Finite Group Databasebeta

← #11860575

Subgroups — #11860575

Order 1152.

1410 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64127C211yesmaximal, characteristic
2#10596045C211yesmaximal, characteristic
3#10596043C211yesmaximal, characteristic, complemented
4C32×#441C211yesmaximal, characteristic, complemented
5Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C4×#3756C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592560C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592503C211yesmaximal, characteristic
12C3⋊D3×#103C211yesmaximal, characteristic, complemented
13#10592488C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592407C211yesmaximal, characteristic, complemented
16#79830—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26#64127C418yescomplemented
27C2×#3744C2211yescharacteristic
28C2×#3743C2211yescharacteristic
29C2×C8×C3⋊D3C2211yescharacteristic
30#64102—21no—
31#64102C2211yescharacteristic
32#64101—21no—
33#64101C2211yescharacteristic
34C4⋊C4×C3⋊D3—21no—
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64096—21no—
37#64096C2211yescharacteristic
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64081—21no—
41#64081—21no—
42#64081C2211yescharacteristic
43C4×#634—21no—
44C4×#634C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#97C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60C4×C3⋊(C3⋊C8)C2211yescharacteristic
61C2×#918—34no—
62#5574—34no—
63#5572—34no—
64C3×#441D314yescomplemented
65Dic3×Q16—34no—
66C4×#216—34no—
67C4×#215—34no—
68#4861—34no—
69#4852—34no—
70#4817—34no—
71#4804—34no—
72D3×#103—34no—
73#4789—34no—
74#4710—34no—
75#4708—34no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78#3832—22no—
79#3832C2×C414yes—
80Q8×C3⋊D3—22no—
81Q8×C3⋊D3C2×C414yescomplemented
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C2×#634C2311yescharacteristic
92C32×Q16C2×C414yescomplemented
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C42—21no—
100C32×C42—21no—
101C32×C42C2311yescharacteristic
102#3756C2×C414yescomplemented
103#3755C2×C414yescomplemented
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752D411yescharacteristic
108#3752D411yescharacteristic
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744C2×C414yescomplemented
127#3743C2×C414yescomplemented
128C8×C3⋊D3—22no—
129#2947—91noSylow
130C2×#239—34no—
131C2×D3×Q8—34no—
132C2×C3×Q16C2×D314yes—
133C3×C4×Q8C2×D314yes—
134C3×C4×Q8C2×D314yes—
135Q8×Dic3—34no—
136Q8×Dic3—34no—
137C2×#216—34no—
138C2×#215—34no—
139#918—332no—
140C2×#204—34no—
141C2×ΓL(1,𝔽25)—34no—
142C2×D3×C8—34no—
143#893—34no—
144#893—64no—
145#892—34no—
146#892—64no—
147D3×C4⋊C4—34no—
148D3×C4⋊C4—64no—
149#887—34no—
150#887—64no—
151C4×D12—34no—
152C4×D12—64no—
153#872—34no—
154#872—64no—
155#872—64no—
156C4×Dic6—34no—
157C4×Dic6—64no—
158C3×#106C2×D314yes—
159C3×#103C2×D314yes—
160C3×#103C2×D314yes—
161C3×#97C2×D314yes—
162#835—34no—
163#835—34no—
164#821—34no—
165#818—34no—
166#816—34no—
167#815—34no—
168C8×Dic3—34no—
169#810—34no—
170#809—34no—
171#808—34no—
172#807—34no—
173C4×C3⋊C8—34no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8C22×C412yes—
179C32×Q8C22×C412yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—24no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)C22×C412yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—24no—
198C4×C3⋊D3—81no—
199C4×C3⋊D3—81no—
200C4×C3⋊D3—81no—
201C4×C3⋊D3C22×C412yes—
202C4×C3⋊D3#4112yes—
203#634—21no—
204#634—24no—
205#634C22×C412yes—
206C32×C8—21no—
207C32×C8C22×C412yes—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)C22×C412yes—
210C2×#137—91no—
211#520—91no—
212#519—91no—
213#441—91no—
214#441C3⋊D311yescharacteristic, complemented
215#440—91no—
216#440—91no—
217C4×Q16—91no—
218C4×Q16—91no—
219C4×SD16—91no—
220C4×SD16—91no—
221#428—91no—
222#416—91no—
223C2×#103—91no—
224#405—91no—
225C2×C3×Q8C22×D314yes—
226C2×C3×Q8C22×D314yes—
227#239—316no—
228#239—68no—
229D3×Q8—316no—
230D3×Q8—68no—
231C2×D12—34no—
232C2×D12—64no—
233C2×C4×D3—34no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C3×Q16C4×D3116yescomplemented
242C2×C3×C8C22×D314yes—
243C2×C3×C8C22×D314yes—
244C3×C4⋊C4—24no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C42—24no—
249C3×C42—24no—
250C3×C42C22×D314yes—
251#216—316no—
252#215—316no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262Dic3⋊C4—34no—
263Dic3⋊C4—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275#204—316no—
276ΓL(1,𝔽25)—316no—
277D3×C8—68no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3C4×D412yes—
285C32×C4—22no—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C23×C411yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3C4×D412yes—
299C2×#41—91no—
300C22×Q8—91no—
301#137—98no—
302C2×Q16—91no—
