Finite Group Databasebeta

← #25112329

Subgroups — #25112329

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063346C211yesmaximal, characteristic
2C2×#14583000C211yesmaximal, characteristic, complemented
3#19137433C211yesmaximal, characteristic, complemented
4#19137420C211yesmaximal, characteristic, complemented
5#19135476C211yesmaximal, characteristic, complemented
6#19135474C211yesmaximal, characteristic, complemented
7#19134943C211yesmaximal, characteristic, complemented
8#19134941C211yesmaximal, characteristic, complemented
9#19134936C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134621C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621900C2211yescharacteristic
18C2×#13063346—24no—
19C2×#13063346—24no—
20C2×#13063346C418yescomplemented
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27#14583000—24no—
28C2×#13063259C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582801—21no—
40#14582801C2211yescharacteristic
41#14582800—21no—
42#14582800C2211yescharacteristic
43#14582778—21no—
44#14582776—21no—
45#14582760—21no—
46#14582756—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C2×C43⋊#95—21no—
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#440—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yescomplemented
70C2×#10621900—22no—
71C2×#10621900—22no—
72C2×#10621900—22no—
73C2×#10621900—41no—
74C2×#10621900—41no—
75C2×#10621900C2×C414yes—
76C22×Dic86C2311yescharacteristic
77C22×D172—21no—
78C22×D172C2311yescharacteristic
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84#13063346—232no—
85C2×#10621885—22no—
86C2×#10621885—22no—
87C2×#10621885C2×C414yescomplemented
88C2×#10621873—22no—
89C2×#10621873—22no—
90C2×#10621873C2×C414yescomplemented
91C2×#10621882—22no—
92C2×#10621882—22no—
93C2×#10621882C2×C414yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—22no—
97C2×C8×D43—22no—
98C2×C8×D43C2×C414yescomplemented
99Q8×Dic43—22no—
100Q8×Dic43—41no—
101D4×Dic43—22no—
102D4×Dic43—41no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063259—22no—
118#13063250—41no—
119#13063249—22no—
120#13063248—41no—
121#13063247—41no—
122#13063246—22no—
123#13063245—41no—
124(C2×D43)⋊C8—22no—
125#13063235—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95D411yescharacteristic
133C43⋊#95D411yescharacteristic
134C22×Q8×C43C2311yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C2×SD16×C43C2×C414yes—
138C2×SD16×C43D414yes—
139C2×SD16×C43D414yes—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×Q8×C43—22no—
143C4×Q8×C43—41no—
144C4×D4×C43—22no—
145C4×D4×C43—41no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#107×C43—22no—
153#103×C43—22no—
154#102×C43—22no—
155#97×C43—22no—
156C24×C43—21no—
157C23×D43—21no—
158C23×D43C2×D411yescharacteristic
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43C2×D412yes—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C22×C412yes—
169C2×D4×C43C2×D412yes—
170C2×D4×C43C2×D412yes—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—81no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—24no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C22×Dic43—24no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—81no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195#10621902—28no—
196#10621902—44no—
197#10621902—44no—
198#10621902—44no—
199#10621900—28no—
200#10621900—44no—
201#10621900—44no—
202#10621900—44no—
203C2×D172—21no—
204C2×D172—24no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—42no—
210C2×D172—42no—
211C2×D172C22×C412yes—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—24no—
217C2×C4×D43—42no—
218C2×C4×D43—42no—
219C2×C4×D43C22×C412yes—
220C2×C4×D43#4112yes—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22×C412yes—
227SD16×C43C22⋊C4116yescomplemented
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43C22×C412yes—
232C2×C8×C43C2×D412yes—
233C2×C8×C43C2×D412yes—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—42no—
243C22⋊Dic43—42no—
244#10621885—28no—
245#10621882—28no—
246(C2×D43)⋊C4—41no—
247(C2×D43)⋊C4—41no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—42no—
250(C2×D43)⋊C4—81no—
251(C2×D43)⋊C4—81no—
252(C2×D43)⋊C4—81no—
253(C2×D43)⋊C4—81no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—42no—
259C4×Dic43—21no—
260C4×Dic43—21no—
261C4×Dic43—42no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268#10621873—28no—
269C8×D43—28no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43C22×D411yescharacteristic
