Finite Group Databasebeta

← #25112279

Subgroups — #25112279

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D172C211yesmaximal, characteristic
2#19143330C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19137036C211yesmaximal, characteristic, complemented
6#19135513C211yesmaximal, characteristic, complemented
7#19135426C211yesmaximal, characteristic, complemented
8#19135042C211yesmaximal, characteristic, complemented
9#19135037C211yesmaximal, characteristic, complemented
10#19134896C211yesmaximal, characteristic, complemented
11#19134896C211yesmaximal, characteristic, complemented
12#19134537C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134405C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic, complemented
19C2×M16×D43C2211yescharacteristic, complemented
20#14583571C411yescharacteristic, complemented
21Q8×D172C411yescharacteristic, complemented
22#14583561C411yescharacteristic, complemented
23#14583561C411yescharacteristic, complemented
24#14583553—21no—
25#14583553C411yescharacteristic, complemented
26#14583544—21no—
27#14583544—21no—
28#14583544C411yescharacteristic, complemented
29#14583544C411yescharacteristic, complemented
30D4×D172—21no—
31D4×D172C411yescharacteristic, complemented
32#14583449—21no—
33#14583449C2211yescharacteristic
34#14583411—21no—
35#14583411—21no—
36#14583411C2211yescharacteristic
37#14583411C2211yescharacteristic
38C2×C4×D172—21no—
39C2×C4×D172C2211yescharacteristic
40C2×#13063282C2211yescharacteristic, complemented
41C2×C42×D43C2211yescharacteristic, complemented
42#14582976—21no—
43#14582969—21no—
44#14582969—21no—
45#14582964—21no—
46#14582914—24no—
47C2×#13063253C2211yescharacteristic, complemented
48C2×#13063253C2211yescharacteristic, complemented
49C2×#13063253C2211yescharacteristic, complemented
50C2×#13063253C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic
52C2×#13063252C2211yescharacteristic
53C2×#13063251C2211yescharacteristic, complemented
54C2×#13063251C2211yescharacteristic, complemented
55C2×#13063251C2211yescharacteristic, complemented
56C2×#13063251C2211yescharacteristic, complemented
57#104×D43—24no—
58#14582862C2211yescharacteristic, complemented
59#14582862C2211yescharacteristic, complemented
60C4×#10621877C2211yescharacteristic, complemented
61#14582789—21no—
62#14582782—21no—
63#14582777—21no—
64#14582770—21no—
65C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
66C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
67#14582745C2211yescharacteristic, complemented
68#14582658C2211yescharacteristic, complemented
69#14582658C2211yescharacteristic, complemented
70C4×#41×C43C2211yescharacteristic
71C43×#423C2211yescharacteristic, complemented
72C2×#104×C43C2211yescharacteristic
73C2×#104×C43C2211yescharacteristic
74C4×C4⋊C4×C43C2211yescharacteristic, complemented
75C43×#339C2211yescharacteristic, complemented
76C43×#339C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic
78C2×#10621902C2×C411yescharacteristic, complemented
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898C2311yescharacteristic
82C2×#10621898C2311yescharacteristic
83C2×#10621900—21no—
84C2×#10621900—21no—
85C2×#10621900C2×C411yescharacteristic
86C2×#10621900C2×C411yescharacteristic, complemented
87#41×D43—22no—
88#41×D43—22no—
89#41×D43—22no—
90#41×D43—22no—
91#41×D43—41no—
92#41×D43—41no—
93#41×D43—41no—
94#41×D43—41no—
95C2×Q8×D43C2×C411yescharacteristic
96C2×Q8×D43C2×C411yescharacteristic, complemented
