Finite Group Databasebeta

← #25102427

Subgroups — #25102427

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583378C211yesmaximal, characteristic
2C2×#14583062C211yesmaximal, characteristic
3C2×#14582999C211yesmaximal, characteristic, complemented
4C2×C4×Dic172C211yesmaximal, characteristic, complemented
5#19137278C211yesmaximal, characteristic, complemented
6#19134937C211yesmaximal, characteristic, complemented
7#19134927C211yesmaximal, characteristic, complemented
8#19134901C211yesmaximal, characteristic, complemented
9#19134850C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic
13#19134428C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20#14583378—24no—
21#14583378—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×#13063290C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063282C2211yescharacteristic
29C2×#13063281—21no—
30C22×Dic43⋊C4—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583062C418yescomplemented
33#14582999—24no—
34C4×Dic172—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582797—21no—
49#14582791—21no—
50#14582790—21no—
51#14582784—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×Dic86C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×Dic172—22no—
78C2×Dic172—22no—
79C2×Dic172C2×C414yescomplemented
80C2×#10621883—22no—
81C2×#10621883—22no—
82C2×#10621883C2×C414yescomplemented
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063305—22no—
86#13063305C2×C414yescomplemented
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86D414yes—
91#13063290—22no—
92#13063290—22no—
93D4×Dic43—22no—
94D4×Dic43—22no—
95C4×C22⋊D43—28no—
96(C22⋊D43)⋊C4—28no—
97#13063282—22no—
98#13063282—22no—
99#13063281—28no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—28no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C2×Dic43⋊C4D411yescharacteristic
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122#13063259—22no—
123#13063258—22no—
124#13063250—22no—
125#13063250—22no—
126#13063248—22no—
127#13063248—22no—
128#13063248C2×C414yescomplemented
129#13063246—22no—
130(C2×D43)⋊C8—22no—
131(C2×D43)⋊C8C2×C414yescomplemented
132#13063236—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43D414yes—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#102×C43—22no—
150#102×C43C2×C414yescomplemented
151C4×C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C23×D43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C22×C412yes—
159C2×D4×C43C2×D412yes—
160C2×D4×C43#4112yes—
161C22×C4×C43—24no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—81no—
166C22×C4×C43—81no—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C22×Dic43—24no—
174C22×Dic43—24no—
175C22×Dic43—24no—
176C22×Dic43—24no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186#10621900—28no—
187#10621900—28no—
188#10621900—28no—
189#10621900—28no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—24no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43C22×C412yes—
198C2×C4×D43#4112yes—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86C22×C412yes—
208C2×Dic86C22×C412yes—
209C2×Dic86C2×D412yes—
210C2×Dic86#4112yes—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43C22×C412yes—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C22×C412yes—
222C4⋊C4×C43C2×D412yes—
223C22⋊C4×C43—24no—
224C42×C43—81no—
225C42×C43C2×D412yes—
226C42×C43C2×D412yes—
227C22⋊Dic43—24no—
228#10621883—28no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—81no—
233C4⋊Dic43—21no—
234C4⋊Dic43—24no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—81no—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—22no—
242Dic43⋊C4—24no—
243Dic43⋊C4—22no—
244Dic43⋊C4—42no—
245C4×Dic43—24no—
246C4×Dic43—24no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—42no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256Dic172—28no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43C22×D411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43C4×D412yes—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43C4×D414yes—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
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—84no—
290C2×C4×C43#12012yes—
291C2×C4×C43#12012yes—
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C22⋊D43—216no—
299C2×Dic43—216no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—84no—
321C2×Dic43C4×D412yes—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—84no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—41no—
333Dic86—41no—
334Dic86C4×D414yes—
335C8×C43—22no—
336C8×C43—41no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339#21465—431nomaximal, Sylow
340C22×C43—24no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43C2×#12011yescharacteristic
349C22×C43#52511yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C22×C43#57811yescharacteristic
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—81no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43C2×C4×D411yescharacteristic
368C4×C43#52511yescharacteristic
369C4×C43#52511yescharacteristic
370Dic43—24no—
371Dic43—22no—
372Dic43—41no—
373Dic43—42no—
374Dic43—41no—
375Dic43—42no—
376Dic43—81no—
377C2×#520—431no—
378C2×#452—431no—
379C2×#440—431no—
380C2×C4×Q16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872—431no—
385#1863—431no—
386#1862—431no—
387#1852—431no—
388#1788—431no—
389#1763—431no—
390C4×#102D4311yescharacteristic, complemented
391#1750—431no—
392C2×C43—44no—
393C2×C43C4×#12011yescharacteristic
394C2×C43#294711yescharacteristic
395C2×C43#295111yescharacteristic
396C2×C43#301111yescharacteristic
397C2×C43#301211yescharacteristic
398C2×C43#312011yescharacteristic
399C2×C43#312411yescharacteristic
400D43—42no—
401C22×#41—431no—
