Finite Group Databasebeta

← #11787116

Subgroups — #11787116

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594776C211yesmaximal, characteristic
2C3×#5006C211yesmaximal, characteristic
3C3×#4999C211yesmaximal, characteristic, complemented
4#10591116C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic
6#10589399C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70546—31nomaximal
9#70044—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63815—22no—
18#63814—22no—
19D3×#208—22no—
20C3×#806C414yes—
21C3×C4⋊(C3⋊C8)—22no—
22Dic3⋊(C3⋊C8)—22no—
23(C2×D3)⋊(C3⋊C8)—22no—
24#5819—31no—
25#5745—31no—
26C3×#424—31no—
27C3×#410—31no—
28#5234—31no—
29#5110—31no—
30#5102—31no—
31#5006D311yescharacteristic
32#4999—31no—
33#4999D311yescharacteristic, complemented
34#4556—31no—
35#4533—31no—
36#4533—31no—
37#4533—31no—
38#4533—61no—
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—
53#3748—21no—
54#3748—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—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—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—
72C22×C3×C8—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—31no—
83C2×#208—31no—
84C2×#208—61no—
85C2×#208—61no—
86C2×#208—62no—
87C2×#208C2×D311yescharacteristic
88C22×C3⋊C8C2×D311yescharacteristic
89#907—62no—
90D3×M16—62no—
91#901—62no—
92C3×C4⋊C8—62no—
93C3×#99—34no—
94#830—62no—
95(C2×D3)⋊C8—62no—
96Dic3⋊C8—62no—
97#806Dic314yes—
98C4⋊(C3⋊C8)—22no—
99C4⋊(C3⋊C8)—62no—
100C23×C32C22×C411yescharacteristic
101C22×C3×D3C4⋊C412yes—
102C2×C32×C4—22no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C3×#67—22no—
110C3×#67—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3C4⋊C412yes—
113C3×D12—21no—
114C3×D12—21no—
115C3×C4×D3—22no—
116C3×C4×D3—22no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3⋊(C3⋊C8)—22no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—41no—
123#568—91no—
124#424—31no—
125#424—91no—
126#410—31no—
127#408—91no—
128#344—91no—
129#344—91no—
130C3×#41—61no—
131C3×#41—61no—
132C3×#41—61no—
133C3×#41—61no—
134C2×C3×Q8—31no—
135C2×C3×D4—32no—
136C2×C3×D4—31no—
137C22×C3×C4—21no—
138C22×C3×C4—32no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C2×#67C2×Dic312yes—
142#235—21no—
143#235—21no—
144#235—21no—
145#235—21no—
146C2×D12Dic611yescharacteristic
147C2×C4×D3D1212yes—
148C2×Dic6Dic611yescharacteristic
149C3×M16—61no—
150C3×M16—61no—
151C2×C3×C8—32no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—61no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—32no—
161C3×C22⋊C4C4×D312yes—
162C3×C22⋊C4C2×Dic312yes—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—41no—
166C3×C42—61no—
167#217C2×Dic312yes—
168C4⋊Dic3—21no—
169C4×Dic3—21no—
170#208—21no—
171#208—21no—
172#208—64no—
173#208—61no—
174#208—61no—
175#208—61no—
176#208—61no—
177#208—62no—
178#208—61no—
179#208—61no—
180#208—61no—
181#208—61no—
182#208—121no—
183#208—121no—
184#208—121no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—64no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8#6712yes—
196ΓL(1,𝔽25)—64no—
197D3×C8—64no—
198C22×C32—41no—
199C22×C32C2×C4⋊C411yescharacteristic
200C22×C32C4×D411yescharacteristic
201C22×C32C4×D411yescharacteristic
202C2×C3×D3—22no—
203C2×C3×D3—42no—
204C32×C4—42no—
205C32×C4#12011yescharacteristic
206C32×C4C22⋊Q811yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4#12311yescharacteristic
209C3×Dic3—22no—
210C3×Dic3—42no—
211C2×#41—31no—
212#131—182no—
213#131—182no—
214C2×M16—31no—
215C2×M16—91no—
216C2×M16—91no—
217C2×M16—182no—
218C22×C8—31no—
219#117—31no—
220#117D3211yescharacteristic
221C4⋊C8—62no—
222C4⋊C8—182no—
223#99—34no—
224C22⋊C8—182no—
225C23×C3—21no—
226C23×C3—32no—
227C23×C3C2×C4×D311yescharacteristic
228C23×C3C22×Dic311yescharacteristic
