Finite Group Databasebeta

← #25117383

Subgroups — #25117383

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583016C211yesmaximal, characteristic, complemented
2#19143322C211yesmaximal, characteristic, complemented
3C2×#14582916C211yesmaximal, characteristic, complemented
4#19143044C211yesmaximal, characteristic, complemented
5#19135489C211yesmaximal, characteristic, complemented
6#19135301C211yesmaximal, characteristic, complemented
7#19135245C211yesmaximal, characteristic, complemented
8#19135044C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134924C211yesmaximal, characteristic, complemented
11#19134872C211yesmaximal, characteristic, complemented
12#19134802C211yesmaximal, characteristic, complemented
13#19134442C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#3002C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic, complemented
19C22×#10621877C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583016—24no—
22#14582977—21no—
23#14582971—21no—
24#14582971—21no—
25D4×C43⋊C8—21no—
26C2×#13063261C2211yescharacteristic, complemented
27C2×#13063261C2211yescharacteristic, complemented
28#14582926C2211yescharacteristic, complemented
29#14582916—24no—
30C2×#13063252C2211yescharacteristic
31C2×#13063252C2211yescharacteristic
32C2×#13063252C2211yescharacteristic
33C2×#13063252C2211yescharacteristic
34C2×#13063252C2211yescharacteristic, complemented
35C2×#13063252C2211yescharacteristic, complemented
36#14582866—21no—
37#14582866—21no—
38#14582866C2211yescharacteristic
39#14582866C2211yescharacteristic
40#14582866C2211yescharacteristic, complemented
41#14582863—21no—
42#14582863C2211yescharacteristic
43C2×C22⋊(C43⋊C8)—21no—
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45#14582855C2211yescharacteristic, complemented
46C2×#13063235C2211yescharacteristic, complemented
47C2×C8×Dic43C2211yescharacteristic, complemented
48#14582664C2211yescharacteristic, complemented
49#14582664C2211yescharacteristic, complemented
50#14582658C2211yescharacteristic, complemented
51#14582658C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C22×#41×C43C2211yescharacteristic
55C2×#135×C43C2211yescharacteristic
56C2×#135×C43C2211yescharacteristic
57C43×#525C2211yescharacteristic
58C43×#452C411yescharacteristic, complemented
59C43×#452C411yescharacteristic, complemented
60C43×#451C411yescharacteristic, complemented
61C43×#450C411yescharacteristic, complemented
62C43×#449C411yescharacteristic, complemented
63C43×#449C411yescharacteristic, complemented
64C43×#448C411yescharacteristic, complemented
65C43×#447C411yescharacteristic, complemented
66C43×#416C2211yescharacteristic
67C43×#416C2211yescharacteristic
68C2×C22⋊C8×C43C2211yescharacteristic
69#13063332—22no—
70#13063332—22no—
71#13063332—22no—
72#13063332—41no—
73#13063332—41no—
74#13063332—41no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—22no—
80C2×#10621877—41no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C22×C43⋊C8—21no—
86C22×C43⋊C8—21no—
87C22×C43⋊C8—21no—
88C22×C43⋊C8—21no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91#13063284—22no—
92#13063284—41no—
93C2×C4⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063261—22no—
98#13063261—41no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101#13063252—22no—
102#13063252—22no—
103#13063252—22no—
104#13063252—22no—
105#13063252—41no—
106#13063252D414yescomplemented
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)—21no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)D411yescharacteristic
116C22⋊(C43⋊C8)D411yescharacteristic
117C22⋊(C43⋊C8)D411yescharacteristic
118C22⋊(C43⋊C8)D411yescharacteristic
119#13063236—21no—
120#13063235—41no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C2×#41×C43—21no—
124C2×#41×C43—21no—
125C2×#41×C43—22no—
126C2×#41×C43—22no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C2×#41×C43C2×C411yescharacteristic
130C2×#41×C43C2×C411yescharacteristic
131C2×#41×C43C2311yescharacteristic
132C2×#41×C43C2311yescharacteristic
133C2×#41×C43C2311yescharacteristic
134C22×Q8×C43C2×C411yescharacteristic
135C22×D4×C43—21no—
136C22×D4×C43C2×C411yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139#135×C43—22no—
140#135×C43—22no—
