Finite Group Databasebeta

← #11898395

Subgroups — #11898395

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595387C212yesmaximal, complemented
2#10592890C211yesmaximal, characteristic
3C3×#5183C211yesmaximal, characteristic, complemented
4C3×Dic3×Q16C211yesmaximal, characteristic, complemented
5#10591607C212yesmaximal, complemented
6#10591579C212yesmaximal, complemented
7#10591565C212yesmaximal, complemented
8#10590865C211yesmaximal, characteristic
9#10590818C211yesmaximal, characteristic, complemented
10C8×#627C211yesmaximal, characteristic, complemented
11#10590763C211yesmaximal, characteristic
12#81795—31nomaximal
13#79710—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64156C2212yes—
16C2×#3755C2212yes—
17C2×#3745C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C2×C3×#216C2212yes—
21C2×C3×Dic12C2211yescharacteristic
22C4×#627C2211yescharacteristic
23#63895—22no—
24#63894C2212yes—
25#63868—22no—
26#63864C2212yes—
27#63848—22no—
28#63843C2212yes—
29#63836—22no—
30C2×#3717C2212yes—
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#835C2212yes—
33C3×#818C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63572C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63565C2212yes—
40#63564C2212yes—
41#5732—32no—
42#5568—32no—
43C3×#494—31no—
44C3×C4×Q16—31no—
45#5191—31no—
46#5191—31no—
47#5191—31no—
48#5191—61no—
49#5185—32no—
50#5185—32no—
51#5183D311yescharacteristic, complemented
52Dic3×Q16—31no—
53Dic3×Q16D311yescharacteristic, complemented
54#5083—32no—
55#5028—32no—
56#4873—31no—
57#4872—31no—
58#4818—32no—
59#4798—32no—
60#4696—31no—
61C4×D24—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×C32×Q8C2312yes—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C3×Dic6C2312yes—
67C2×#627D411yescharacteristic
68C2×#624—22no—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71#3755—42no—
72#3752—22no—
73#3752—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3745—22no—
77C3×#216—42no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×Dic12—22no—
88#3724D411yescharacteristic
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3D411yescharacteristic
91Dic3⋊Dic3D411yescharacteristic
92#3722—22no—
93#3722—22no—
94#3722—22no—
95Dic32—22no—
96#3717—42no—
97#3393—91noSylow
98C2×C3×Q16—21no—
99C2×C3×Q16—32no—
100C2×C3×Q16—31no—
101C2×C3×Q16C2×D311yescharacteristic
102C2×C3×Q16C2×D311yescharacteristic
103C3×C4⋊Q8—32no—
104C3×C4×Q8—32no—
105#947—32no—
106#947—32no—
107#947—32no—
108#947—62no—
109Q8×Dic3—32no—
110Q8×Dic3C2×D312yes—
111#944C2×D312yes—
112C2×#216C2×D312yes—
113C2×#215—32no—
114C2×#215—32no—
115C2×#215—32no—
116C2×#215—62no—
117C2×Dic12C2×D311yescharacteristic
118C2×D24—31no—
119C2×D24—31no—
120C2×D24—61no—
121C2×#204—32no—
122#898—62no—
123#898—62no—
124#898—62no—
125#897—62no—
126#896—62no—
127#893—32no—
128#892—62no—
129#887—32no—
130#876—62no—
131#875—32no—
132C4×D12—32no—
133#872—62no—
134C4×Dic6—31no—
135C4×Dic6—31no—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#835—32no—
141#835C2×D312yes—
142#821—32no—
143#818C2×D311yescharacteristic
144Dic3⋊C8—31no—
145Dic3⋊C8—31no—
146Dic3⋊C8—31no—
147Dic3⋊C8—31no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—61no—
151C8×Dic3C2×D311yescharacteristic
152C8×Dic3C2×D311yescharacteristic
153#810—32no—
154#809—32no—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C22×C3⋊D3—22no—
158C32×Q8—22no—
159C32×Q8—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D411yescharacteristic
170C2×C3×Dic3C2×D411yescharacteristic
171C2×C3×Dic3C2×D411yescharacteristic
172C3×Dic6—22no—
173C3×Dic6—22no—
174#627—22no—
175#624—44no—
176C32×C8#4112yes—
177C3⋊(C3⋊C8)—21no—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—91no—
182#495—91no—
183#494—31no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—91no—
188C4×Q16—31no—
189C4×Q16—91no—
190C4×D8—91no—
191C2×C3×Q8—22no—
192C2×C3×Q8—32no—
193C2×C3×Q8C22×D312yes—
194C2×C3×Q8C22×D312yes—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×Dic6—31no—
201C2×Dic6—31no—
202C2×Dic6C22×D312yes—
203C3×Q16—22no—
204C3×Q16—22no—
205C3×Q16—42no—
206C3×Q16—62no—
207C3×Q16—122no—
208C2×C3×C8—21no—
209C2×C3×C8—31no—
210C2×C3×C8—31no—
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C3×C4⋊C4—32no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4—62no—
216C3×C4⋊C4—62no—
217C3×C42—31no—
218C3×C42—31no—
219C3×C42—62no—
220#216—42no—
221#215—122no—
222#215—122no—
223#215—122no—
224#215—124no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237C4⋊Dic3—22no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—62no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—22no—
243Dic3⋊C4—22no—
244Dic3⋊C4—31no—
245Dic3⋊C4—31no—
246Dic3⋊C4—31no—
