Finite Group Databasebeta

← #11787114

Subgroups — #11787114

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
1#10594776C211yesmaximal, characteristic
2#10592698C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic
4#10591117C211yesmaximal, characteristic, complemented
5#10591071C211yesmaximal, characteristic
6C3×#4533C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70044—31nomaximal
9#69034—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63815—22no—
18#63814—22no—
19D3×#208—22no—
20C4⋊(C3⋊(C3⋊C8))—22no—
21C3×#806C414yes—
22Dic3⋊(C3⋊C8)—22no—
23(C2×D3)⋊(C3⋊C8)—22no—
24#5819—31no—
25#5745—31no—
26C3×#410—31no—
27#5234—31no—
28#5129—31no—
29#5119—31no—
30#5006D311yescharacteristic
31#4999—31no—
32#4999—31no—
33#4999—31no—
34#4999—61no—
35C3×#344—31no—
36#4559—31no—
37#4533—31no—
38#4533D311yescharacteristic, 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×C4⋊C4—21no—
49C32×C22⋊C4C2×C412yes—
50C32×C42—21no—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
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—
66#3711—24no—
67D3×C3⋊C8—24no—
68#1868—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C3×#117—21no—
74C3×#117—31no—
75C3×#117C2×D311yescharacteristic
76C3×#117C2×D311yescharacteristic
77#948—62no—
78#948—62no—
79#926C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208—62no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88C22×C3⋊C8—61no—
89#907—62no—
90D3×M16—62no—
91#901—62no—
92C3×#99—34no—
93#830—62no—
94(C2×D3)⋊C8—62no—
95Dic3⋊C8—62no—
96#806Dic314yes—
97C4⋊(C3⋊C8)—62no—
98C4⋊(C3⋊C8)—62no—
99C4⋊(C3⋊C8)—64no—
100C4⋊(C3⋊C8)—62no—
101C23×C32C22×C411yescharacteristic
102C22×C3×D3C4⋊C412yes—
103C2×C32×C4—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×Q811yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
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—
120C3⋊(C3⋊C8)—22no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124#568—91no—
125#424—91no—
126#424—91no—
127#410—31no—
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×#67C2×Dic312yes—
143#235—21no—
144#235—21no—
145#235—21no—
146#235—21no—
147C2×D12Dic611yescharacteristic
148C2×C4×D3D1212yes—
149C2×Dic6Dic611yescharacteristic
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C3×M16—61no—
154C2×C3×C8—32no—
155C2×C3×C8—61no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—32no—
162C3×C22⋊C4C4×D312yes—
163C3×C22⋊C4C2×Dic312yes—
164C3×C42—22no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—61no—
168#217C2×Dic312yes—
169C4⋊Dic3—21no—
170C4×Dic3—21no—
171#208—21no—
172#208—21no—
173#208—21no—
174#208—21no—
175#208—64no—
176#208—61no—
177#208—61no—
178#208—61no—
179#208—61no—
180#208—121no—
181#208—121no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—64no—
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⋊C8D1212yes—
197ΓL(1,𝔽25)—64no—
198D3×C8—64no—
199C22×C32—41no—
200C22×C32C2×C4⋊C411yescharacteristic
201C22×C32C4×D411yescharacteristic
202C22×C32C4×D411yescharacteristic
203C2×C3×D3—22no—
204C2×C3×D3—42no—
205C32×C4—42no—
206C32×C4#12011yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4C22⋊Q811yescharacteristic
209C32×C4#12311yescharacteristic
210C3×Dic3—22no—
211C3×Dic3—42no—
212C2×#41—31no—
213#131—182no—
214#131—182no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—91no—
218C2×M16—182no—
219C22×C8—91no—
220#117—31no—
221#117D3211yescharacteristic
222C4⋊C8—182no—
223C4⋊C8—182no—
224#99—34no—
225C22⋊C8—182no—
226C23×C3—21no—
227C23×C3—32no—
228C23×C3C2×C4×D311yescharacteristic
229C23×C3C22×Dic311yescharacteristic
230C22×D3C4⋊Dic312yes—
231C3×Q8—61no—
232C3×Q8—61no—
233C3×D4—62no—
234C3×D4—62no—
235C3×D4—61no—
236C3×D4—61no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—32no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4C2×Dic611yescharacteristic
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4#23511yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4D3×Q811yescharacteristic
262#67—22no—
263#67—22no—
264C2×Dic3—22no—
265C2×Dic3C4⋊Dic312yes—
266D12—21no—
267D12—21no—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6—21no—
272C3×C8—62no—
273C3×C8—121no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—62no—
277C3⋊C8—62no—
278C3⋊C8—122no—
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—61no—
297M16—61no—
298M16—61no—
299M16—61no—
300M16—184no—
301M16—181no—
302M16—181no—
303C2×C8—32no—
304C2×C8—61no—
305C2×C8—92no—
306C2×C8—184no—
307C2×C8—181no—
308C2×C8—181no—
309C2×C8—181no—
310C4⋊C4—21no—
311C4⋊C4—61no—
312C22⋊C4—32no—
313C22⋊C4D3×Dic312yes—
314C42—21no—
315C42—61no—
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×C4⋊Dic311yescharacteristic
328C22×C3D4×Dic311yescharacteristic
329C22×C3D4×Dic311yescharacteristic
330C2×D3—22no—
331C2×D3—42no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—44no—
337C3×C4—42no—
338C3×C4—42no—
339C3×C4—62no—
340C3×C4—122no—
341C3×C4#87811yescharacteristic
342C3×C4#87811yescharacteristic
343C3×C4#88211yescharacteristic
344C3×C4#88211yescharacteristic
345C3×C4#88311yescharacteristic
346C3×C4#88611yescharacteristic
347C3×C4#89611yescharacteristic
348C3×C4#89711yescharacteristic
349Dic3—22no—
350Dic3—42no—
351C32#186811yescharacteristic, complemented, Sylow
352C23—32no—
353C23C2×D3×Dic311yescharacteristic
354Q8—61no—
355Q8—61no—
356D4—62no—
357D4—62no—
358D4—61no—
359D4—61no—
360C2×C4—22no—
361C2×C4—32no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4D3×Dic611yescharacteristic
366C2×C4#379511yescharacteristic
367C2×C4D3×D1211yescharacteristic
368C2×C4D3×D1211yescharacteristic
369C2×C4#380511yescharacteristic
370C2×C4#381111yescharacteristic
371C8—62no—
372C8—121no—
373C8—182no—
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#495011yescharacteristic
388D3—42no—
389C22—41no—
390C22—62no—
391C22—122no—
392C22D3×C4⋊Dic311yescharacteristic
393C22Dic3×D1211yescharacteristic
394C22#67⋊Dic311yescharacteristic
395C4—42no—
396C4—62no—
397C4—122no—
398C4#6389111yescharacteristic
399C4#6389311yescharacteristic
400C4#6389611yescharacteristic
401C4#6392311yescharacteristic
402C3—21no—
403C3#6903411yescharacteristic, complemented
404C3#7004411yescharacteristic, complemented
405C2—21no—
406C2—21no—
407C2—21no—
408C2—122no—
409C2#1059137911yescharacteristic
subgroupG/H
centerC4#63923
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#385
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592698C2semidirect
4. #10591117C2semidirect
6. C3×#4533C2semidirect
7. #10589170C2semidirect
38. #4533D3semidirect
351. C32#1868semidirect
403. C3#69034semidirect
404. C3#70044semidirect

Maximal subgroups

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

subgroupindex
#105947762
#105926982
C3×#50062
#105911172
#105910712
C3×#45332
#105891702
#700443
#690343