Finite Group Databasebeta

← #11784940

Subgroups — #11784940

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4#10591113C212yesmaximal, complemented
5#10591105C212yesmaximal, complemented
6#70054—31nomaximal
7#70010—31nomaximal
8C2×C32×#41C2211yescharacteristic
9#64367—22no—
10#64366—22no—
11#41×C3⋊D3—24no—
12#64364C412yescomplemented
13#64361—22no—
14#64361C412yescomplemented
15C2×#3828—22no—
16C2×#3828C2212yes—
17C3×#926C2212yescomplemented
18C2×C3×#208C2211yescharacteristic, complemented
19C22×C3×C3⋊C8C2211yescharacteristic, complemented
20C3×#834—22no—
21C3×#830—22no—
22#63570—24no—
23#63567—22no—
24#63564—22no—
25#5964—31no—
26#5964—31no—
27#5964—61no—
28C3×#410—31no—
29C3×#408—31no—
30#5240D311yescharacteristic, complemented
31#5234D311yescharacteristic, complemented
32#5139—32no—
33#5113—32no—
34#5005—32no—
35#5002—32no—
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×D4C2×C411yescharacteristic
40C2×C32×D4D412yes—
41C22×C32×C4D412yes—
42C22×C32×C4C2311yescharacteristic
43C2×#638—24no—
44C2×#638—22no—
45#3832—24no—
46Q8×C3⋊D3—24no—
47#3830—28no—
48#3830—24no—
49D4×C3⋊D3—28no—
50D4×C3⋊D3—24no—
51#3828—24no—
52#3828—24no—
53#3828—24no—
54#3828—22no—
55#3828—22no—
56#3828C2×C414yes—
57#3828D414yes—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)D412yes—
60C2×C4×C3⋊D3—24no—
61C2×C4×C3⋊D3—22no—
62C2×#634—22no—
63C2×#634D412yes—
64C3×#217—22no—
65C3×C4⋊Dic3—22no—
66C3×C4×Dic3—22no—
67C3×#208—22no—
68C2×C3×C3⋊C8—22no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1794—91noSylow
72C2×C3×#41—21no—
73C2×C3×#41C2×D311yescharacteristic
74C2×C3×#41C2×D311yescharacteristic
75#1010—62no—
76#1010—62no—
77#1010—64no—
78#1009—62no—
79#1009—62no—
80#1009—64no—
81D3×#41—64no—
82D3×#41—64no—
83D3×#41—68no—
84#1007—32no—
85#1007—32no—
86#1007—62no—
87#1004—32no—
88#1004—32no—
89#1004—62no—
90#1004—64no—
91#1004—62no—
92#1004—62no—
93C2×#235—32no—
94C2×#235—32no—
95C2×#235—62no—
96C2×#235—64no—
97C2×#235—62no—
98C2×#235—62no—
99C2×C3×M16—31no—
100C22×C3×C8—31no—
101C3×#117—32no—
102#926C2×D312yescomplemented
103C2×#208C2×D311yescharacteristic, complemented
104C22×C3⋊C8C2×D311yescharacteristic, complemented
105C3×#99—62no—
106C3×C22⋊C8—62no—
107#834—22no—
108#830—22no—
109#825—64no—
110#821—62no—
111#816—62no—
112#810—62no—
113#809—62no—
114#805—64no—
115C23×C32C22⋊C412yes—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—24no—
118C22×C3⋊D3—22no—
119C32×Q8—22no—
120C32×D4—24no—
121C32×D4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22⋊C412yes—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D412yes—
129#638—28no—
130#638—24no—
131#638—24no—
132C2×C3⋊Dic3—24no—
133C2×C3⋊Dic3—22no—
134C4⋊(C3⋊D3)—24no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)C22⋊C414yes—
137C4×C3⋊D3—28no—
138C4×C3⋊D3—24no—
139C4×C3⋊D3—24no—
140#634—24no—
141#634—22no—
142#634C22⋊C414yes—
143C2×C3×Dic3—42no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146#585—91no—
147#421—92no—
148#416—92no—
149#410—31no—
150#408—31no—
151C3×#41—24no—
152C3×#41—24no—
153C3×#41—22no—
154C3×#41—22no—
155C3×#41—22no—
156C3×#41—22no—
157C2×C3×Q8—21no—
158C2×C3×Q8C4×D311yescharacteristic
159C2×C3×Q8C4×D311yescharacteristic
160C2×C3×D4—21no—
161C2×C3×D4—22no—
162C2×C3×D4C4×D311yescharacteristic
163C2×C3×D4C4×D311yescharacteristic
164C2×C3×D4D1212yes—
