Finite Group Databasebeta

← #11860913

Subgroups — #11860913

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64125C211yesmaximal, characteristic
2#10596045C211yesmaximal, characteristic, complemented
3#10596017C211yesmaximal, characteristic, complemented
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592729C211yesmaximal, characteristic, complemented
7#10592713C211yesmaximal, characteristic, complemented
8C3⋊D3×#106C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592502C211yesmaximal, characteristic, complemented
11#10592488C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic, complemented
13#10592470C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15#10592388C211yesmaximal, characteristic, complemented
16#79650—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C4×#638—21no—
27C2×#3750—21no—
28#64125C418yescomplemented
29C2×#3744C2211yescharacteristic
30C2×#3743C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic
32#64102—21no—
33#64102C2211yescharacteristic
34C4⋊C4×C3⋊D3—21no—
35C4⋊C4×C3⋊D3C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64096C2211yescharacteristic
38#64090—21no—
39#64086—21no—
40C4×C4⋊(C3⋊D3)—21no—
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42#64081—21no—
43#64081C2211yescharacteristic
44C4×#634C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49#63662C2211yescharacteristic
50#63659C2211yescharacteristic
51#63648C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63635C2211yescharacteristic
60#63630C2211yescharacteristic
61C2×#916—34no—
62#5574—34no—
63#5546—34no—
64C3×C4×SD16D314yescomplemented
65Dic3×SD16—34no—
66#5030—34no—
67#5014—34no—
68D3×#106—34no—
69#4852—34no—
70#4803—34no—
71#4789—34no—
72#4785—34no—
73#4771—34no—
74C4×#204—34no—
75#4689—34no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82#3832—22no—
83#3832C2×C414yescomplemented
84#3830—22no—
85#3830C2×C414yescomplemented
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C32×SD16C2×C414yescomplemented
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C42—21no—
103C32×C42C2311yescharacteristic
104#3757—21no—
105#3756C2×C414yescomplemented
106#3753C2×C414yescomplemented
107#3752—21no—
108#3752—21no—
109#3752D411yescharacteristic
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119#3750D411yescharacteristic
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#3743—22no—
128C8×C3⋊D3C2×C414yescomplemented
129#2952—91noSylow
130C2×#239—34no—
131C2×#237—34no—
132C2×C3×SD16C2×D314yes—
133C3×C4×Q8C2×D314yes—
134C3×C4×D4C2×D314yes—
135Q8×Dic3—34no—
136C2×#216—34no—
137D4×Dic3—34no—
138C2×#213—34no—
139C4×#67—64no—
140C2×Dic3⋊C4—64no—
141#916—332no—
142C2×#204—34no—
143C2×ΓL(1,𝔽25)—34no—
144C2×D3×C8—34no—
145#893—34no—
146#893—64no—
147D3×C4⋊C4—34no—
148D3×C4⋊C4—34no—
149D3×C4⋊C4—64no—
150#887—34no—
151#67⋊C4—64no—
152#877—64no—
153C4×D12—34no—
154C4×D12—64no—
155#872—34no—
156#872—64no—
157C4×Dic6—34no—
158C3×#106C2×D314yes—
159C3×#103C2×D314yes—
160C3×#102C2×D314yes—
161C3×C4×C8C2×D314yes—
162#835—34no—
163#832—34no—
164#821—34no—
165#817—34no—
166#816—34no—
167#815—34no—
168C8×Dic3—34no—
169#810—34no—
170#809—34no—
171#808—34no—
172#808—34no—
173#803—34no—
174C23×C32—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3C2×D411yescharacteristic
177C32×Q8—21no—
178C32×Q8C22×C412yes—
179C32×D4—21no—
180C32×D4C22×C412yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—81no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188#638—24no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—24no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—81no—
