Finite Group Databasebeta

← #25140412

Subgroups — #25140412

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583038C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3#19138109C211yesmaximal, characteristic
4#19136138C211yesmaximal, characteristic, complemented
5#19136032C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic
8#19135274C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134863C211yesmaximal, characteristic, complemented
13#19134600C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063307—21no—
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583038—24no—
22C4×#10621884—24no—
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582826—21no—
38#14582815—21no—
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582773—21no—
42#14582769C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C23×Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C43×#391—21no—
54C43×#391—21no—
55C43×#391C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#380—21no—
58C43×#380C2211yescharacteristic
59C4×C22⋊C4×C43—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—41no—
69C2×#10621884D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063307—44no—
75#13063299—22no—
76#13063299—41no—
77C4×D172—22no—
78C4×D172—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90#13063256—22no—
91#13063256—41no—
92C4⋊(C43⋊C8)—41no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063249—22no—
98#13063249—41no—
99#13063245—22no—
100#13063245—41no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—41no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43—22no—
107C22×Q8×C43—22no—
108C22×Q8×C43—21no—
109C22×Q8×C43—22no—
110C22×Q8×C43—22no—
111C22×Q8×C43—41no—
112C22×Q8×C43—41no—
113C22×Q8×C43C2311yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C4×Q8×C43—22no—
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120C4×Q8×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C2×Q8×C43—24no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—42no—
151C2×Q8×C43—42no—
152C2×Q8×C43—44no—
153C2×Q8×C43—44no—
154C2×Q8×C43—44no—
155C2×Q8×C43—44no—
156C2×Q8×C43C2×D412yes—
157C2×Q8×C43#4112yes—
158C2×Q8×C43#4112yes—
159C2×Q8×C43#4112yes—
160C22×C4×C43—24no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—81no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172C2×D412yes—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—81no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—42no—
199C4⋊C4×C43—42no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43SD1614yescomplemented
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—42no—
208C42×C43—42no—
209C22⋊Dic43—42no—
210#10621884—28no—
211#10621884—44no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43—81no—
224Dic43⋊C4—42no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8C2×D412yes—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43C2×SD1612yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—22no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252Q8×C43—22no—
253Q8×C43—22no—
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—48no—
258Q8×C43—41no—
259Q8×C43—41no—
260Q8×C43#12314yescomplemented
261C2×C4×C43—22no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—48no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43C2×SD1612yes—
292C2×C4×C43C2×SD1612yes—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C22⋊D43—84no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309D172—22no—
310D172—22no—
311D172—41no—
312D172—41no—
313C4×D43—84no—
314C43⋊C8—22no—
315C43⋊C8—41no—
316C43⋊C8—41no—
317C43⋊C8—41no—
318#24898—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43#52511yescharacteristic
327C22×C43D4211yescharacteristic
328C22×C43#54611yescharacteristic
329C22×C43C22×SD1611yescharacteristic
330C22×C43#57511yescharacteristic
331C22×C43#57711yescharacteristic
332C22×C43#57811yescharacteristic
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—81no—
337C2×D43—81no—
338C2×D43—81no—
339C2×D43—81no—
340C4×C43—24no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—41no—
344C4×C43—42no—
345C4×C43—41no—
346C4×C43—41no—
347C4×C43—81no—
348C4×C43—81no—
349C4×C43C2×#12311yescharacteristic
350C4×C43#53811yescharacteristic
351C4×C43#54611yescharacteristic
352C4×C43#55111yescharacteristic
353Dic43—81no—
354Dic43—81no—
355Dic43—81no—
356C2×#448—431no—
357C2×C4×SD16—431no—
358#2422—431no—
359Q8×C22⋊C4D4311yescharacteristic, complemented
360#2096—431no—
361#2077—431no—
362#2055—431no—
363#2034—431no—
364#1933—431no—
365#1923—431no—
366#1880—431no—
367#1877—431no—
368#1865—431no—
369#1803—431no—
370#1787—431no—
371C2×C43—42no—
372C2×C43#241811yescharacteristic
373C2×C43#310311yescharacteristic
374C2×C43#312111yescharacteristic
375C2×C43#326911yescharacteristic
376C2×C43D4×SD1611yescharacteristic
377C2×C43#329811yescharacteristic
378C2×C43#332611yescharacteristic
379D43—82no—
380C23×Q8C2×D4311yescharacteristic
381C22×SD16—431no—
382C22×SD16—431no—
383C2×#123—861no—
384C2×#121—431no—
385C2×C4×Q8C2×D4311yescharacteristic
386C2×C4×Q8C2×D4311yescharacteristic
387C2×C4×D4—431no—
388#448—864no—
389C4×SD16—864no—
390C2×#106—431no—
391C2×#106—431no—
392C2×C4⋊C8—431no—
393C2×#103—431no—