303C2×Q16C2×C3⋊D311yescharacteristic
304C2×SD16—91no—
305C2×SD16—91no—
306C2×M16—91no—
307C22×C8—91no—
308C4×Q8—91no—
309C4×Q8—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—181no—
313C4×Q8—181no—
314C4×Q8C2×C3⋊D311yescharacteristic
315C4×Q8C2×C3⋊D311yescharacteristic
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—181no—
319C4×D4—181no—
320#117—91no—
321#117—91no—
322#117—181no—
323#117—181no—
324#117—181no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—181no—
327#107—91no—
328#107—91no—
329#106—91no—
330#106C2×C3⋊D311yescharacteristic
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103C2×C3⋊D311yescharacteristic
336#103C2×C3⋊D311yescharacteristic
337#102—91no—
338#102—91no—
339#97—91no—
340#97C2×C3⋊D311yescharacteristic
341C4×C8—91no—
342C4×C8—91no—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8C2×C4×D318yes—
348C3×Q8C2×C4×D318yes—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4D3×D414yes—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362D12—38no—
363D12—616no—
364D12—64no—
365C4×D3—38no—
366C4×D3—38no—
367C4×D3—616no—
368C4×D3—616no—
369C4×D3—244no—
370C4×D3—244no—
371C4×D3—244no—
372Dic6—38no—
373Dic6—616no—
374Dic6—64no—
375C3×C8—24no—
376C3×C8C2×C4×D318yes—
377C3⋊C8—38no—
378C3⋊C8—64no—
379C2×C32C2×C4×D411yescharacteristic
380C2×C32#57711yescharacteristic
381C2×C32#57811yescharacteristic
382C3⋊D3—22no—
383C3⋊D3—42no—
384#41—94no—
385#41—182no—
386C2×Q8—94no—
387C2×Q8—91no—
388C2×Q8—181no—
389C2×Q8—182no—
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×Q8C22×C3⋊D311yescharacteristic
392C2×D4—91no—
393C2×D4—181no—
394C22×C4—91no—
395C22×C4—181no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400Q16—94no—
401Q16C4×C3⋊D314yescomplemented
402SD16—94no—
403SD16—94no—
404M16—94no—
405C2×C8—91no—
406C2×C8—91no—
407C2×C8—182no—
408C2×C8C22×C3⋊D311yescharacteristic
409C2×C8C22×C3⋊D311yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×C3⋊D311yescharacteristic
422C4⋊C4C22×C3⋊D311yescharacteristic
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C42—21no—
429C42—21no—
430C42—91no—
431C42—181no—
432C42—181no—
433C42—181no—
434C42—181no—
435C42—181no—
436C42C22×C3⋊D311yescharacteristic
437C22×C3C2×D3×D414yes—
438C2×D3—38no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—68no—
442C2×D3—124no—
443C2×D3—124no—
444C3×C4—24no—
445C3×C4—24no—
446C3×C4—28no—
447C3×C4—28no—
448C3×C4—44no—
449C3×C4—44no—
450C3×C4C22×C4×D314yes—
451C3×C4D3×#4114yes—
452Dic3—38no—
453Dic3—64no—
454Dic3—64no—
455Dic3—68no—
456Dic3—124no—
457Dic3—124no—
458C32#294711yescharacteristic, complemented, Sylow
459C23—91no—
460C23—181no—
461Q8—21no—
462Q8—21no—
463Q8—92no—
464Q8—184no—
465Q8—181no—
466Q8C2×C4×C3⋊D312yes—
467Q8C2×C4×C3⋊D312yes—
468D4—92no—
469D4—184no—
470D4—181no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—91no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—91no—
479C2×C4—91no—
480C2×C4—184no—
481C2×C4—184no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—721no—
486C2×C4—721no—
487C2×C4—721no—
488C2×C4D4×C3⋊D311yescharacteristic
489C2×C4D4×C3⋊D311yescharacteristic
490C2×C4C23×C3⋊D311yescharacteristic
491C8—21no—
492C8—92no—
493C8—181no—
494C8C2×C4×C3⋊D312yes—
495C2×C3C4×D3×D414yes—
496C2×C3#577814yes—
497C2×C3#577914yes—
498D3—68no—
499D3—128no—
500C22—92no—
501C22—181no—
502C22—181no—
503C22—182no—
504C22—361no—
505C22—361no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—92no—
514C4—181no—
515C4—181no—
516C4—182no—
517C4—361no—
518C4—361no—
519C4C22×C4×C3⋊D311yescharacteristic
520C4#41×C3⋊D311yescharacteristic
521C3#7983014yescomplemented
522C2—182no—
523C2—362no—
524C2C4×D4×C3⋊D311yescharacteristic
525C2#1059624911yescharacteristic
526C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC2×#3832C22
cosocleC2×C32×C4C24
hypercenter#441C3⋊D3
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #10596043C2semidirect
4. C32×#441C2semidirect
5. Q16×C3⋊Dic3C2semidirect
6. C4×#3756C2semidirect
7. C4×#3755C2semidirect
8. #10592560C2semidirect
9. #10592551C2semidirect
10. #10592516C2semidirect
12. C3⋊D3×#103C2semidirect
13. #10592488C2semidirect
14. #10592409C2semidirect
15. #10592407C2semidirect
26. #64127C4semidirect
64. C3×#441D3semidirect
81. Q8×C3⋊D3C2×C4semidirect
92. C32×Q16C2×C4semidirect
102. #3756C2×C4semidirect
103. #3755C2×C4semidirect
126. #3744C2×C4semidirect
127. #3743C2×C4semidirect
214. #441C3⋊D3semidirect
241. C3×Q16C4×D3semidirect
401. Q16C4×C3⋊D3semidirect
458. C32#2947semidirect
521. C3#79830semidirect

Maximal subgroups

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

subgroupindex
C2×#641272
#105960452
#105960432
C32×#4412
Q16×C3⋊Dic32
C4×#37562
C4×#37552
#105925602
#105925512
#105925162
#105925032
C3⋊D3×#1032
#105924882
#105924092
#105924072
#798303