97C22×D172—21no—
98C22×D172D411yescharacteristic
99C2×D4×D43—21no—
100C2×D4×D43—21no—
101C2×D4×D43C2×C411yescharacteristic
102C2×D4×D43C2×C411yescharacteristic, complemented
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43C2311yescharacteristic
107C22×C4×D43C2311yescharacteristic
108C2×#10621877C2311yescharacteristic
109C2×#10621877C2311yescharacteristic
110C2×#10621872—21no—
111C2×#10621872—21no—
112M16×D43—22no—
113M16×D43—22no—
114M16×D43—41no—
115M16×D43—41no—
116C2×C8×D43—21no—
117C2×C8×D43—21no—
118#13063325—21no—
119#13063325C2×C411yescharacteristic, complemented
120#13063322—21no—
121#13063322C2×C411yescharacteristic, complemented
122#13063313—21no—
123#13063313—21no—
124#13063313C2×C411yescharacteristic, complemented
125#13063313C2×C411yescharacteristic, complemented
126#13063309—21no—
127#13063309—21no—
128#13063309—21no—
129#13063309—21no—
130#13063309—21no—
131#13063309—21no—
132#13063305—21no—
133#13063305—21no—
134#13063305—21no—
135#13063305—21no—
136#13063305C2×C411yescharacteristic
137#13063305C2×C411yescharacteristic
138#13063305C2×C411yescharacteristic, complemented
139#13063305C2×C411yescharacteristic, complemented
140#13063300—21no—
141#13063300—21no—
142#13063300—21no—
143#13063300—21no—
144#13063300C2×C411yescharacteristic
145#13063300C2×C411yescharacteristic
146#13063300C2×C411yescharacteristic, complemented
147#13063300C2×C411yescharacteristic, complemented
148#13063299—21no—
149#13063299—21no—
150#13063299—21no—
151#13063299—21no—
152#13063299—21no—
153#13063299—21no—
154#13063295—21no—
155#13063295—21no—
156#13063295—21no—
157#13063295—21no—
158#13063295—21no—
159#13063295—21no—
160C4×D172—21no—
161C4×D172—21no—
162C4×D172—21no—
163C4×D172—21no—
164C4×D172—21no—
165C4×D172—21no—
166C4×D172—21no—
167C4×D172—21no—
168C4×D172—21no—
169C4×D172—21no—
170C4×D172C2×C411yescharacteristic
171C4×D172C2×C411yescharacteristic
172C4×D172C2×C411yescharacteristic
173C4×D172C2×C411yescharacteristic
174C4×D172D411yescharacteristic
175C4×D172D411yescharacteristic
176C4×D172D411yescharacteristic
177C4×D172D411yescharacteristic
178#13063282—22no—
179#13063282—41no—
180C2×C4⋊Dic43—21no—
181C2×C4⋊Dic43D411yescharacteristic
182C2×Dic43⋊C4—21no—
183C2×(C2×D43)⋊C4—21no—
184C2×(C2×D43)⋊C4—21no—
185C2×(C2×D43)⋊C4—21no—
186C2×(C2×D43)⋊C4—21no—
187C2×(C2×D43)⋊C4—21no—
188C2×(C2×D43)⋊C4D411yescharacteristic
189C2×(C2×D43)⋊C4D411yescharacteristic
190C2×C4×Dic43—21no—
191C2×C4×Dic43C2311yescharacteristic
192C2×C4×Dic43C2311yescharacteristic
193C42×D43—22no—
194C42×D43—41no—
195#13063253—22no—
196#13063253—22no—
197#13063253—41no—
198#13063253—41no—
199#13063252—22no—
200#13063252D414yescomplemented
201#13063251—22no—
202#13063251—22no—
203#13063251—41no—
204#13063251—41no—
205(C2×D43)⋊C8—21no—
206(C2×D43)⋊C8—21no—
207(C2×D43)⋊C8—21no—
208(C2×D43)⋊C8—21no—
209#13063236—21no—
210C4×C43⋊C8—21no—
211C43⋊#95—21no—
212C43⋊#95—21no—
213C43⋊#95—21no—
214C43⋊#95—21no—
215C2×#41×C43C2311yescharacteristic
216C2×M16×C43C2311yescharacteristic
217C2×M16×C43C2311yescharacteristic
218C4×Q8×C43C2×C411yescharacteristic, complemented
219C4×Q8×C43C2×C411yescharacteristic, complemented
220C4×D4×C43—21no—
221C4×D4×C43—21no—
222C4×D4×C43C2×C411yescharacteristic, complemented
223C4×D4×C43C2×C411yescharacteristic, complemented
224#117×C43—21no—
225#117×C43C2311yescharacteristic
226C2×C4⋊C4×C43—21no—
227C2×C42×C43—21no—
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231C4⋊C8×C43—21no—
232C4⋊C8×C43—21no—