165C2×C3×D4#6712yes—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4D1212yes—
169C22×C3×C4#6712yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—68no—
173C2×#67—64no—
174C2×#67—64no—
175C2×#67—64no—
176C2×#67—62no—
177C2×#67—62no—
178#239—64no—
179#239—64no—
180#239—68no—
181D3×Q8—64no—
182D3×Q8—64no—
183D3×Q8—68no—
184#237—64no—
185#237—64no—
186#237—68no—
187#237—616no—
188#237—68no—
189#237—68no—
190D3×D4—64no—
191D3×D4—64no—
192D3×D4—68no—
193D3×D4—616no—
194D3×D4—68no—
195D3×D4—68no—
196#235—34no—
197#235—34no—
198#235—34no—
199#235—34no—
200#235—64no—
201#235—64no—
202#235—64no—
203#235—68no—
204#235—68no—
205#235—64no—
206#235—64no—
207#235—68no—
208#235—64no—
209#235—64no—
210#235—64no—
211#235—64no—
212#235—64no—
213#235—62no—
214#235—62no—
215#235—62no—
216#235—62no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—64no—
221C2×D12—62no—
222C2×D12—62no—
223C2×C4×D3—68no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—62no—
232C2×Dic6—64no—
233C2×Dic6—62no—
234C2×Dic6—62no—
235C3×M16—62no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—62no—
239C3×C4⋊C4—62no—
240C3×C22⋊C4—62no—
241C3×C42—62no—
242#217—22no—
243C4⋊Dic3—22no—
244C4×Dic3—22no—
245#208—22no—
246C2×C3⋊C8—22no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C22×C32—22no—
250C22×C32—41no—
251C22×C32—42no—
252C22×C32C2×C22⋊C411yescharacteristic
253C22×C32#12012yes—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—82no—
256C2×C3⋊D3—84no—
257C32×C4—22no—
258C32×C4C2×C22⋊C412yes—
259C32×C4#12011yescharacteristic
260C32×C4#12011yescharacteristic
261C3⋊Dic3—24no—
262C3×Dic3—82no—
2632−1+4—92no—
2642−1+4—182no—
265H(5,𝔽2)—92no—
266H(5,𝔽2)—182no—
267H(5,𝔽2)—182no—
268C2×#41—92no—
269C2×#41—184no—
270C2×#41—182no—
271C2×#41D3211yescharacteristic
272C2×M16—31no—
273C22×C8—31no—
274#117—32no—
275#104—184no—
276#103—182no—
277#102—182no—
278#99—62no—
279C22⋊C8—62no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3(C2×D3)⋊C412yes—
283C23×C3(C2×D3)⋊C412yes—
284C23×C3C2×D1211yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—68no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—62no—
291C22×D3—62no—
292C3×Q8—24no—
293C3×Q8—22no—
294C3×Q8—22no—
295C3×D4—28no—
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—122no—
313C2×C3×C4(C2×D3)⋊C412yes—
314C2×C3×C4(C2×D3)⋊C412yes—
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4D3×D412yes—
319C2×C3×C4D3×D412yes—
320C2×C3×C4D3×D412yes—
321C2×C3×C4D3×D412yes—
322C2×C3×C4C2×#6711yescharacteristic
323#67—68no—
324#67—616no—
325#67—68no—
326#67—68no—
327#67—68no—
328#67—64no—
329#67—64no—
330#67—64no—
331#67—64no—
332C2×Dic3—42no—
333C2×Dic3—68no—
334C2×Dic3—64no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339D12—34no—
340D12—34no—
341D12—64no—
342D12—64no—
343D12—68no—
344D12—64no—
345D12—64no—
346D12—62no—
347D12—62no—
348C4×D3—68no—
349C4×D3—616no—
350C4×D3—68no—
351C4×D3—68no—
352C4×D3—68no—
353C4×D3—64no—
354C4×D3—64no—
355C4×D3—64no—
356C4×D3—64no—
357Dic6—34no—
358Dic6—34no—
359Dic6—64no—
360Dic6—64no—
361Dic6—68no—
362Dic6—64no—
363Dic6—64no—
364Dic6—62no—
365Dic6—62no—
366C3×C8—121no—
367C3×C8—121no—
368C3⋊C8—41no—
369C3⋊C8—41no—
370C2×C32—22no—
371C2×C32—21no—
372C2×C32—42no—
373C2×C32#37911yescharacteristic
374C3⋊D3—44no—
375#41—22no—
376#41—22no—
