Finite Group Databasebeta

← #11865224

Subgroups — #11865224

Order 1152.

1483 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
1C3×#5964C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C2×#63827C212yesmaximal, complemented
4#10592936C211yesmaximal, characteristic, complemented
5#10591648C214yesmaximal, complemented
6#10591512C214yesmaximal, complemented
7#10591111C212yesmaximal, complemented
8#84123—31nomaximal
9#83416—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1010—22no—
12C3×#1009—22no—
13C3×D3×#41—24no—
14C3×#1007C2212yes—
15C3×#1004—22no—
16C3×#1004C2212yes—
17C2×C3×#235—22no—
18C2×C3×#235C2212yes—
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×#3748C2212yescomplemented
21C3×#944C2212yescomplemented
22C3×#936C2212yescomplemented
23C3×#935—22no—
24C3×#926C2211yescharacteristic, complemented
25C3×#924—22no—
26C2×#3718—22no—
27#63827—24no—
28#63827C2218yescomplemented
29C2×#3715—22no—
30#63663C2212yescomplemented
31#63660C2212yescomplemented
32#63569C2218yescomplemented
33C3×#585—31no—
34#5964D311yescharacteristic
35C3×#536—31no—
36#5825D311yescharacteristic, complemented
37C2×#951—32no—
38C2×#942—32no—
39#5246—34no—
40#5242—34no—
41#5237—31no—
42#5237—31no—
43#5237—61no—
44#5236—32no—
45#5095—34no—
46#5061—34no—
47#5005—32no—
48C32×#41—22no—
49C32×#41—22no—
50C2×C32×Q8C2311yescharacteristic
51C2×C32×D4D412yes—
52C2×C32×D4C2311yescharacteristic
53C22×C32×C4D412yes—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—24no—
56C2×C3×#67—22no—
57C22×C3×Dic3—21no—
58C3×#239—24no—
59C3×D3×Q8—24no—
60C3×#237—28no—
61C3×#237—24no—
62C3×D3×D4—28no—
63C3×D3×D4—24no—
64C3×#235—24no—
65C3×#235—24no—
66C3×#235—22no—
67C3×#235—24no—
68C3×#235—22no—
69C3×#235D414yes—
70C3×#235C2314yes—
71C2×C3×D12—22no—
72C2×C3×D12D412yes—
73C2×C3×C4×D3—24no—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D412yes—
80C2×C3×Dic6C2312yes—
81#3748—22no—
82#3748C2314yes—
83C2×C3⋊(C3⋊C8)—22no—
84C3×#217—24no—
85C3×#217—21no—
86C3×C4⋊Dic3—21no—
87C3×Dic3⋊C4—24no—
88C3×C4×Dic3C2312yes—
89#3718—28no—
90#3715—28no—
91#3022—91noSylow
92C3×2−1+4—32no—
93C3×2−1+4—62no—
94C3×H(5,𝔽2)—32no—
95C3×H(5,𝔽2)—62no—
96C3×H(5,𝔽2)—62no—
97C2×C3×#41—21no—
98C2×C3×#41—32no—
99C2×C3×#41—64no—
100C2×C3×#41—62no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C2×D311yescharacteristic
103C22×C3×Q8—31no—
104#1010—22no—
105#1009—22no—
106D3×#41—24no—
107#1007C2×D312yes—
108#1004—22no—
109#1004C2×D312yes—
110C2×#235—22no—
111C2×#235C2×D312yes—
112C22×Dic6C2×D311yescharacteristic, complemented
113C3×C4⋊Q8—32no—
114C3×#124—32no—
115C3×#123—62no—
116C3×C22⋊Q8—62no—
117C3×#117—31no—
118#951—38no—
119#951—64no—
120#944C2×D312yescomplemented
121C2×#216—62no—
122C2×#216—62no—
123#942—38no—
124#942—64no—
125C2×#215—62no—
126#936C2×D312yescomplemented
127#935—22no—
128C2×#214—62no—
129#926C2×D311yescharacteristic, complemented
130#924—22no—
131C2×#208—32no—
132C2×#208—32no—
133C2×#208—62no—
134#837—38no—
135#836—32no—
136#836—32no—
137#836—62no—
138#833—32no—
139#833—32no—
140#833—62no—
141#805—38no—
142C23×C32C2×D412yes—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—24no—
145C22×C3×D3—22no—
146C32×Q8—22no—
147C32×D4—24no—
148C32×D4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C3×#67—28no—
157C3×#67—24no—
158C3×#67—24no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12C2×D414yes—
167C3×C4×D3—28no—
168C3×C4×D3—24no—
169C3×C4×D3—24no—
170C3×Dic6—24no—
171C3×Dic6—22no—
172C3×Dic6—24no—
173C3×Dic6—41no—
174C3×Dic6—41no—
175C3×Dic6C2×D414yes—
176C3⋊(C3⋊C8)—24no—
177#585—31no—
178C2×#137—92no—
179#536—31no—
180#456—94no—
181#455—94no—
182#421—92no—