394C2×#103—431no—
395C2×#103—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×C4×C8—431no—
404#397—861no—
405#394—861no—
406#391—21no—
407#391—21no—
408#391C2×D4311yescharacteristic
409#391C2×D4311yescharacteristic
410#390—431no—
411#389—431no—
412#385—861no—
413#384—431no—
414#380—21no—
415#380—431no—
416#380C2×D4311yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C2×D4311yescharacteristic
419#340—431no—
420#340—431no—
421#340—431no—
422#340—431no—
423#336—431no—
424#336—431no—
425C43#2489811yescharacteristic, complemented, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C22×D4311yescharacteristic
434C22×Q8C22×D4311yescharacteristic
435C22×D4—431no—
436C22×D4—861no—
437C23×C4—21no—
438C23×C4—861no—
439C23×C4C22×D4311yescharacteristic
440C2×SD16—434no—
441C2×SD16—862no—
442C2×SD16—862no—
443C2×SD16—862no—
444C2×SD16—862no—
445C2×SD16—1721no—
446C22×C8—431no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—431no—
450#123—1724no—
451#121—862no—
452#121—1721no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×D4—862no—
458C4×D4—1721no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4C22⋊D4311yescharacteristic
476C2×C22⋊C4C22⋊D4311yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C22×D4311yescharacteristic
480C2×C42C22×D4311yescharacteristic
481#106—862no—
482#106—1721no—
483C4⋊C8—1721no—
484#103—862no—
485#103—862no—
486#103—862no—
487#103—862no—
488#103—862no—
489#103—1721no—
490#102—862no—
491#102—1721no—
492C22⋊C8—862no—
493C22⋊C8—1721no—
494C4×C8—862no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—861no—
501#95—861no—
502#95C22⋊D4311yescharacteristic
503#95C22⋊D4311yescharacteristic
504C24—861no—
505C24C2×C22⋊D4311yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8#1062189812yes—
522C2×Q8#1062189812yes—
523C2×Q8D4×D4312yes—
524C2×Q8#1062190012yes—
525C2×D4—432no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—3441no—
532C2×D4—1722no—
533C2×D4—1722no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—3441no—
551C22×C4—1722no—
552C22×C4—1722no—
553C22×C4C2×C22⋊D4311yescharacteristic
554C22×C4C2×C22⋊D4311yescharacteristic
555C22×C4C2×C22⋊D4311yescharacteristic
556C22×C4C2×C22⋊D4311yescharacteristic
557C22×C4C2×C22⋊D4311yescharacteristic
558C22×C4C23×D4311yescharacteristic
559SD16—868no—
560SD16—1724no—
561C2×C8—432no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—3441no—
586C4⋊C4—1722no—
587C4⋊C4—1722no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—1722no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C22⋊C4#1062188414yescomplemented
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—862no—
609C23—1721no—
610C23—1721no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23C2×#1062188412yes—
616C23C22×C22⋊D4311yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#1306330714yescomplemented
626D4—862no—
627D4—862no—
628D4—3444no—
629D4—1721no—
630D4—1721no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—3444no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4C2×#1062188412yes—
672C2×C4C2×#1062188412yes—
673C2×C4C2×D4×D4311yescharacteristic
674C2×C4C2×#1062190011yescharacteristic
675C2×C4C2×#1062189811yescharacteristic
676C2×C4C2×#1062189811yescharacteristic
677C2×C4#1306337011yescharacteristic
678C2×C4#1306337011yescharacteristic
679C8—862no—
680C8—1721no—
681C8—1721no—
682C8—1721no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—3441no—
691C22—3441no—
692C22—3441no—
693C22—3441no—
694C22—1722no—
695C22—1722no—
696C22—1722no—
697C22#1458341011yescharacteristic
698C22D4×C22⋊D4311yescharacteristic
699C22#1458354311yescharacteristic
700C22C22×#1062188411yescharacteristic
701C22#1458369711yescharacteristic
702C22#1458370711yescharacteristic
703C22#1458371411yescharacteristic
704C4—24no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—3441no—
714C4—3441no—
715C4—3441no—
716C4C2×#1306330711yescharacteristic
717C4#1458348711yescharacteristic
718C4#1458353911yescharacteristic
719C4#1458357511yescharacteristic
720C2—42no—
721C2—3442no—
722C2#1913805711yescharacteristic
723C2#1914462611yescharacteristic
724C2#1914482411yescharacteristic
725C2#1914615111yescharacteristic
726C2D4×#1062188411yescharacteristic
727C2#1914646011yescharacteristic
728C2#1914684811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingQ8×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterQ8×C22⋊C4D43
hypocenterC43#24898
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621884C2semidirect
4. #19136138C2semidirect
5. #19136032C2semidirect
6. #19135910C2semidirect
8. #19135274C2semidirect
9. #19135203C2semidirect
10. #19134950C2semidirect
11. #19134932C2semidirect
12. #19134863C2semidirect
13. #19134600C2semidirect
14. #19134530C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
202. C22⋊C4×C43SD16semidirect
260. Q8×C43#123semidirect
359. Q8×C22⋊C4D43semidirect
425. C43#24898semidirect
595. C22⋊C4#10621884semidirect
625. Q8#13063307semidirect

Maximal subgroups

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

subgroupindex
C2×#145830382
C2×C4×#106218842
#191381092
#191361382
#191360322
#191359102
#191357842
#191352742
#191352032
#191349502
#191349322
#191348632
#191346002
#191345302
Q8×C22⋊C4×C432
#2489843