Finite Group Databasebeta

← #26235732

Subgroups — #26235732

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094046C211yesmaximal, characteristic
2#20252053C211yesmaximal, characteristic, complemented
3#20251953C211yesmaximal, characteristic, complemented
4#20244099C212yesmaximal, complemented
5#20243988C212yesmaximal, complemented
6#20243714C212yesmaximal
7#20243526C211yesmaximal, characteristic, complemented
8#20243409C211yesmaximal, characteristic, complemented
9#20243409C211yesmaximal, characteristic, complemented
10#20243232C212yesmaximal, complemented
11C47×#1770C211yesmaximal, characteristic, complemented
12C2×#13094046C2211yescharacteristic
13C2×#13094030C2212yes—
14C4×#10625350C2211yescharacteristic
15C4×#10625350C2211yescharacteristic
16C4×Dic188C411yescharacteristic, complemented
17C4×Dic188C411yescharacteristic, complemented
18C4×#10625325C411yescharacteristic, complemented
19C4×#10625325C411yescharacteristic, complemented
20C4×#10625325C411yescharacteristic, complemented
21C4×#10625325C411yescharacteristic, complemented
22C4×D376C411yescharacteristic, complemented
23C4×D376C411yescharacteristic, complemented
24#15689183—22no—
25#15689179—21no—
26#15689175—21no—
27#15689161C2211yescharacteristic
28#15689149C2212yes—
29#15689148—22no—
30#15689147C2211yescharacteristic
31#15689147C2211yescharacteristic
32#15689145—21no—
33C4⋊C8×D47—21no—
34C2×#13093952C2212yes—
35C2×#13093952C2212yes—
36#15689120C2211yescharacteristic
37#15689120C2211yescharacteristic
38#15689089C2212yes—
39#15689078C2212yes—
40#15688888C2212yes—
41#15688888C2212yes—
42#15688883C2212yes—
43#15688883C2212yes—
44C2×C4⋊C8×C47C2211yescharacteristic
45C2×#97×C47C2212yes—
46C2×C4×C8×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C47×#336C2212yes—
49C2×#10625350C2311yescharacteristic
50C2×#10625350C2311yescharacteristic
51#13094046—22no—
52#13094046—22no—
53C2×Dic188C2×C411yescharacteristic
54C2×#10625325C2×C411yescharacteristic
55C2×#10625325C2×C411yescharacteristic
56C2×D376C2×C411yescharacteristic
57#13094030—24no—
58#13094030—42no—
59C2×#10625329C2312yes—
60C2×#10625329C2312yes—
61C2×#10625324—22no—
62C2×C8×D47—22no—
63C4×Dic94C2×C411yescharacteristic
64C4×Dic94C2×C411yescharacteristic
65C4×Dic94C2×C411yescharacteristic
66C4×Dic94C2×C411yescharacteristic
67C4×D188C2×C411yescharacteristic
68C4×D188C2×C411yescharacteristic
69C4×D188C2×C411yescharacteristic
70C4×D188C2×C411yescharacteristic
71C4×C22⋊D47—21no—
72C4×C22⋊D47—21no—
73C4×C22⋊D47—21no—
74C4×C22⋊D47—21no—
75#13093983C2311yescharacteristic
76#13093983C2311yescharacteristic
77#13093981—21no—
78#13093981—21no—
79C42×D47—21no—
80C42×D47—21no—
81#13093958C2×C411yescharacteristic
82#13093958C2×C411yescharacteristic
83#13093956C2×C411yescharacteristic
84#13093956C2×C411yescharacteristic
85C4⋊(C47⋊C8)—21no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91#13093952—24no—
92#13093952—42no—
93#13093949C2×C411yescharacteristic
94#13093949C2×C411yescharacteristic
95#13093949C2×C411yescharacteristic
96#13093949C2×C411yescharacteristic
97#13093946C2×C411yescharacteristic
98#13093946C2×C411yescharacteristic
99#13093946C2×C411yescharacteristic
100#13093946C2×C411yescharacteristic
101(C2×D47)⋊C8—22no—
102(C2×D47)⋊C8—22no—
103#13093934—22no—
104C8×Dic47—22no—
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2312yes—
