Finite Group Databasebeta

← #11898394

Subgroups — #11898394

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595389C212yesmaximal, complemented
2#10592882C211yesmaximal, characteristic, complemented
3C3×#5191C211yesmaximal, characteristic
4C3×Dic3×Q16C211yesmaximal, characteristic, complemented
5#10591604C212yesmaximal, complemented
6#10591577C212yesmaximal, complemented
7#10591569C212yesmaximal, complemented
8#10590864C211yesmaximal, characteristic
9#10590807C211yesmaximal, characteristic, complemented
10C8×#627C211yesmaximal, characteristic, complemented
11#10590777C211yesmaximal, characteristic
12#81813—31nomaximal
13#79710—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64153C2212yes—
16C2×#3756C2212yes—
17C2×#3746C2211yescharacteristic
18C3×#947C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2212yes—
21C2×C3×D24C2211yescharacteristic
22C4×#627C2211yescharacteristic
23#63899—22no—
24#63898C2212yes—
25#63877—22no—
26#63860C2212yes—
27#63859—22no—
28#63858—22no—
29#63844C2212yes—
30C2×#3716C2212yes—
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#835C2212yes—
33C3×#818C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63572C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63567C2212yes—
40#63562C2212yes—
41#5671—32no—
42#5568—32no—
43C3×#495—31no—
44C3×C4×Q16—31no—
45#5191D311yescharacteristic
46#5183—31no—
47#5183—31no—
48#5183—61no—
49Dic3×Q16D311yescharacteristic, complemented
50#5166—32no—
51#5162—32no—
52#5155—31no—
53Dic3×D8—31no—
54#5054—32no—
55#5028—32no—
56#4873—31no—
57#4872—31no—
58#4818—32no—
59#4798—32no—
60C4×Dic12—31no—
61#4696—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×C32×Q8C2312yes—
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×#627D411yescharacteristic
68C2×D3×Dic3—22no—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71#3756—42no—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3746—22no—
77C3×#215—42no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×D24—22no—
88#3724—22no—
89#3724D411yescharacteristic
90Dic3⋊Dic3D411yescharacteristic
91Dic3⋊Dic3D411yescharacteristic
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3716—42no—
97#3393—91noSylow
98C2×C3×Q16—21no—
99C2×C3×Q16C2×D311yescharacteristic
100C2×C3×Q16C2×D311yescharacteristic
101C2×C3×SD16—32no—
102C2×C3×D8—31no—
103C3×#124—32no—
104C3×C4×Q8—32no—
105#947C2×D312yes—
106Q8×Dic3C2×D312yes—
107#944—32no—
108#944—32no—
109#944—62no—
110C2×#216—32no—
111C2×#216—32no—
112C2×#216—62no—
113C2×#215C2×D312yes—
114#936—32no—
115D4×Dic3—32no—
116C2×#214—32no—
117C2×Dic12—31no—
118C2×Dic12—31no—
119C2×Dic12—61no—
120C2×D24C2×D311yescharacteristic
121C2×#204—32no—
122#898—62no—
123#896—62no—
124#893—32no—
125#887—32no—
126#879—62no—
127#879—62no—
128#878—62no—
129#877—62no—
130#876—62no—
131#875—32no—
132#872—62no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—32no—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#835C2×D312yes—
141#832—32no—
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#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⋊Dic3—22no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2×D411yescharacteristic
165#634—22no—
166#634—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D411yescharacteristic
170C2×C3×Dic3C2×D411yescharacteristic
171C2×C3×Dic3C2×D411yescharacteristic
172C3×D12—22no—
173C3×D12—22no—
174#627—22no—
175D3×Dic3—44no—
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—31no—
189C4×Q16—91no—
190C4×D8—91no—
191C2×C3×Q8—22no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—32no—
195C22×Dic3—62no—
196C2×D12C22×D312yes—
197C2×C4×D3—62no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—32no—
201C2×Dic6—32no—
202C2×Dic6—62no—
203C3×Q16—22no—
204C3×Q16—22no—
205C3×Q16—42no—
206C3×SD16—122no—
207C3×D8—62no—
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×C22⋊C4—62no—
216C3×C22⋊C4—62no—
217C3×C42—31no—
218C3×C42—31no—
219C3×C42—62no—
220#217—62no—
221#217—62no—
222#217—62no—
223#216—122no—
224#216—122no—
225#216—124no—
226#215—42no—
227#214—122no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—22no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—22no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—31no—
