Finite Group Databasebeta

← #11860965

Subgroups — #11860965

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2#10594990C212yesmaximal, complemented
3C2×C3×#817C211yesmaximal, characteristic, complemented
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591106C212yesmaximal, complemented
6#10590810C212yesmaximal, complemented
7#10590768C212yesmaximal, complemented
8#10590758C214yesmaximal, complemented
9#79106—31nomaximal
10#78574—31nomaximal
11C2×#3828C2212yes—
12C22×C32×C8C2211yescharacteristic
13C2×#3746C2211yescharacteristic
14#64113C418yescomplemented
15C2×#3745C2211yescharacteristic
16C2×#3744C2212yes—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×#208C2211yescharacteristic
20#63952—24no—
21#63900—22no—
22#63894C2214yes—
23#63849—22no—
24#63844C2214yes—
25C3×#817C2212yes—
26C3×#817C2212yes—
27C3×#815C2212yes—
28C3×C8×Dic3C2212yes—
29#63567C2214yes—
30#63564C2214yes—
31C2×#904—31no—
32C2×#904—31no—
33C2×#904—61no—
34#5523—32no—
35#5504—32no—
36C2×C3×#106—31no—
37C3×#405—31no—
38#5133—32no—
39C2×#817D311yescharacteristic, complemented
40#5101D311yescharacteristic, complemented
41#4966—32no—
42#4869—32no—
43#4853—32no—
44#4852—34no—
45#4716—32no—
46#4711—32no—
47C4×#204—34no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—22no—
50#3828—24no—
51#3828C2×C418yescomplemented
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×#634C2312yes—
55C22×C3×Dic3—22no—
56C2×#624—24no—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3746C2×C414yescomplemented
61#3745C2×C414yescomplemented
62#3744C2×C418yescomplemented
63C3×#217D412yes—
64C3×C4⋊Dic3—22no—
65C3×C4⋊Dic3D412yes—
66C3×C4⋊Dic3C2314yes—
67C3×C4×Dic3C2312yes—
68C3×#208—22no—
69C2×C3×C3⋊C8C2312yes—
70#3724—24no—
71#3722—24no—
72Dic32—24no—
73#2952—91noSylow
74C2×#235—32no—
75C2×#235—32no—
76C2×#235—62no—
77C2×C3×M16—31no—
78C22×C3×C8—21no—
79C22×C3×C8C2×D311yescharacteristic
80C22×C3×C8C2×D311yescharacteristic
81C3×#117—31no—
82C2×C3×C4⋊C4—32no—
83C4×#67—64no—
84#926C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D312yes—
86C2×#208C2×D311yescharacteristic
87C2×Dic12—31no—
88C2×Dic12—31no—
89C2×Dic12—61no—
90#904—38no—
91#904—38no—
92#904—68no—
93C2×D24—31no—
94C2×D24—31no—
95C2×D24—61no—
96C2×#204—32no—
97C2×#204—32no—
98C2×#204—62no—
99#893—34no—
100#892—62no—
101#892—62no—
102D3×C4⋊C4—62no—
103D3×C4⋊C4—62no—
104#887—34no—
105#67⋊C4—64no—
106C4×D12—34no—
107C4×Dic6—34no—
108C3×#106—32no—
109C3×#106—32no—
110C3×#97—32no—
111C3×C4×C8—32no—
112#821—34no—
113#817C2×D312yes—
114#817C2×D312yes—
115#816—34no—
116#815C2×D312yes—
117C8×Dic3C2×D312yes—
118#810—34no—
119#809—34no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4112yes—
125C2×C32×C4C2411yescharacteristic
126#638—28no—
127C2×C3⋊Dic3—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)C22×C414yes—
130C4×C3⋊D3—28no—
131#634—22no—
132#634C22×C414yes—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—82no—
135C2×C3×Dic3C2×D414yes—
136#624—84no—
137C32×C8C22×C412yes—
138C32×C8C22×C412yes—
