Finite Group Databasebeta

← #11785463

Subgroups — #11785463

Order 1152.

597 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
1C22×#3711C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C3×#5126C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#69983—31nomaximal
9#68940—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—22no—
18C2×#3711—22no—
19C2×#3711C414yes—
20#63649—22no—
21C3×(C2×D3)⋊C8—22no—
22#63578—22no—
23(C2×D3)⋊(C3⋊C8)—22no—
24C22×#208—31no—
25C22×ΓL(1,𝔽25)—31no—
26C3×#407—31no—
27#5207—31no—
28#5126—31no—
29#5126D311yescharacteristic
30C2×#822—31no—
31C2×#822—31no—
32C2×#822—31no—
33C2×#822—31no—
34C2×#822—61no—
35C3×#341—31no—
36#4558—31no—
37#4558D311yescharacteristic, complemented
38#4552—31no—
39C23×C3×D3Q811yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3Q811yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3C2×C412yes—
47C2×C3×C4×D3D412yes—
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)C2×C412yes—
55C2×C3⋊(C3⋊C8)D412yes—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66#3711—28no—
67#1811—91noSylow
68C23×C3×C4—31no—
69C22×C4×D3C2×D311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C22×C3×C8—31no—
76C2×#208—34no—
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—61no—
80C2×#208—62no—
81C2×#208—62no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8C2×D311yescharacteristic
88C2×ΓL(1,𝔽25)—34no—
89C2×ΓL(1,𝔽25)—62no—
90C2×ΓL(1,𝔽25)—62no—
91C3×C22⋊C8—62no—
92#830—62no—
93#822—62no—
94#822—62no—
95#822—62no—
96#822—62no—
97#822—64no—
98(C2×D3)⋊C8—22no—
99(C2×D3)⋊C8—62no—
100C23×C32C2×Q811yescharacteristic
101C22×C3×D3—21no—
102C22×C3×D3—21no—
103C22×C3×D3—42no—
104C22×C3×D3C4⋊C412yes—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3C4⋊C412yes—
114C3×C4×D3—22no—
115C3×C4×D3—22no—
116C3×C4×D3—22no—
117C3×C4×D3—22no—
118C32×C8—41no—
119C3⋊(C3⋊C8)—41no—
120C3⋊(C3⋊C8)C22⋊C414yes—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8—41no—
124C22×M16—91no—
125C2×#108—91no—
126C2×#108—91no—
127#407—31no—
128#407—91no—
129#341—31no—
130#341—91no—
131C24×C3—31no—
132C23×D3Dic611yescharacteristic
133C22×C3×C4—21no—
134C22×C3×C4—31no—
135C22×C3×C4—32no—
136C22×C3×C4—32no—
137C22×C3×C4—61no—
138C22×C3×C4—61no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3Dic611yescharacteristic
144C2×C4×D3—21no—
145C2×C4×D3—21no—
146C2×C4×D3—21no—
147C2×C4×D3—21no—
148C2×C4×D3C4×D312yes—
149C2×C4×D3#6712yes—
150C3×M16—22no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—21no—
155C3×M16—41no—
156C3×M16—61no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—32no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168#208—21no—
169#208—21no—
170#208—21no—
171#208—21no—
172#208—68no—
173#208—62no—
174#208—61no—
175#208—61no—
176#208—61no—
177#208—61no—
178#208—121no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8C4×D312yes—
196ΓL(1,𝔽25)—68no—
197C22×C32—22no—
198C22×C32C2×C4⋊C411yescharacteristic
199C22×C32C22⋊Q811yescharacteristic
200C22×C32C22⋊Q811yescharacteristic
201C2×C3×D3—22no—
202C2×C3×D3—24no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C32×C4C2×C22⋊C411yescharacteristic
206C32×C4#11711yescharacteristic
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C3×Dic3—22no—
210C23×C4—31no—
211C2×M16—31no—
212C2×M16—31no—
213C2×M16—94no—
214C2×M16—91no—
215C2×M16—182no—
216C2×M16—182no—
217C2×M16D3211yescharacteristic
218C22×C8—31no—
219C22×C8—91no—
220#108—182no—
221#108—182no—
222C22⋊C8—62no—
223C22⋊C8—182no—
224C23×C3—21no—
225C23×C3—32no—
226C23×C3—61no—
227C23×C3—61no—
228C23×C3—122no—
229C23×C3C2×Dic611yescharacteristic
230C23×C3D3×Q811yescharacteristic
231C22×D3—21no—