233#104×C43—22no—
234#104×C43—22no—
235#95×C43—21no—
236C23×D43—21no—
237C23×D43—21no—
238C23×D43C2×D411yescharacteristic
239C23×D43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43C2×D412yes—
243#41×C43#4112yes—
244C2×Q8×C43C22×C411yescharacteristic
245C2×D4×C43—21no—
246C2×D4×C43C22×C411yescharacteristic
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2411yescharacteristic
255C2×C22⋊D43—21no—
256C2×C22⋊D43—21no—
257C2×C22⋊D43—21no—
258C2×C22⋊D43—21no—
259C2×C22⋊D43—21no—
260C2×C22⋊D43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43C2×D411yescharacteristic
266C22×Dic43C2×D411yescharacteristic
267#10621902—22no—
268#10621902—22no—
269#10621902—41no—
270#10621902—41no—
271Q8×D43—22no—
272Q8×D43—22no—
273Q8×D43—41no—
274Q8×D43—41no—
275#10621900—22no—
276#10621900—22no—
277#10621900—41no—
278#10621900—41no—
279#10621900—42no—
280#10621900—42no—
281#10621900—42no—
282#10621900—42no—
283D4×D43—22no—
284D4×D43—22no—
285D4×D43—42no—
286D4×D43—42no—
287D4×D43—42no—
288D4×D43—42no—
289D4×D43—41no—
290D4×D43—41no—
291#10621898—21no—
292#10621898—21no—
293#10621898—21no—
294#10621898—21no—
295#10621898—21no—
296#10621898—21no—
297#10621898—21no—
298#10621898—21no—
299#10621898—42no—
300#10621898—42no—
301#10621898—42no—
302#10621898—42no—
303C2×D172—21no—
304C2×D172—21no—
305C2×D172—21no—
306C2×D172—21no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172—21no—
310C2×D172—21no—
311C2×D172—42no—
312C2×D172—44no—
313C2×D172C22⋊C411yescharacteristic
314C2×D172C22⋊C411yescharacteristic
315C2×D172C22⋊C411yescharacteristic
316C2×D172C22⋊C411yescharacteristic
317C2×D172C22×C411yescharacteristic
318C2×D172C22×C411yescharacteristic
319C2×C4×D43—21no—
320C2×C4×D43—21no—
321C2×C4×D43—21no—
322C2×C4×D43—21no—
323C2×C4×D43—21no—
324C2×C4×D43—21no—
325C2×C4×D43—21no—
326C2×C4×D43—21no—
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—21no—
330C2×C4×D43—21no—
331C2×C4×D43—21no—
332C2×C4×D43—21no—
333C2×C4×D43—42no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—42no—
337C2×C4×D43—42no—
338C2×C4×D43—42no—
339C2×C4×D43—42no—
340C2×C4×D43C22×C411yescharacteristic
341C2×C4×D43C22×C411yescharacteristic
342C2×C4×D43C22×C411yescharacteristic
343C2×C4×D43C22×C411yescharacteristic
344C2×C4×D43C2×D411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43C2×D411yescharacteristic
347C2×C4×D43C2×D411yescharacteristic
348C2×Dic86—21no—
349C2×Dic86—21no—
350C2×Dic86C22×C411yescharacteristic
351C2×Dic86C22×C411yescharacteristic
352M16×C43—21no—
353M16×C43—21no—
354M16×C43—21no—
355M16×C43—21no—
356C2×C8×C43—21no—
357C2×C8×C43—21no—
358C4⋊C4×C43—21no—
359C4⋊C4×C43—21no—
360C4⋊C4×C43—42no—
361C4⋊C4×C43C22×C411yescharacteristic
362C4⋊C4×C43C22×C411yescharacteristic
363C22⋊C4×C43—21no—
364C22⋊C4×C43—21no—
365C22⋊C4×C43—21no—
366C42×C43—21no—
367C42×C43—21no—
368C42×C43—21no—
369C42×C43—21no—
370C42×C43—21no—
371C42×C43—21no—
372C42×C43—21no—
373C42×C43C22×C411yescharacteristic
374C42×C43C22×C411yescharacteristic
375C42×C43C2×D411yescharacteristic
376C42×C43C2×D411yescharacteristic
377(C2×D43)⋊C4—21no—
378(C2×D43)⋊C4—21no—
379(C2×D43)⋊C4—21no—
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383(C2×D43)⋊C4—21no—
384(C2×D43)⋊C4—21no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4—21no—
388(C2×D43)⋊C4—21no—
389(C2×D43)⋊C4—42no—
390(C2×D43)⋊C4—42no—
391(C2×D43)⋊C4—42no—
392(C2×D43)⋊C4C22⋊C411yescharacteristic
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394(C2×D43)⋊C4C22⋊C411yescharacteristic
