Finite Group Databasebeta

← #25269184

Subgroups — #25269184

Order 11008.

2866 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583525C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3#19142931C212yesmaximal, complemented
4#19142881C212yesmaximal, complemented
5#19140414C212yesmaximal, complemented
6#19140406C212yesmaximal, complemented
7#19138421C214yesmaximal, complemented
8#19138419C214yesmaximal, complemented
9#19138406C214yesmaximal, complemented
10#19138404C214yesmaximal, complemented
11#19137207C211yesmaximal, characteristic, complemented
12#19137170C211yesmaximal, characteristic
13#19137170C211yesmaximal, characteristic
14C2×#14582772C211yesmaximal, characteristic, complemented
15C2×C43×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18#14583525—28no—
19C2×#13063304C2212yescomplemented
20C2×#13063304C2212yescomplemented
21C2×#13063303C2214yescomplemented
22C2×#13063302C2212yes—
23C2×#13063302C2212yes—
24C2×#13063302C2212yescomplemented
25C2×#13063302C2212yescomplemented
26C2×C4×C22⋊D43—28no—
27C2×C4×C22⋊D43C2214yes—
28C2×C4×C22⋊D43C2214yes—
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2212yescomplemented
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582840C2214yescomplemented
37#14582834C2214yescomplemented
38#14582833C2214yescomplemented
39#14582830C2214yescomplemented
40#14582823C2214yescomplemented
41#14582821C2214yescomplemented
42#14582819C2214yescomplemented
43#14582812C2214yescomplemented
44#14582803C2214yescomplemented
45#14582794C2214yescomplemented
46#14582785C2214yescomplemented
47#14582781C2214yescomplemented
48#14582778C2212yes—
49#14582778C2214yes—
50#14582778C2212yes—
51#14582776C2212yes—
52#14582776C2214yes—
53#14582776C2212yes—
54#14582773C2214yescomplemented
55#14582772C2212yes—
56#14582772C2212yes—
57#14582772C2214yescomplemented
58#14582772C2214yescomplemented
59#14582771C2214yescomplemented
60#14582770C2214yescomplemented
61#14582760C2212yes—
62#14582760C2212yes—
63#14582758C2214yescomplemented
64#14582757C2212yes—
65#14582757C2212yes—
66#14582754C2212yes—
67#14582754C2212yes—
68C2×C43⋊#95C2212yescomplemented
69C24×C4×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2212yescomplemented
71C22×C22⋊C4×C43C2211yescharacteristic
72C22×C22⋊C4×C43C2211yescharacteristic
73C43×#385C2212yes—
74C43×#385C2212yes—
75C43×#385C2214yescomplemented
76C2×#95×C43C2212yescomplemented
77C24×D43C2311yescharacteristic
78C22×Dic86C2312yes—
79C22×Dic86C2312yes—
80C22×C22⋊D43—24no—
81C22×C22⋊D43—24no—
82C22×C22⋊D43Q818yescomplemented
83C22×C22⋊D43C2312yes—
84C22×C22⋊D43C2312yes—
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2312yes—
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C22×C4×D43—24no—
92C22×C4×D43—44no—
93C22×C4×D43C2314yes—
94#13063304—28no—
95#13063304—28no—
96#13063303—48no—
97#13063302—28no—
98#13063302—28no—
99#13063302—28no—
100#13063302—28no—
101C4×C22⋊D43—216no—
102C4×C22⋊D43—216no—
103C2×C4⋊Dic43C2312yes—
104C2×C4⋊Dic43C2312yes—
105C2×Dic43⋊C4—24no—
106C2×Dic43⋊C4—44no—
107C2×Dic43⋊C4C2312yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2312yes—
111C2×Dic43⋊C4C2312yes—
112C2×Dic43⋊C4C2312yes—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C2×C22⋊Dic43—24no—
117C2×C22⋊Dic43—24no—
118C2×C22⋊Dic43D418yes—
119C2×C22⋊Dic43C2312yes—
120C2×C22⋊Dic43C2312yes—
121C2×C22⋊Dic43C2312yes—
122C2×C22⋊Dic43C2312yes—
123C2×C22⋊Dic43C2312yes—
124C2×C22⋊Dic43C2312yes—
125C2×(C2×D43)⋊C4—24no—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2314yes—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2314yes—
131C2×C4×Dic43—24no—
132C2×C4×Dic43C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2314yes—
141C25×C43C2311yescharacteristic
142C23×C4×C43—24no—
143C23×C4×C43—44no—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2312yes—
146C23×C4×C43C2312yes—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2312yes—
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43—44no—