108C2×C4⋊C4×C47—21no—
109C2×C42×C47C2312yes—
110C2×C42×C47C2311yescharacteristic
111C4⋊C8×C47D411yescharacteristic
112C4⋊C8×C47D411yescharacteristic
113C4⋊C8×C47D412yes—
114#97×C47—42no—
115C4×C8×C47C2×C411yescharacteristic
116C4×C8×C47C2×C411yescharacteristic
117C4×C8×C47C2×C411yescharacteristic
118C4×C8×C47C2×C411yescharacteristic
119#95×C47—21no—
120C22×C4×C47—22no—
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47C2411yescharacteristic
124C2×C22⋊D47—21no—
125C2×C22⋊D47—21no—
126#10625350—21no—
127#10625350—21no—
128#10625350—21no—
129#10625350—21no—
130#10625350—21no—
131#10625350—21no—
132#10625350#4112yes—
133#10625350#4112yes—
134C2×D188C22×C411yescharacteristic
135C2×D188C22×C411yescharacteristic
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—21no—
141C2×C4×D47—21no—
142C2×Dic94C22×C411yescharacteristic
143C2×Dic94C22×C411yescharacteristic
144C2×C8×C47—22no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—22no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47C22×C411yescharacteristic
151C2×C8×C47C22×C411yescharacteristic
152C2×C8×C47C22×C411yescharacteristic
153C2×C8×C47C22×C411yescharacteristic
154C2×C8×C47C2×D412yes—
155C2×C8×C47C2×D412yes—
156C4⋊C4×C47—42no—
157C42×C47—22no—
158C42×C47—22no—
159C42×C47C22×C411yescharacteristic
160C42×C47C22×C411yescharacteristic
161C42×C47C2×D411yescharacteristic
162C42×C47C2×D411yescharacteristic
163C22⋊Dic47—21no—
164C22⋊Dic47—21no—
165(C2×D47)⋊C4—21no—
166(C2×D47)⋊C4—21no—
167(C2×D47)⋊C4—21no—
168(C2×D47)⋊C4—21no—
169C4⋊Dic47C22×C411yescharacteristic
170C4⋊Dic47C22×C411yescharacteristic
171C4⋊Dic47C22×C411yescharacteristic
172C4⋊Dic47C22×C411yescharacteristic
173Dic47⋊C4—21no—
174Dic47⋊C4—21no—
175Dic47⋊C4—21no—
176Dic47⋊C4—21no—
177C4×Dic47—21no—
178C4×Dic47—21no—
179C4×Dic47—21no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183#10625329—22no—
184#10625329—22no—
185#10625329—22no—
186#10625329—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189Dic188—22no—
190D376—22no—
191#10625325—22no—
192#10625325—22no—
193#10625324—44no—
194C8×D47—44no—
195C23×C47C2×#4111yescharacteristic
196C22×D47—21no—
197C22×D47—21no—
198C2×C4×C47—22no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47C4×D411yescharacteristic
204C2×C4×C47C4×D411yescharacteristic
205C2×C4×C47C4×D411yescharacteristic
206C2×C4×C47C4×D411yescharacteristic
207C2×C4×C47C23×C411yescharacteristic
208C2×C4×C47C22×D411yescharacteristic
209C2×C4×C47C2×#4111yescharacteristic
210C2×C4×C47C2×#4111yescharacteristic
211C2×C4×C47H(5,𝔽2)11yescharacteristic
212C2×C4×C472−1+411yescharacteristic
213C22⋊D47—22no—
214C22⋊D47—22no—
215C22⋊D47—41no—
216C22⋊D47—41no—
217C2×Dic47—21no—
218C2×Dic47—21no—
219C2×Dic47—21no—
220C2×Dic47—21no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223D188—21no—
224D188—21no—
225D188—21no—
226D188#11712yes—
227C4×D47—22no—
228C4×D47—22no—
229C4×D47—41no—
230C4×D47—41no—
231C4×D47—42no—
232C4×D47—42no—
233C4×D47—81no—
234C4×D47—81no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94#11712yes—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—22no—
244C8×C47—22no—
245C47⋊C8—42no—
246C47⋊C8—42no—
247#22782—471nomaximal, Sylow
248C22×C47—21no—
249C22×C47—21no—
250C22×C47C2×C4×D411yescharacteristic
251C22×C47#55211yescharacteristic
252C22×C47#55311yescharacteristic
253C2×D47—22no—
254C2×D47—41no—
