Finite Group Databasebeta

← #25117294

Subgroups — #25117294

Order 11008.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583046C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4#19137609C211yesmaximal, characteristic, complemented
5#19137435C211yesmaximal, characteristic, complemented
6#19135471C211yesmaximal, characteristic, complemented
7#19135278C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135033C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic, complemented
11#19134942C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134426C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25#14583046C418yescomplemented
26C4×#10621873—24no—
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29#14582901—24no—
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582797C2211yescharacteristic
44#14582791—21no—
45#14582776—21no—
46#14582773—21no—
47#14582759C2211yescharacteristic
48#14582758—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C22⋊C4×C43C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C2×#10621873—22no—
77C2×#10621873—22no—
78C2×#10621873C2×C414yescomplemented
79C2×D344—41no—
80C2×D344—41no—
81C2×D344C2×C414yescomplemented
82#13063299—22no—
83#13063299C2×C414yes—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86—41no—
87C4×Dic86—41no—
88C4×D172—22no—
89C4×D172—41no—
90(C22⋊D43)⋊C4—44no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114#13063257—22no—
115#13063257—41no—
116#13063250—22no—
117#13063250C2×C414yescomplemented
118#13063250D414yescomplemented
119#13063247—22no—
120#13063247—22no—
121#13063247—22no—
122#13063247—41no—
123#13063247C2×C414yescomplemented
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—22no—
129C2×M16×C43—22no—
130C2×M16×C43—41no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C22⋊C8×C43C2×C414yescomplemented
140#97×C43—41no—
141C4×C8×C43—22no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C23×D43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—81no—
174#10621898—28no—
175#10621898—44no—
176#10621898—44no—
177#10621898—44no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172C22×C412yes—
189C2×D172C22×C412yes—
190C2×C4×D43—24no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86C22×C412yes—
200C2×Dic86C2×D412yes—
201C2×Dic86#4112yes—
202M16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43C22×C412yes—
213C2×C8×C43C22×C412yes—
214C2×C8×C43C2×D412yes—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—41no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—42no—
239C4⋊Dic43C22×C412yes—
240C4⋊Dic43C2×D412yes—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—42no—
245C4×Dic43—42no—
246C4×Dic43—42no—
247D344—44no—
248#10621873—28no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43C4×D412yes—
256C23×C43C22×D411yescharacteristic
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43AGL(1,ℤ/8)12yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C22⋊D43—48no—
297C22⋊D43—48no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—84no—
317D172—22no—
318D172—22no—
319D172—22no—
320D172—22no—
321D172—41no—
322D172—41no—
323D172—41no—
324D172—41no—
325C4×D43—48no—
326C4×D43—84no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86C4×D414yescomplemented
331C8×C43—22no—
332C8×C43—22no—
333C8×C43—22no—
334C8×C43—41no—
335#22883—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43C2×C4×D411yescharacteristic
344C22×C43D4211yescharacteristic
345C22×C43#54611yescharacteristic
346C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43C2×C4×D411yescharacteristic
370C4×C43#51811yescharacteristic
371C4×C43#54611yescharacteristic
372C4×C43#55111yescharacteristic
373Dic43—24no—
374Dic43—42no—
375Dic43—42no—
376Dic43—81no—
377Dic43—81no—
378Dic43—81no—
379C2×#449—431no—
380C2×C4×SD16—431no—
381C2×#417—431no—
382#2361—431no—
383#2341—431no—
384#1972—431no—
385#1934—431no—
386#1926—431no—
387#1895—431no—
388#1880—431no—
389#1879—431no—
390#1865—431no—
391#1853—431no—
392#1763—431no—
393#1753D4311yescharacteristic, complemented
394C2×C43—42no—
395C2×C43#235811yescharacteristic
396C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
397C2×C43#295211yescharacteristic
398C2×C43#326511yescharacteristic
399C2×C43#327111yescharacteristic
400C2×C43#332611yescharacteristic
401C2×C43#333211yescharacteristic
402D43—82no—
403D43—82no—
404C22×#41—431no—
405C22×SD16—431no—
406C22×D8—431no—
407C22×M16C2×D4311yescharacteristic
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C22×C4⋊C4—431no—
414#449—438no—
415C4×SD16—864no—
416C2×#106—431no—
417C2×#106—431no—
418#417—864no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×C22⋊C8C2×D4311yescharacteristic
428C2×#97C2×D4311yescharacteristic
429C2×C4×C8C2×D4311yescharacteristic
430#390—431no—
431#390—431no—
432#390—431no—
433#390—861no—
434#390—861no—
435#389—431no—
436#388—861no—
437#386—861no—
438#385—861no—
439#380—431no—
440#380—861no—
441C4×C4⋊C4—431no—
442C4×C22⋊C4—861no—
443C4×C22⋊C4C2×D4311yescharacteristic
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#336C2×D4311yescharacteristic
449#336C2×D4311yescharacteristic