395(C2×D43)⋊C4C22⋊C411yescharacteristic
396(C2×D43)⋊C4C22⋊C411yescharacteristic
397(C2×D43)⋊C4C22⋊C411yescharacteristic
398(C2×D43)⋊C4C22⋊C411yescharacteristic
399(C2×D43)⋊C4C22⋊C411yescharacteristic
400C4⋊Dic43—21no—
401C4⋊Dic43—21no—
402C4⋊Dic43—21no—
403C4⋊Dic43—21no—
404C4⋊Dic43—21no—
405C4⋊Dic43—21no—
406C4⋊Dic43C22⋊C411yescharacteristic
407C4⋊Dic43C22⋊C411yescharacteristic
408C4⋊Dic43C22⋊C411yescharacteristic
409C4⋊Dic43C22⋊C411yescharacteristic
410Dic43⋊C4—42no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—21no—
414C4×Dic43—42no—
415C4×Dic43C2×D412yescomplemented
416#10621877—21no—
417#10621877—21no—
418#10621877—21no—
419#10621877C2×D412yescomplemented
420C2×C43⋊C8—21no—
421C2×C43⋊C8—21no—
422#10621872—42no—
423#10621872—42no—
424C8×D43—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43C22×D411yescharacteristic
428C22×D43—21no—
429C22×D43—21no—
430C22×D43—21no—
431C22×D43—21no—
432C22×D43—22no—
433C22×D43—21no—
434C22×D43—21no—
435C22×D43—41no—
436C22×D43—41no—
437C22×D43—41no—
438C22×D43—42no—
439C22×D43—42no—
440C22×D43—42no—
441C22×D43—42no—
442C22×D43—81no—
443C22×D43—81no—
444C22×D43C2×C22⋊C411yescharacteristic
445C22×D43C2×C22⋊C411yescharacteristic
446C22×D43C2×C22⋊C411yescharacteristic
447C22×D43C2×C22⋊C411yescharacteristic
448Q8×C43—21no—
449Q8×C43C4×D412yes—
450D4×C43—22no—
451D4×C43—22no—
452D4×C43—21no—
453D4×C43C4×D412yes—
454C2×C4×C43—21no—
455C2×C4×C43—22no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—21no—
459C2×C4×C43—21no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—42no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43—81no—
469C2×C4×C43C2×C22⋊C411yescharacteristic
470C2×C4×C43C2×C22⋊C411yescharacteristic
471C2×C4×C43C2×C22⋊C411yescharacteristic
472C2×C4×C43C2×C22⋊C411yescharacteristic
473C2×C4×C43C23×C411yescharacteristic
474C2×C4×C43C22×D411yescharacteristic
475C2×C4×C43C22×D411yescharacteristic
476C2×C4×C43C2×#4111yescharacteristic
477C2×C4×C43H(5,𝔽2)11yescharacteristic
478C2×C4×C43H(5,𝔽2)11yescharacteristic
479C22⋊D43—42no—
480C22⋊D43—42no—
481C22⋊D43—42no—
482C22⋊D43—42no—
483C22⋊D43—41no—
484C22⋊D43—41no—
485C22⋊D43—41no—
486C22⋊D43—41no—
487C2×Dic43—21no—
488C2×Dic43—21no—
489C2×Dic43—21no—
490C2×Dic43—21no—
491C2×Dic43—21no—
492C2×Dic43—21no—
493C2×Dic43—22no—
494C2×Dic43—42no—
495C2×Dic43—42no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43C2×C22⋊C411yescharacteristic
502C2×Dic43C2×C22⋊C411yescharacteristic
503C2×Dic43C2×C22⋊C411yescharacteristic
504C2×Dic43C2×C22⋊C411yescharacteristic
505D172—22no—
506D172—22no—
507D172—21no—
508D172—21no—
509D172—21no—
510D172—21no—
511D172—41no—
512D172—41no—
513D172—42no—
514D172—42no—
515D172—42no—
516D172—42no—
517D172—42no—
518D172—81no—
519D172—81no—
520D172—81no—
521C4×D43—21no—
522C4×D43—21no—
523C4×D43—21no—
524C4×D43—21no—
525C4×D43—21no—
526C4×D43—21no—
527C4×D43—21no—
528C4×D43—21no—
529C4×D43—21no—
530C4×D43—21no—
531C4×D43—21no—
532C4×D43—21no—
533C4×D43—21no—
534C4×D43—21no—
535C4×D43—21no—
536C4×D43—21no—
537C4×D43—42no—
538C4×D43—42no—
539C4×D43—42no—
540C4×D43—42no—
541C4×D43—48no—
542C4×D43—41no—
543C4×D43—41no—
544C4×D43—41no—
545C4×D43—41no—
546Dic86—21no—
547Dic86—21no—
548Dic86—21no—
549Dic86—21no—
550Dic86—42no—
551Dic86—42no—
552C8×C43—41no—
553C8×C43—41no—
554C43⋊C8—22no—
555C43⋊C8—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—22no—
560C22×C43—41no—
561C22×C43—41no—
562C22×C43C22×C22⋊C411yescharacteristic