141#135×C43—41no—
142#135×C43—41no—
143C2×Q16×C43C2×C411yescharacteristic
144C2×Q16×C43C2×C411yescharacteristic
145C2×SD16×C43C2×C411yescharacteristic
146C2×SD16×C43C2×C411yescharacteristic
147C2×SD16×C43C2×C411yescharacteristic
148C2×SD16×C43C2×C411yescharacteristic
149C2×D8×C43C2×C411yescharacteristic
150C2×D8×C43C2×C411yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C22×C8×C43C2311yescharacteristic
153#123×C43—21no—
154C22⋊Q8×C43C2×C411yescharacteristic
155C22⋊Q8×C43C2×C411yescharacteristic
156#121×C43C2×C411yescharacteristic
157#121×C43C2×C411yescharacteristic
158#120×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161#117×C43C2311yescharacteristic
162#103×C43C2×C411yescharacteristic
163#103×C43C2×C411yescharacteristic
164#103×C43C2×C411yescharacteristic
165#103×C43C2×C411yescharacteristic
166#102×C43C2×C411yescharacteristic
167#102×C43C2×C411yescharacteristic
168#102×C43C2×C411yescharacteristic
169#102×C43C2×C411yescharacteristic
170C22⋊C8×C43C2×C411yescharacteristic
171C22⋊C8×C43C2×C411yescharacteristic
172C22⋊C8×C43C2×C411yescharacteristic
173C22⋊C8×C43C2×C411yescharacteristic
174C24×C43—21no—
175C24×C43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—22no—
179#41×C43—22no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43—41no—
191#41×C43—41no—
192#41×C43—42no—
193#41×C43—42no—
194#41×C43C2×D412yes—
195#41×C43#4112yes—
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43—41no—
199C2×Q8×C43C22×C411yescharacteristic
200C2×Q8×C43C22×C411yescharacteristic
201C2×Q8×C43C22×C411yescharacteristic
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—22no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—41no—
214C2×D4×C43C22×C411yescharacteristic
215C2×D4×C43C22×C411yescharacteristic
216C2×D4×C43C22×C411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—42no—
228C22×C4×C43—42no—
229C22×C4×C43C22×C411yescharacteristic
230C22×C4×C43C22×C411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43#4111yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237Q16×C43—22no—
238Q16×C43—41no—
239SD16×C43—22no—
240SD16×C43—22no—
241SD16×C43—41no—
242SD16×C43—41no—
243D8×C43—22no—
244D8×C43—41no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43C22×C411yescharacteristic
250C2×C8×C43C22×C411yescharacteristic
251C2×C8×C43C22×C411yescharacteristic
252C2×C8×C43C22×C411yescharacteristic
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C22×C411yescharacteristic
256C4⋊C4×C43C22×C411yescharacteristic
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C42×C43—21no—
263C22⋊Dic43—42no—
264C4⋊Dic43—42no—
265C4×Dic43—21no—
266C4×Dic43—21no—
267C4×Dic43—21no—
268C4×Dic43C2×D412yes—
269#10621877—21no—
270#10621877—21no—
271#10621877—21no—
272#10621877—21no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—42no—
277#10621877—42no—
278#10621877—42no—
279#10621877—42no—
280#10621877C2×D412yes—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—42no—
290C2×C43⋊C8—42no—
291C2×C43⋊C8—42no—
292C2×C43⋊C8—42no—
293C2×C43⋊C8C2×D411yescharacteristic
294C2×C43⋊C8C2×D411yescharacteristic
295C2×C43⋊C8C2×D411yescharacteristic
296C2×C43⋊C8C2×D411yescharacteristic
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—81no—
307C23×C43C4×D411yescharacteristic
308C23×C43C4×D411yescharacteristic
309C23×C43C2×#4111yescharacteristic
310Q8×C43—21no—
311Q8×C43—21no—
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43—42no—
316Q8×C43C4×D412yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—21no—
320D4×C43—21no—
321D4×C43—21no—
322D4×C43—21no—
323D4×C43—21no—
324D4×C43—42no—
325D4×C43—42no—
326D4×C43—42no—
327D4×C43—42no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—81no—
333D4×C43C4×D412yes—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43C4×D411yescharacteristic
359C2×C4×C43C4×D411yescharacteristic
360C2×C4×C43C23×C411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43H(5,𝔽2)11yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×Dic43—22no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—21no—
376C43⋊C8—21no—
377C43⋊C8—21no—
378C43⋊C8—22no—
379C43⋊C8—21no—
380C43⋊C8—21no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22889—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—84no—