450C43#2288311yescharacteristic, complemented, Sylow
451C2×#41—434no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—1721no—
456C2×#41—1721no—
457C22×Q8—431no—
458C22×D4—431no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C2×SD16—434no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×D8—434no—
470C2×D8—1721no—
471C2×D8—1721no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—41no—
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479#121—434no—
480#121—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—1721no—
484C4×Q8—1721no—
485C4×D4—862no—
486C4×D4—1721no—
487C4×D4—1724no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—1721no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4D17211yescharacteristic
509C2×C22⋊C4D17211yescharacteristic
510C2×C42—861no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42C22×D4311yescharacteristic
514C2×C42C22×D4311yescharacteristic
515#106—862no—
516#106—1721no—
517#103—434no—
518#103—434no—
519#103—862no—
520#102—434no—
521#102—862no—
522#102—862no—
523#102—862no—
524#102—1721no—
525C22⋊C8C4×D4314yescomplemented
526#97—41no—
527C4×C8—22no—
528#95—861no—
529#95—861no—
530#95—861no—
531#95D17211yescharacteristic
532#95D17211yescharacteristic
533C24—861no—
534C24—861no—
535C24C2×D17211yescharacteristic
536#41—868no—
537#41—1724no—
538#41—1724no—
539#41—1724no—
540C2×Q8—432no—
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×D4—432no—
547C2×D4—432no—
548C2×D4—864no—
549C2×D4—864no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4—1722no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—864no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—3441no—
576C22×C4—3441no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4C2×C4×D4312yes—
584C22×C4C2×D17211yescharacteristic
585C22×C4C2×D17211yescharacteristic
586C22×C4C2×D17211yescharacteristic
587C22×C4C2×D17211yescharacteristic
588C22×C4C2×D17211yescharacteristic
589C22×C4#1062189812yes—
590C22×C4C23×D4311yescharacteristic
591SD16—868no—
592D8—1724no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8C2×C4×D4312yes—
604C2×C8C2×C4×D4312yes—
605C2×C8D4×D4312yes—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4—1722no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—864no—
623C22⋊C4—3441no—
624C22⋊C4—3441no—
625C22⋊C4—3441no—
626C22⋊C4—3441no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—1722no—
636C42—1722no—
637C42—1722no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—862no—
645C23—862no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23C4×D17212yes—
659C23C22×D17211yescharacteristic
660Q8—434no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664D4—862no—
665D4—862no—
666D4—862no—
667D4—862no—
668D4—1728no—
669D4—1728no—
670D4—1721no—
671D4—1721no—
672D4—1721no—
673D4—1721no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—3444no—
697C2×C4—3444no—
698C2×C4—1728no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4C4×D17212yes—
713C2×C4#1306335312yes—
714C2×C4C22×C4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4C2×#1062189811yescharacteristic
718C2×C4#1306337011yescharacteristic
719C2×C4#1306337111yescharacteristic
720C8—22no—
721C8—22no—
722C8—22no—
723C8—41no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—3441no—
735C22—3441no—
736C22—3441no—
737C22—3441no—
738C22—3441no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22C2×C4×D17211yescharacteristic
746C22D4×D17211yescharacteristic
747C22#1458354411yescharacteristic
748C22C2×#1306335311yescharacteristic
749C22#1458369911yescharacteristic
750C22#1458371111yescharacteristic
751C22#1458371111yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—864no—
758C4—3441no—
759C4—3441no—
760C4—3441no—
761C4—1722no—
762C4—1722no—
763C4C4×D4×D4311yescharacteristic
764C4#1458337111yescharacteristic
765C4#1458353911yescharacteristic
766C4#1458357311yescharacteristic
767C2—42no—
768C2—3442no—
769C2—3442no—
770C2#1913757711yescharacteristic
771C2C4×#1306335311yescharacteristic
772C2#1914348011yescharacteristic
773C2#1914609511yescharacteristic
774C2#1914618511yescharacteristic
775C2#1914685011yescharacteristic
776C2#1914692311yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621873C2semidirect
3. C2×#14582901C2semidirect
4. #19137609C2semidirect
5. #19137435C2semidirect
6. #19135471C2semidirect
7. #19135278C2semidirect
8. #19135223C2semidirect
9. #19135033C2semidirect
10. #19134949C2semidirect
11. #19134942C2semidirect
12. #19134866C2semidirect
13. #19134790C2semidirect
14. #19134426C2semidirect
15. C43×#1753C2semidirect
25. #14583046C4semidirect
67. C2×#10621898C2×C4semidirect
78. C2×#10621873C2×C4semidirect
81. C2×D344C2×C4semidirect
117. #13063250C2×C4semidirect
118. #13063250D4semidirect
123. #13063247C2×C4semidirect
139. C22⋊C8×C43C2×C4semidirect
330. Dic86C4×D4semidirect
393. #1753D43semidirect
450. C43#22883semidirect
525. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830462
C2×C4×#106218732
C2×#145829012
#191376092
#191374352
#191354712
#191352782
#191352232
#191350332
#191349492
#191349422
#191348662
#191347902
#191344262
C43×#17532
#2288343