Finite Group Databasebeta

← #11786652

Subgroups — #11786652

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2C3×#5124C211yesmaximal, characteristic, complemented
3#10591143C211yesmaximal, characteristic, complemented
4#10591076C211yesmaximal, characteristic
5#10591071C211yesmaximal, characteristic
6#10589424C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#72027—31nomaximal
9#70734—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20C3×#822—22no—
21#63578—22no—
22#63560C412yes—
23#63558C412yes—
24(C2×D3)⋊(C3⋊C8)—22no—
25C3×#568—31no—
26#5745D311yescharacteristic
27C3×#430—31no—
28#5237—31no—
29#5234—31no—
30#5132—31no—
31#5129—31no—
32#5124—31no—
33#5124—31no—
34#5124D311yescharacteristic, complemented
35#4558—31no—
36#4558—31no—
37#4558—31no—
38#4558—31no—
39#4558—61no—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67Q812yes—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3D412yes—
48C2×C3×Dic6C2×C411yescharacteristic
49C32×M16—21no—
50C32×M16D412yes—
51C2×C32×C8—21no—
52#3748—21no—
53#3748C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C3×#208D412yes—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C3×ΓL(1,𝔽25)—24no—
68C3×D3×C8—24no—
69#1858—91noSylow
70C2×C3×#41—31no—
71C2×#235C2×D311yescharacteristic
72C3×#131—62no—
73C3×#131—62no—
74C2×C3×M16—21no—
75C2×C3×M16—31no—
76C2×C3×M16—31no—
77C2×C3×M16—31no—
78C2×C3×M16—62no—
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×M16C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C2×#208C2×D311yescharacteristic
87C22×C3⋊C8—31no—
88C22×C3⋊C8—31no—
89C22×C3⋊C8—61no—
90#907—22no—
91D3×M16—22no—
92#901—22no—
93C3×#108—62no—
94#836—32no—
95#833—32no—
96#830—62no—
97#824—32no—
98#823—32no—
99#822—22no—
100#822—62no—
101#822—62no—
102(C2×D3)⋊C8—62no—
103C23×C32C2×Q811yescharacteristic
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
111C3×#67—22no—
112C3×#67—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—
120C32×C8—22no—
121C3⋊(C3⋊C8)—22no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126#568—31no—
127#430—31no—
128#430—91no—
129#413—91no—
130#408—91no—
131#341—91no—
132#341—91no—
133C3×#41—61no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C2×C3×Q8—31no—
138C2×C3×D4—32no—
139C2×C3×D4—31no—
140C22×C3×C4—21no—
141C22×C3×C4—32no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67Dic612yes—
145#235—21no—
146#235—21no—
147#235—21no—
148#235—21no—
149C2×D12C4×D311yescharacteristic
150C2×C4×D3#6712yes—
151C2×Dic6C4×D311yescharacteristic
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—22no—
155C3×M16—32no—
156C3×M16—32no—
157C3×M16—41no—
158C3×M16—64no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16#6712yes—
164C3×M16#6712yes—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—64no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172#208—21no—
173#208—21no—
174#208—21no—
175#208—21no—
176#208—32no—
177#208—32no—
178#208—62no—
179#208—61no—
180#208—61no—
181#208—121no—
182#208C4×D312yes—
183#208#6712yes—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197C2×C3⋊C8—121no—
198C2×C3⋊C8—121no—
199ΓL(1,𝔽25)—24no—
200D3×C8—24no—
201C22×C32—41no—
202C22×C32C2×C4⋊C411yescharacteristic
203C22×C32C22⋊Q811yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C2×C3×D3—22no—
206C2×C3×D3—42no—
207C32×C4C4×D411yescharacteristic
208C32×C4C4×D411yescharacteristic
209C32×C4#12011yescharacteristic
210C32×C4#12311yescharacteristic