238Dic3⋊C4—31no—
239Dic3⋊C4—31no—
240Dic3⋊C4—31no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—122no—
248Dic3⋊C4—122no—
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—62no—
263Dic12—62no—
264Dic12—122no—
265D24—22no—
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—42no—
276C3⋊Dic3#13512yes—
277C3×Dic3—21no—
278C3×Dic3—21no—
279C3×Dic3—21no—
280C3×Dic3—21no—
281C3×Dic3—42no—
282C2×Q16—92no—
283C2×Q16—91no—
284C2×Q16D3211yescharacteristic
285C2×SD16—32no—
286C2×SD16—92no—
287C2×D8—31no—
288C4⋊Q8—92no—
289#126—182no—
290#126—182no—
291#124—32no—
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—
309C23×C3—62no—
310C22×D3—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—42no—
316C3×Q8—42no—
317C3×D4—62no—
318C3×D4—62no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—31no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—122no—
340C2×Dic3—124no—
341C2×Dic3D3×D411yescharacteristic
342C2×Dic3D3×D411yescharacteristic
343C2×Dic3D3×D411yescharacteristic
344C2×Dic3D3×D411yescharacteristic
345D12—22no—
346D12—22no—
347C4×D3—124no—
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#55011yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32#57811yescharacteristic
369C3×D3—82no—
370C2×Q8—91no—
371C2×Q8—92no—
372C2×Q8C2×D3212yes—
373C2×D4—32no—
374C22×C4—182no—
375Q16—22no—
376Q16—182no—
377Q16—362no—
378SD16—122no—
379SD16—362no—
380D8—62no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8—91no—
384C2×C8C2×D3211yescharacteristic
385C4⋊C4—32no—
386C4⋊C4—62no—
387C4⋊C4—91no—
388C4⋊C4—91no—
389C4⋊C4—91no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C22⋊C4—62no—
394C22⋊C4—62no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C42—31no—
399C42—31no—
400C42—62no—
401C42—91no—
402C42—182no—
403C22×C3—21no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3C2×D3×D411yescharacteristic
408C22×C3C2×D3×D411yescharacteristic
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—42no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—82no—
421C3×C4—122no—
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×#23711yescharacteristic
424C3×C4#100411yescharacteristic
425C3×C4#100911yescharacteristic
426Dic3—21no—
427Dic3—21no—
428Dic3—21no—
429Dic3—21no—
430Dic3—32no—
431Dic3—32no—
432Dic3—42no—
433Dic3—62no—
434Dic3—62no—
435Dic3—61no—
436Dic3—61no—
437Dic3—122no—
438Dic3—122no—
439Dic3—242no—
440C32#339311yescharacteristic, complemented, Sylow
441C23—62no—
442Q8—22no—
443Q8—22no—
444Q8—182no—
445Q8—182no—
446Q8—182no—
447D4—62no—
448D4—62no—
449C2×C4—22no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—62no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—182no—
458C2×C4—364no—
459C2×C4C22×D3211yescharacteristic
460C8—61no—
461C8—61no—
462C8—181no—
463C8#380412yes—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—242no—
468C2×C3#555311yescharacteristic
469C2×C3#571811yescharacteristic
470C2×C3#576611yescharacteristic
471C2×C3D3×#13511yescharacteristic
472C2×C3D3×#13511yescharacteristic
473C2×C3#577111yescharacteristic
474D3—82no—
475C22—122no—
476C22—122no—
477C22—122no—
478C22D32×D411yescharacteristic
479C4—42no—
480C4—61no—
481C4—61no—
482C4—61no—
483C4—61no—
484C4—92no—
485C4—122no—
486C4—181no—
487C4—362no—
488C4#6431411yescharacteristic
489C4C2×#380411yescharacteristic
490C3—21no—
491C3#7971011yescharacteristic, complemented
492C3#8181311yescharacteristic, complemented
493C2—242no—
494C2#1059476411yescharacteristic
495C2#1059476811yescharacteristic
496C2#1059514311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
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. #10595389C2semidirect
2. #10592882C2semidirect
4. C3×Dic3×Q16C2semidirect
5. #10591604C2semidirect
6. #10591577C2semidirect
7. #10591569C2semidirect
9. #10590807C2semidirect
10. C8×#627C2semidirect
49. Dic3×Q16D3semidirect
440. C32#3393semidirect
491. C3#79710semidirect
492. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105953892
#105928822
C3×#51912
C3×Dic3×Q162
#105916042
#105915772
#105915692
#105908642
#105908072
C8×#6272
#105907772
#818133
#797103