Finite Group Databasebeta

← #11787108

Subgroups — #11787108

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2#10592818C211yesmaximal, characteristic, complemented
3#10591231C211yesmaximal, characteristic
4#10591117C211yesmaximal, characteristic, complemented
5#10591071C211yesmaximal, characteristic
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#72026—31nomaximal
9#69034—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63641—22no—
21#63580C414yes—
22Dic3⋊(C3⋊C8)—22no—
23(C2×D3)⋊(C3⋊C8)—22no—
24C3×#568—31no—
25#5745D311yescharacteristic
26#5240—31no—
27#5234—31no—
28#5129—31no—
29#5119—31no—
30#5119—31no—
31#5119—31no—
32#5119—61no—
33#5006—31no—
34#4999—31no—
35C3×#344—31no—
36#4559—31no—
37#4556—31no—
38#4556D311yescharacteristic, complemented
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67C2×C412yes—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12Q811yescharacteristic
46C2×C3×C4×D3D412yes—
47C2×C3×Dic6Q811yescharacteristic
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8D412yes—
51#3757C2×C412yes—
52C4⋊(C3⋊Dic3)—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217C2×C412yes—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8D412yes—
66C3×ΓL(1,𝔽25)—24no—
67C3×D3×C8—24no—
68#1868—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C3×#131—62no—
72C3×#131—62no—
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16—62no—
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C2×D311yescharacteristic
79C3×#117—31no—
80#926—31no—
81#926—31no—
82#926—61no—
83#926C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88C22×C3⋊C8—61no—
89#907—22no—
90D3×M16—22no—
91#901—22no—
92#834—34no—
93#830—62no—
94(C2×D3)⋊C8—62no—
95Dic3⋊C8—62no—
96Dic3⋊C8—64no—
97Dic3⋊C8—62no—
98Dic3⋊C8—62no—
99#806—34no—
100C4⋊(C3⋊C8)—62no—
101C23×C32C22×C411yescharacteristic
102C22×C3×D3C4⋊C412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—22no—
110C3×#67—22no—
111C3×#67—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3C4⋊C412yes—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—22no—
117C3×C4×D3—22no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C32×C8—22no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124#568—31no—
125#424—91no—
126#424—91no—
127#410—91no—
128#408—91no—
129#344—31no—
130#344—91no—
131C3×#41—61no—
132C3×#41—61no—
133C3×#41—61no—
134C3×#41—61no—
135C2×C3×Q8—31no—
136C2×C3×D4—32no—
137C2×C3×D4—31no—
138C22×C3×C4—21no—
139C22×C3×C4—32no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×#67C4×D312yes—
143#235—21no—
144#235—21no—
145#235—21no—
146#235—21no—
147C2×D12Dic611yescharacteristic
148C2×C4×D3#6712yes—
149C2×Dic6Dic611yescharacteristic
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—41no—
155C3×M16—41no—
156C3×M16—64no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—22no—
162C2×C3×C8—32no—
163C2×C3×C8—64no—
164C2×C3×C8—61no—
165C2×C3×C8D1212yes—
166C2×C3×C8#6712yes—
167C3×C4⋊C4—61no—
168C3×C22⋊C4—32no—
169C3×C42—61no—
170#217—32no—
171#217—32no—
172#217—62no—
173#217C4×D312yes—
174C4⋊Dic3—21no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4×Dic3—21no—
179C4×Dic3—62no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182#208—21no—
183#208—21no—
184#208—21no—
185#208—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8#6712yes—
197ΓL(1,𝔽25)—24no—
198D3×C8—24no—
199C22×C32—41no—
200C22×C32C2×C4⋊C411yescharacteristic
201C22×C32C4×D411yescharacteristic
202C22×C32C4×D411yescharacteristic
203C2×C3×D3—22no—
204C2×C3×D3—42no—
205C32×C4#12011yescharacteristic
206C32×C4C22⋊Q811yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4#12311yescharacteristic
209C3⋊Dic3—42no—
210C3×Dic3—22no—
211C3×Dic3—42no—
212C2×#41—31no—
213#131—62no—
214#131—62no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—62no—
218C2×M16D3211yescharacteristic
219C22×C8—91no—
220#117—31no—
