Finite Group Databasebeta

← #11786587

Subgroups — #11786587

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4#10591130C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#70068—31nomaximal
7#69642—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C2×#3757—22no—
10D4×C3⋊Dic3—22no—
11D4×C3⋊Dic3—22no—
12#64135C2212yes—
13C2×C3×#217—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2212yes—
17C3×#833C414yescomplemented
18#63575—22no—
19#63573—22no—
20#5798—31no—
21#5798—31no—
22#5798—61no—
23C2×C3×#100—31no—
24C3×#390—31no—
25#5221D311yescharacteristic
26C2×#833D311yescharacteristic
27#5121—32no—
28#4964—32no—
29#4555—32no—
30#4523—32no—
31C24×C32D412yes—
32C2×C32×D4—22no—
33C2×C32×D4—22no—
34C2×C32×D4C2×C412yes—
35C2×C32×D4Q812yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41#3757—24no—
42#3757—22no—
43C4⋊(C3⋊Dic3)D412yes—
44C4⋊(C3⋊Dic3)D412yes—
45C4×C3⋊Dic3—22no—
46C3×#217—44no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—22no—
49C3×#208—22no—
50C3×#208C2×C414yescomplemented
51C2×C3×C3⋊C8—22no—
52#1856—91noSylow
53C22×C3×D4—21no—
54C22×C3×D4C2×D311yescharacteristic
55C22×C3×D4C2×D311yescharacteristic
56C2×C3×M16—32no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C22⋊C4—62no—
59C2×C3×C42—31no—
60C2×#217—22no—
61C2×#217—64no—
62C2×#217—62no—
63C2×#217—62no—
64D4×Dic3—62no—
65D4×Dic3—62no—
66D4×Dic3—62no—
67D4×Dic3—62no—
68D4×Dic3—64no—
69D4×Dic3—64no—
70#926—32no—
71#926—32no—
72#926—62no—
73C2×C4⋊Dic3C2×D311yescharacteristic
74C2×C4×Dic3C2×D311yescharacteristic
75C2×#208C2×D312yes—
76C3×#100—34no—
77#833Dic314yescomplemented
78#818—62no—
79#817—62no—
80#808—62no—
81#807—62no—
82C23×C32—22no—
83C23×C32—22no—
84C23×C32—42no—
85C23×C32—42no—
86C23×C32C4⋊C414yes—
87C23×C32C2×D411yescharacteristic
88C32×D4—24no—
89C32×D4—24no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D412yes—
92C2×C32×C4C2×Q811yescharacteristic
93C2×C32×C4#4112yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—82no—
97C2×C3⋊Dic3—82no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—41no—
103C3×C3⋊C8—24no—
104#518—91no—
105#428—92no—
106C2×#100—31no—
107#390—31no—
108#339—92no—
109C24×C3—22no—
110C24×C3D1212yes—
111C24×C3#6712yes—
112C2×C3×D4—24no—
113C2×C3×D4—24no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4Dic612yes—
121C2×C3×D4Dic612yes—
122C2×C3×D4C4×D312yes—
123C2×C3×D4C2×Dic312yes—
124C22×C3×C4—21no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—21no—
130C22×Dic3—21no—
131C22×Dic3—64no—
132C22×Dic3—64no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C3×M16—34no—
138C3×M16—62no—
139C2×C3×C8—62no—
140C3×C4⋊C4—62no—
141C3×C22⋊C4—124no—
142C3×C42—62no—
143#217—44no—
144#217—64no—
145#217—68no—
146#217—64no—
147#217—64no—
148#217—62no—
149#217—62no—
150C4⋊Dic3—22no—
151C4⋊Dic3—32no—
152C4⋊Dic3—32no—
153C4⋊Dic3—32no—
154C4⋊Dic3—32no—
155C4⋊Dic3—62no—
156C4⋊Dic3—62no—
157C4×Dic3—22no—
158C4×Dic3—64no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161#208—22no—
162#208C2×Dic314yescomplemented
163C2×C3⋊C8—22no—
164C22×C32—24no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—42no—
168C22×C32—42no—
169C22×C32—44no—
170C22×C32—82no—
171C22×C32C2×C4⋊C411yescharacteristic
172C22×C32#12011yescharacteristic
173C22×C32#12311yescharacteristic
174C32×C4C4×D412yes—
175C32×C4C22⋊Q812yes—
176C3⋊Dic3—42no—
177C3⋊Dic3—42no—
178C3×Dic3—42no—
179C3×Dic3—81no—
180C22×D4D3211yescharacteristic
181C2×M16—32no—
182C4×D4—182no—
183C4×D4—182no—
184#117—92no—
185C2×C4⋊C4—31no—
186C2×C22⋊C4—62no—
187C2×C22⋊C4—182no—
188C2×C42—31no—
189#107—182no—
190#106—182no—
191#100—34no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—24no—
199C23×C3—21no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3—42no—
203C23×C3—42no—