402C22×Q16—431no—
403C22×SD16—431no—
404C2×C22⋊Q8—431no—
405#520—864no—
406#520—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×D4—431no—
411C2×C4×D4—861no—
412C2×C4×D4—861no—
413C2×C4×D4C2×D4311yescharacteristic
414C2×#117—431no—
415C2×#117—861no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—861no—
418#452—438no—
419#440—864no—
420C4×Q16—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102C2×D4311yescharacteristic
430C2×#102C2×D4311yescharacteristic
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×#97—431no—
434C2×C4×C8C2×D4311yescharacteristic
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380—431no—
442C4×C4⋊C4C2×D4311yescharacteristic
443#340—431no—
444#340—431no—
445#340C2×D4311yescharacteristic
446#340C2×D4311yescharacteristic
447#336—431no—
448#336—431no—
449C43#2146511yescharacteristic, complemented, Sylow
450C2×#41—434no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—862no—
456C22×Q8—431no—
457C22×Q8—431no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—431no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4—861no—
465C2×Q16—434no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×SD16—434no—
469C2×SD16—862no—
470C2×SD16—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×D4—22no—
484C4×D4—868no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—862no—
488C4×D4D17214yes—
489#117—868no—
490#117—862no—
491#117—862no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—868no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—21no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520#107—862no—
521#107—862no—
522#103—434no—
523#103—862no—
524#103—862no—
525#103—862no—
526#103—862no—
527#102—22no—
528#102—862no—
529#102C4×D4314yescomplemented
530C22⋊C8—434no—
531C22⋊C8—862no—
532#97—862no—
533C4×C8—22no—
534#95—21no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—431no—
541#41—868no—
542#41—868no—
543#41—868no—
544#41—868no—
545C2×Q8—432no—
546C2×Q8—432no—
547C2×Q8—432no—
548C2×Q8—432no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4C2×C4×D4312yes—
564C2×D4C2×D17212yes—
565C2×D4#1062189812yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—81no—
571C22×C4—81no—
572C22×C4—431no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—864no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—3441no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—3441no—
594C22×C4D4×D4311yescharacteristic
595C22×C4D4×D4311yescharacteristic
596C22×C4C23×D4311yescharacteristic
597Q16—868no—
598SD16—868no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—432no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8C2×C4×D4312yes—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—432no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—862no—
620C4⋊C4—862no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—3441no—
626C4⋊C4—1722no—
627C4⋊C4C2×C4×D4312yes—
628C4⋊C4C2×D17212yes—
629C22⋊C4—24no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—862no—
633C22⋊C4—862no—
634C22⋊C4—3441no—
635C42—81no—
636C42—864no—
637C42—864no—
638C42—861no—
639C42—861no—
640C42—1722no—
641C42C2×D17212yes—
642C42D4×D4312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—432no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23C2×D4×D4311yescharacteristic
658Q8—434no—
659Q8—862no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—1721no—
665Q8—1721no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—8616no—
670D4C4×D17214yes—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—84no—
685C2×C4—432no—
686C2×C4—8616no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4#1306329512yes—
714C2×C4#1306329512yes—
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C22×D17211yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4C2×#1062189811yescharacteristic
721C8—22no—
722C8—41no—
723C8—862no—
724C8—1721no—
725C22—24no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—862no—
733C22—862no—
734C22—862no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22C4×D4×D4311yescharacteristic
740C22C2×#1306329511yescharacteristic
741C22#1458340811yescharacteristic
742C22#1458370011yescharacteristic
743C22#1458370511yescharacteristic
744C22#1458371311yescharacteristic
745C22#1458371311yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—81no—
751C4—862no—
752C4—864no—
753C4—3441no—
754C4—1722no—
755C4—1721no—
756C4—1721no—
757C4—1722no—
758C4C4×D4×D4311yescharacteristic
759C4C2×C4×D17211yescharacteristic
760C4#1458340811yescharacteristic
761C4#1458341111yescharacteristic
762C2—44no—
763C2—1722no—
764C2C4×#1306329511yescharacteristic
765C2#1914343111yescharacteristic
766C2#1914346511yescharacteristic
767C2#1914389311yescharacteristic
768C2#1914390411yescharacteristic
769C2#1914480511yescharacteristic
770C2#1914485311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#21465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C2×#14582999C2semidirect
4. C2×C4×Dic172C2semidirect
5. #19137278C2semidirect
6. #19134937C2semidirect
7. #19134927C2semidirect
8. #19134901C2semidirect
9. #19134850C2semidirect
10. #19134844C2semidirect
11. #19134784C2semidirect
13. #19134428C2semidirect
14. #19134362C2semidirect
15. C4×#102×C43C2semidirect
32. #14583062C4semidirect
79. C2×Dic172C2×C4semidirect
82. C2×#10621883C2×C4semidirect
86. #13063305C2×C4semidirect
128. #13063248C2×C4semidirect
131. (C2×D43)⋊C8C2×C4semidirect
150. #102×C43C2×C4semidirect
390. C4×#102D43semidirect
449. C43#21465semidirect
529. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
C2×#145830622
C2×#145829992
C2×C4×Dic1722
#191372782
#191349372
#191349272
#191349012
#191348502
#191348442
#191347842
#191345322
#191344282
#191343622
C4×#102×C432
#2146543