255C2×D47—41no—
256C2×D47—41no—
257C2×D47—41no—
258C2×D47—41no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—82no—
263C4×C47#44412yes—
264C4×C47C2×#11711yescharacteristic
265C4×C47#52011yescharacteristic
266C4×C47#54611yescharacteristic
267C4×C47#54811yescharacteristic
268Dic47—22no—
269Dic47—41no—
270Dic47—41no—
271Dic47—41no—
272Dic47—41no—
273Dic47—41no—
274C4×#135—471no—
275#2925—471no—
276#2906—471no—
277#1938—472no—
278#1922—472no—
279#1876—472no—
280#1837—471no—
281#1806—471no—
282#1806—471no—
283#1770D4711yescharacteristic, complemented
284#1765—472no—
285C2×C47—21no—
286C2×C47—21no—
287C2×C47#235211yescharacteristic
288C2×C47C2×#44411yescharacteristic
289C2×C47#295711yescharacteristic
290D47—42no—
291D47—81no—
292C2×#135—471no—
293C2×#131—472no—
294C4×#41—471no—
295C4×#41—471no—
296C4×Q16—471no—
297C4×Q16—471no—
298C4×SD16—471no—
299C4×SD16—471no—
300C4×SD16—471no—
301C4×SD16—471no—
302C4×D8—471no—
303C4×D8—471no—
304#433—942no—
305#432—941no—
306#431—941no—
307#427—471no—
308#424—472no—
309#424—942no—
310#423—471no—
311#423—471no—
312#423—941no—
313C2×C4⋊C8—941no—
314C2×C4⋊C8C2×D4711yescharacteristic
315C2×#104—472no—
316C2×#104—472no—
317#416—471no—
318#416—471no—
319#408—472no—
320#405—472no—
321C2×#97C2×D4712yes—
322C2×C4×C8C2×D4711yescharacteristic
323C4×C4⋊C4C2×D4711yescharacteristic
324#341—472no—
325#341—472no—
326#339—472no—
327#339—472no—
328#336C2×D4712yes—
329C47#2278211yescharacteristic, complemented, Sylow
330C2×#41—471no—
331C2×#41—471no—
332#135—942no—
333#135—942no—
334C2×Q16—471no—
335C2×SD16—471no—
336C2×SD16—471no—
337C2×D8—471no—
338#131—944no—
339#131—1882no—
340C2×M16—472no—
341C2×M16—472no—
342C2×M16—942no—
343C22×C8—942no—
344C22×C8C22×D4711yescharacteristic
345C22×C8C22×D4711yescharacteristic
346C22×C8C22×D4712yes—
347C4×Q8—471no—
348C4×Q8—471no—
349C4×Q8—471no—
350C4×Q8—471no—
351C4×D4—471no—
352C4×D4—471no—
353C4×D4—471no—
354C4×D4—471no—
355C4×D4—941no—
356C4×D4—941no—
357C4×D4—941no—
358C4×D4—941no—
359#117—471no—
360#117—471no—
361#117—941no—
362#117—941no—
363C2×C4⋊C4—21no—
364C2×C42—941no—
365C2×C42—941no—
366C2×C42C22×D4712yes—
367C2×C42C22×D4711yescharacteristic
368#107—471no—
369#107—471no—
370#106—471no—
371#106—471no—
372C4⋊C8—942no—
373C4⋊C8—942no—
374C4⋊C8—941no—
375C4⋊C8—941no—
376C4⋊C8—941no—
377C4⋊C8—941no—
378C4⋊C8D18811yescharacteristic
379C4⋊C8D18811yescharacteristic
380C4⋊C8D18812yes—
381#104—944no—
382#104—1882no—
383#103—471no—
384#103—471no—
385#103—471no—
386#103—471no—
387#102—471no—
388#102—471no—
389#102—471no—
390#102—471no—
391C22⋊C8—942no—
392C22⋊C8—942no—
393#97—42no—
394#97—942no—
395C4×C8—942no—
396C4×C8C4×D4711yescharacteristic
397C4×C8C4×D4711yescharacteristic
398C4×C8C4×D4711yescharacteristic
399C4×C8C4×D4711yescharacteristic
400#95—21no—
401#41—472no—
402#41—472no—
403#41—941no—
404#41—941no—
405#41—941no—
406#41—941no—
407#41—941no—
408#41—941no—
409C2×Q8—471no—
410C2×Q8—471no—
411C2×D4—471no—
412C2×D4—471no—
413C2×D4—941no—
414C2×D4—941no—
415C22×C4—22no—
416C22×C4—941no—
417C22×C4—941no—
418C22×C4—941no—
419C22×C4—941no—
420C22×C4—941no—
421C22×C4—941no—
422C22×C4#1062535011yescharacteristic
423C22×C4#1062535011yescharacteristic
424C22×C4C23×D4711yescharacteristic
425Q16—942no—
426SD16—942no—
427SD16—942no—
428D8—942no—
429M16—942no—
430M16—942no—
431M16—942no—