152C2×C4⋊C4×C43C2314yes—
153C2×C4⋊C4×C43C2314yes—
154C2×C22⋊C4×C43—24no—
155C2×C22⋊C4×C43—24no—
156C2×C22⋊C4×C43C2312yes—
157C2×C22⋊C4×C43C2312yes—
158C2×C22⋊C4×C43C2312yes—
159C2×C22⋊C4×C43C2312yes—
160#95×C43C2314yes—
161#95×C43C2314yes—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43C2×D414yes—
165C24×C43C2×Q814yes—
166C24×C43#4114yes—
167C24×C43C2411yescharacteristic
168C24×C43C2411yescharacteristic
169C24×C43C2411yescharacteristic
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—42no—
173C23×D43—42no—
174C23×D43C2×Q814yes—
175C23×D43C2412yes—
176C22×C4×C43—24no—
177C22×C4×C43—24no—
178C22×C4×C43—24no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—24no—
182C22×C4×C43—24no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—24no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43—416no—
194C22×C4×C43C2412yes—
195C22×C4×C43C2414yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C2×C22⋊D43—232no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43C2×Q818yes—
205C2×C22⋊D43C2×Q818yes—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—24no—
211C22×Dic43—42no—
212C22×Dic43—42no—
213C22×Dic43—42no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43C2×D414yes—
218C22×Dic43C2×D414yes—
219C22×Dic43C2×Q814yes—
220C22×Dic43C2414yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C2×C4×D43—28no—
227C2×C4×D43—28no—
228C2×C4×D43—44no—
229C2×C4×D43—416no—
230C2×Dic86—24no—
231C2×Dic86—24no—
232C2×Dic86—44no—
233C2×Dic86—44no—
234C4⋊C4×C43—28no—
235C4⋊C4×C43—44no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244C22⋊Dic43C2×D418yes—
245C22⋊Dic43C2×D418yes—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4—44no—
249(C2×D43)⋊C4—44no—
250(C2×D43)⋊C4—44no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253Dic43⋊C4—28no—
254Dic43⋊C4—28no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—44no—
260Dic43⋊C4—44no—
261Dic43⋊C4—44no—
262C4×Dic43—28no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—44no—
270C23×C43—44no—
271C23×C43—48no—
272C23×C43—48no—
273C23×C43C22⋊Q8116yescomplemented
274C23×C43C22×D412yes—
275C23×C43C22×D412yes—
276C23×C43C22×D412yes—
277C23×C43C22×Q812yes—
278C23×C43C22×Q812yes—
279C23×C43C22×Q812yes—
280C23×C43C2×#4112yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4112yes—
283C23×C43C2511yescharacteristic
284C22×D43—28no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—24no—
288C22×D43—24no—
289C22×D43—48no—
290C22×D43—44no—
291C22×D43—48no—
292C22×D43—44no—
293C22×D43C22×Q814yes—
294C2×C4×C43—28no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—24no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43—24no—
304C2×C4×C43—22no—
305C2×C4×C43—24no—
306C2×C4×C43—24no—
307C2×C4×C43—48no—
308C2×C4×C43—48no—
309C2×C4×C43—48no—
310C2×C4×C43—44no—
311C2×C4×C43—82no—
312C2×C4×C43—82no—
313C2×C4×C43H(5,𝔽2)14yes—
314C22⋊D43—216no—
315C22⋊D43—216no—
316C2×Dic43—28no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43—48no—
331C2×Dic43—82no—
332C2×Dic43—82no—
333C2×Dic43C22×D414yes—
334C2×Dic43C22×D414yes—
335C2×Dic43C22×Q814yes—
336C4×D43—416no—
337Dic86—84no—
338Dic86—84no—
339#34985—431nomaximal, Sylow
340C22×C43—24no—
341C22×C43—24no—
342C22×C43—24no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—24no—
352C22×C43—416no—
353C22×C43C2×C22⋊Q814yes—
354C22×C43C2×C22⋊Q814yes—
355C22×C43C2×C22⋊Q814yes—
356C22×C43C23×D411yescharacteristic
357C22×C43C23×Q811yescharacteristic
358C22×C43C22×#4111yescharacteristic
359C22×C43C2×H(5,𝔽2)12yes—
360C22×C43#58512yes—
361C2×D43—24no—
362C2×D43—28no—
363C2×D43—416no—
364C2×D43—44no—
365C2×D43—42no—
366C2×D43—42no—
367C4×C43—24no—
368C4×C43—44no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43—42no—
372Dic43—24no—
373Dic43—24no—
374Dic43—24no—
375Dic43—44no—
376Dic43—42no—
377Dic43—42no—
378C2×#543—431no—
379C22×C4×D4—431no—
380#2855—432no—
381#2848—432no—
382#2627—432no—
383#2626—432no—
384#2450—434no—
