Finite Group Databasebeta

← #11898396

Subgroups — #11898396

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#10595273C212yesmaximal, complemented
2#10592854C211yesmaximal, characteristic
3C3×#5155C211yesmaximal, characteristic
4C3×Dic3×D8C211yesmaximal, characteristic
5#10591489C212yesmaximal, complemented
6#10591443C212yesmaximal, complemented
7#10591441C212yesmaximal, complemented
8#10590896C211yesmaximal, characteristic, complemented
9#10590818C211yesmaximal, characteristic, complemented
10#10590807C211yesmaximal, characteristic, complemented
11C8×#627C211yesmaximal, characteristic, complemented
12#81813—31nomaximal
13#79579—31nomaximal
14C2×C32×D8C2211yescharacteristic
15#64145C2212yes—
16C2×#3754C2212yes—
17C2×#3746C2211yescharacteristic
18C3×#936C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×#214C2212yes—
21C2×C3×Dic12C2211yescharacteristic
22#63964—22no—
23#63956—22no—
24#63956—22no—
25#63955—22no—
26C4×#627C2211yescharacteristic
27#63866C2212yes—
28#63844C2212yes—
29#63843C2212yes—
30C2×#3719C2212yes—
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#832C2212yes—
33C3×#818C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63572C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63567C2212yes—
40#63565C2212yes—
41#5671—32no—
42#5542—32no—
43C3×#495—31no—
44C3×C4×D8—31no—
45#5183—31no—
46Dic3×Q16—31no—
47#5166—32no—
48#5162—32no—
49#5155—31no—
50#5155—31no—
51#5155—61no—
52#5155D311yescharacteristic
53Dic3×D8D311yescharacteristic
54#5054—32no—
55#5019—32no—
56#4873—31no—
57#4873—31no—
58#4767—32no—
59#4767—32no—
60#4699—31no—
61C4×Dic12—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×C32×D4C2312yes—
65C2×#634C2312yes—
66C22×C3×Dic3—22no—
67C2×C3×Dic6C2312yes—
68C2×#627D411yescharacteristic
69C32×D8—22no—
70C2×C32×C8C2311yescharacteristic
71#3757—22no—
72#3757—22no—
73#3754—42no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3746—22no—
77C3×#217—22no—
78C3×#217—22no—
79C3×#217—22no—
80C3×#214—42no—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3C2311yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×Dic12—22no—
87#3724—22no—
88#3724D411yescharacteristic
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3D411yescharacteristic
93Dic3⋊Dic3D411yescharacteristic
94Dic32—22no—
95Dic32—22no—
96#3719—42no—
97#3393—91noSylow
98C2×C3×Q16—31no—
99C2×C3×SD16—32no—
100C2×C3×D8—21no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C2×D311yescharacteristic
103C3×#124—32no—
104C3×C4×D4—32no—
105Q8×Dic3—32no—
106#944—32no—
107C2×#216—32no—
108#936—32no—
109#936—32no—
110#936—62no—
111#936C2×D312yes—
112D4×Dic3C2×D312yes—
113C2×#214—32no—
114C2×#214—32no—
115C2×#214—62no—
116C2×#214C2×D312yes—
117#926—62no—
118#924—62no—
119C2×Dic12—31no—
120C2×Dic12—31no—
121C2×Dic12—32no—
122C2×Dic12—61no—
123C2×Dic12C2×D311yescharacteristic
124#887—32no—
125#887—32no—
126#879—62no—
127#879—62no—
128#879—62no—
129#879—62no—
130#878—62no—
131#877—62no—
132#869—32no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—32no—
136C3×#107—31no—
137C3×#102—32no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#835—32no—
141#832C2×D312yes—
142#818C2×D311yescharacteristic
143#816—32no—
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#810—32no—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C23×C32—22no—
158C32×D4—22no—
159C32×D4—22no—
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164#634—22no—
165#634—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—44no—
169C2×C3×Dic3C2×D411yescharacteristic
170C2×C3×Dic3C2×D411yescharacteristic
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C3×Dic6—22no—
174C3×Dic6—22no—
175#627—22no—
176C32×C8#4112yes—
177C3⋊(C3⋊C8)—21no—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—31no—
182#495—91no—
183#494—91no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—91no—
188C4×Q16—91no—
189C4×Q16—91no—
190C4×D8—31no—
191C2×C3×Q8—32no—
192C2×C3×D4—22no—
193C2×C3×D4C22×D312yes—
194C2×C3×D4C22×D312yes—
195C22×C3×C4—62no—
196C22×Dic3—22no—
197C2×Dic6—31no—
198C2×Dic6—31no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6C22×D312yes—
203C3×Q16—62no—
204C3×SD16—122no—
205C3×D8—22no—
206C3×D8—22no—
207C3×D8—42no—
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×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C22⋊C4—62no—
217C3×C42—31no—
218C3×C42—31no—
219#217—22no—
220#217—22no—
221#217—22no—