232C22×D3—21no—
233C22×D3—42no—
234C22×D3Dic3⋊C412yes—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—32no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4C2×C4×D311yescharacteristic
249C2×C3×C4C2×C4×D311yescharacteristic
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×C4D3×D411yescharacteristic
257C2×C3×C4#23711yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3Dic3⋊C412yes—
263C4×D3—22no—
264C4×D3—22no—
265C4×D3—22no—
266C4×D3—22no—
267C3×C8—42no—
268C3×C8—41no—
269C3×C8—41no—
270C3×C8—62no—
271C3×C8—121no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—34no—
275C3⋊C8—34no—
276C3⋊C8—41no—
277C3⋊C8—41no—
278C3⋊C8—64no—
279C3⋊C8—122no—
280C3⋊C8—121no—
281C3⋊C8—121no—
282C2×C32—21no—
283C2×C32—21no—
284C2×C32#38011yescharacteristic
285C2×C32#43012yes—
286C3×D3—42no—
287C24—31no—
288C22×C4—31no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—61no—
294C22×C4—61no—
295C22×C4C2×D3211yescharacteristic
296M16—21no—
297M16—21no—
298M16—61no—
299M16—61no—
300M16—61no—
301M16—61no—
302M16—188no—
303M16—181no—
304M16—181no—
305C2×C8—21no—
306C2×C8—32no—
307C2×C8—61no—
308C2×C8—61no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—92no—
312C2×C8—92no—
313C2×C8—92no—
314C2×C8—181no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—42no—
321C22×C3—64no—
322C22×C3—62no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3#87811yescharacteristic
326C22×C3#87811yescharacteristic
327C22×C3D3×C4⋊C411yescharacteristic
328C22×C3#89611yescharacteristic
329C22×C3#89611yescharacteristic
330C22×C3C2×Dic3⋊C411yescharacteristic
331C2×D3—24no—
332C2×D3—22no—
333C2×D3—42no—
334C2×D3—42no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—62no—
340C3×C4#87211yescharacteristic
341C3×C4#87711yescharacteristic
342C3×C4D3×C22⋊C411yescharacteristic
343C3×C4D3×C22⋊C411yescharacteristic
344C3×C4#88411yescharacteristic
345C3×C4#88411yescharacteristic
346C3×C4#93911yescharacteristic
347C3×C4#93911yescharacteristic
348Dic3—22no—
349C32#181111yescharacteristic, complemented, Sylow
350C23—32no—
351C23—61no—
352C23—61no—
353C23—122no—
354C23D3×Dic611yescharacteristic
355C2×C4—32no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4#379511yescharacteristic
363C2×C4C4×D3211yescharacteristic
364C2×C4#380211yescharacteristic
365C2×C4#380411yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C2×C4#381111yescharacteristic
368C8—41no—
369C8—62no—
370C8—94no—
371C8—121no—
372C8—121no—
373C8—361no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—22no—
380C2×C3—41no—
381C2×C3—41no—
382C2×C3—122no—
383C2×C3#466711yescharacteristic
384C2×C3#489312yes—
385C2×C3#494211yescharacteristic
386C2×C3#512412yes—
387D3—42no—
388C22—22no—
389C22—62no—
390C22—64no—
391C22—122no—
392C22—122no—
393C22D3×Dic3⋊C411yescharacteristic
394C22#6389611yescharacteristic
395C22#6389911yescharacteristic
396C4—62no—
397C4#6387711yescharacteristic
398C4#6388511yescharacteristic
399C4#6392111yescharacteristic
400C4#6397111yescharacteristic
401C3—21no—
402C3#6894011yescharacteristic, complemented
403C3#6998311yescharacteristic, complemented
404C2—21no—
405C2—21no—
406C2—122no—
407C2#1059097312yes—
408C2#1059136911yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C3×D3Q8
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63649C2semidirect
4. C2×#63578C2semidirect
6. C3×#4558C2semidirect
7. #10589166C2semidirect
37. #4558D3semidirect
349. C32#1811semidirect
402. C3#68940semidirect
403. C3#69983semidirect

Maximal subgroups

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

subgroupindex
C22×#37112
C2×#636492
C3×#51262
C2×#635782
#105910692
C3×#45582
#105891662
#699833
#689403