139C3×C3⋊C8—22no—
140C2×#135—91no—
141#520—92no—
142#442—92no—
143#441—92no—
144C4×SD16—94no—
145C2×#106—31no—
146#417—92no—
147#405—31no—
148C22×C3×C4—21no—
149C22×C3×C4—62no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—122no—
155C22×Dic3—22no—
156#235—38no—
157#235—38no—
158#235—68no—
159#235—64no—
160#235—64no—
161#235—124no—
162C2×D12—32no—
163C2×D12—32no—
164C2×D12—62no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×C4×D3—122no—
170C2×Dic6—32no—
171C2×Dic6—32no—
172C2×Dic6—62no—
173C3×M16—62no—
174C2×C3×C8—24no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—32no—
178C2×C3×C8C4×D314yescomplemented
179C2×C3×C8C4×D314yescomplemented
180C2×C3×C8C22×D311yescharacteristic
181C2×C3×C8C22×D311yescharacteristic
182C2×C3×C8C22×D311yescharacteristic
183C2×C3×C8C22×D311yescharacteristic
184C3×C4⋊C4—32no—
185C3×C4⋊C4—34no—
186C3×C4⋊C4—62no—
187C3×C22⋊C4—32no—
188C3×C42—32no—
189#217D1212yes—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192C4⋊Dic3—22no—
193C4⋊Dic3D1212yes—
194C4⋊Dic3C22×D314yes—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3C22×D312yes—
200#208—22no—
201C2×C3⋊C8C22×D312yes—
202Dic12—34no—
203Dic12—34no—
204Dic12—64no—
205D24—34no—
206D24—34no—
207D24—64no—
208#204—38no—
209#204—38no—
210#204—68no—
211C22×C32—22no—
212C22×C32C4×D412yes—
213C22×C32C22×D411yescharacteristic
214C2×C3⋊D3—24no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—42no—
217C32×C4C4×D412yes—
218C32×C4C23×C411yescharacteristic
219C32×C4C2×#4111yescharacteristic
220C3⋊Dic3—24no—
221C3×Dic3—24no—
222C3×Dic3—44no—
223C2×#41—92no—
224#135—98no—
225C2×Q16—91no—
226C2×SD16—92no—
227C2×D8—91no—
228C2×M16—31no—
229C22×C8D3211yescharacteristic
230C4×Q8—94no—
231C4×D4—94no—
232C4×D4—184no—
233#117—31no—
234#117—182no—
235C2×C4⋊C4—32no—
236C2×C4⋊C4—182no—
237#106—32no—
238#106—32no—
239#103—94no—
240#102—94no—
241#97—32no—
242C4×C8—32no—
243C23×C3—21no—
244C23×C3C2×D1211yescharacteristic
245C23×C3D3×D411yescharacteristic
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C2×C3×C4—21no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—34no—
254C2×C3×C4—64no—
255C2×C3×C4—242no—
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4C2×C4×D312yes—
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4#23512yes—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4#23912yes—
262C2×C3×C4C23×D311yescharacteristic
263C2×C3×C4C23×D311yescharacteristic
264#67—68no—
265#67—68no—
266#67—128no—
267C2×Dic3—24no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—82no—
271C2×Dic3—122no—
272C2×Dic3C2×D1214yes—
273D12—34no—
274D12—34no—
275D12—64no—
276D12—62no—
277D12—62no—
278D12—122no—
279C4×D3—68no—
280C4×D3—68no—
281C4×D3—128no—
282C4×D3—244no—
283C4×D3—244no—
284Dic6—34no—
285Dic6—34no—
286Dic6—64no—
287Dic6—62no—
288Dic6—62no—
289Dic6—122no—
290C3×C8—22no—
291C3×C8—22no—
292C3×C8—62no—
293C3×C8C2×C4×D312yes—
294C3×C8C2×C4×D312yes—
295C3×C8C2×C4×D312yes—
296C3×C8C2×C4×D312yes—
297C3⋊C8—22no—
298C2×C32—22no—