222#217—62no—
223#217—62no—
224#217—62no—
225#217—62no—
226#217—122no—
227#217—122no—
228#216—122no—
229#214—42no—
230#214—122no—
231#214—122no—
232#214—124no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—31no—
240Dic3⋊C4—31no—
241Dic3⋊C4—31no—
242Dic3⋊C4—31no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—61no—
251C4×Dic3—62no—
252C4×Dic3—62no—
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—
263Dic12—62no—
264Dic12—62no—
265Dic12—122no—
266Dic12—122no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C32×C4H(5,𝔽2)11yescharacteristic
273C3⋊Dic3—21no—
274C3⋊Dic3—21no—
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—32no—
286C2×SD16—92no—
287C2×D8D3211yescharacteristic
288C4⋊Q8—92no—
289#126—182no—
290#126—182no—
291#124—32no—
292#124—92no—
293C22⋊Q8—182no—
294C4×Q8—91no—
295C4×Q8—92no—
296C4×Q8—92no—
297C4×D4—32no—
298#117—182no—
299#107—31no—
300C4⋊C8—91no—
301C4⋊C8—91no—
302C4⋊C8—91no—
303#103—92no—
304#103—92no—
305#102—32no—
306C4×C8—31no—
307C4×C8—31no—
308C4×C8—91no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—42no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—42no—
320C2×C3×C4—21no—
321C2×C3×C4—31no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—124no—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—44no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—122no—
342C2×Dic3D3×D411yescharacteristic
343C2×Dic3D3×D411yescharacteristic
344C2×Dic3D3×D411yescharacteristic
345C2×Dic3D3×D411yescharacteristic
346Dic6—22no—
347Dic6—22no—
348Dic6—62no—
349Dic6—62no—
350Dic6—62no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—122no—
355Dic6—122no—
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—82no—
367C2×C32#55011yescharacteristic
368C2×C32C2×#13511yescharacteristic
369C2×C32#57811yescharacteristic
370C2×Q8—32no—
371C2×Q8—91no—
372C2×Q8—92no—
373C2×D4C2×D3212yes—
374C22×C4—62no—
375Q16—62no—
376Q16—182no—
377Q16—362no—
378SD16—122no—
379SD16—362no—
380D8—22no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8—91no—
384C2×C8C2×D3211yescharacteristic
385C4⋊C4—32no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—91no—
389C4⋊C4—182no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C22⋊C4—62no—
394C22⋊C4—62no—
395C22⋊C4—62no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C42—31no—
399C42—31no—
400C42—91no—
401C42—182no—
402C42—182no—
403C22×C3—21no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—32no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4C2×#23511yescharacteristic
424C3×C4C2×#23711yescharacteristic
425C3×C4#100411yescharacteristic
426C3×C4#100911yescharacteristic
427Dic3—21no—
428Dic3—21no—
429Dic3—21no—
430Dic3—42no—
431Dic3—42no—
432Dic3—61no—
433Dic3—61no—
434Dic3—61no—
435Dic3—61no—
436Dic3—121no—
437Dic3—121no—
438Dic3—122no—
439Dic3—122no—
440Dic3—242no—
441Dic3#91212yes—
442C32#339311yescharacteristic, complemented, Sylow
443C23—22no—
444Q8—62no—
445Q8—62no—
446Q8—182no—
447Q8—182no—
448Q8—182no—
449D4—22no—
450D4—22no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—124no—
460C2×C4—182no—
461C2×C4C22×D3211yescharacteristic
462C8—61no—
463C8—61no—
464C8—181no—
465C8#380412yes—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—82no—
470C2×C3—82no—
471C2×C3—162no—
472C2×C3#555311yescharacteristic
473C2×C3#571811yescharacteristic
474C2×C3C2×#91211yescharacteristic
475C2×C3D3×#13511yescharacteristic
476C2×C3#577111yescharacteristic
477C2×C3#577111yescharacteristic
478C22—42no—
479C22—42no—
480C22—42no—
481C22D32×D411yescharacteristic
482C4—32no—
483C4—61no—
484C4—61no—
485C4—61no—
486C4—122no—
487C4—122no—
488C4—181no—
489C4—181no—
490C4—362no—
491C4#6431411yescharacteristic
492C4C2×#380411yescharacteristic
493C3—21no—
494C3#7957911yescharacteristic, complemented
495C3#8181311yescharacteristic, complemented
496C2—82no—
497C2D3×#91211yescharacteristic
498C2#1059473711yescharacteristic
499C2#1059514311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595273C2semidirect
5. #10591489C2semidirect
6. #10591443C2semidirect
7. #10591441C2semidirect
8. #10590896C2semidirect
9. #10590818C2semidirect
10. #10590807C2semidirect
11. C8×#627C2semidirect
442. C32#3393semidirect
494. C3#79579semidirect
495. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105952732
#105928542
C3×#51552
C3×Dic3×D82
#105914892
#105914432
#105914412
#105908962
#105908182
#105908072
C8×#6272
#818133
#795793