563C22×C43D4211yescharacteristic
564C22×C43#54611yescharacteristic
565C2×D43—21no—
566C2×D43—21no—
567C2×D43—21no—
568C2×D43—21no—
569C2×D43—21no—
570C2×D43—21no—
571C2×D43—21no—
572C2×D43—21no—
573C2×D43—21no—
574C2×D43—21no—
575C2×D43—21no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—41no—
579C2×D43—41no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—84no—
585C2×D43—81no—
586C2×D43—81no—
587C2×D43—84no—
588C2×D43#42112yescomplemented
589C4×C43—22no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—21no—
593C4×C43—21no—
594C4×C43—42no—
595C4×C43—41no—
596C4×C43—41no—
597C4×C43—81no—
598C4×C43C2×C4×D411yescharacteristic
599C4×C43#51811yescharacteristic
600C4×C43D4211yescharacteristic
601C4×C43#54611yescharacteristic
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—21no—
606Dic43—42no—
607Dic43—41no—
608Dic43—41no—
609Dic43—81no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871—431no—
621#1806D4311yescharacteristic, complemented
622#1789—431no—
623#1789—431no—
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—42no—
628C2×C43D4×C22⋊C411yescharacteristic
629C2×C43C2×#42111yescharacteristic
630C2×C43#290111yescharacteristic
631D43—22no—
632D43—41no—
633D43—41no—
634D43—41no—
635D43—81no—
636D43—81no—
637C22×#41—431no—
638C22×#41—431no—
639C22×M16—431no—
640C22×M16—431no—
641#550—431no—
642D4×Q8—431no—
643#548—431no—
644#548—431no—
645#547—431no—
646#547—861no—
647#546—431no—
648#546—431no—
649#546—861no—
650#546—861no—
651D42—431no—
652D42—861no—
653#532—431no—
654#532—861no—
655#525—431no—
656#525—431no—
657#525—861no—
658#525—861no—
659C4×#41C2×D4311yescharacteristic
660C2×C4×D4—431no—
661C2×C4×D4—861no—
662C2×#117—431no—
663C22×C42—431no—
664#436—861no—
665#435—861no—
666#435—861no—
667C8×D4—861no—
668#423C2×D4311yescharacteristic, complemented
669#421—864no—
670C2×#104—431no—
671C2×#104—431no—
672C2×#104—431no—
673C2×#104—431no—
674C2×#104—431no—
675C2×#104—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—864no—
681C2×#104C2×D4311yescharacteristic
682C2×#104C2×D4311yescharacteristic
683#407—431no—
684#407—431no—
685C4×M16—431no—
686#388—861no—
687#387—861no—
688#386—861no—
689#385—861no—
690C4×C4⋊C4C2×D4311yescharacteristic, complemented
691C4×C22⋊C4—431no—
692C4×C22⋊C4—431no—
693#376—431no—
694#339—431no—
695#339—431no—
696#339C2×D4311yescharacteristic, complemented
697#339C2×D4311yescharacteristic, complemented
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—431no—
700C2×#41—431no—
701C2×#41—431no—
702C2×#41—431no—
703C2×#41—431no—
704C2×#41—431no—
705C2×#41—861no—
706C2×#41—861no—
707C2×#41—861no—
708C2×#41—861no—
709C2×#41—862no—
710C2×#41—862no—
711C2×#41—862no—
712C2×#41—862no—
713C2×#41—1721no—
714C2×#41—1721no—
715C2×#41—1721no—
716C2×#41—1721no—
717C2×#41C22×D4311yescharacteristic
718C22×Q8—431no—
719C22×Q8—431no—
720C22×D4—431no—
721C22×D4—431no—
722C22×D4—431no—
723C22×D4—861no—
724C22×D4—861no—
725C22×D4—861no—
726C23×C4—431no—
727C23×C4—431no—
728C23×C4—861no—
729C23×C4—861no—
730C23×C4—861no—
731C2×M16—431no—
732C2×M16—431no—
733C2×M16—861no—
734C2×M16—861no—
735C2×M16—862no—
736C2×M16—862no—
737C2×M16—1721no—
738C2×M16—1721no—
739C2×M16C22×D4311yescharacteristic
740C2×M16C22×D4311yescharacteristic
741C22×C8—861no—
742C22×C8—861no—
743C4⋊Q8—431no—
744C4⋊Q8—861no—
745#127—431no—
746#127—861no—
747#124—431no—
748#124—431no—
749#124—861no—
750#124—861no—
751#123—861no—
752#123—861no—
753#123—861no—
754#123—861no—