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—22no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43C4×D412yes—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—22no—
295Q8×C43C2×C22⋊C414yes—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43C2×C22⋊C414yes—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C22⋊D43—48no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—48no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—84no—
342C2×Dic43C4×D412yes—
343D172—22no—
344D172—22no—
345D172—48no—
346D172—41no—
347D172—41no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—48no—
353Dic86—22no—
354Dic86—22no—
355Dic86—41no—
356Dic86—41no—
357C8×C43—41no—
358C8×C43C2×C22⋊C414yes—
359C43⋊C8—22no—
360C43⋊C8—41no—
361#22439—431nomaximal, Sylow
362C22×C43—24no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43C2×C4×D411yescharacteristic
370C22×C43D4211yescharacteristic
371C22×C43D4211yescharacteristic
372C22×C43#57511yescharacteristic
373C22×C43#57511yescharacteristic
374C22×C43#57611yescharacteristic
375C22×C43#57811yescharacteristic
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C2×D43—81no—
390C4×C43—24no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43C22×C22⋊C411yescharacteristic
396C4×C43#51811yescharacteristic
397C4×C43#54611yescharacteristic
398C4×C43#54611yescharacteristic
399Dic43—22no—
400Dic43—42no—
401Dic43—41no—
402Dic43—41no—
403Dic43—81no—
404Dic43—81no—
405C22×#135—431no—
406C2×#440—431no—
407C2×#440D4311yescharacteristic, complemented
408#2341—431no—
409#2339—431no—
410#1973—431no—
411#1973—431no—
412#1879—431no—
413#1879—431no—
414#1878—431no—
415#1878—431no—
416#1808—431no—
417#1788—431no—
418#1788—431no—
419#1752—431no—
420C2×C43—44no—
421C2×C43D4×C22⋊C411yescharacteristic
422C2×C43#294311yescharacteristic
423C2×C43#295111yescharacteristic
424C2×C43#326811yescharacteristic
425C2×C43#326811yescharacteristic
426C2×C43#326911yescharacteristic
427C2×C43#326911yescharacteristic
428D43—42no—
429D43—82no—
430C22×#41—431no—
431C22×#41—431no—
432C2×#135—438no—
433C2×#135—864no—
434C2×#135—864no—
435C22×Q16—431no—
436C22×SD16—431no—
437C22×SD16C2×D4311yescharacteristic
438C22×D8—431no—
439C23×C8—431no—
440C2×C4×Q8—431no—
441C2×C4×Q8C2×D4311yescharacteristic
442C2×C4×D4—431no—
443C2×C4×D4C2×D4311yescharacteristic
444#440—24no—
445#440—864no—
446C2×#107—431no—
447C2×#107C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103C2×D4311yescharacteristic
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102C2×D4311yescharacteristic
456C2×C22⋊C8—431no—
457C2×#97—431no—
458C2×#97C2×D4311yescharacteristic
459#391—431no—
460#391—431no—
461#390—431no—
462#390—431no—
463#390—861no—
464#390—861no—
465#386—861no—
466#386—861no—
467#381—861no—
468#380—431no—
469#380—431no—
470#380—861no—
471C4×C22⋊C4—431no—
472C4×C22⋊C4—861no—
473C2×#95—861no—
474#340—431no—
475#340—431no—
476#336—431no—
477#336—431no—
478C43#2243911yescharacteristic, complemented, Sylow
479C2×#41—434no—
480C2×#41—434no—
481C2×#41—862no—
482C2×#41—862no—
483C2×#41—862no—
484C2×#41—862no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41—1721no—
488C2×#41—1721no—
489C2×#41—1721no—
490C2×#41—1721no—
491C22×Q8—431no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—431no—
494C22×D4—861no—
495C22×D4—861no—
496C22×D4C22×D4311yescharacteristic
497C23×C4—21no—
498C23×C4—431no—
499C23×C4—861no—
500C23×C4—861no—
501C23×C4—861no—
502#135—8632no—
503C2×Q16—434no—
504C2×Q16—862no—
505C2×Q16—862no—
506C2×SD16—434no—
507C2×SD16—862no—
508C2×SD16—862no—
509C2×SD16C4×D4314yes—
510C2×SD16D17214yes—
511C2×SD16C22⋊D4314yes—
512C2×D8—434no—
513C2×D8—862no—
514C2×D8—862no—
515C22×C8—431no—
516C22×C8—434no—
517C22×C8—431no—
518C22×C8—862no—
519C22×C8—862no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522C4×Q8—22no—
523C4×Q8—41no—
524C4×Q8—862no—
525C4×Q8—1721no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—862no—
529C4×D4—1721no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C42—21no—
547C2×C42—431no—
548C2×C42—861no—
549C2×C42C22×D4311yescharacteristic
550#107—22no—
551#107—862no—
552#103—22no—
553#103—862no—
554#103—1721no—
555#103—1721no—
556#102—22no—
557#102—862no—
558#102—1721no—
559#102—1721no—
560C22⋊C8—862no—
561#97—22no—
562#97—862no—
563#95—431no—
564#95—431no—
565#95—861no—
566#95—861no—
567#95—861no—
568#95—861no—
569#95—861no—
570#95—861no—
571C24—21no—
572C24—431no—