204C23×C3—82no—
205C23×C3—82no—
206C23×C3Dic3⋊C414yes—
207C23×C3C4⋊Dic314yes—
208C23×C3C2×D1211yescharacteristic
209C23×C3C2×#6711yescharacteristic
210C3×D4—28no—
211C3×D4—28no—
212C3×D4—24no—
213C3×D4—24no—
214C3×D4—24no—
215C3×D4—24no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—62no—
221C2×C3×C4—121no—
222C2×C3×C4—121no—
223C2×C3×C4—122no—
224C2×C3×C4—121no—
225C2×C3×C4C2×Dic611yescharacteristic
226C2×C3×C4C2×Dic611yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4D3×D412yes—
229C2×C3×C4D3×D412yes—
230C2×C3×C4#23712yes—
231C2×C3×C4#23712yes—
232C2×C3×C4C22×Dic311yescharacteristic
233C2×Dic3—22no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—42no—
237C2×Dic3—41no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—244no—
245C2×Dic3—244no—
246C2×Dic3—242no—
247C2×Dic3—242no—
248C2×Dic3—242no—
249C2×Dic3—242no—
250C3×C8—64no—
251C3⋊C8—24no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—44no—
255C2×C32#38511yescharacteristic
256C2×C32#45311yescharacteristic
257C2×C32#45511yescharacteristic
258C24#62612yes—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4D3×Dic312yes—
262C2×D4#62712yes—
263C22×C4—61no—
264C22×C4—61no—
265C22×C4—182no—
266C22×C4—182no—
267C22×C4C2×D3211yescharacteristic
268M16—34no—
269M16—62no—
270C2×C8—62no—
271C4⋊C4—62no—
272C4⋊C4—92no—
273C4⋊C4—92no—
274C22⋊C4—124no—
275C22⋊C4—184no—
276C22⋊C4—182no—
277C42—62no—
278C42—182no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—28no—
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—84no—
300C22×C3—82no—
301C22×C3—82no—
302C22×C3—84no—
303C22×C3#88211yescharacteristic
304C22×C3#88611yescharacteristic
305C22×C3C2×Dic3⋊C411yescharacteristic
306C22×C3C2×C4⋊Dic311yescharacteristic
307C22×C3#93511yescharacteristic
308C22×C3#93711yescharacteristic
309C3×C4—22no—
310C3×C4—22no—
311C3×C4—122no—
312C3×C4—241no—
313C3×C4#87812yes—
314C3×C4#87812yes—
315C3×C4#67⋊C412yes—
316C3×C4D4×Dic312yes—
317Dic3—42no—
318Dic3—81no—
319Dic3—124no—
320Dic3—124no—
321Dic3—122no—
322Dic3—122no—
323Dic3—122no—
324Dic3—122no—
325C32#185611yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—42no—
329C23—42no—
330C23Dic3⋊Dic314yes—
331C23C2×#62611yescharacteristic
332D4—24no—
333D4—24no—
334C2×C4—62no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4—122no—
338C2×C4—121no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—722no—
342C2×C4—722no—
343C2×C4C2×D3×Dic311yescharacteristic
344C2×C4#380512yes—
345C2×C4C2×#62711yescharacteristic
346C2×C4#381112yes—
347C8—64no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—48no—
358C2×C3—44no—
359C2×C3—44no—
360C2×C3#474611yescharacteristic
361C2×C3#474711yescharacteristic
362C2×C3#494611yescharacteristic
363C2×C3#495011yescharacteristic
364C2×C3#506111yescharacteristic
365C2×C3#507711yescharacteristic
366C22—21no—
367C22—21no—
368C22—24no—
369C22—44no—
370C22—42no—
371C22—42no—
372C22—82no—
373C22#6396211yescharacteristic
374C22C2×Dic3⋊Dic311yescharacteristic
375C22#6398111yescharacteristic
376C4—122no—
377C4—241no—
378C4—362no—
379C4—362no—
380C4#67⋊Dic312yes—
381C4#6398212yes—
382C3—21no—
383C3#6964211yescharacteristic, complemented
384C3#7006811yescharacteristic, complemented
385C2—21no—
386C2—21no—
387C2—44no—
388C2#1059151111yescharacteristic
389C2#1059151411yescharacteristic
390C2#1059171911yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591130C2semidirect
5. #10589162C2semidirect
17. C3×#833C4semidirect
50. C3×#208C2×C4semidirect
77. #833Dic3semidirect
162. #208C2×Dic3semidirect
325. C32#1856semidirect
383. C3#69642semidirect
384. C3#70068semidirect

Maximal subgroups

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

subgroupindex
#105962692
C3×#52212
C2×C3×#8332
#105911302
#105891622
#700683
#696423