755#123—861no—
756#123—861no—
757C22⋊Q8—431no—
758C22⋊Q8—431no—
759C22⋊Q8—431no—
760C22⋊Q8—431no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763C22⋊Q8—861no—
764C22⋊Q8—861no—
765#121—431no—
766#121—431no—
767#121—431no—
768#121—431no—
769#121—861no—
770#121—861no—
771#121—861no—
772#121—861no—
773#121—861no—
774#121—861no—
775#121—861no—
776#121—861no—
777#121—861no—
778#121—861no—
779#120—861no—
780#120—861no—
781#120—861no—
782#120—861no—
783#120—861no—
784#120—861no—
785C4×Q8C4×D4311yescharacteristic, complemented
786C4×Q8C4×D4311yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—431no—
790C4×D4—431no—
791C4×D4—431no—
792C4×D4—431no—
793C4×D4—431no—
794C4×D4—431no—
795C4×D4—431no—
796C4×D4—431no—
797C4×D4—861no—
798C4×D4—861no—
799C4×D4—861no—
800C4×D4—861no—
801C4×D4—861no—
802C4×D4—861no—
803C4×D4—861no—
804C4×D4—861no—
805C4×D4—861no—
806C4×D4—861no—
807C4×D4C4×D4311yescharacteristic, complemented
808C4×D4C4×D4311yescharacteristic, complemented
809#117—21no—
810#117—862no—
811#117—1721no—
812#117C22×D4311yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—431no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C22⋊C4—431no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—861no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C42—21no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—862no—
828C2×C42—861no—
829C2×C42—1721no—
830C2×C42C22×D4311yescharacteristic
831C2×C42C22×D4311yescharacteristic
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—21no—
834C4⋊C8—21no—
835#104—22no—
836#104—22no—
837#104—434no—
838#104—862no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—1721no—
844#104—1721no—
845#104—1721no—
846#104—1721no—
847C22⋊C8—861no—
848C22⋊C8—861no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—21no—
854#95—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—431no—
859C24—431no—
860C24—861no—
861C24—861no—
862#41—21no—
863#41—21no—
864#41—862no—
865#41—862no—
866#41—862no—
867#41—862no—
868#41—861no—
869#41—861no—
870#41—861no—
871#41—861no—
872#41—861no—
873#41—861no—
874#41—861no—
875#41—861no—
876#41—1722no—
877#41—1722no—
878#41—1722no—
879#41—1722no—
880#41—1721no—
881#41—1721no—
882#41—1722no—
883#41—1722no—
884#41—1722no—
885#41—1722no—
886#41—1721no—
887#41—1721no—
888#41D4×D4312yes—
889#41#1062190212yes—
890C2×Q8—431no—
891C2×Q8—431no—
892C2×Q8—861no—
893C2×Q8—861no—
894C2×Q8—862no—
895C2×Q8—862no—
896C2×Q8—1721no—
897C2×Q8—1721no—
898C2×Q8C2×C4×D4311yescharacteristic
899C2×D4—21no—
900C2×D4—431no—
901C2×D4—431no—
902C2×D4—431no—
903C2×D4—431no—
904C2×D4—431no—
905C2×D4—431no—
906C2×D4—861no—
907C2×D4—861no—
908C2×D4—861no—
909C2×D4—861no—
910C2×D4—861no—
911C2×D4—861no—
912C2×D4—861no—
913C2×D4—861no—
914C2×D4—862no—
915C2×D4—862no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—1722no—
923C2×D4—1724no—
924C2×D4—1721no—
925C2×D4—1721no—
926C2×D4—1722no—
927C2×D4—1722no—
928C2×D4—1722no—
929C2×D4—1722no—
930C2×D4C2×C4×D4311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—431no—
937C22×C4—431no—
938C22×C4—431no—
939C22×C4—431no—
940C22×C4—431no—
941C22×C4—431no—
942C22×C4—431no—
943C22×C4—431no—
944C22×C4—431no—
945C22×C4—431no—
946C22×C4—861no—
947C22×C4—861no—
948C22×C4—861no—
949C22×C4—861no—
950C22×C4—861no—
951C22×C4—861no—
952C22×C4—861no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—861no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4—1722no—
969C22×C4—1722no—
970C22×C4—1722no—
