Finite Group Databasebeta

← #11777907

Subgroups — #11777907

Order 1152.

385 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3744C211yesmaximal, characteristic
2#10590338C211yesmaximal, characteristic
3#10590296C211yesmaximal, characteristic, complemented
4C3×#4458C211yesmaximal, characteristic, complemented
5C3×#4455C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#68565—31nomaximal
9#68082—31nomaximal
10C2×#3744C411yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C2×#3712—21no—
14C32×C4×C8C2211yescharacteristic
15#63648C411yescharacteristic
16#63644C411yescharacteristic
17#63643C411yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63572—21no—
23#63557—21no—
24#63555—21no—
25#4838—31no—
26#4831—31no—
27C4×#204—31no—
28C4×#204—31no—
29C4×#204—61no—
30#4688—31no—
31#4679—31no—
32C3×#335—31no—
33C3×#322—31no—
34#4484—31no—
35#4483—31no—
36#4459—31no—
37#4458D311yescharacteristic, complemented
38#4456—31no—
39#4455D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634C2×C411yescharacteristic
43C2×C32×C8C2×C411yescharacteristic
44C2×C32×C8C2×C411yescharacteristic
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3—21no—
51#3744—22no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3712—42no—
58#1592—91noSylow
59C2×#204—31no—
60C2×#204—31no—
61C2×#204—61no—
62C2×ΓL(1,𝔽25)—61no—
63C2×ΓL(1,𝔽25)—61no—
64C4×D12—31no—
65C4×D12—31no—
66C4×D12—61no—
67C4×Dic6—31no—
68C4×Dic6—31no—
69C4×Dic6—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4×C8—21no—
73C3×C4×C8—31no—
74C3×C4×C8—31no—
75C3×C4×C8C2×D311yescharacteristic
76C3×C4×C8C2×D311yescharacteristic
77#821—31no—
78#821—31no—
79#821—61no—
80(C2×D3)⋊C8—61no—
81(C2×D3)⋊C8—61no—
82#817—31no—
83#817—31no—
84#817—61no—
85#816—31no—
86#816—31no—
87#816—61no—
88#815—61no—
89#815—61no—
90Dic3⋊C8—61no—
91Dic3⋊C8—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊D3—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C4⋊(C3⋊D3)—21no—
104C4⋊(C3⋊D3)—21no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—41no—
107#634—21no—
108#634—21no—
109C32×C8—21no—
110C32×C8M1612yescomplemented
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#446—91no—
117C4×SD16—91no—
118#436—91no—
119#335—31no—
120Q8⋊C8—91no—
121D4⋊C8—91no—
122#322—31no—
123C2×D12—31no—
124C2×D12—31no—
125C2×D12—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—121no—
129C2×Dic6—31no—
130C2×Dic6—31no—
131C2×Dic6—61no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8C4×D311yescharacteristic
140C2×C3×C8C4×D311yescharacteristic
141C2×C3×C8C4×D311yescharacteristic
142C2×C3×C8C4×D311yescharacteristic
143C3×C42—21no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146(C2×D3)⋊C4—61no—
147(C2×D3)⋊C4—61no—
148(C2×D3)⋊C4—121no—
149C4⋊Dic3—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155Dic3⋊C4—61no—
156Dic3⋊C4—61no—
157Dic3⋊C4—121no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—121no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8D1211yescharacteristic
165C2×C3⋊C8D1211yescharacteristic
166#204—64no—
167#204—62no—
168#204—62no—
169ΓL(1,𝔽25)—122no—
170ΓL(1,𝔽25)—122no—
171C22×C32C4×D411yescharacteristic
172C2×C3⋊D3—41no—
173C2×C3⋊D3—41no—
174C2×C3⋊D3—41no—
175C32×C4—21no—
176C32×C4C2×M1611yescharacteristic
177C32×C4#13111yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C3⋊Dic3—41no—
181C3⋊Dic3—41no—
182C3⋊Dic3—41no—
183C2×SD16—91no—
184C2×M16—181no—
185C4×Q8—91no—
186C4×D4—91no—
187#106—91no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—181no—
191#103—91no—
192#102—91no—
193C22⋊C8—181no—
194#97—181no—
195C4×C8—31no—
196C4×C8—31no—
197C4×C8D3211yescharacteristic
198C22×D3—61no—
199C22×D3—61no—