183#413—91no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—22no—
188C3×#41—34no—
189C3×#41—34no—
190C3×#41—42no—
191C3×#41—42no—
192C3×#41—64no—
193C3×#41—64no—
194C3×#41—64no—
195C3×#41—68no—
196C3×#41—64no—
197C3×#41—62no—
198C3×#41—62no—
199C3×#41—64no—
200C2×C3×Q8—21no—
201C2×C3×Q8—32no—
202C2×C3×Q8—32no—
203C2×C3×Q8—62no—
204C2×C3×Q8—64no—
205C2×C3×Q8—61no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—32no—
213C2×C3×D4—62no—
214C2×C3×D4—64no—
215C2×C3×D4—68no—
216C2×C3×D4—62no—
217C2×C3×D4—64no—
218C2×C3×D4#6712yes—
219C2×C3×D4#6712yes—
220C2×C3×D4C22×D311yescharacteristic
221C2×C3×D4C22×D311yescharacteristic
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—64no—
225C22×C3×C4—62no—
226C22×C3×C4—61no—
227C22×C3×C4#6712yes—
228C22×C3×C4#6712yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—24no—
232C2×#67—22no—
233C22×Dic3—21no—
234#239—24no—
235D3×Q8—24no—
236#237—28no—
237#237—24no—
238D3×D4—28no—
239D3×D4—24no—
240#235—24no—
241#235—24no—
242#235—22no—
243#235—24no—
244#235—22no—
245#235#6714yes—
246#235C22×D314yes—
247C2×D12—22no—
248C2×D12#6712yes—
249C2×C4×D3—24no—
250C2×C4×D3—22no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—22no—
254C2×Dic6—21no—
255C2×Dic6#6712yes—
256C2×Dic6C22×D312yes—
257C3×C4⋊C4—64no—
258C3×C4⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—64no—
261C3×C42—32no—
262#217—24no—
263#217—21no—
264#216—68no—
265#216—68no—
266#215—68no—
267#214—68no—
268C4⋊Dic3—21no—
269Dic3⋊C4—24no—
270C4×Dic3C22×D312yes—
271#208—34no—
272#208—34no—
273#208—64no—
274#208—62no—
275#208—62no—
276#208—122no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—42no—
283C22×C32#12012yes—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—24no—
286C2×C3×D3—82no—
287C2×C3×D3—84no—
288C32×C4—22no—
289C32×C4#12011yescharacteristic
290C32×C4#12011yescharacteristic
291C32×C4C22×D412yes—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
2952−1+4—32no—
2962−1+4—62no—
297H(5,𝔽2)—32no—
298H(5,𝔽2)—62no—
299H(5,𝔽2)—62no—
300C2×#41—32no—
301C2×#41—64no—
302C2×#41—62no—
303C2×#41D3211yescharacteristic
304C22×Q8—31no—
305#137—98no—
306#137—184no—
307C2×Q16—182no—
308C2×SD16—182no—
309C2×M16—92no—
310C4⋊Q8—32no—
311#124—32no—
312#123—62no—
313C22⋊Q8—62no—
314#117—31no—
315#104—98no—
316#101—92no—
317#100—92no—
318C23×C3—21no—
319C23×C3—22no—
320C23×C3—64no—
321C23×C3—62no—
322C23×C3C2×#6712yes—
323C23×C3C2×#6712yes—
324C23×C3C2×#6711yescharacteristic
325C23×C3C2×#6711yescharacteristic
326C22×D3—24no—
327C22×D3—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—34no—
331C3×Q8—42no—
332C3×Q8—64no—
333C3×Q8—62no—
334C3×Q8—64no—
335C3×Q8—121no—
336C3×Q8—121no—
337C3×D4—24no—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—34no—
342C3×D4—42no—
343C3×D4—44no—
344C3×D4—64no—
345C3×D4—68no—
346C3×D4—64no—
347C3×D4—64no—
348C3×D4—62no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—68no—
361C2×C3×C4—64no—
362C2×C3×C4—62no—
363C2×C3×C4—64no—
364C2×C3×C4—64no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—122no—
368C2×C3×C4D3×D412yes—
369C2×C3×C4D3×D412yes—
370C2×C3×C4C2×#6712yes—
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6712yes—
375C2×C3×C4C2×#6712yes—
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—28no—
379#67—24no—
380#67—24no—
381C2×Dic3—24no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—42no—
386D12—24no—
387D12—22no—
388D12C2×#6714yes—
389C4×D3—28no—
390C4×D3—24no—
391C4×D3—24no—
392Dic6—24no—
393Dic6—22no—
394Dic6—24no—
395Dic6—41no—
396Dic6—41no—
397Dic6C2×#6714yes—
398C3⋊C8—64no—
399C3⋊C8—64no—
400C3⋊C8—124no—
401C2×C32—21no—
402C2×C32—22no—
403C2×C32—42no—
