Finite Group Databasebeta

← #11870704

Subgroups — #11870704

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2#10596019C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4#10592869C211yesmaximal, characteristic, complemented
5#10592862C211yesmaximal, characteristic, complemented
6C4×#3755C211yesmaximal, characteristic, complemented
7C4×#3754C211yesmaximal, characteristic, complemented
8#10592562C211yesmaximal, characteristic, complemented
9#10592553C211yesmaximal, characteristic, complemented
10#10592505C211yesmaximal, characteristic, complemented
11#10592490C211yesmaximal, characteristic, complemented
12#10592476C211yesmaximal, characteristic, complemented
13#10592461C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15#10592384C211yesmaximal, characteristic, complemented
16#79653—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×#3828—21no—
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64149C2211yescharacteristic
25#64147C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C4×#638—21no—
28C2×#3744C2211yescharacteristic
29#64104C2211yescharacteristic
30C4⋊C4×C3⋊D3—21no—
31C4⋊C4×C3⋊D3C2211yescharacteristic
32#64097C2211yescharacteristic
33#64096—21no—
34#64096C2211yescharacteristic
35#64094—21no—
36#64093—21no—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C42×C3⋊D3—21no—
39C42×C3⋊D3C2211yescharacteristic
40C4×#634—21no—
41C4×#634C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C4×C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51#63644C2211yescharacteristic
52#63643C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55#63637C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63635C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60C4×D3×Q8—34no—
61#5548—34no—
62C3×C4×SD16D314yescomplemented
63#5170—34no—
64#5163—34no—
65C4×#215—34no—
66C4×#214—34no—
67#4863—34no—
68#4854—34no—
69#4806—34no—
70#4791—34no—
71#4777—34no—
72#4762—34no—
73C4×#204—34no—
74#4685—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C2×#638—21no—
79C2×#638—21no—
80C2×#638—21no—
81Q8×C3⋊D3—22no—
82Q8×C3⋊D3—22no—
83#3828—44no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3D411yescharacteristic
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×#634—21no—
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C32×SD16—22no—
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#3755—22no—
106#3754—22no—
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—22no—
125#3103—91noSylow
126C2×D3×Q8—34no—
127C2×#235—64no—
128C2×C3×SD16C2×D314yes—
129C3×C4×Q8C2×D314yes—
130C3×C4×D4C2×D314yes—
131Q8×Dic3—34no—
132C2×#215—34no—
133#940—34no—
134#938—34no—
135C2×#214—34no—
136C4×#67—64no—
137C2×#204—34no—
138#895—34no—
139D3×C4⋊C4—34no—
140D3×C4⋊C4—64no—
141#888—34no—
142#887—34no—
143#887—64no—
144#885—64no—
145#884—64no—
146C4×D12—34no—
147C42×D3—34no—
148C42×D3—64no—
149C4×Dic6—34no—
150C4×Dic6—64no—
151C3×#106C2×D314yes—
152C3×#103C2×D314yes—
153C3×#102C2×D314yes—
154C3×C4×C8C2×D314yes—
155#835—34no—
156#832—34no—
157#821—34no—
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160#817—34no—
161#816—34no—
162Dic3⋊C8—34no—
163Dic3⋊C8—34no—
164#810—34no—
165#809—34no—
166#808—34no—
167#808—34no—
168C4×C3⋊C8—34no—
169C23×C32—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C2×D411yescharacteristic
172C32×Q8—21no—
173C32×Q8#4112yescomplemented
174C32×D4—21no—
175C32×D4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—42no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183#638—42no—
184#638—42no—
185#638—42no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—42no—
195C4×C3⋊D3—24no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—41no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3SD1614yescomplemented
202#634—24no—
203#634—21no—
204#634—42no—
205#634#4112yescomplemented
206C32×C8—21no—
207C32×C8—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210#532—91no—
211C2×C4×Q8—91no—
212#481—91no—
213#481—91no—
214#475—91no—
215#475—91no—
216#460—91no—
217#460—91no—
218#448—91no—
219#448—91no—
220C4×SD16—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×SD16C3⋊D311yescharacteristic, complemented
224#431—91no—
225C2×C3×Q8C22×D314yes—
226C2×C3×D4C22×D314yes—
227C22×C3×C4—24no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—64no—
231D3×Q8—68no—
232D3×Q8—68no—
233#235—1216no—
234C2×D12—34no—
235C2×D12—64no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—34no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×Dic6—34no—
243C2×Dic6—64no—
244C2×Dic6—64no—
245C3×SD16—28no—
246C2×C3×C8C22×D314yes—
247C2×C3×C8C22×D314yes—
248C3×C4⋊C4—24no—
249C3×C4⋊C4C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252C3×C42—24no—
253C3×C42C22×D314yes—
254#217—64no—
255#215—68no—
256#214—68no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266C4×Dic3—34no—
267C4×Dic3—34no—
268C4×Dic3—34no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274#204—68no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3C2×SD1612yes—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4C2×SD1612yes—
