Finite Group Databasebeta

← #11787115

Subgroups — #11787115

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594780C211yesmaximal, characteristic
2#10592705C211yesmaximal, characteristic
3C3×#4999C211yesmaximal, characteristic, complemented
4#10591119C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic
6C3×#4533C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70546—31nomaximal
9#69034—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63818—22no—
18#63817—22no—
19#63817—22no—
20#63633C414yes—
21C3×C4⋊(C3⋊C8)—22no—
22#63572—22no—
23#63557—22no—
24#5745—31no—
25#5745—31no—
26C3×#424—31no—
27#5129—31no—
28#5119—31no—
29#5110—31no—
30#5102—31no—
31#5006—31no—
32#5006—31no—
33#5006—61no—
34#4999D311yescharacteristic, complemented
35C3×#344—31no—
36#4559—31no—
37#4556—31no—
38#4533D311yescharacteristic, complemented
39C22×C32×C4C2311yescharacteristic
40C2×#638C2×C412yes—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45C2×C4⋊(C3⋊D3)Q811yescharacteristic
46C2×C4×C3⋊D3D412yes—
47C2×#634Q811yescharacteristic
48C32×C4⋊C4—21no—
49C32×C22⋊C4C2×C412yes—
50C32×C42—21no—
51#3757C2×C412yes—
52C4⋊(C3⋊Dic3)—21no—
53C4×C3⋊Dic3—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65C2×C3×C3⋊C8D412yes—
66#3712—24no—
67#3710—24no—
68#1868—91noSylow
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C22×C3×C8—31no—
76C3×#117—21no—
77C3×#117C2×D311yescharacteristic
78C3×#117C2×D311yescharacteristic
79#926—31no—
80#926—31no—
81#926—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C22×C3⋊C8C2×D311yescharacteristic
86#907—62no—
87#907—62no—
88D3×M16—62no—
89D3×M16—62no—
90#901—62no—
91#901—62no—
92C3×C4⋊C8—62no—
93(C2×D3)⋊C8—62no—
94(C2×D3)⋊C8—62no—
95Dic3⋊C8—62no—
96Dic3⋊C8—62no—
97#806—34no—
98#806—34no—
99#806—64no—
100C4⋊(C3⋊C8)—22no—
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
110#638—22no—
111#638—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3C4⋊C412yes—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118#634—21no—
119#634—21no—
120C3×C3⋊C8—22no—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8—41no—
124#568—91no—
125#424—31no—
126#424—91no—
127#410—91no—
128#408—91no—
129#344—31no—
130#344—91no—
131C22×C3×C4—21no—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C2×#67—32no—
135C2×#67—32no—
136C2×#67—62no—
137#235—61no—
138#235—61no—
139#235—61no—
140#235—61no—
141#235—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—121no—
146#235—121no—
147#235—121no—
148#235—121no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—61no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—62no—
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—41no—
173C3×C22⋊C4—22no—
174C3×C22⋊C4C4×D312yes—
175C3×C22⋊C4C4×D312yes—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—41no—
179#217—32no—
180#217—32no—
181#217—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—121no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188#208—21no—
189#208—21no—
190#208—21no—
191#208—21no—
192#208—21no—
193#208—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8D1212yes—
199C2×C3⋊C8#6712yes—
200ΓL(1,𝔽25)—64no—
201ΓL(1,𝔽25)—64no—
202D3×C8—64no—
203D3×C8—64no—
204C22×C32—41no—
205C22×C32C2×C4⋊C411yescharacteristic
206C22×C32C4×D411yescharacteristic
207C22×C32C4×D411yescharacteristic
208C2×C3⋊D3—22no—
209C2×C3⋊D3—42no—
210C32×C4—42no—
211C32×C4#12011yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4#12311yescharacteristic
215C3⋊Dic3—22no—
216C3⋊Dic3—42no—
217C2×#41—91no—
218#131—182no—
219#131—182no—
220C2×M16—31no—
221C2×M16—31no—
222C2×M16—31no—
223C2×M16—182no—
224C22×C8—31no—
225#117—91no—
226#117D3211yescharacteristic
227C4⋊C8—62no—
228C4⋊C8—182no—
229#99—94no—
230C22⋊C8—182no—
231C23×C3—21no—
232C23×C3C2×C4×D311yescharacteristic
233C23×C3C2×C4×D311yescharacteristic
234C22×D3—32no—
235C22×D3—32no—