200C22×D3—121no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4C2×C4×D311yescharacteristic
205C2×C3×C4C2×C4×D311yescharacteristic
206C2×C3×C4C2×D1211yescharacteristic
207C2×C3×C4#23511yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4#23911yescharacteristic
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219D12—62no—
220D12—61no—
221D12—61no—
222D12—61no—
223D12—61no—
224D12—121no—
225C4×D3—121no—
226C4×D3—121no—
227C4×D3—121no—
228C4×D3—121no—
229C4×D3—241no—
230C4×D3—241no—
231Dic6—62no—
232Dic6—61no—
233Dic6—61no—
234Dic6—61no—
235Dic6—61no—
236Dic6—121no—
237C3×C8—21no—
238C3×C8—21no—
239C3×C8—22no—
240C3×C8—41no—
241C3×C8—61no—
242C3×C8—61no—
243C3×C8—121no—
244C3×C8—121no—
245C3×C8—121no—
246C3×C8ΓL(1,𝔽25)12yescomplemented
247C3×C8ΓL(1,𝔽25)12yescomplemented
248C3⋊C8—21no—
249C3⋊C8—21no—
250C3⋊C8—41no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C2×C32#43611yescharacteristic
254C2×C32#44011yescharacteristic
255C2×C32#44411yescharacteristic
256C3⋊D3—81no—
257C2×Q8—91no—
258C2×D4—91no—
259C22×C4—181no—
260SD16—182no—
261M16—362no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—61no—
267C2×C8#62411yescharacteristic
268C2×C8#62411yescharacteristic
269C4⋊C4—91no—
270C4⋊C4—91no—
271C4⋊C4—181no—
272C22⋊C4—181no—
273C42—181no—
274C42C2×D3211yescharacteristic
275C22×C3—21no—
276C22×C3C4×D1211yescharacteristic
277C22×C3#89311yescharacteristic
278C2×D3—122no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—241no—
286C2×D3—241no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
295C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
296C3×C4#90111yescharacteristic
297C3×C4#90711yescharacteristic
298C3×C4#90811yescharacteristic
299C3×C4#90911yescharacteristic
300C3×C4#91111yescharacteristic
301C3×C4#91811yescharacteristic
302Dic3—122no—
303Dic3—121no—
304Dic3—121no—
305Dic3—121no—
306Dic3—121no—
307Dic3—121no—
308Dic3—121no—
309Dic3—241no—
310Dic3—241no—
311C32#159211yescharacteristic, complemented, Sylow
312C23—181no—
313Q8—181no—
314Q8—181no—
315D4—181no—
316D4—181no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4#379911yescharacteristic
323C2×C4D3×D1211yescharacteristic
324C2×C4C2×#62411yescharacteristic
325C8—21no—
326C8—61no—
327C8—61no—
328C8—121no—
329C8—121no—
330C8—121no—
331C8#371212yescomplemented
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#468811yescharacteristic
336C2×C3#471011yescharacteristic
337C2×C3#471711yescharacteristic
338C2×C3#483811yescharacteristic
339C2×C3#488911yescharacteristic
340C2×C3#489411yescharacteristic
341D3—242no—
342D3—241no—
343D3—241no—
344C22—361no—
345C22—361no—
346C22—361no—
347C22#6389411yescharacteristic
348C4—21no—
349C4—361no—
350C4—361no—
351C4—361no—
352C4#6379511yescharacteristic
353C4#6380111yescharacteristic
354C4#6381711yescharacteristic
355C4C2×#371211yescharacteristic
356C3—21no—
357C3#6808211yescharacteristic, complemented
358C3#6856511yescharacteristic, complemented
359C2—721no—
360C2#1059033811yescharacteristic
361C2#1059077311yescharacteristic
362C2#1059091811yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C4×D4
prime radicalC2×C4⋊(C3⋊D3)C2×C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1592
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10590296C2semidirect
4. C3×#4458C2semidirect
5. C3×#4455C2semidirect
6. #10589085C2semidirect
37. #4458D3semidirect
39. #4455D3semidirect
110. C32×C8M16semidirect
246. C3×C8ΓL(1,𝔽25)semidirect
247. C3×C8ΓL(1,𝔽25)semidirect
311. C32#1592semidirect
331. C8#3712semidirect
357. C3#68082semidirect
358. C3#68565semidirect

Maximal subgroups

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

subgroupindex
C4×#37442
#105903382
#105902962
C3×#44582
C3×#44552
#105890852
#105890822
#685653
#680823