Finite Group Databasebeta

← #11867762

Subgroups — #11867762

Order 1152.

1416 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic, complemented
2C2×#64116C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4#10595981C211yesmaximal, characteristic
5C32×#428C211yesmaximal, characteristic, complemented
6#10592701C211yesmaximal, characteristic, complemented
7C2×#63637C211yesmaximal, characteristic, complemented
8#10592586C212yesmaximal, complemented
9#10592585C212yesmaximal, complemented
10#10592566C212yesmaximal, complemented
11#10592563C212yesmaximal, complemented
12#79214—34nomaximal
13C2×#3828C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19#64139—22no—
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#64118—24no—
22#64116—24no—
23C2×#3746C2212yes—
24C2×#3744C2212yes—
25C2×#3743C2212yes—
26C2×C8×C3⋊D3C2212yes—
27#64106—21no—
28#64106C2212yes—
29#64106C2212yes—
30#64106C2212yes—
31#64104—21no—
32#64104C2212yes—
33#64095—22no—
34#64084—21no—
35#64078—21no—
36C32×#107C2212yes—
37C32×#106C2212yes—
38#63637C2212yes—
39#63637C2211yescharacteristic
40#63637C2212yes—
41#63637C2211yescharacteristic
42#63636C2211yescharacteristic
43#63636C2211yescharacteristic
44C2×#909—34no—
45C2×#907—34no—
46#5526—34no—
47#5510—34no—
48C3×#428D314yescomplemented
49#5002—34no—
50C2×#810—34no—
51#4887—38no—
52#4886—38no—
53#4867—38no—
54#4864—38no—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58C2×#638D412yes—
59C22×C3⋊Dic3—21no—
60#3828—22no—
61#3828—22no—
62#3828—22no—
63#3828—22no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)D411yescharacteristic
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3C2312yes—
69C2×#634—22no—
70C2×#634—22no—
71C2×#634—21no—
72C2×#634D411yescharacteristic
73C2×#634C2312yes—
74C2×#634C2311yescharacteristic
75C32×M16D414yescomplemented
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42—21no—
83#3752—22no—
84#3752—22no—
85#3752—22no—
86#3752—22no—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)—22no—
89C4⋊(C3⋊Dic3)—22no—
90C2×C3⋊(C3⋊C8)—22no—
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93#3746—24no—
94#3744—24no—
95#3743—24no—
96C8×C3⋊D3—24no—
97#3063—91noSylow
98C2×#235—34no—
99C2×#235—34no—
100C22×Dic6—34no—
101C2×C3×M16C2×D314yes—
102C3×#117C2×D314yes—
103C2×C3×C4⋊C4C2×D314yes—
104#930—68no—
105C22×C3⋊C8—34no—
106#909—616no—
107#907—616no—
108C2×Dic12—38no—
109C2×#204—38no—
110C2×ΓL(1,𝔽25)—38no—
111C2×D3×C8—38no—
112#897—38no—
113#897—38no—
114#897—38no—
115#897—64no—
116#895—38no—
117#895—64no—
118#886—68no—
119#875—64no—
120#869—64no—
121C3×#107C2×D318yes—
122C3×#106C2×D318yes—
123#810—38no—
124#810—34no—
125#810—38no—
126#810—34no—
127#809—34no—
128#809—34no—
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3C2×D412yes—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4—81no—
136C2×C32×C4C2×D412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140#638—24no—