404C2×C32C2×#12011yescharacteristic
405C3×D3—44no—
406#41—22no—
407#41—22no—
408#41—34no—
409#41—34no—
410#41—64no—
411#41—64no—
412#41—64no—
413#41—68no—
414#41—64no—
415#41—62no—
416#41—64no—
417#41—62no—
418C2×Q8—32no—
419C2×Q8—32no—
420C2×Q8—62no—
421C2×Q8—64no—
422C2×Q8—61no—
423C2×Q8—62no—
424C2×Q8—62no—
425C2×Q8C2×D3211yescharacteristic
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—64no—
429C2×D4—68no—
430C2×D4—62no—
431C2×D4—64no—
432C2×D4#62512yes—
433C2×D4C2×D3211yescharacteristic
434C22×C4—64no—
435C22×C4—62no—
436C22×C4—61no—
437C22×C4#62512yes—
438C22×C4C2×D3211yescharacteristic
439Q16—188no—
440SD16—188no—
441M16—94no—
442M16—182no—
443C2×C8—182no—
444C4⋊C4—61no—
445C4⋊C4—64no—
446C22⋊C4—61no—
447C22⋊C4—64no—
448C42—32no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—42no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—64no—
459C22×C3—81no—
460C22×C3—82no—
461C22×C3—242no—
462C22×C3—244no—
463C22×C3#93712yes—
464C22×C3#95312yes—
465C22×C3C22×#6711yescharacteristic
466C22×C3C22×#6711yescharacteristic
467C2×D3—24no—
468C2×D3—82no—
469C2×D3—84no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—42no—
476C3×C4—64no—
477C3×C4—122no—
478C3×C4—122no—
479C3×C4#93711yescharacteristic
480C3×C4#93711yescharacteristic
481C3×C4#95311yescharacteristic
482C3×C4#95311yescharacteristic
483C3×C4C2×D3×D412yes—
484C3×C4C22×#6712yes—
485Dic3—24no—
486Dic3—42no—
487Dic3—42no—
488C32#302211yescharacteristic, complemented, Sylow
489C23—64no—
490C23—62no—
491C23C2×#62512yes—
492C23C2×#62511yescharacteristic
493Q8—22no—
494Q8—34no—
495Q8—64no—
496Q8—62no—
497Q8—64no—
498Q8—121no—
499Q8—121no—
500D4—24no—
501D4—22no—
502D4—34no—
503D4—64no—
504D4—68no—
505D4—64no—
506D4—64no—
507D4—62no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—68no—
511C2×C4—64no—
512C2×C4—62no—
513C2×C4—64no—
514C2×C4—64no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—122no—
518C2×C4C2×#62512yes—
519C2×C4C2×#62511yescharacteristic
520C2×C4D3×#6712yes—
521C2×C4D3×#6712yes—
522C2×C4C22×D3211yescharacteristic
523C8—184no—
524C2×C3—21no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—41no—
530C2×C3—42no—
531C2×C3—42no—
532C2×C3—42no—
533C2×C3—82no—
534C2×C3—124no—
535C2×C3C2×#93711yescharacteristic
536C2×C3C2×#95311yescharacteristic
537D3—44no—
538C22—22no—
539C22—41no—
540C22—42no—
541C22—64no—
542C22—242no—
543C22—244no—
544C22#6397612yes—
545C22C22×#62511yescharacteristic
546C4—22no—
547C4—64no—
548C4—122no—
549C4—122no—
550C4#6397611yescharacteristic
551C4#6397611yescharacteristic
552C4C2×D3×#6712yes—
553C3—21no—
554C3#8341611yescharacteristic, complemented
555C3#8412311yescharacteristic, complemented
556C2—21no—
557C2—22no—
558C2—42no—
559C2—124no—
560C2C2×#6397611yescharacteristic
subgroupG/H
centerC2C2×#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
prime radicalC3×#5964C2
hypercenterC2×#41D32
hypocenterC32#3022
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C2×#63827C2semidirect
4. #10592936C2semidirect
5. #10591648C2semidirect
6. #10591512C2semidirect
7. #10591111C2semidirect
19. C22×C3×Dic6C22semidirect
20. C2×#3748C22semidirect
21. C3×#944C22semidirect
22. C3×#936C22semidirect
24. C3×#926C22semidirect
28. #63827C22semidirect
30. #63663C22semidirect
31. #63660C22semidirect
32. #63569C22semidirect
36. #5825D3semidirect
112. C22×Dic6C2×D3semidirect
120. #944C2×D3semidirect
126. #936C2×D3semidirect
129. #926C2×D3semidirect
488. C32#3022semidirect
554. C3#83416semidirect
555. C3#84123semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C3×#58252
C2×#638272
#105929362
#105916482
#105915122
#105911112
#841233
#834163