385#2450—434no—
386#2449—434no—
387#2449—434no—
388#2315—431no—
389#2308—431no—
390#2308—431no—
391C2×#385—431no—
392C2×#385D4311yescharacteristic, complemented
393C2×C43—24no—
394C2×C43—24no—
395C2×C43—24no—
396C2×C43C22×C22⋊Q811yescharacteristic
397C2×C43#345912yes—
398C2×C43#348411yescharacteristic
399C2×C43#348511yescharacteristic
400C2×C43#350112yes—
401D43—44no—
402C23×D4—431no—
403C24×C4—431no—
404C24×C4C2×D4311yescharacteristic
405#543—868no—
406C2×C22⋊Q8—432no—
407C2×C22⋊Q8—432no—
408C2×C22⋊Q8—434no—
409C2×C22⋊Q8—432no—
410C2×C22⋊Q8—432no—
411C2×C22⋊Q8—432no—
412C2×C22⋊Q8—432no—
413C2×C4×D4—434no—
414C2×C4×D4—434no—
415C2×C4×D4—868no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—432no—
418C22×C4⋊C4C2×D4312yescomplemented
419C22×C22⋊C4—431no—
420C22×C22⋊C4—431no—
421C22×C22⋊C4—431no—
422C22×C22⋊C4—431no—
423C22×C22⋊C4C2×D4311yescharacteristic
424C22×C22⋊C4C2×D4311yescharacteristic
425C22×C42—431no—
426#400—434no—
427#399—434no—
428#398—434no—
429#398—434no—
430#396—434no—
431#396—434no—
432#395—434no—
433#393—434no—
434#391—434no—
435#389—434no—
436#387—434no—
437#387—434no—
438#386—432no—
439#386—434no—
440#386—432no—
441#386—432no—
442#386—434no—
443#386—432no—
444#385—434no—
445#385—432no—
446#385—432no—
447#385—434no—
448#385—434no—
449#385—434no—
450#385—434no—
451#385C2×D4312yes—
452#385C2×D4312yes—
453#385C2×D4314yescomplemented
454#381—432no—
455#381—432no—
456#380—432no—
457#380—432no—
458#380—434no—
459#379—432no—
460#379—432no—
461C2×#95—432no—
462C2×#95C2×D4312yescomplemented
463C43#3498511yescharacteristic, complemented, Sylow
464C25—431no—
465C25C22×D4311yescharacteristic
466C22×Q8—432no—
467C22×Q8—432no—
468C22×D4—438no—
469C22×D4—432no—
470C22×D4—432no—
471C22×D4—864no—
472C22×D4—864no—
473C23×C4—24no—
474C23×C4—44no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—432no—
480C23×C4—431no—
481C23×C4—434no—
482C23×C4—864no—
483C23×C4—1724no—
484C23×C4C22×D4311yescharacteristic
485C23×C4C22×D4312yes—
486C23×C4C22×D4312yes—
487C23×C4C22×D4311yescharacteristic
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4312yes—
490C23×C4C22×D4311yescharacteristic
491C22⋊Q8—868no—
492C22⋊Q8—868no—
493C22⋊Q8—868no—
494C22⋊Q8—868no—
495C22⋊Q8—868no—
496C22⋊Q8—868no—
497C22⋊Q8—1728no—
498C4×D4—8616no—
499C4×D4—8616no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—432no—
504C2×C4⋊C4—432no—
505C2×C4⋊C4—432no—
506C2×C4⋊C4—432no—
507C2×C4⋊C4—432no—
508C2×C4⋊C4—432no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—434no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—864no—
513C2×C4⋊C4—1724no—
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—438no—
519C2×C22⋊C4—432no—
520C2×C22⋊C4—432no—
521C2×C22⋊C4—432no—
522C2×C22⋊C4—432no—
523C2×C22⋊C4—432no—
524C2×C22⋊C4—432no—
525C2×C22⋊C4—434no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—434no—
528C2×C22⋊C4—434no—
529C2×C22⋊C4—434no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—864no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4C22×D4312yes—
534C2×C22⋊C4C22×D4312yes—
535C2×C22⋊C4C22×D4312yes—
536C2×C22⋊C4C22×D4312yes—
537C2×C42—434no—
538C2×C42—864no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95C22×D4314yes—
548#95C22×D4314yes—
549C24—42no—
550C24—42no—
551C24—432no—
552C24—434no—
553C24—862no—
554C24—862no—
555C24—1722no—
556C24—1722no—
557C24#1062189814yes—
558C24D4×D4314yes—
559C24Q8×D4314yes—
560C24C23×D4311yescharacteristic
561C24C23×D4311yescharacteristic
562C24C23×D4311yescharacteristic
563C2×Q8—864no—
564C2×Q8—864no—
565C2×Q8—1724no—
566C2×Q8—1724no—
567C2×D4—438no—
568C2×D4—438no—
569C2×D4—8632no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—864no—
573C2×D4—864no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—416no—
592C22×C4—434no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—434no—
597C22×C4—434no—
598C22×C4—434no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—864no—