377#41—94no—
378#41—94no—
379#41—184no—
380#41—184no—
381#41—184no—
382#41—188no—
383#41—184no—
384#41—184no—
385#41—182no—
386#41—182no—
387C2×Q8—92no—
388C2×Q8—182no—
389C2×Q8—184no—
390C2×Q8#62411yescharacteristic
391C2×D4—92no—
392C2×D4—182no—
393C2×D4—184no—
394C2×D4—188no—
395C2×D4—184no—
396C2×D4—182no—
397C2×D4#62411yescharacteristic
398C2×D4#62612yes—
399C22×C4—184no—
400C22×C4—182no—
401C22×C4#62612yes—
402C22×C4C2×D3211yescharacteristic
403M16—62no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—62no—
407C4⋊C4—62no—
408C22⋊C4—62no—
409C42—62no—
410C22×C3—24no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—81no—
420C22×C3—82no—
421C22×C3#88212yes—
422C22×C3C2×(C2×D3)⋊C411yescharacteristic
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C22×C3#93712yes—
425C2×D3—68no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—242no—
429C2×D3—242no—
430C2×D3—244no—
431C2×D3—248no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—24no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—242no—
441C3×C4D3×C22⋊C412yes—
442C3×C4D3×C22⋊C412yes—
443C3×C4#88211yescharacteristic
444C3×C4#88211yescharacteristic
445C3×C4#93711yescharacteristic
446C3×C4#93711yescharacteristic
447Dic3—68no—
448Dic3—64no—
449Dic3—64no—
450Dic3—82no—
451C32#179411yescharacteristic, complemented, Sylow
452C23—184no—
453C23—182no—
454C23#372212yes—
455C23C2×#62611yescharacteristic
456Q8—22no—
457Q8—94no—
458Q8—184no—
459Q8—182no—
460D4—24no—
461D4—22no—
462D4—94no—
463D4—184no—
464D4—188no—
465D4—184no—
466D4—184no—
467D4—182no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—122no—
471C2×C4—188no—
472C2×C4—184no—
473C2×C4—182no—
474C2×C4—184no—
475C2×C4—184no—
476C2×C4#372212yes—
477C2×C4C2×#62411yescharacteristic
478C2×C4C2×#62611yescharacteristic
479C2×C4#381112yes—
480C2×C4#381112yes—
481C8—121no—
482C8—121no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—42no—
489C2×C3—41no—
490C2×C3—44no—
491C2×C3—42no—
492C2×C3—42no—
493C2×C3#495511yescharacteristic
494C2×C3#495511yescharacteristic
495D3—128no—
496D3—124no—
497D3—124no—
498C22—22no—
499C22—41no—
500C22—42no—
501C22—184no—
502C22—722no—
503C22—724no—
504C22C2×#372211yescharacteristic
505C22#6398112yes—
506C4—22no—
507C4—184no—
508C4—242no—
509C4#6397412yes—
510C4#6398111yescharacteristic
511C4#6398111yescharacteristic
512C3—21no—
513C3#7001011yescharacteristic, complemented
514C3#7005411yescharacteristic, complemented
515C2—22no—
516C2—21no—
517C2—42no—
518C2—364no—
519C2#1059171411yescharacteristic
subgroupG/H
centerC4#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#379
prime radical#10596756C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1794
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5240C2semidirect
3. C3×#5234C2semidirect
4. #10591113C2semidirect
5. #10591105C2semidirect
12. #64364C4semidirect
14. #64361C4semidirect
17. C3×#926C22semidirect
18. C2×C3×#208C22semidirect
19. C22×C3×C3⋊C8C22semidirect
30. #5240D3semidirect
31. #5234D3semidirect
102. #926C2×D3semidirect
103. C2×#208C2×D3semidirect
104. C22×C3⋊C8C2×D3semidirect
451. C32#1794semidirect
513. C3#70010semidirect
514. C3#70054semidirect

Maximal subgroups

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

subgroupindex
#105967562
C3×#52402
C3×#52342
#105911132
#105911052
#700543
#700103