405C22×C43C2×C4×D411yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43#55111yescharacteristic
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—41no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43D4211yescharacteristic
418C4×C43#54611yescharacteristic
419Dic43—42no—
420Dic43—81no—
421#3002D4311yescharacteristic
422C2×#443—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1975—431no—
427#1937—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855—431no—
434#1765—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43—81no—
443C2×C43#235811yescharacteristic
444C2×C43#295511yescharacteristic
445C2×C43#295711yescharacteristic
446C22×#41C2×D4311yescharacteristic
447C2×#135C2×D4311yescharacteristic
448C2×#135C2×D4311yescharacteristic
449C2×#131—431no—
450C2×#131—431no—
451C2×#131—431no—
452C22×M16—431no—
453#525C2×D4311yescharacteristic
454C2×#117—431no—
455#452Dic4311yescharacteristic, complemented
456#452Dic4311yescharacteristic, complemented
457#451Dic4311yescharacteristic, complemented
458#450Dic4311yescharacteristic, complemented
459#449Dic4311yescharacteristic, complemented
460#449Dic4311yescharacteristic, complemented
461#448Dic4311yescharacteristic, complemented
462#447Dic4311yescharacteristic, complemented
463#443—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108—431no—
469C2×#108—431no—
470#424—431no—
471#421—864no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478#416C2×D4311yescharacteristic
479#416C2×D4311yescharacteristic
480#408—431no—
481#408—431no—
482#408—431no—
483#408—861no—
484#408—861no—
485#407—431no—
486#407—861no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—861no—
489C2×C22⋊C8C2×D4311yescharacteristic
490#405—431no—
491C2×#97—431no—
492C2×C4×C8—431no—
493#341—431no—
494#341—431no—
495#339—431no—
496#339—431no—
497#336—431no—
498#336—431no—
499C43#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic4311yescharacteristic
507C2×#41C2×Dic4311yescharacteristic
508C2×#41C22×D4311yescharacteristic
509C2×#41C22×D4311yescharacteristic
510C2×#41C22×D4311yescharacteristic
511C22×Q8C2×Dic4311yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic4311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D4311yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic4311yescharacteristic
521C2×Q16C2×Dic4311yescharacteristic
522C2×SD16C2×Dic4311yescharacteristic
523C2×SD16C2×Dic4311yescharacteristic
524C2×SD16C2×Dic4311yescharacteristic
525C2×SD16C2×Dic4311yescharacteristic
526C2×D8C2×Dic4311yescharacteristic
527C2×D8C2×Dic4311yescharacteristic
528#131—862no—
529#131—862no—
530#131—862no—
531#131—1721no—
532#131—1721no—
533#131—1721no—
534C2×M16—431no—
535C2×M16—431no—
536C2×M16—431no—
537C2×M16—431no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—862no—
543C2×M16—1721no—
544C22×C8—431no—
545C22×C8—431no—
546C22×C8—861no—
547C22×C8—861no—
548C22×C8—861no—
549C22×C8—861no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic4311yescharacteristic
554C22⋊Q8C2×Dic4311yescharacteristic
555#121C2×Dic4311yescharacteristic
556#121C2×Dic4311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—862no—
561#117—1721no—
562#117C22×D4311yescharacteristic
563C2×C4⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42—431no—
567#108—862no—
568#108—1721no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—434no—
572#104—862no—
573#104—862no—
574#104—862no—
575#104—862no—
576#104—1721no—
577#103C2×Dic4311yescharacteristic
578#103C2×Dic4311yescharacteristic
579#103C2×Dic4311yescharacteristic
580#103C2×Dic4311yescharacteristic
581#102C2×Dic4311yescharacteristic
582#102C2×Dic4311yescharacteristic
583#102C2×Dic4311yescharacteristic
584#102C2×Dic4311yescharacteristic
585C22⋊C8—431no—
586C22⋊C8—431no—
587C22⋊C8—431no—
588C22⋊C8—431no—
589C22⋊C8—861no—
590C22⋊C8—861no—
591C22⋊C8—861no—
592C22⋊C8—861no—
593C22⋊C8—861no—
594C22⋊C8—861no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8C2×Dic4311yescharacteristic
598C22⋊C8C2×Dic4311yescharacteristic
599C22⋊C8C2×Dic4311yescharacteristic
600C22⋊C8C2×Dic4311yescharacteristic
601#97—861no—
602#97—1721no—
603C4×C8—861no—
604C4×C8—862no—
605C24—21no—
606C24#1062190011yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D4312yes—
