Finite Group Databasebeta

← #11898367

Subgroups — #11898367

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#10593850C212yesmaximal, complemented
2#10592395C211yesmaximal, characteristic
3C3×C4×Dic12C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590896C211yesmaximal, characteristic, complemented
6#10590865C211yesmaximal, characteristic
7#10590813C212yesmaximal, complemented
8#10590807C211yesmaximal, characteristic, complemented
9#10590763C211yesmaximal, characteristic
10#10590760C212yesmaximal, complemented
11#10590368C212yesmaximal, complemented
12#79912—31nomaximal
13#79710—31nomaximal
14C2×#3746C2211yescharacteristic
15C2×#3745C2211yescharacteristic
16C2×#3744C2212yes—
17#64084C2212yes—
18C2×C3×Dic12C2211yescharacteristic
19C3×C4×Dic6C2212yes—
20C3×C4×Dic6C2211yescharacteristic
21#63894C2212yes—
22#63888—22no—
23#63868—22no—
24#63866C2212yes—
25#63864C2212yes—
26#63848—22no—
27#63844C2212yes—
28#63836—22no—
29C2×#3719C2212yes—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32C3×#818C2211yescharacteristic
33C3×#816C2212yes—
34C3×Dic3⋊C8C2211yescharacteristic
35C3×Dic3⋊C8C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63567C2212yes—
40#63564C2212yes—
41#5584—32no—
42#5568—32no—
43C3×C8×Q8—31no—
44C3×C4×Q16—31no—
45#5191—31no—
46#5183—31no—
47#5028—32no—
48#4873—31no—
49#4872—31no—
50#4845—32no—
51#4845—32no—
52#4841—32no—
53#4818—32no—
54#4798—32no—
55#4699—31no—
56C4×Dic12—31no—
57C4×Dic12D311yescharacteristic, complemented
58#4696—31no—
59#4696—31no—
60#4696—31no—
61#4696—61no—
62C4×D24—31no—
63C8×Dic6D311yescharacteristic, complemented
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×#634C2312yes—
66C2×C3×Dic6D411yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#624—22no—
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C32×C42C2311yescharacteristic
72#3752—22no—
73#3752—22no—
74#3746—22no—
75#3745—22no—
76#3744—42no—
77C3×C4⋊Dic3D411yescharacteristic
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4D411yescharacteristic
81C3×Dic3⋊C4D411yescharacteristic
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×Dic12—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91#3722—22no—
92#3722—22no—
93#3722—22no—
94Dic32—22no—
95#3719—42no—
96#3717—42no—
97#3393—91noSylow
98C2×C3×Q16—31no—
99C3×C4×Q8—31no—
100C3×C4×Q8—32no—
101#947—32no—
102#946—62no—
103#944—32no—
104C2×#216—32no—
105C2×#215—32no—
106C2×Dic12—31no—
107C2×Dic12—31no—
108C2×Dic12—32no—
109C2×Dic12—61no—
110C2×Dic12C2×D311yescharacteristic
111C2×D24—31no—
112C2×D24—31no—
113C2×D24—61no—
114C2×#204—32no—
115C2×#204—32no—
116C2×#204—32no—
117C2×#204—62no—
118#898—62no—
119#898—62no—
120#898—62no—
121#896—62no—
122#893—32no—
123#892—62no—
124#887—32no—
125#876—62no—
126#875—32no—
127#875—32no—
128#875—32no—
129#875—62no—
130C4×D12—32no—
131#872—62no—
132#869—32no—
133C4×Dic6—32no—
134C4×Dic6C2×D312yes—
135C4×Dic6C2×D311yescharacteristic
136C3×#107—31no—
137C3×C4⋊C8—31no—
138C3×C4⋊C8—31no—
139C3×C4⋊C8—31no—
140C3×#103—32no—
141C3×C4×C8—21no—
142C3×C4×C8—31no—
143C3×C4×C8—31no—
144C3×C4×C8C2×D311yescharacteristic
145C3×C4×C8C2×D311yescharacteristic
146#821—32no—
147#818C2×D311yescharacteristic
148#816—32no—
149#816C2×D312yes—
150Dic3⋊C8C2×D311yescharacteristic
151Dic3⋊C8C2×D311yescharacteristic
152C8×Dic3C2×D311yescharacteristic
153C8×Dic3C2×D311yescharacteristic
154#810—32no—
155#809—32no—
156C4⋊(C3⋊C8)C2×D311yescharacteristic
157C22×C3⋊D3—22no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—22no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)—22no—
164#634—22no—
165#634—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—
174C3×Dic6—22no—
175#624—44no—
176C32×C8—21no—
177C32×C8#4112yes—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—91no—
182#495—91no—
183#494—91no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—31no—
188C4×Q16—31no—
189C4×Q16—91no—
190C4×D8—91no—
191C2×C3×Q8—31no—
192C2×C3×Q8—32no—
193C2×D12—32no—
194C2×D12—32no—
195C2×D12—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6D1211yescharacteristic
202C2×Dic6C22×D312yes—
203C3×Q16—62no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C4⋊C4—31no—
213C3×C4⋊C4—31no—
214C3×C4⋊C4—31no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—62no—
217C3×C42—21no—
218C3×C42—31no—
219C3×C42—31no—
220C3×C42—62no—
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223#216—122no—
224#215—122no—
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—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3D1211yescharacteristic
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4D1211yescharacteristic
247Dic3⋊C4D1211yescharacteristic