236C22×D3—62no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—42no—
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4D3×Q811yescharacteristic
255C2×C3×C4D3×Q811yescharacteristic
256C2×C3×C4#23911yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258#67—62no—
259#67—62no—
260#67—62no—
261#67—62no—
262#67—122no—
263#67—122no—
264C2×Dic3—32no—
265C2×Dic3—32no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—122no—
270D12—61no—
271D12—61no—
272D12—61no—
273D12—61no—
274D12—121no—
275D12—121no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—122no—
281C4×D3—122no—
282Dic6—61no—
283Dic6—61no—
284Dic6—61no—
285Dic6—61no—
286Dic6—121no—
287Dic6—121no—
288C3×C8—62no—
289C3×C8—62no—
290C3×C8—121no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—22no—
294C3⋊C8—41no—
295C3⋊C8—41no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—21no—
299C2×C32#38511yescharacteristic
300C3⋊D3—42no—
301#41—181no—
302#41—181no—
303#41—181no—
304#41—181no—
305C2×Q8—91no—
306C2×D4—92no—
307C2×D4—91no—
308C22×C4—92no—
309C22×C4C2×D3211yescharacteristic
310M16—61no—
311M16—61no—
312M16—61no—
313M16—61no—
314M16—61no—
315M16—61no—
316M16—184no—
317C2×C8—32no—
318C2×C8—32no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—184no—
324C4⋊C4—21no—
325C4⋊C4—181no—
326C22⋊C4—92no—
327C22⋊C4#62412yes—
328C42—21no—
329C42—181no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—81no—
336C22×C3C4×D1211yescharacteristic
337C22×C3#67⋊C411yescharacteristic
338C22×C3D3×C4⋊C411yescharacteristic
339C22×C3D3×C4⋊C411yescharacteristic
340C22×C3#89311yescharacteristic
341C22×C3C4×#6711yescharacteristic
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—122no—
345C2×D3—122no—
346C2×D3—122no—
347C2×D3—242no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—82no—
355C3×C4#88211yescharacteristic
356C3×C4#88311yescharacteristic
357C3×C4#89411yescharacteristic
358C3×C4#89611yescharacteristic
359C3×C4#89611yescharacteristic
360C3×C4#89711yescharacteristic
361C3×C4#93711yescharacteristic
362C3×C4#94611yescharacteristic
363Dic3—62no—
364Dic3—62no—
365Dic3—122no—
366Dic3—122no—
367Dic3—122no—
368Dic3—242no—
369C32#186811yescharacteristic, complemented, Sylow
370C23—92no—
371C23C2×#62411yescharacteristic
372Q8—181no—
373Q8—181no—
374D4—182no—
375D4—182no—
376D4—181no—
377D4—181no—
378C2×C4—22no—
379C2×C4—92no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4#379711yescharacteristic
384C2×C4#379911yescharacteristic
385C2×C4D3×D1211yescharacteristic
386C2×C4#380211yescharacteristic
387C2×C4#380411yescharacteristic
388C2×C4D3×#6711yescharacteristic
389C8—62no—
390C8—62no—
391C8—121no—
392C8—121no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—41no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3#466811yescharacteristic
404C2×C3#498911yescharacteristic
405D3—122no—
406D3—122no—
407D3—242no—
408C22—41no—
409C22—182no—
410C22—362no—
411C22#6389411yescharacteristic
412C22#6390011yescharacteristic
413C22#6395211yescharacteristic
414C4—42no—
415C4—182no—
416C4—362no—
417C4#6385411yescharacteristic
418C4#6388811yescharacteristic
419C4#6389511yescharacteristic
420C4#6392211yescharacteristic
421C3—21no—
422C3#6903411yescharacteristic, complemented
423C3#7054611yescharacteristic, complemented
424C2—21no—
425C2—21no—
426C2—21no—
427C2—362no—
428C2#1059137811yescharacteristic
subgroupG/H
centerC4#63922
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#385
prime radicalC2×#3828C22
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. #10591119C2semidirect
6. C3×#4533C2semidirect
7. #10589171C2semidirect
34. #4999D3semidirect
38. #4533D3semidirect
369. C32#1868semidirect
422. C3#69034semidirect
423. C3#70546semidirect

Maximal subgroups

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

subgroupindex
#105947802
#105927052
C3×#49992
#105911192
#105910732
C3×#45332
#105891712
#705463
#690343