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4⋊(C3⋊D3)—24no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)C22×C412yes—
200C4×C3⋊D3—24no—
201C4×C3⋊D3—81no—
202C4×C3⋊D3—81no—
203C4×C3⋊D3—81no—
204C4×C3⋊D3—81no—
205C4×C3⋊D3C22×C412yes—
206C4×C3⋊D3#4112yes—
207#634—21no—
208#634C22×C412yes—
209C32×C8—21no—
210C32×C8C22×C412yes—
211C3⋊(C3⋊C8)—21no—
212C3⋊(C3⋊C8)C22×C412yes—
213C2×#135—91no—
214#520—91no—
215#520—91no—
216#442—91no—
217#442—91no—
218#441—91no—
219#441—91no—
220C4×SD16—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×SD16C3⋊D311yescharacteristic, complemented
224C2×#106—91no—
225#417—91no—
226#417—91no—
227#405—91no—
228C2×C3×Q8C22×D314yes—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—24no—
231C2×#67—64no—
232C22×Dic3—64no—
233C22×Dic3—64no—
234#239—316no—
235#239—68no—
236#237—316no—
237#237—68no—
238C2×D12—34no—
239C2×D12—64no—
240C2×C4×D3—34no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—64no—
246C2×Dic6—34no—
247C3×SD16C4×D3116yescomplemented
248C2×C3×C8C22×D314yes—
249C2×C3×C8C22×D314yes—
250C3×C4⋊C4—24no—
251C3×C4⋊C4C22×D314yes—
252C3×C4⋊C4C22×D314yes—
253C3×C22⋊C4—24no—
254C3×C42—24no—
255C3×C42C22×D314yes—
256#217—64no—
257#216—316no—
258#213—316no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—64no—
266Dic3⋊C4—34no—
267Dic3⋊C4—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272C4×Dic3—34no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278#204—316no—
279ΓL(1,𝔽25)—68no—
280D3×C8—316no—
281C22×C32—22no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3C4×D412yes—
291C32×C4—22no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C23×C411yescharacteristic
297C32×C4C2×#4111yescharacteristic
298C3⋊Dic3—22no—
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3C4×D412yes—
304C2×#41—91no—
305C2×#41—91no—
306#135—98no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16C2×C3⋊D311yescharacteristic
310C2×D8—91no—
311C2×M16—91no—
312C22×C8—91no—
313C4×Q8—91no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×Q8C2×C3⋊D311yescharacteristic
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4—181no—
324C4×D4C2×C3⋊D311yescharacteristic
325#117—91no—
326#117—181no—
327#117—181no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—181no—
331C2×C4⋊C4—181no—
332#106—91no—
333#106—91no—
334#106—91no—
335#106C2×C3⋊D311yescharacteristic
336#103—91no—
337#103—91no—
338#103—91no—
339#103C2×C3⋊D311yescharacteristic
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×C3⋊D311yescharacteristic
344#97—91no—
345#97—91no—
346C4×C8—91no—
347C4×C8C2×C3⋊D311yescharacteristic
348C23×C3—24no—
349C22×D3—34no—
350C22×D3—64no—
351C3×Q8—24no—
352C3×Q8C2×C4×D318yes—
353C3×D4—24no—
354C3×D4C2×C4×D318yes—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—84no—
359C2×C3×C4D3×D414yes—
360C2×C3×C4D3×D414yes—
361C2×C3×C4C23×D314yes—
362#67—616no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—616no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—244no—
371D12—38no—
372D12—616no—
373D12—64no—
374C4×D3—38no—
375C4×D3—38no—
376C4×D3—616no—
377C4×D3—244no—
378C4×D3—244no—
379C4×D3—244no—
380C4×D3—244no—
381Dic6—38no—
382Dic6—64no—
383C3×C8—24no—
384C3×C8C2×C4×D318yes—
385C3⋊C8—38no—
386C3⋊C8—64no—
387C2×C32—42no—
388C2×C32C2×C4×D411yescharacteristic
389C2×C32#57711yescharacteristic
390C2×C32#57711yescharacteristic
391C3⋊D3—22no—
392C3⋊D3—42no—
393#41—94no—
394#41—94no—
395#41—182no—
396#41—182no—
397C2×Q8—91no—
398C2×Q8C22×C3⋊D311yescharacteristic