229C22×D3C4⋊Dic312yes—
230C3×Q8—61no—
231C3×Q8—61no—
232C3×D4—62no—
233C3×D4—62no—
234C3×D4—61no—
235C3×D4—61no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—32no—
245C2×C3×C4—42no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4C2×Dic611yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4#23711yescharacteristic
257C2×C3×C4#23711yescharacteristic
258C2×C3×C4D3×Q811yescharacteristic
259C2×C3×C4#23911yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261#67—22no—
262#67—22no—
263C2×Dic3—22no—
264C2×Dic3C4⋊Dic312yes—
265D12—21no—
266D12—21no—
267C4×D3—22no—
268C4×D3—22no—
269Dic6—21no—
270Dic6—21no—
271C3×C8—62no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C3⋊C8—62no—
276C3⋊C8—62no—
277C3⋊C8—122no—
278C3⋊C8—122no—
279C3⋊C8—121no—
280C3⋊C8—121no—
281C2×C32—21no—
282C2×C32—21no—
283C2×C32—21no—
284C2×C32#38511yescharacteristic
285C3×D3—42no—
286#41—61no—
287#41—61no—
288#41—61no—
289#41—61no—
290C2×Q8—31no—
291C2×D4—32no—
292C2×D4—31no—
293C22×C4—32no—
294C22×C4C2×D3211yescharacteristic
295M16—61no—
296M16—61no—
297M16—184no—
298M16—181no—
299M16—181no—
300M16—181no—
301M16—181no—
302C2×C8—32no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—61no—
306C2×C8—92no—
307C2×C8—184no—
308C2×C8—181no—
309C4⋊C4—21no—
310C4⋊C4—61no—
311C22⋊C4—32no—
312C22⋊C4D3×Dic312yes—
313C42—21no—
314C42—61no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—62no—
321C22×C3—81no—
322C22×C3—122no—
323C22×C3D3×C4⋊C411yescharacteristic
324C22×C3#89311yescharacteristic
325C22×C3C2×C4⋊Dic311yescharacteristic
326C22×C3C4×#6711yescharacteristic
327C22×C3D4×Dic311yescharacteristic
328C22×C3D4×Dic311yescharacteristic
329C2×D3—22no—
330C2×D3—42no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—42no—
336C3×C4—42no—
337C3×C4—62no—
338C3×C4—82no—
339C3×C4—122no—
340C3×C4#87811yescharacteristic
341C3×C4#87811yescharacteristic
342C3×C4#88211yescharacteristic
343C3×C4#88611yescharacteristic
344C3×C4#89411yescharacteristic
345C3×C4#89611yescharacteristic
346C3×C4#93711yescharacteristic
347C3×C4#94611yescharacteristic
348Dic3—22no—
349Dic3—42no—
350C32#186811yescharacteristic, complemented, Sylow
351C23—32no—
352C23C2×D3×Dic311yescharacteristic
353Q8—61no—
354Q8—61no—
355D4—62no—
356D4—62no—
357D4—61no—
358D4—61no—
359C2×C4—22no—
360C2×C4—32no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4D3×Dic611yescharacteristic
365C2×C4#379611yescharacteristic
366C2×C4D3×D1211yescharacteristic
367C2×C4#380211yescharacteristic
368C2×C4#380411yescharacteristic
369C2×C4D3×#6711yescharacteristic
370C8—62no—
371C8—121no—
372C8—182no—
373C8—361no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—41no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3—122no—
385C2×C3#495011yescharacteristic
386C2×C3#498911yescharacteristic
387D3—42no—
388C22—41no—
389C22—62no—
390C22—122no—
391C22D3×C4⋊Dic311yescharacteristic
392C22#6389811yescharacteristic
393C22Dic3×#6711yescharacteristic
394C4—42no—
395C4—62no—
396C4—122no—
397C4#6388711yescharacteristic
398C4#6389011yescharacteristic
399C4#6389911yescharacteristic
400C4#6392211yescharacteristic
401C3—21no—
402C3#7004411yescharacteristic, complemented
403C3#7054611yescharacteristic, complemented
404C2—21no—
405C2—21no—
406C2—21no—
407C2—122no—
408C2#1059137711yescharacteristic
subgroupG/H
centerC4#63922
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
3. C3×#4999C2semidirect
4. #10591116C2semidirect
6. #10589399C2semidirect
7. #10589169C2semidirect
33. #4999D3semidirect
350. C32#1868semidirect
402. C3#70044semidirect
403. C3#70546semidirect

Maximal subgroups

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

subgroupindex
#105947762
C3×#50062
C3×#49992
#105911162
#105910702
#105893992
#105891692
#705463
#700443