248C4×Dic3—22no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3C22×D311yescharacteristic
252C4×Dic3C22×D311yescharacteristic
253C2×C3⋊C8C22×D311yescharacteristic
254C2×C3⋊C8C22×D311yescharacteristic
255Dic12—22no—
256Dic12—62no—
257Dic12—62no—
258Dic12—122no—
259Dic12—122no—
260D24—62no—
261D24—62no—
262D24—122no—
263#204—122no—
264#204—122no—
265#204—124no—
266#204—122no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4C2×#4111yescharacteristic
274C32×C4H(5,𝔽2)11yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—21no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3#13512yes—
282C2×Q16—31no—
283C2×Q16—92no—
284C2×Q16—91no—
285C2×SD16—92no—
286C2×SD16—92no—
287C2×D8—91no—
288C4⋊Q8—92no—
289#126—182no—
290#126—182no—
291#124—92no—
292#124—92no—
293C22⋊Q8—182no—
294C4×Q8—31no—
295C4×Q8—32no—
296C4×Q8—92no—
297C4×D4—92no—
298#117—182no—
299#107—31no—
300C4⋊C8—31no—
301C4⋊C8—31no—
302C4⋊C8—31no—
303#103—32no—
304#103—92no—
305#102—92no—
306C4×C8—31no—
307C4×C8—31no—
308C4×C8D3211yescharacteristic
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8—62no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—31no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4C2×D1211yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3C2×D1211yescharacteristic
336C2×Dic3C2×D1211yescharacteristic
337C2×Dic3C2×D1211yescharacteristic
338C2×Dic3C2×D1211yescharacteristic
339D12—62no—
340D12—62no—
341D12—62no—
342D12—62no—
343D12—122no—
344D12—122no—
345C4×D3—124no—
346C4×D3—124no—
347Dic6—22no—
348Dic6—22no—
349Dic6—22no—
350Dic6—62no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—122no—
355Dic6—122no—
356C3×C8—22no—
357C3×C8—21no—
358C3×C8—21no—
359C3×C8—22no—
360C3×C8—61no—
361C3×C8—61no—
362C3×C8#23512yes—
363C3×C8#23912yes—
364C3⋊C8—21no—
365C3⋊C8—21no—
366C2×C32#55011yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32#57811yescharacteristic
369C3⋊D3—82no—
370C2×Q8—31no—
371C2×Q8—32no—
372C2×Q8—92no—
373C2×D4—92no—
374C22×C4—182no—
375Q16—62no—
376Q16—182no—
377Q16—362no—
378SD16—362no—
379SD16—362no—
380D8—182no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8C2×D3211yescharacteristic
384C2×C8C2×D3211yescharacteristic
385C4⋊C4—31no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—62no—
390C4⋊C4—182no—
391C4⋊C4—182no—
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—182no—
402C42C2×D3211yescharacteristic
403C22×C3—21no—
404C22×C3C22×D1211yescharacteristic
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—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—61no—
425C3×C4—61no—
426C3×C4—61no—
427C3×C4—122no—
428C3×C4—122no—
429C3×C4C2×#23511yescharacteristic
430C3×C4C2×#23911yescharacteristic
431C3×C4#100911yescharacteristic
432C3×C4#100911yescharacteristic
433Dic3—21no—
434Dic3—21no—
435Dic3—21no—
436Dic3—42no—
437Dic3—42no—
438Dic3—122no—
439Dic3—122no—
440Dic3—242no—
441Dic3#90412yes—
442C32#339311yescharacteristic, complemented, Sylow
443C23—182no—
444Q8—62no—
445Q8—62no—
446Q8—62no—
447Q8—182no—
448Q8—182no—
449D4—182no—
450D4—182no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—182no—
458C2×C4—364no—
459C2×C4D3×D1211yescharacteristic
460C2×C4D3×D1211yescharacteristic
461C2×C4C22×D3211yescharacteristic
462C8—21no—
463C8—61no—
464C8—61no—
465C8#379912yes—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#555311yescharacteristic
470C2×C3#557711yescharacteristic
471C2×C3C2×#90411yescharacteristic
472C2×C3#575311yescharacteristic
473C2×C3#576611yescharacteristic
474C2×C3D3×#13511yescharacteristic
475D3—242no—
476D3—242no—
477D3—482no—
478C22—362no—
479C22—362no—
480C22—362no—
481C22C2×D3×D1211yescharacteristic
482C4—21no—
483C4—21no—
484C4—32no—
485C4—61no—
486C4—61no—
487C4—61no—
488C4—122no—
489C4—122no—
490C4—362no—
491C4C2×#379911yescharacteristic
492C4#6430811yescharacteristic
493C3—21no—
494C3#7971011yescharacteristic, complemented
495C3#7991211yescharacteristic, complemented
496C2—722no—
497C2#1059390211yescharacteristic
498C2D3×#90411yescharacteristic
499C2#1059469111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×C8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593850C2semidirect
3. C3×C4×Dic12C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590896C2semidirect
7. #10590813C2semidirect
8. #10590807C2semidirect
10. #10590760C2semidirect
11. #10590368C2semidirect
57. C4×Dic12D3semidirect
63. C8×Dic6D3semidirect
442. C32#3393semidirect
494. C3#79710semidirect
495. C3#79912semidirect

Maximal subgroups

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

subgroupindex
#105938502
#105923952
C3×C4×Dic122
C3×C8×Dic62
#105908962
#105908652
#105908132
#105908072
#105907632
#105907602
#105903682
#799123
#797103