141#638—42no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3C2×D412yes—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—82no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—42no—
153#634—22no—
154#634—22no—
155#634—21no—
156#634—22no—
157#634—21no—
158#634—42no—
159C32×C8C2×D414yes—
160C3⋊(C3⋊C8)—21no—
161C3⋊(C3⋊C8)—21no—
162C2×#137—91no—
163C2×#131—91no—
164#537—91no—
165#536—91no—
166#470—92no—
167#468—92no—
168#467—92no—
169#465—92no—
170#428C3⋊D311yescharacteristic, complemented
171#416—91no—
172C2×#103—91no—
173C22×C3×C4—24no—
174C22×C3×C4C22×D314yes—
175C2×#67—38no—
176C2×#67—64no—
177C22×Dic3—64no—
178#235—68no—
179#235—68no—
180#235—68no—
181#235—68no—
182C2×D12—34no—
183C2×D12—34no—
184C2×D12—68no—
185C2×C4×D3—38no—
186C2×C4×D3—64no—
187C2×Dic6—34no—
188C2×Dic6—38no—
189C2×Dic6—34no—
190C2×Dic6—68no—
191C2×Dic6—68no—
192C2×Dic6—64no—
193C3×M16D12116yescomplemented
194C2×C3×C8C22×D318yes—
195C3×C4⋊C4—24no—
196C3×C4⋊C4C22×D314yes—
197C3×C4⋊C4C22×D314yes—
198C3×C4⋊C4C22×D318yes—
199C3×C22⋊C4—24no—
200C3×C42—24no—
201(C2×D3)⋊C4—68no—
202(C2×D3)⋊C4—68no—
203(C2×D3)⋊C4—68no—
204(C2×D3)⋊C4—68no—
205C4⋊Dic3—68no—
206C4⋊Dic3—68no—
207C4⋊Dic3—68no—
208C2×C3⋊C8—34no—
209C2×C3⋊C8—34no—
210C2×C3⋊C8—68no—
211Dic12—616no—
212#204—616no—
213ΓL(1,𝔽25)—616no—
214D3×C8—616no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32#12112yes—
218C22×C32C22×D411yescharacteristic
219C2×C3⋊D3—22no—
220C2×C3⋊D3—22no—
221C2×C3⋊D3—22no—
222C2×C3⋊D3—41no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C32×C4—42no—
226C32×C4—41no—
227C32×C4—41no—
228C32×C4#12112yes—
229C32×C4C22×D411yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—22no—
232C3⋊Dic3—42no—
233C3⋊Dic3—41no—
234C2×#41—91no—
235C2×#41—91no—
236C22×Q8—91no—
237#137—184no—
238C2×Q16—92no—
239C2×SD16—92no—
240#131—184no—
241C2×M16—92no—
242C2×M16C2×C3⋊D311yescharacteristic
243C22×C8—91no—
244C22×C8—92no—
245C4⋊Q8—181no—
246#124—181no—
247#123—182no—
248C22⋊Q8—92no—
249C22⋊Q8—92no—
250C22⋊Q8—92no—
251C22⋊Q8—181no—
252#121—92no—
253#121—181no—
254#121—182no—
255#117C2×C3⋊D311yescharacteristic
256C2×C4⋊C4C2×C3⋊D311yescharacteristic
257#107C2×C3⋊D312yes—
258#106C2×C3⋊D312yes—
259#103—92no—
260#103—92no—
261#103—91no—
262#103—91no—
263#102—91no—
264#102—91no—
265C23×C3D3×D414yes—
266C22×D3—38no—
267C22×D3—64no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—28no—
271C2×C3×C4—84no—
272C2×C3×C4C2×D1218yes—
273C2×C3×C4D3×D414yes—
274C2×C3×C4#23918yes—
275C2×C3×C4C23×D314yes—
276#67—616no—
277#67—128no—
278C2×Dic3—38no—
279C2×Dic3—68no—
280C2×Dic3—64no—
281C2×Dic3—128no—
282D12—68no—
283D12—64no—
284D12—64no—
285D12—248no—
286C4×D3—68no—
287C4×D3—68no—
288C4×D3—128no—
289Dic6—68no—
290Dic6—68no—
291Dic6—64no—
292Dic6—68no—
293Dic6—64no—
294Dic6—128no—
295C3×C8C2×D12116yes—
296C3⋊C8—64no—
297C3⋊C8—64no—
298C2×C32—22no—
299C2×C32C2×#12111yescharacteristic
300C2×C32#57711yescharacteristic
301C2×C32#57811yescharacteristic
302C3⋊D3—42no—
303C3⋊D3—81no—
304#41—182no—
305#41—182no—
306#41—182no—
