
453C22×D4—431no—
454C23×C4—432no—
455C23×C4—432no—
456C23×C4C22×D4311yescharacteristic
457#131—868no—
458#131—868no—
459#131—868no—
460#131—868no—
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—432no—
470C2×M16—432no—
471C2×M16—432no—
472C2×M16—432no—
473C2×M16—864no—
474C2×M16—868no—
475C2×M16—868no—
476C2×M16—861no—
477C2×M16—861no—
478C2×M16—861no—
479C2×M16—861no—
480C2×M16—861no—
481C2×M16—861no—
482C2×M16—861no—
483C2×M16—861no—
484C2×M16D17212yes—
485C2×M16D17212yes—
486C2×M16C22×D4312yes—
487C2×M16C22×D4312yes—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—864no—
491C22×C8—861no—
492C22×C8—861no—
493C4⋊Q8—864no—
494C4⋊Q8—864no—
495#124—864no—
496#124—864no—
497#123—4316no—
498#123—868no—
499C22⋊Q8—868no—
500C22⋊Q8—868no—
501#117—21no—
502#117—21no—
503#117C4×D4312yes—
504#117C22×D4312yes—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—864no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4C4×D4312yes—
509C2×C42—21no—
510#101—868no—
511#101—864no—
512#101—868no—
513#100—864no—
514C24—432no—
515C24C2×C4×D4311yescharacteristic
516#41—862no—
517#41—862no—
518#41—862no—
519#41—862no—
520#41—862no—
521#41—862no—
522#41—862no—
523#41—862no—
524#41—862no—
525#41—862no—
526#41—862no—
527#41—862no—
528#41—862no—
529#41—862no—
530#41—862no—
531#41—862no—
532C2×Q8—432no—
533C2×Q8—432no—
534C2×Q8—862no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×Q8—862no—
538C2×Q8—862no—
539C2×Q8—862no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—862no—
545C2×Q8—862no—
546C2×Q8—862no—
547C2×Q8—862no—
548C2×Q8—862no—
549C2×Q8—862no—
550C2×Q8—1721no—
551C2×Q8—1721no—
552C2×Q8—1721no—
553C2×Q8—1721no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×Q8—1721no—
557C2×Q8—1721no—
558C2×Q8—1721no—
559C2×Q8—1721no—
560C2×Q8—1721no—
561C2×Q8—1721no—
562C2×Q8—1721no—
563C2×Q8—1721no—
564C2×Q8—1721no—
565C2×Q8—1721no—
566C2×D4—434no—
567C2×D4—434no—
568C2×D4—432no—
569C2×D4—432no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—861no—
578C22×C4—22no—
579C22×C4—432no—
580C22×C4—434no—
581C22×C4—434no—
582C22×C4—434no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4C2×C4×D4311yescharacteristic
594C22×C4C2×D17211yescharacteristic
595C22×C4C2×D17211yescharacteristic
596C22×C4#1062189811yescharacteristic
597C22×C4#1062189811yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4D4×D4311yescharacteristic
604C22×C4#1062190211yescharacteristic
605C22×C4#1062190211yescharacteristic
606C22×C4C23×D4311yescharacteristic
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—434no—
615M16—8616no—
616M16—862no—
617M16—862no—
618M16—862no—
619M16—862no—
620M16—862no—
621M16—1721no—
622M16—1721no—
623M16C2×D17214yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—8616no—
631C2×C8—862no—
632C2×C8—862no—
633C2×C8—862no—
634C2×C8—862no—
635C2×C8—1721no—
636C2×C8—1721no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—8616no—
640C22⋊C4—22no—
641C22⋊C4—8616no—
642C22⋊C4C2×C4×D4314yes—
643C42—22no—
644C42—22no—
645C23—42no—
646C23—434no—
647C23—862no—
648C23—862no—
649C23—1724no—
650C23C22⋊C4×D4311yescharacteristic
651C23C22⋊C4×D4311yescharacteristic
652C23#1306328711yescharacteristic
653C23#1306328711yescharacteristic
654C23C4×D17211yescharacteristic
655C23C4×D17211yescharacteristic
656C23C22×C4×D4311yescharacteristic
657Q8—862no—
658Q8—862no—
659Q8—862no—
660Q8—862no—
661Q8—1722no—
662Q8—1722no—
663Q8—1722no—
664Q8—1722no—
665Q8—1722no—
666Q8—1722no—
667Q8—1722no—
668Q8—1722no—
669D4—864no—
670D4—864no—
671D4—864no—
672D4—864no—
673D4—862no—
674D4—862no—
675D4—862no—
676D4—862no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—434no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—864no—
683C2×C4—864no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—864no—
687C2×C4—864no—
688C2×C4—864no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4C22⋊C4×D4311yescharacteristic
694C2×C4C22⋊C4×D4311yescharacteristic
695C2×C4#1306328711yescharacteristic
696C2×C4#1306328711yescharacteristic
697C2×C4C4×D17211yescharacteristic
698C2×C4C4×D17211yescharacteristic
699C2×C4#1306329511yescharacteristic
700C2×C4#1306329511yescharacteristic
701C2×C4#1306329511yescharacteristic
702C2×C4#1306329511yescharacteristic
703C2×C4#1306329811yescharacteristic
704C2×C4#1306329811yescharacteristic
705C2×C4#1306329811yescharacteristic
706C2×C4#1306329811yescharacteristic
707C2×C4#1306330011yescharacteristic
708C2×C4#1306330011yescharacteristic
709C2×C4#1306330011yescharacteristic
710C2×C4#1306330011yescharacteristic
711C2×C4#1306331011yescharacteristic
712C2×C4#1306331011yescharacteristic
713C2×C4#1306331011yescharacteristic
714C2×C4#1306331011yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C22×D17211yescharacteristic
719C2×C4C2×#1062189811yescharacteristic
720C2×C4C2×#1062190211yescharacteristic
721C8—24no—
722C8—42no—
723C8—864no—
724C8—1722no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—864no—
733C22—3442no—
734C22—1724no—
735C22—1724no—
736C22#1458277711yescharacteristic
737C22#1458277711yescharacteristic
738C22#1458277711yescharacteristic
739C22#1458277711yescharacteristic
740C22C2×C22⋊C4×D4311yescharacteristic
741C22C2×#1306328711yescharacteristic
742C22C2×C4×D17211yescharacteristic
743C4—44no—
744C4—864no—
745C4—1724no—
746C4#1458277711yescharacteristic
747C4#1458277711yescharacteristic
748C4#1458277711yescharacteristic
749C4#1458277711yescharacteristic
750C4C2×#1306329511yescharacteristic
751C4C2×#1306329811yescharacteristic
752C4C2×#1306330011yescharacteristic
753C4C2×#1306331011yescharacteristic
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—1724no—
761C2#1913514612yesdirect product factor
762C2C2×#1458277711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1915
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C22×#13063243C2semidirect
5. C22×#13063243C2semidirect
6. #19135146C2direct (N × H)
7. C2×#14582669C2semidirect
8. C2×C43×#344C2semidirect
35. C2×#13063243C22semidirect
36. C2×#13063243C22semidirect
38. #14582669C22semidirect
42. C43×#344C22semidirect
380. C2×#344D43semidirect
387. C2×C43#1915semidirect
423. #344C2×D43semidirect
424. C43C2×#1915semidirect
761. C2#19135146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834752
C2×#145828812
C22×#130632432
#191351462
C2×#145826692
C2×C43×#3442
C2×#191543