290C32×C4C2×#4111yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—22no—
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3C2×SD1612yes—
298C2×#41—181no—
299C22×Q8—91no—
300C2×SD16—91no—
301C2×SD16—91no—
302C2×SD16—91no—
303C2×SD16C2×C3⋊D311yescharacteristic
304C4⋊Q8—91no—
305#127—91no—
306#124—181no—
307#121—91no—
308#121—91no—
309#121—181no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—91no—
313C4×Q8—181no—
314C4×Q8—181no—
315C4×Q8C2×C3⋊D311yescharacteristic
316C4×D4—91no—
317C4×D4—181no—
318C4×D4C2×C3⋊D311yescharacteristic
319C2×C4⋊C4—91no—
320C2×C4⋊C4—181no—
321C2×C42—91no—
322C2×C42—181no—
323#106—91no—
324#106—91no—
325#106—91no—
326#106C2×C3⋊D311yescharacteristic
327C4⋊C8—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103C2×C3⋊D311yescharacteristic
333#102—91no—
334#102—91no—
335#102—91no—
336#102C2×C3⋊D311yescharacteristic
337C22⋊C8—91no—
338C22⋊C8—91no—
339C4×C8—91no—
340C4×C8C2×C3⋊D311yescharacteristic
341C23×C3—24no—
342C22×D3—34no—
343C22×D3—64no—
344C3×Q8—24no—
345C3×Q8#23518yescomplemented
346C3×D4—24no—
347C3×D4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—48no—
352C2×C3×C4D3×D414yes—
353C2×C3×C4D3×D414yes—
354C2×C3×C4C23×D314yes—
355#67—128no—
356#67—128no—
357#67—128no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364D12—64no—
365D12—64no—
366D12—128no—
367C4×D3—316no—
368C4×D3—616no—
369C4×D3—64no—
370C4×D3—64no—
371C4×D3—124no—
372C4×D3—128no—
373C4×D3—128no—
374Dic6—38no—
375Dic6—616no—
376Dic6—64no—
377Dic6—128no—
378C3×C8—24no—
379C3×C8—24no—
380C3⋊C8—64no—
381C3⋊C8—64no—
382C2×C32—81no—
383C2×C32#52511yescharacteristic
384C2×C32C22×SD1611yescharacteristic
385C2×C32#57511yescharacteristic
386C3⋊D3—22no—
387C3⋊D3—81no—
388#41—364no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—182no—
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×D4—91no—
396C2×D4—181no—
397C2×D4—181no—
398C2×D4—181no—
399C2×D4—181no—
400C2×D4C22×C3⋊D311yescharacteristic
401C22×C4—21no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408SD16—22no—
409SD16—182no—
410SD16—182no—
411SD16—182no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8C22×C3⋊D311yescharacteristic
415C2×C8C22×C3⋊D311yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C22×C3⋊D311yescharacteristic
425C4⋊C4C22×C3⋊D311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C42—21no—
431C42—91no—
432C42—91no—
433C42—91no—
434C42—181no—
435C42—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3C2×D3×D414yes—
442C2×D3—38no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—28no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4D3×SD1618yes—
453C3×C4C2×#23514yes—
454C3×C4D3×#4114yes—
455Dic3—38no—
456Dic3—64no—
457Dic3—68no—
458Dic3—64no—
459Dic3—124no—
460Dic3—124no—
461C32#310311yescharacteristic, complemented, Sylow
462C23—21no—
463C23—91no—
464C23—181no—
465Q8—21no—
466Q8—92no—
467Q8—184no—
468Q8—181no—
469Q8—362no—
470Q8#382812yescomplemented
471D4—21no—
472D4—21no—
473D4—181no—
474D4—181no—
475D4—362no—
476D4—362no—
477D4—362no—
478D4—362no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—91no—
484C2×C4—94no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—184no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—361no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4D4×C3⋊D311yescharacteristic
497C2×C4D4×C3⋊D311yescharacteristic
498C2×C4C23×C3⋊D311yescharacteristic
499C8—21no—
500C8—21no—
501C8—181no—
502C8—181no—
503C2×C3—84no—
504C2×C3#554714yes—
505C2×C3C2×D3×SD1614yes—
506C2×C3#576814yes—
507D3—68no—
508D3—244no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—92no—
513C22—181no—
514C22—181no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22C2×D4×C3⋊D311yescharacteristic
519C4—21no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—92no—
524C4—181no—
525C4—181no—
526C4—182no—
527C4—361no—
528C4—361no—
529C4SD16×C3⋊D312yes—
530C4C2×#382811yescharacteristic
531C4#41×C3⋊D311yescharacteristic
532C3#7965314yescomplemented
533C2—81no—
534C2—182no—
535C2—721no—
536C2#1059601811yescharacteristic
537C2C2×SD16×C3⋊D311yescharacteristic
538C2#1059623911yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radical#10596019C2
hypercenterC4×SD16C3⋊D3
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
3. C32×C4×SD16C2semidirect
4. #10592869C2semidirect
5. #10592862C2semidirect
6. C4×#3755C2semidirect
7. C4×#3754C2semidirect
8. #10592562C2semidirect
9. #10592553C2semidirect
10. #10592505C2semidirect
11. #10592490C2semidirect
12. #10592476C2semidirect
13. #10592461C2semidirect
14. C4×#3744C2semidirect
15. #10592384C2semidirect
62. C3×C4×SD16D3semidirect
173. C32×Q8#41semidirect
201. C4×C3⋊D3SD16semidirect
205. #634#41semidirect
223. C4×SD16C3⋊D3semidirect
345. C3×Q8#235semidirect
461. C32#3103semidirect
470. Q8#3828semidirect
532. C3#79653semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105960192
C32×C4×SD162
#105928692
#105928622
C4×#37552
C4×#37542
#105925622
#105925532
#105925052
#105924902
#105924762
#105924612
C4×#37442
#105923842
#796533