307#41—182no—
308C2×Q8—91no—
309C2×Q8—92no—
310C2×Q8—91no—
311C2×Q8—181no—
312C2×Q8—182no—
313C2×Q8—182no—
314C2×D4—92no—
315C2×D4—91no—
316C2×D4—91no—
317C2×D4—182no—
318C2×D4—181no—
319C22×C4—21no—
320C22×C4—92no—
321C22×C4—181no—
322C22×C4—181no—
323C22×C4C22×C3⋊D311yescharacteristic
324Q16—184no—
325SD16—184no—
326M16—184no—
327M16C4⋊(C3⋊D3)14yescomplemented
328C2×C8—91no—
329C2×C8—91no—
330C2×C8—182no—
331C2×C8—184no—
332C2×C8C22×C3⋊D312yes—
333C4⋊C4—21no—
334C4⋊C4—182no—
335C4⋊C4—182no—
336C4⋊C4—182no—
337C4⋊C4C22×C3⋊D311yescharacteristic
338C4⋊C4C22×C3⋊D311yescharacteristic
339C4⋊C4C22×C3⋊D312yes—
340C22⋊C4—21no—
341C22⋊C4—182no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C42—21no—
346C22×C3—24no—
347C22×C3—24no—
348C22×C3#89518yes—
349C22×C3C2×D3×D414yes—
350C2×D3—68no—
351C2×D3—68no—
352C2×D3—68no—
353C2×D3—124no—
354C2×D3—124no—
355C2×D3—124no—
356C3×C4—48no—
357C3×C4—44no—
358C3×C4—44no—
359C3×C4#89518yes—
360C3×C4C22×D1214yes—
361C3×C4C2×#23914yes—
362Dic3—68no—
363Dic3—128no—
364Dic3—124no—
365C32#306311yescharacteristic, complemented, Sylow
366C23—92no—
367C23—181no—
368C23D4×C3⋊D311yescharacteristic
369Q8—182no—
370Q8—182no—
371Q8—181no—
372Q8—182no—
373Q8—181no—
374Q8—362no—
375D4—184no—
376D4—181no—
377D4—182no—
378D4—181no—
379D4—362no—
380D4—722no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—81no—
385C2×C4—92no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—181no—
389C2×C4—182no—
390C2×C4—362no—
391C2×C4—362no—
392C2×C4C2×C4⋊(C3⋊D3)12yes—
393C2×C4D4×C3⋊D311yescharacteristic
394C2×C4#383212yes—
395C2×C4C23×C3⋊D311yescharacteristic
396C8—181no—
397C8—181no—
398C8C2×C4⋊(C3⋊D3)14yes—
399C2×C3—28no—
400C2×C3C2×#89514yes—
401C2×C3#577514yes—
402C2×C3#577914yes—
403D3—128no—
404D3—244no—
405C22—21no—
406C22—21no—
407C22—182no—
408C22—182no—
409C22—182no—
410C22—361no—
411C22—361no—
412C22—361no—
413C22#6410412yes—
414C22C2×D4×C3⋊D311yescharacteristic
415C4—42no—
416C4—41no—
417C4—41no—
418C4—182no—
419C4—361no—
420C4—362no—
421C4#6410412yes—
422C4C22×C4⋊(C3⋊D3)11yescharacteristic
423C4C2×#383211yescharacteristic
424C3#7921414yescomplemented
425C2—22no—
426C2—362no—
427C2—721no—
428C2C2×#6410411yescharacteristic
429C2#1059624611yescharacteristic
430C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radical#10595981C2
hypercenter#428C3⋊D3
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#64118C2semidirect
2. C2×#64116C2semidirect
3. #10595997C2semidirect
5. C32×#428C2semidirect
6. #10592701C2semidirect
7. C2×#63637C2semidirect
8. #10592586C2semidirect
9. #10592585C2semidirect
10. #10592566C2semidirect
11. #10592563C2semidirect
48. C3×#428D3semidirect
75. C32×M16D4semidirect
170. #428C3⋊D3semidirect
193. C3×M16D12semidirect
327. M16C4⋊(C3⋊D3)semidirect
365. C32#3063semidirect
424. C3#79214semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
C2×#641162
#105959972
#105959812
C32×#4282
#105927012
C2×#636372
#105925862
#105925852
#105925662
#105925632
#792143