626#41#1062190012yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic4311yescharacteristic
631C2×Q8C22×Dic4311yescharacteristic
632C2×Q8C22×Dic4311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic4311yescharacteristic
646C2×D4C22×Dic4311yescharacteristic
647C2×D4C22×Dic4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4#1062190011yescharacteristic
665C22×C4C22×Dic4311yescharacteristic
666C22×C4C22×Dic4311yescharacteristic
667C22×C4C23×D4311yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—432no—
677M16—861no—
678M16—861no—
679M16—861no—
680M16—861no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—1722no—
685M16—1722no—
686M16—1722no—
687M16—1722no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—431no—
693C2×C8—431no—
694C2×C8—431no—
695C2×C8—431no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—1722no—
705C2×C8—1722no—
706C2×C8—1722no—
707C2×C8—1722no—
708C2×C8C22×Dic4311yescharacteristic
709C2×C8C22×Dic4311yescharacteristic
710C2×C8C22×Dic4311yescharacteristic
711C2×C8C22×Dic4311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—1722no—
715C4⋊C4C22×Dic4311yescharacteristic
716C4⋊C4C22×Dic4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—1722no—
723C42—21no—
724C42—432no—
725C42—861no—
726C42—861no—
727C42—861no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic4311yescharacteristic
739C23D4×Dic4311yescharacteristic
740C23C2×#1062190011yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic4312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic4312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—862no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4D4×Dic4311yescharacteristic
796C2×C4D4×Dic4311yescharacteristic
797C2×C4C23×Dic4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4C2×#1062190011yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337011yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—861no—
808C8—861no—
809C8—862no—
810C8—861no—
811C8—861no—
812C8—1721no—
813C8—1721no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic4311yescharacteristic
836C22#1458353611yescharacteristic
837C22#1458358011yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—3441no—
846C4—1722no—
847C4C2×D4×Dic4311yescharacteristic
848C4#1458337411yescharacteristic
849C4#1458353111yescharacteristic
850C4#1458353611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#1913757911yescharacteristic
859C2#1914349811yescharacteristic
860C2#1914351211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3002C2
socleC22×C43C2×C4×D4
cosocleC22×C4×C43C24
hypercenter#3002D43
hypocenterC43#22889
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#14583016C2semidirect
2. #19143322C2semidirect
3. C2×#14582916C2semidirect
4. #19143044C2semidirect
5. #19135489C2semidirect
6. #19135301C2semidirect
7. #19135245C2semidirect
8. #19135044C2semidirect
9. #19134924C2semidirect
10. #19134924C2semidirect
11. #19134872C2semidirect
12. #19134802C2semidirect
13. #19134442C2semidirect
14. #19134363C2semidirect
18. C2×#13063332C22semidirect
26. C2×#13063261C22semidirect
27. C2×#13063261C22semidirect
28. #14582926C22semidirect
34. C2×#13063252C22semidirect
35. C2×#13063252C22semidirect
40. #14582866C22semidirect
45. #14582855C22semidirect
46. C2×#13063235C22semidirect
47. C2×C8×Dic43C22semidirect
48. #14582664C22semidirect
49. #14582664C22semidirect
50. #14582658C22semidirect
51. #14582658C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
58. C43×#452C4semidirect
59. C43×#452C4semidirect
60. C43×#451C4semidirect
61. C43×#450C4semidirect
62. C43×#449C4semidirect
63. C43×#449C4semidirect
64. C43×#448C4semidirect
65. C43×#447C4semidirect
106. #13063252D4semidirect
455. #452Dic43semidirect
456. #452Dic43semidirect
457. #451Dic43semidirect
458. #450Dic43semidirect
459. #449Dic43semidirect
460. #449Dic43semidirect
461. #448Dic43semidirect
462. #447Dic43semidirect
499. C43#22889semidirect

Maximal subgroups

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

subgroupindex
C2×#145830162
#191433222
C2×#145829162
#191430442
#191354892
#191353012
#191352452
#191350442
#191349242
#191348722
#191348022
#191344422
#191343632
C43×#30022
#2288943