Finite Group Databasebeta

← #11787109

Subgroups — #11787109

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic
2C3×#5119C211yesmaximal, characteristic, complemented
3#10591232C211yesmaximal, characteristic
4#10591116C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70546—31nomaximal
9#69034—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13#64116—22no—
14M16×C3⋊D3—22no—
15#64110—22no—
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×Dic3⋊C8—22no—
21#63581C414yes—
22Dic3⋊(C3⋊C8)—22no—
23#63557—22no—
24#5745—31no—
25#5745—31no—
26#5745—61no—
27C3×#424—31no—
28#5129—31no—
29#5119D311yescharacteristic, complemented
30#5110—31no—
31#5102—31no—
32#5006—31no—
33#5006—31no—
34#4999—31no—
35C3×#344—31no—
36#4559—31no—
37#4556D311yescharacteristic, complemented
38#4533—31no—
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×M16—21no—
49C32×M16—21no—
50C2×C32×C8D412yes—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)D412yes—
54#3743—24no—
55C8×C3⋊D3—24no—
56C3×#217C2×C412yes—
57C3×#217C2×C412yes—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1868—91noSylow
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C22×C3×C8—31no—
77C3×#117—31no—
78C3×#117—31no—
79#926C2×D311yescharacteristic
80#926C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C22×C3⋊C8C2×D311yescharacteristic
86#907—62no—
87#907—62no—
88#907—64no—
89D3×M16—62no—
90D3×M16—62no—
91D3×M16—64no—
92#901—64no—
93#901—62no—
94#901—62no—
95C3×C4⋊C8—62no—
96(C2×D3)⋊C8—62no—
97(C2×D3)⋊C8—62no—
98Dic3⋊C8—22no—
99Dic3⋊C8—62no—
100#806—34no—
101#806—34no—
102C4⋊(C3⋊C8)—62no—
103C23×C32C22×C411yescharacteristic
104C22×C3⋊D3C4⋊C412yes—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×Q811yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111#638—22no—
112#638—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—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C32×C8—22no—
123C3⋊(C3⋊C8)—22no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126#568—91no—
127#424—31no—
128#424—91no—
129#410—91no—
130#408—91no—
131#344—31no—
132#344—91no—
133C22×C3×C4—21no—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C2×#67—32no—
137C2×#67—32no—
138C2×#67—62no—
139#235—62no—
140#235—62no—
141#235—62no—
142#235—62no—
143#235—61no—
144#235—61no—
145#235—61no—
146#235—61no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—61no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—62no—
157C2×Dic6—31no—
158C2×Dic6—31no—
159C2×Dic6—61no—
160C3×M16—22no—
161C3×M16—22no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—61no—
167C3×M16—61no—
168C2×C3×C8—22no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8D1212yes—
174C2×C3×C8#6712yes—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—32no—
178C3×C22⋊C4—32no—
179C3×C42—61no—
180C3×C42—61no—
181#217C4×D312yes—
182#217C4×D312yes—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4×Dic3—21no—
186C4×Dic3—21no—
187#208—21no—
188#208—21no—
189#208—62no—
190#208—62no—
191#208—61no—
192#208—61no—
193#208—61no—
194#208—61no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—62no—
202ΓL(1,𝔽25)—68no—
203ΓL(1,𝔽25)—64no—
204ΓL(1,𝔽25)—64no—
205D3×C8—68no—
206D3×C8—64no—
207D3×C8—64no—
208C22×C32—41no—
209C22×C32C2×C4⋊C411yescharacteristic
210C22×C32C4×D411yescharacteristic
211C22×C32C4×D411yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
214C32×C4#12011yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C32×C4C22⋊Q811yescharacteristic
217C32×C4#12311yescharacteristic
218C3⋊Dic3—22no—
219C3×Dic3—42no—
220C3×Dic3—42no—
221C2×#41—91no—
222#131—182no—
223#131—182no—
224C2×M16—31no—
225C2×M16—91no—
226C2×M16—182no—
227C2×M16D3211yescharacteristic
228C22×C8—31no—
229#117—31no—
230#117—31no—
231C4⋊C8—62no—
232C4⋊C8—182no—
233#99—94no—
234C22⋊C8—182no—
235C23×C3—21no—
236C23×C3C2×C4×D311yescharacteristic
237C23×C3C2×C4×D311yescharacteristic