399C2×D4—91no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4C22×C3⋊D311yescharacteristic
403C22×C4—21no—
404C22×C4—91no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412Q16—94no—
413SD16—94no—
414SD16C4×C3⋊D314yescomplemented
415D8—94no—
416M16—182no—
417C2×C8—91no—
418C2×C8—94no—
419C2×C8—91no—
420C2×C8C22×C3⋊D311yescharacteristic
421C2×C8C22×C3⋊D311yescharacteristic
422C4⋊C4—21no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4C22×C3⋊D311yescharacteristic
433C4⋊C4C22×C3⋊D311yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—91no—
436C22⋊C4—91no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C42—21no—
441C42—91no—
442C42—181no—
443C42—181no—
444C42—181no—
445C42C22×C3⋊D311yescharacteristic
446C22×C3—28no—
447C22×C3—44no—
448C22×C3—44no—
449C22×C3C2×D3×D414yes—
450C2×D3—38no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—68no—
454C2×D3—124no—
455C2×D3—124no—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—28no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4C22×C4×D314yes—
462C3×C4D3×#4114yes—
463Dic3—38no—
464Dic3—64no—
465Dic3—64no—
466Dic3—68no—
467Dic3—124no—
468Dic3—124no—
469C32#295211yescharacteristic, complemented, Sylow
470C23—21no—
471C23—91no—
472C23—181no—
473Q8—21no—
474Q8—92no—
475Q8—181no—
476Q8C2×C4×C3⋊D312yes—
477D4—21no—
478D4—92no—
479D4—184no—
480D4—184no—
481D4—181no—
482D4C2×C4×C3⋊D312yes—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—81no—
487C2×C4—91no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—184no—
493C2×C4—184no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—721no—
498C2×C4—721no—
499C2×C4—721no—
500C2×C4—721no—
501C2×C4—721no—
502C2×C4D4×C3⋊D311yescharacteristic
503C2×C4D4×C3⋊D311yescharacteristic
504C2×C4C23×C3⋊D311yescharacteristic
505C8—21no—
506C8—92no—
507C8—181no—
508C8C2×C4×C3⋊D312yes—
509C2×C3—48no—
510C2×C3C4×D3×D414yes—
511C2×C3#576214yes—
512C2×C3#577014yes—
513D3—68no—
514D3—128no—
515C22—22no—
516C22—41no—
517C22—41no—
518C22—92no—
519C22—181no—
520C22—181no—
521C22—182no—
522C22—361no—
523C22—361no—
524C22C2×D4×C3⋊D311yescharacteristic
525C4—21no—
526C4—21no—
527C4—22no—
528C4—41no—
529C4—41no—
530C4—92no—
531C4—181no—
532C4—181no—
533C4—182no—
534C4—361no—
535C4—361no—
536C4C22×C4×C3⋊D311yescharacteristic
537C4#41×C3⋊D311yescharacteristic
538C3#7965014yescomplemented
539C2—42no—
540C2—182no—
541C2—362no—
542C2C4×D4×C3⋊D311yescharacteristic
543C2#1059623311yescharacteristic
544C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×#64125C2
cosocleC2×C32×C4C24
hypercenterC4×SD16C3⋊D3
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10596045C2semidirect
3. #10596017C2semidirect
4. C32×C4×SD16C2semidirect
5. SD16×C3⋊Dic3C2semidirect
6. #10592729C2semidirect
7. #10592713C2semidirect
8. C3⋊D3×#106C2semidirect
9. #10592551C2semidirect
10. #10592502C2semidirect
11. #10592488C2semidirect
12. #10592484C2semidirect
13. #10592470C2semidirect
14. C4×#3744C2semidirect
15. #10592388C2semidirect
28. #64125C4semidirect
64. C3×C4×SD16D3semidirect
83. #3832C2×C4semidirect
85. #3830C2×C4semidirect
95. C32×SD16C2×C4semidirect
105. #3756C2×C4semidirect
106. #3753C2×C4semidirect
126. #3744C2×C4semidirect
128. C8×C3⋊D3C2×C4semidirect
223. C4×SD16C3⋊D3semidirect
247. C3×SD16C4×D3semidirect
414. SD16C4×C3⋊D3semidirect
469. C32#2952semidirect
538. C3#79650semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
#105960452
#105960172
C32×C4×SD162
SD16×C3⋊Dic32
#105927292
#105927132
C3⋊D3×#1062
#105925512
#105925022
#105924882
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