221#117—91no—
222C4⋊C8—182no—
223C4⋊C8—182no—
224#99—94no—
225C22⋊C8—182no—
226C23×C3—21no—
227C23×C3—32no—
228C23×C3C2×C4×D311yescharacteristic
229C23×C3C2×C4×D311yescharacteristic
230C22×D3Dic3⋊C412yes—
231C3×Q8—61no—
232C3×Q8—61no—
233C3×D4—62no—
234C3×D4—62no—
235C3×D4—61no—
236C3×D4—61no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—32no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4C2×Dic611yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4#23511yescharacteristic
250C2×C3×C4#23511yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4D3×Q811yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259#67—22no—
260#67—22no—
261C2×Dic3—22no—
262C2×Dic3—64no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3Dic3⋊C412yes—
266D12—21no—
267D12—21no—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6—21no—
272C3×C8—22no—
273C3×C8—22no—
274C3×C8—42no—
275C3×C8—62no—
276C3×C8—121no—
277C3⋊C8—22no—
278C3⋊C8—41no—
279C3⋊C8—122no—
280C3⋊C8—121no—
281C3⋊C8—121no—
282C2×C32—21no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#38511yescharacteristic
286C3×D3—42no—
287#41—61no—
288#41—61no—
289#41—61no—
290#41—61no—
291C2×Q8—31no—
292C2×D4—32no—
293C2×D4—31no—
294C22×C4—32no—
295C22×C4C2×D3211yescharacteristic
296M16—21no—
297M16—21no—
298M16—64no—
299M16—61no—
300M16—61no—
301M16—61no—
302M16—61no—
303C2×C8—32no—
304C2×C8—64no—
305C2×C8—61no—
306C2×C8—181no—
307C2×C8—181no—
308C2×C8—181no—
309C2×C8#62612yes—
310C4⋊C4—61no—
311C4⋊C4—181no—
312C22⋊C4—32no—
313C22⋊C4—92no—
314C42—61no—
315C42—181no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—42no—
322C22×C3—62no—
323C22×C3—122no—
324C22×C3C4×D1211yescharacteristic
325C22×C3#67⋊C411yescharacteristic
326C22×C3D3×C4⋊C411yescharacteristic
327C22×C3C2×Dic3⋊C411yescharacteristic
328C22×C3C4×#6711yescharacteristic
329C22×C3C4×#6711yescharacteristic
330C2×D3—22no—
331C2×D3—42no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—62no—
337C3×C4—122no—
338C3×C4#88211yescharacteristic
339C3×C4#88311yescharacteristic
340C3×C4#89611yescharacteristic
341C3×C4#89711yescharacteristic
342C3×C4#92411yescharacteristic
343C3×C4#92411yescharacteristic
344C3×C4#92911yescharacteristic
345C3×C4#95311yescharacteristic
346Dic3—22no—
347Dic3—42no—
348Dic3—124no—
349Dic3—122no—
350Dic3—122no—
351C32#186811yescharacteristic, complemented, Sylow
352C23—32no—
353C23C4×D3211yescharacteristic
354Q8—61no—
355Q8—61no—
356D4—62no—
357D4—62no—
358D4—61no—
359D4—61no—
360C2×C4—32no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—182no—
365C2×C4D3×Dic611yescharacteristic
366C2×C4#379511yescharacteristic
367C2×C4#379811yescharacteristic
368C2×C4C2×#62611yescharacteristic
369C2×C4D3×#6711yescharacteristic
370C2×C4D3×#6711yescharacteristic
371C8—22no—
372C8—62no—
373C8—121no—
374C8—361no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—41no—
384C2×C3—41no—
385C2×C3—122no—
386C2×C3#466811yescharacteristic
387C2×C3#521011yescharacteristic
388D3—42no—
389C22—41no—
390C22—62no—
391C22—122no—
392C22D3×Dic3⋊C411yescharacteristic
393C22#6387911yescharacteristic
394C22C4×#62611yescharacteristic
395C4—62no—
396C4—122no—
397C4—362no—
398C4#6385111yescharacteristic
399C4#6385711yescharacteristic
400C4#6390511yescharacteristic
401C4#6397711yescharacteristic
402C3—21no—
403C3#6903411yescharacteristic, complemented
404C3#7202611yescharacteristic, complemented
405C2—21no—
406C2—21no—
407C2—21no—
408C2—122no—
409C2#1059127811yescharacteristic
subgroupG/H
centerC4#63977
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592818C2semidirect
4. #10591117C2semidirect
6. C3×#4556C2semidirect
7. #10589171C2semidirect
38. #4556D3semidirect
351. C32#1868semidirect
403. C3#69034semidirect
404. C3#72026semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105928182
#105912312
#105911172
#105910712
C3×#45562
#105891712
#720263
#690343