573C24—861no—
574#41—868no—
575#41—868no—
576#41—1724no—
577#41—1724no—
578#41—1724no—
579#41—1724no—
580#41—1724no—
581#41—1724no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—432no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8C2×C4×D4312yes—
592C2×Q8C2×D17212yes—
593C2×Q8C2×C22⋊D4312yes—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—432no—
598C2×D4—864no—
599C2×D4—864no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—1722no—
606C2×D4—1722no—
607C2×D4—1722no—
608C2×D4—1722no—
609C2×D4C2×C4×D4312yes—
610C2×D4C2×D17212yes—
611C2×D4C2×C22⋊D4312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—431no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—3441no—
633C22×C4—1722no—
634C22×C4—1722no—
635C22×C4—1722no—
636C22×C4—1722no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4C23×D4311yescharacteristic
642Q16—868no—
643SD16—868no—
644SD16(C2×D43)⋊C4116yescomplemented
645D8—868no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—432no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—868no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8C2×C4×D4312yes—
657C2×C8C2×D17212yes—
658C2×C8C2×C22⋊D4312yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—1722no—
669C22⋊C4—42no—
670C22⋊C4—3441no—
671C22⋊C4—3441no—
672C22⋊C4—3441no—
673C22⋊C4—3441no—
674C22⋊C4—1721no—
675C22⋊C4—1721no—
676C22⋊C4—1722no—
677C22⋊C4—1722no—
678C22⋊C4—1722no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—861no—
683C42—861no—
684C42—1722no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—432no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23—862no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23C2×D4×D4311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—862no—
711Q8—862no—
712Q8—1721no—
713Q8—1721no—
714Q8C2×(C2×D43)⋊C414yes—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—862no—
719D4—862no—
720D4—1728no—
721D4—1728no—
722D4—1721no—
723D4—1721no—
724D4C2×(C2×D43)⋊C414yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—432no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—3444no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4C22×C4×D4311yescharacteristic
767C2×C4C22×C22⋊D4311yescharacteristic
768C2×C4C22×D17211yescharacteristic
769C2×C4#41×D4311yescharacteristic
770C2×C4#1306337011yescharacteristic
771C2×C4#1306337111yescharacteristic
772C8—41no—
773C8—862no—
774C8—1721no—
775C8C2×(C2×D43)⋊C414yes—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—3441no—
787C22—3441no—
788C22—3441no—
789C22—3441no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1721no—
794C22—1721no—
795C22—1721no—
796C22—1721no—
797C22C4×D4×D4311yescharacteristic
798C22D4×C22⋊D4311yescharacteristic
799C22D4×D17211yescharacteristic
800C22#1458369511yescharacteristic
801C22#1458369811yescharacteristic
802C22#1458370311yescharacteristic
803C22#1458371511yescharacteristic
804C4—24no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4—862no—
810C4—3441no—
811C4—3441no—
812C4—1722no—
813C4—1721no—
814C4—1721no—
815C4C22×(C2×D43)⋊C411yescharacteristic
816C4#1458337111yescharacteristic
817C4#1458353711yescharacteristic
818C4#1458354411yescharacteristic
819C2—44no—
820C2—3442no—
821C2—1722no—
822C2D4×(C2×D43)⋊C411yescharacteristic
823C2#1914339011yescharacteristic
824C2#1914346711yescharacteristic
825C2#1914612911yescharacteristic
826C2#1914613711yescharacteristic
827C2#1914614411yescharacteristic
828C2#1914615211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×#13063346C2
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#22439
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#14583000C2semidirect
3. #19137433C2semidirect
4. #19137420C2semidirect
5. #19135476C2semidirect
6. #19135474C2semidirect
7. #19134943C2semidirect
8. #19134941C2semidirect
9. #19134936C2semidirect
10. #19134934C2semidirect
11. #19134621C2semidirect
12. #19134534C2semidirect
13. #19134532C2semidirect
14. #19134372C2semidirect
15. C2×C43×#440C2semidirect
20. C2×#13063346C4semidirect
69. C2×#10621902C2×C4semidirect
87. C2×#10621885C2×C4semidirect
90. C2×#10621873C2×C4semidirect
98. C2×C8×D43C2×C4semidirect
227. SD16×C43C22⋊C4semidirect
407. C2×#440D43semidirect
478. C43#22439semidirect
644. SD16(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633462
C2×#145830002
#191374332
#191374202
#191354762
#191354742
#191349432
#191349412
#191349362
#191349342
#191346212
#191345342
#191345322
#191343722
C2×C43×#4402
#2243943