238C22×D3—32no—
239C22×D3—32no—
240C22×D3—62no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4#23511yescharacteristic
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×C4D3×Q811yescharacteristic
258C2×C3×C4D3×Q811yescharacteristic
259C2×C3×C4#23911yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261#67—64no—
262#67—64no—
263#67—62no—
264#67—62no—
265#67—62no—
266#67—62no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—62no—
272D12—62no—
273D12—62no—
274D12—61no—
275D12—61no—
276D12—61no—
277D12—61no—
278C4×D3—64no—
279C4×D3—64no—
280C4×D3—62no—
281C4×D3—62no—
282C4×D3—62no—
283C4×D3—62no—
284Dic6—62no—
285Dic6—62no—
286Dic6—61no—
287Dic6—61no—
288Dic6—61no—
289Dic6—61no—
290C3×C8—24no—
291C3×C8—22no—
292C3×C8—22no—
293C3×C8—121no—
294C3×C8—121no—
295C3⋊C8—41no—
296C3⋊C8—41no—
297C3⋊C8—64no—
298C3⋊C8—62no—
299C3⋊C8—62no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#38511yescharacteristic
304C3⋊D3—42no—
305#41—181no—
306#41—181no—
307#41—181no—
308#41—181no—
309C2×Q8—91no—
310C2×D4—92no—
311C2×D4—91no—
312C22×C4—92no—
313C22×C4C2×D3211yescharacteristic
314M16—21no—
315M16—21no—
316M16—61no—
317M16—61no—
318M16—184no—
319M16—181no—
320M16—181no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—92no—
326C2×C8—184no—
327C2×C8#62612yes—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C22⋊C4—32no—
331C22⋊C4—32no—
332C42—61no—
333C42—61no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—81no—
340C22×C3C4×D1211yescharacteristic
341C22×C3#67⋊C411yescharacteristic
342C22×C3D3×C4⋊C411yescharacteristic
343C22×C3D3×C4⋊C411yescharacteristic
344C22×C3#89311yescharacteristic
345C22×C3C4×#6711yescharacteristic
346C2×D3—64no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—242no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—122no—
357C3×C4—122no—
358C3×C4#88211yescharacteristic
359C3×C4#88311yescharacteristic
360C3×C4#89411yescharacteristic
361C3×C4#89611yescharacteristic
362C3×C4#89611yescharacteristic
363C3×C4#89711yescharacteristic
364C3×C4#93711yescharacteristic
365C3×C4#94611yescharacteristic
366Dic3—42no—
367Dic3—42no—
368Dic3—64no—
369Dic3—62no—
370Dic3—62no—
371C32#186811yescharacteristic, complemented, Sylow
372C23—92no—
373C23C4×D3211yescharacteristic
374Q8—181no—
375Q8—181no—
376D4—182no—
377D4—182no—
378D4—181no—
379D4—181no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—92no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4#379611yescharacteristic
386C2×C4#379711yescharacteristic
387C2×C4#379811yescharacteristic
388C2×C4C2×#62611yescharacteristic
389C2×C4#381111yescharacteristic
390C2×C4#381111yescharacteristic
391C8—22no—
392C8—121no—
393C8—121no—
394C8—182no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—41no—
405C2×C3#466811yescharacteristic
406C2×C3#498911yescharacteristic
407D3—124no—
408D3—122no—
409D3—122no—
410C22—41no—
411C22—182no—
412C22—362no—
413C22#6388111yescharacteristic
414C22#6388311yescharacteristic
415C22C4×#62611yescharacteristic
416C4—122no—
417C4—122no—
418C4—182no—
419C4#6385311yescharacteristic
420C4#6386511yescharacteristic
421C4#6387111yescharacteristic
422C4#6398111yescharacteristic
423C3—21no—
424C3#6903411yescharacteristic, complemented
425C3#7054611yescharacteristic, complemented
426C2—21no—
427C2—21no—
428C2—21no—
429C2—362no—
430C2#1059129011yescharacteristic
subgroupG/H
centerC4#63981
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×#3828C22
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. C3×#5119C2semidirect
4. #10591116C2semidirect
6. C3×#4556C2semidirect
7. #10589170C2semidirect
29. #5119D3semidirect
37. #4556D3semidirect
371. C32#1868semidirect
424. C3#69034semidirect
425. C3#70546semidirect

Maximal subgroups

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

subgroupindex
#105962162
C3×#51192
#105912322
#105911162
#105910732
C3×#45562
#105891702
#705463
#690343