247Dic3⋊C4—31no—
248Dic3⋊C4—62no—
249C4×Dic3—22no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—61no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3C22×D311yescharacteristic
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8C22×D311yescharacteristic
261C2×C3⋊C8C22×D311yescharacteristic
262Dic12—22no—
263D24—62no—
264D24—62no—
265D24—122no—
266#204—122no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C32×C4—42no—
272C32×C4C2×#4111yescharacteristic
273C32×C4H(5,𝔽2)11yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—21no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3#13512yes—
282C2×Q16—32no—
283C2×Q16—31no—
284C2×Q16D3211yescharacteristic
285C2×SD16—92no—
286C2×SD16—92no—
287C2×D8—91no—
288C4⋊Q8—32no—
289#126—182no—
290#126—182no—
291#124—92no—
292#124—92no—
293C22⋊Q8—182no—
294C4×Q8—32no—
295C4×Q8—91no—
296C4×Q8—92no—
297C4×D4—92no—
298#117—182no—
299#107—31no—
300C4⋊C8—91no—
301C4⋊C8—91no—
302C4⋊C8—91no—
303#103—32no—
304#103—92no—
305#102—92no—
306C4×C8—31no—
307C4×C8—31no—
308C4×C8—91no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—62no—
319C3×Q8—62no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—31no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3D3×D411yescharacteristic
341C2×Dic3D3×D411yescharacteristic
342C2×Dic3D3×D411yescharacteristic
343C2×Dic3D3×D411yescharacteristic
344D12—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—122no—
350C4×D3—124no—
351C4×D3—124no—
352Dic6—22no—
353Dic6—22no—
354Dic6—62no—
355Dic6—62no—
356C3×C8—22no—
357C3×C8—61no—
358C3×C8—61no—
359C3×C8#23512yes—
360C3×C8#23712yes—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C3⋊C8—62no—
364C3⋊C8—61no—
365C3⋊C8—61no—
366C2×C32#55011yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32#57811yescharacteristic
369C3⋊D3—82no—
370C2×Q8—32no—
371C2×Q8—91no—
372C2×Q8C2×D3212yes—
373C2×D4—92no—
374C22×C4—182no—
375Q16—22no—
376Q16—62no—
377Q16—122no—
378SD16—362no—
379SD16—362no—
380D8—182no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8—91no—
384C2×C8C2×D3211yescharacteristic
385C4⋊C4—32no—
386C4⋊C4—62no—
387C4⋊C4—62no—
388C4⋊C4—62no—
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—182no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C42—31no—
399C42—31no—
400C42—62no—
401C42—91no—
402C42—182no—
403C22×C3—21no—
404C22×C3C2×D3×D411yescharacteristic
405C22×C3C2×D3×D411yescharacteristic
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—242no—
413C2×D3—242no—
414C2×D3—242no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—32no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—61no—
423C3×C4—82no—
424C3×C4—122no—
425C3×C4—122no—
426C3×C4C2×#23511yescharacteristic
427C3×C4C2×#23711yescharacteristic
428C3×C4#100411yescharacteristic
429C3×C4#100911yescharacteristic
430Dic3—21no—
431Dic3—21no—
432Dic3—21no—
433Dic3—42no—
434Dic3—42no—
435Dic3—61no—
436Dic3—61no—
437Dic3—61no—
438Dic3—61no—
439Dic3—121no—
440Dic3—121no—
441Dic3#91912yes—
442C32#339311yescharacteristic, complemented, Sylow
443C23—182no—
444Q8—22no—
445Q8—22no—
446Q8—62no—
447Q8—62no—
448Q8—182no—
449D4—182no—
450D4—182no—
451C2×C4—22no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—364no—
461C2×C4C22×D3211yescharacteristic
462C8—61no—
463C8—61no—
464C8—181no—
465C8#380412yes—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#555311yescharacteristic
470C2×C3#571811yescharacteristic
471C2×C3C2×#91911yescharacteristic
472C2×C3#576611yescharacteristic
473C2×C3#576611yescharacteristic
474C2×C3D3×#13511yescharacteristic
475D3—242no—
476D3—242no—
477D3—482no—
478C22—362no—
479C22—362no—
480C22—362no—
481C22D32×D411yescharacteristic
482C4—32no—
483C4—42no—
484C4—61no—
485C4—61no—
486C4—61no—
487C4—122no—
488C4—122no—
489C4—181no—
490C4—181no—
491C4#6431411yescharacteristic
492C4C2×#380411yescharacteristic
493C3—21no—
494C3#7971011yescharacteristic, complemented
495C3#8179511yescharacteristic, complemented
496C2—722no—
497C2D3×#91911yescharacteristic
498C2#1059476511yescharacteristic
499C2#1059514311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC2×Q16D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10595387C2semidirect
3. C3×#5183C2semidirect
4. C3×Dic3×Q16C2semidirect
5. #10591607C2semidirect
6. #10591579C2semidirect
7. #10591565C2semidirect
9. #10590818C2semidirect
10. C8×#627C2semidirect
51. #5183D3semidirect
53. Dic3×Q16D3semidirect
442. C32#3393semidirect
494. C3#79710semidirect
495. C3#81795semidirect

Maximal subgroups

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

subgroupindex
#105953872
#105928902
C3×#51832
C3×Dic3×Q162
#105916072
#105915792
#105915652
#105908652
#105908182
C8×#6272
#105907632
#817953
#797103