432M16—942no—
433M16—1884no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—942no—
441C2×C8—942no—
442C2×C8—1884no—
443C2×C8C2×C4×D4711yescharacteristic
444C2×C8C2×C4×D4711yescharacteristic
445C2×C8C2×C4×D4711yescharacteristic
446C2×C8C2×C4×D4711yescharacteristic
447C2×C8C2×D18812yes—
448C2×C8C2×D18812yes—
449C4⋊C4—42no—
450C4⋊C4—471no—
451C4⋊C4—471no—
452C4⋊C4—471no—
453C4⋊C4—471no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C22⋊C4—941no—
459C22⋊C4—941no—
460C22⋊C4—941no—
461C22⋊C4—941no—
462C22⋊C4—941no—
463C22⋊C4—941no—
464C42—22no—
465C42—22no—
466C42—941no—
467C42—941no—
468C42—941no—
469C42—941no—
470C42—941no—
471C42—941no—
472C42C2×C4×D4711yescharacteristic
473C42C2×C4×D4711yescharacteristic
474C42C2×D18811yescharacteristic
475C42C2×D18811yescharacteristic
476C23—941no—
477C23—941no—
478C23C2×#1062535011yescharacteristic
479Q8—472no—
480Q8—941no—
481Q8—941no—
482Q8—941no—
483D4—472no—
484D4—942no—
485D4—942no—
486D4—941no—
487D4—941no—
488D4—941no—
489D4—1881no—
490D4—1881no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—941no—
497C2×C4—942no—
498C2×C4—942no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—941no—
502C2×C4—941no—
503C2×C4—941no—
504C2×C4—3761no—
505C2×C4—3761no—
506C2×C4—1882no—
507C2×C4—1882no—
508C2×C4—1881no—
509C2×C4—1881no—
510C2×C4C4×D18811yescharacteristic
511C2×C4C4×D18811yescharacteristic
512C2×C4C4×D18811yescharacteristic
513C2×C4C4×D18811yescharacteristic
514C2×C4C22×C4×D4711yescharacteristic
515C2×C4C22×D18811yescharacteristic
516C2×C4#41×D4711yescharacteristic
517C2×C4#41×D4711yescharacteristic
518C2×C4#1309406911yescharacteristic
519C2×C4#1309407211yescharacteristic
520C8—22no—
521C8—22no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—1882no—
527C8—1882no—
528C22—21no—
529C22—21no—
530C22—942no—
531C22—1881no—
532C22—1881no—
533C22—1881no—
534C22—1881no—
535C22—1881no—
536C22C2×C4×D18811yescharacteristic
537C22#1568981411yescharacteristic
538C22#1568982311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—942no—
544C4—1881no—
545C4—1881no—
546C4—1881no—
547C4—1881no—
548C4—1881no—
549C4#1568924612yes—
550C4#117×D4711yescharacteristic
551C4#1568960411yescharacteristic
552C4#1568976811yescharacteristic
553C4#1568978511yescharacteristic
554C2—21no—
555C2—21no—
556C2—3761no—
557C2—1882no—
558C2#2024632011yescharacteristic
559C2C2×#1568924611yescharacteristic
560C2#2025230611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1770C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094046C22
cosocleC22×C4×C47C24
hypercenter#1770D47
hypocenterC47#22782
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #20252053C2semidirect
3. #20251953C2semidirect
4. #20244099C2semidirect
5. #20243988C2semidirect
7. #20243526C2semidirect
8. #20243409C2semidirect
9. #20243409C2semidirect
10. #20243232C2semidirect
11. C47×#1770C2semidirect
16. C4×Dic188C4semidirect
17. C4×Dic188C4semidirect
18. C4×#10625325C4semidirect
19. C4×#10625325C4semidirect
20. C4×#10625325C4semidirect
21. C4×#10625325C4semidirect
22. C4×D376C4semidirect
23. C4×D376C4semidirect
283. #1770D47semidirect
329. C47#22782semidirect

Maximal subgroups

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

subgroupindex
C4×#130940462
#202520532
#202519532
#202440992
#202439882
#202437142
#202435262
#202434092
#202432322
C47×#17702
#2278247