299C2×C32C2×C4×D411yescharacteristic
300C2×C32#57712yes—
301C3⋊D3—44no—
302#41—98no—
303#41—184no—
304C2×Q8—92no—
305C2×D4—92no—
306C2×D4—182no—
307C22×C4—62no—
308C22×C4—184no—
309C22×C4—182no—
310C22×C4C2×D3211yescharacteristic
311Q16—94no—
312SD16—98no—
313D8—94no—
314M16—62no—
315C2×C8—32no—
316C2×C8#62414yescomplemented
317C2×C8C2×D3211yescharacteristic
318C2×C8C2×D3211yescharacteristic
319C4⋊C4—32no—
320C4⋊C4—34no—
321C4⋊C4—62no—
322C4⋊C4—184no—
323C22⋊C4—32no—
324C22⋊C4—184no—
325C42—32no—
326C42—184no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—42no—
332C22×C3C4×D1212yes—
333C22×C3#89312yes—
334C22×C3C22×D1211yescharacteristic
335C22×C3C2×D3×D411yescharacteristic
336C2×D3—64no—
337C2×D3—64no—
338C2×D3—124no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—122no—
342C2×D3—122no—
343C2×D3—242no—
344C2×D3—242no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—22no—
348C3×C4—64no—
349C3×C4—124no—
350C3×C4C4×D1212yes—
351C3×C4#89312yes—
352C3×C4C22×C4×D311yescharacteristic
353C3×C4C22×C4×D311yescharacteristic
354C3×C4C2×#23511yescharacteristic
355C3×C4C2×#23911yescharacteristic
356Dic3—24no—
357Dic3—44no—
358Dic3—64no—
359Dic3—64no—
360Dic3—124no—
361C32#295211yescharacteristic, complemented, Sylow
362C23—182no—
363C23D3×D1211yescharacteristic
364Q8—94no—
365Q8—182no—
366D4—94no—
367D4—188no—
368D4—182no—
369C2×C4—34no—
370C2×C4—64no—
371C2×C4—182no—
372C2×C4—188no—
373C2×C4—242no—
374C2×C4—724no—
375C2×C4#379912yes—
376C2×C4D3×D1211yescharacteristic
377C2×C4C2×#62412yes—
378C2×C4C22×D3211yescharacteristic
379C8—62no—
380C8C2×#62412yes—
381C8C2×#62412yes—
382C2×C3—22no—
383C2×C3—22no—
384C2×C3—21no—
385C2×C3—22no—
386C2×C3—42no—
387C2×C3C2×C4×D1211yescharacteristic
388C2×C3C2×#89311yescharacteristic
389C2×C3#575112yes—
390C2×C3#576212yes—
391D3—124no—
392D3—124no—
393D3—244no—
394C22—22no—
395C22—184no—
396C22—362no—
397C22—362no—
398C22#6389412yes—
399C22C2×D3×D1211yescharacteristic
400C4—64no—
401C4—124no—
402C4—184no—
403C4#6389412yes—
404C4C2×#379911yescharacteristic
405C4C22×#62411yescharacteristic
406C3—21no—
407C3#7857411yescharacteristic, complemented
408C3#7910611yescharacteristic, complemented
409C2—22no—
410C2—364no—
411C2#1059467712yes—
412C2C2×#6389411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#64113C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594990C2semidirect
3. C2×C3×#817C2semidirect
4. C3×#5101C2semidirect
5. #10591106C2semidirect
6. #10590810C2semidirect
7. #10590768C2semidirect
8. #10590758C2semidirect
14. #64113C4semidirect
39. C2×#817D3semidirect
40. #5101D3semidirect
51. #3828C2×C4semidirect
57. C2×C32×C8C2×C4semidirect
60. #3746C2×C4semidirect
61. #3745C2×C4semidirect
62. #3744C2×C4semidirect
178. C2×C3×C8C4×D3semidirect
179. C2×C3×C8C4×D3semidirect
316. C2×C8#624semidirect
361. C32#2952semidirect
407. C3#78574semidirect
408. C3#79106semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105949902
C2×C3×#8172
C3×#51012
#105911062
#105908102
#105907682
#105907582
#791063
#785743