607C22×C4—868no—
608C22×C4—1724no—
609C22×C4—17216no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4C23×D4314yes—
617C22×C4C23×D4312yes—
618C22×C4C23×D4312yes—
619C22×C4C23×D4312yes—
620C22×C4C23×D4312yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—868no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—868no—
631C4⋊C4—1724no—
632C4⋊C4—1724no—
633C4⋊C4—1724no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—438no—
639C22⋊C4—438no—
640C22⋊C4—868no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—1724no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C22⋊C4—1724no—
649C42—868no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—48no—
658C23—44no—
659C23—48no—
660C23—434no—
661C23—868no—
662C23—862no—
663C23—862no—
664C23—864no—
665C23—864no—
666C23—1728no—
667C23—1724no—
668C23—1724no—
669C23—1728no—
670C23#13063303116yescomplemented
671C23C2×D4×D4312yes—
672C23C2×D4×D4312yes—
673C23C2×D4×D4312yes—
674C23C2×Q8×D4312yes—
675C23C2×Q8×D4312yes—
676C23C2×Q8×D4312yes—
677C23C2×#1062189812yes—
678C23C2×#1062189812yes—
679C23C2×#1062189812yes—
680C23C24×D4311yescharacteristic
681Q8—3444no—
682Q8—3444no—
683D4—8616no—
684D4—8616no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—434no—
705C2×C4—434no—
706C2×C4—434no—
707C2×C4—868no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—3442no—
720C2×C4—3442no—
721C2×C4—17216no—
722C2×C4—1724no—
723C2×C4—1724no—
724C2×C4—1728no—
725C2×C4#1306337014yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—416no—
739C22—864no—
740C22—868no—
741C22—17216no—
742C22—1722no—
743C22—1722no—
744C22—1724no—
745C22C2×#1306330314yes—
746C22C2×#1306330314yes—
747C22C2×#1306330314yes—
748C22C22×D4×D4311yescharacteristic
749C22C22×Q8×D4311yescharacteristic
750C22C22×#1062189811yescharacteristic
751C22C2×#1306337012yes—
752C22#1458373512yes—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—864no—
759C4—864no—
760C4—864no—
761C4—1722no—
762C4—1722no—
763C4—1724no—
764C2—24no—
765C2—24no—
766C2—24no—
767C2—1724no—
768C2C22×#1306330311yescharacteristic
769C2#1914800412yes—
770C2#1914822411yescharacteristic
771C2#1914823311yescharacteristic
772C2#1914839112yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC2×C43×#385C2
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43#34985
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#14583525C2semidirect
3. #19142931C2semidirect
4. #19142881C2semidirect
5. #19140414C2semidirect
6. #19140406C2semidirect
7. #19138421C2semidirect
8. #19138419C2semidirect
9. #19138406C2semidirect
10. #19138404C2semidirect
11. #19137207C2semidirect
14. C2×#14582772C2semidirect
15. C2×C43×#385C2semidirect
19. C2×#13063304C22semidirect
20. C2×#13063304C22semidirect
21. C2×#13063303C22semidirect
24. C2×#13063302C22semidirect
25. C2×#13063302C22semidirect
30. C22×Dic43⋊C4C22semidirect
36. #14582840C22semidirect
37. #14582834C22semidirect
38. #14582833C22semidirect
39. #14582830C22semidirect
40. #14582823C22semidirect
41. #14582821C22semidirect
42. #14582819C22semidirect
43. #14582812C22semidirect
44. #14582803C22semidirect
45. #14582794C22semidirect
46. #14582785C22semidirect
47. #14582781C22semidirect
54. #14582773C22semidirect
57. #14582772C22semidirect
58. #14582772C22semidirect
59. #14582771C22semidirect
60. #14582770C22semidirect
63. #14582758C22semidirect
68. C2×C43⋊#95C22semidirect
70. C22×C4⋊C4×C43C22semidirect
75. C43×#385C22semidirect
76. C2×#95×C43C22semidirect
82. C22×C22⋊D43Q8semidirect
273. C23×C43C22⋊Q8semidirect
392. C2×#385D43semidirect
418. C22×C4⋊C4C2×D43semidirect
453. #385C2×D43semidirect
462. C2×#95C2×D43semidirect
463. C43#34985semidirect
670. C23#13063303semidirect

Maximal subgroups

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

subgroupindex
C2×#145835252
C22×C4×C22⋊D432
#191429312
#191428812
#191404142
#191404062
#191384212
#191384192
#191384062
#191384042
#191372072
#191371702
C2×#145827722
C2×C43×#3852
#3498543