971C22×C4D4×D4311yescharacteristic
972C22×C4D4×D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—432no—
979M16—861no—
980M16—861no—
981M16—861no—
982M16—1722no—
983M16—1722no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—861no—
987C2×C8—861no—
988C2×C8—1722no—
989C2×C8—1722no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—42no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—431no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—861no—
1002C4⋊C4—861no—
1003C4⋊C4—1722no—
1004C4⋊C4C2×C4×D4311yescharacteristic
1005C4⋊C4C2×C4×D4311yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—431no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—431no—
1013C22⋊C4—431no—
1014C22⋊C4—431no—
1015C22⋊C4—431no—
1016C22⋊C4—431no—
1017C22⋊C4—861no—
1018C22⋊C4—861no—
1019C22⋊C4—861no—
1020C22⋊C4—861no—
1021C22⋊C4—861no—
1022C22⋊C4—861no—
1023C22⋊C4—861no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—861no—
1028C22⋊C4—861no—
1029C22⋊C4—1722no—
1030C22⋊C4—1722no—
1031C22⋊C4—1722no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—432no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—1722no—
1044C42C2×C4×D4311yescharacteristic
1045C42C2×C4×D4311yescharacteristic
1046C42D4×D4311yescharacteristic
1047C42D4×D4311yescharacteristic
1048C23—21no—
1049C23—431no—
1050C23—431no—
1051C23—431no—
1052C23—431no—
1053C23—862no—
1054C23—861no—
1055C23—861no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—861no—
1060C23—3441no—
1061C23—3441no—
1062C23—1721no—
1063C23—1721no—
1064C23—1721no—
1065C23—1722no—
1066C23—1722no—
1067C23—1722no—
1068C23—1722no—
1069C23C2×D4×D4311yescharacteristic
1070Q8—21no—
1071Q8—861no—
1072Q8—861no—
1073Q8—861no—
1074Q8—861no—
1075Q8—1722no—
1076Q8—1722no—
1077Q8#1306328712yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—862no—
1082D4—862no—
1083D4—861no—
1084D4—861no—
1085D4—861no—
1086D4—861no—
1087D4—3441no—
1088D4—3441no—
1089D4—3441no—
1090D4—1721no—
1091D4—1721no—
1092D4—1722no—
1093D4—1722no—
1094D4—1722no—
1095D4—1722no—
1096D4—1722no—
1097D4—1722no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1721no—
1102D4—1721no—
1103D4—1721no—
1104D4—1721no—
1105D4#1306328712yes—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—81no—
1121C2×C4—431no—
1122C2×C4—431no—
1123C2×C4—431no—
1124C2×C4—431no—
1125C2×C4—861no—
1126C2×C4—861no—
1127C2×C4—861no—
1128C2×C4—861no—
1129C2×C4—861no—
1130C2×C4—861no—
1131C2×C4—861no—
1132C2×C4—861no—
1133C2×C4—861no—
1134C2×C4—861no—
1135C2×C4—861no—
1136C2×C4—861no—
1137C2×C4—861no—
1138C2×C4—861no—
1139C2×C4—861no—
1140C2×C4—861no—
1141C2×C4—861no—
1142C2×C4—861no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—862no—
1148C2×C4—1722no—
1149C2×C4—1722no—
1150C2×C4—1722no—
1151C2×C4—1722no—
1152C2×C4—1728no—
1153C2×C4—1722no—
1154C2×C4—1722no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1721no—
1158C2×C4—1721no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1721no—
1163C2×C4—1721no—
1164C2×C4C22⋊C4×D4311yescharacteristic
1165C2×C4C22⋊C4×D4311yescharacteristic
1166C2×C4C22⋊C4×D4311yescharacteristic
1167C2×C4C22⋊C4×D4311yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C2×D4×D4311yescharacteristic
1171C2×C4C2×#1062190211yescharacteristic
1172C2×C4#1306337111yescharacteristic
1173C2×C4#1306337111yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—862no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—22no—
1181C22—41no—
1182C22—41no—
1183C22—432no—
1184C22—861no—
1185C22—861no—
1186C22—861no—
1187C22—861no—
1188C22—861no—
1189C22—861no—
1190C22—861no—
1191C22—861no—
1192C22—861no—
1193C22—861no—
1194C22—861no—
1195C22—3441no—
1196C22—3441no—
1197C22—3444no—
1198C22—3444no—
1199C22—1722no—
1200C22—1722no—
1201C22—1721no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22—1721no—
1206C22—1721no—
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22#1458353311yescharacteristic
1209C22#1458354011yescharacteristic
1210C4—22no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—42no—
1216C4—41no—
1217C4—41no—
1218C4—81no—
1219C4—861no—
1220C4—861no—
1221C4—861no—
1222C4—861no—
1223C4—3441no—
1224C4—1722no—
1225C4—1721no—
1226C4—1721no—
1227C4C2×#1306328711yescharacteristic
1228C4#1458337311yescharacteristic
1229C4#1458353311yescharacteristic
1230C4#1458354011yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—42no—
1234C2—862no—
1235C2—3441no—
1236C2—3441no—
1237C2—1721no—
1238C2—1721no—
1239C2—1721no—
1240C2#1913741511yescharacteristic
1241C2#421×D4311yescharacteristic
1242C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#41×D172C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143330C2semidirect
3. C2×#14582914C2semidirect
4. C2×#104×D43C2semidirect
5. #19137036C2semidirect
6. #19135513C2semidirect
7. #19135426C2semidirect
8. #19135042C2semidirect
9. #19135037C2semidirect
10. #19134896C2semidirect
11. #19134896C2semidirect
12. #19134537C2semidirect
13. #19134537C2semidirect
14. #19134405C2semidirect
15. C43×#1806C2semidirect
18. C2×M16×D43C22semidirect
19. C2×M16×D43C22semidirect
20. #14583571C4semidirect
21. Q8×D172C4semidirect
22. #14583561C4semidirect
23. #14583561C4semidirect
25. #14583553C4semidirect
28. #14583544C4semidirect
29. #14583544C4semidirect
31. D4×D172C4semidirect
40. C2×#13063282C22semidirect
41. C2×C42×D43C22semidirect
47. C2×#13063253C22semidirect
48. C2×#13063253C22semidirect
49. C2×#13063253C22semidirect
50. C2×#13063253C22semidirect
53. C2×#13063251C22semidirect
54. C2×#13063251C22semidirect
55. C2×#13063251C22semidirect
56. C2×#13063251C22semidirect
58. #14582862C22semidirect
59. #14582862C22semidirect
60. C4×#10621877C22semidirect
65. C4×(C2×D43)⋊C4C22semidirect
66. C4×(C2×D43)⋊C4C22semidirect
67. #14582745C22semidirect
68. #14582658C22semidirect
69. #14582658C22semidirect
71. C43×#423C22semidirect
74. C4×C4⋊C4×C43C22semidirect
75. C43×#339C22semidirect
76. C43×#339C22semidirect
78. C2×#10621902C2×C4semidirect
86. C2×#10621900C2×C4semidirect
96. C2×Q8×D43C2×C4semidirect
102. C2×D4×D43C2×C4semidirect
119. #13063325C2×C4semidirect
121. #13063322C2×C4semidirect
124. #13063313C2×C4semidirect
125. #13063313C2×C4semidirect
138. #13063305C2×C4semidirect
139. #13063305C2×C4semidirect
146. #13063300C2×C4semidirect
147. #13063300C2×C4semidirect
200. #13063252D4semidirect
218. C4×Q8×C43C2×C4semidirect
219. C4×Q8×C43C2×C4semidirect
222. C4×D4×C43C2×C4semidirect
223. C4×D4×C43C2×C4semidirect
415. C4×Dic43C2×D4semidirect
419. #10621877C2×D4semidirect
588. C2×D43#421semidirect
621. #1806D43semidirect
668. #423C2×D43semidirect
690. C4×C4⋊C4C2×D43semidirect
696. #339C2×D43semidirect
697. #339C2×D43semidirect
698. C43#22434semidirect
785. C4×Q8C4×D43semidirect
786. C4×Q8C4×D43semidirect
807. C4×D4C4×D43semidirect
808. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#41×D1722
#191433302
C2×#145829142
C2×#104×D432
#191370362
#191355132
#191354262
#191350422
#191350372
#191348962
#191345372
#191344052
C43×#18062
#2243443