211C3×Dic3—22no—
212C2×#41—31no—
213#131—62no—
214#131—62no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—62no—
219C2×M16—91no—
220C2×M16D3211yescharacteristic
221C22×C8—91no—
222#108—62no—
223#108—182no—
224#101—92no—
225#100—92no—
226C22⋊C8—182no—
227C23×C3—21no—
228C23×C3—32no—
229C23×C3C2×Dic611yescharacteristic
230C23×C3D3×Q811yescharacteristic
231C22×D3Dic3⋊C412yes—
232C3×Q8—61no—
233C3×Q8—61no—
234C3×D4—62no—
235C3×D4—62no—
236C3×D4—61no—
237C3×D4—61no—
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—62no—
246C2×C3×C4—62no—
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4C2×C4×D311yescharacteristic
249C2×C3×C4#23511yescharacteristic
250C2×C3×C4#23511yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4#23911yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259#67—22no—
260#67—22no—
261C2×Dic3Dic3⋊C412yes—
262D12—21no—
263D12—21no—
264C4×D3—22no—
265C4×D3—22no—
266Dic6—21no—
267Dic6—21no—
268C3×C8—22no—
269C3×C8—22no—
270C3×C8—42no—
271C3×C8—62no—
272C3×C8—62no—
273C3×C8—121no—
274C3⋊C8—22no—
275C3⋊C8—22no—
276C3⋊C8—41no—
277C3⋊C8—62no—
278C3⋊C8—62no—
279C3⋊C8—122no—
280C3⋊C8—122no—
281C3⋊C8—121no—
282C3⋊C8—121no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32—21no—
286C2×C32#38511yescharacteristic
287C3×D3—42no—
288#41—61no—
289#41—61no—
290#41—61no—
291#41—61no—
292C2×Q8—31no—
293C2×D4—32no—
294C2×D4—31no—
295C22×C4—32no—
296C22×C4C2×D3211yescharacteristic
297M16—21no—
298M16—32no—
299M16—32no—
300M16—64no—
301M16—61no—
302M16—61no—
303M16—61no—
304M16—61no—
305M16—92no—
306M16—181no—
307M16#62512yes—
308C2×C8—21no—
309C2×C8—64no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—181no—
314C2×C8—181no—
315C2×C8—181no—
316C2×C8—181no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—42no—
323C22×C3—62no—
324C22×C3—122no—
325C22×C3D3×C4⋊C411yescharacteristic
326C22×C3#89611yescharacteristic
327C22×C3C2×Dic3⋊C411yescharacteristic
328C22×C3#92411yescharacteristic
329C22×C3#92411yescharacteristic
330C22×C3#94611yescharacteristic
331C2×D3—22no—
332C2×D3—42no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—62no—
338C3×C4#89311yescharacteristic
339C3×C4#89411yescharacteristic
340C3×C4C4×#6711yescharacteristic
341C3×C4C4×#6711yescharacteristic
342C3×C4C4×#6711yescharacteristic
343C3×C4#92911yescharacteristic
344C3×C4#93711yescharacteristic
345C3×C4#95311yescharacteristic
346Dic3—22no—
347C32#185811yescharacteristic, complemented, Sylow
348C23—32no—
349C23D3×Dic611yescharacteristic
350Q8—61no—
351Q8—61no—
352D4—62no—
353D4—62no—
354D4—61no—
355D4—61no—
356C2×C4—32no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4#379811yescharacteristic
360C2×C4#379911yescharacteristic
361C2×C4C4×D3211yescharacteristic
362C2×C4C2×#62511yescharacteristic
363C2×C4D3×#6711yescharacteristic
364C2×C4D3×#6711yescharacteristic
365C8—22no—
366C8—62no—
367C8—62no—
368C8—121no—
369C8—182no—
370C8—361no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—41no—
380C2×C3—41no—
381C2×C3—122no—
382C2×C3#498911yescharacteristic
383C2×C3#521011yescharacteristic
384D3—42no—
385C22—41no—
386C22—62no—
387C22—122no—
388C22#6385111yescharacteristic
389C22#6385611yescharacteristic
390C22D3×Dic3⋊C411yescharacteristic
391C4—62no—
392C4#6385011yescharacteristic
393C4C4×#62511yescharacteristic
394C4#6390411yescharacteristic
395C4#6397611yescharacteristic
396C3—21no—
397C3#7073411yescharacteristic, complemented
398C3#7202711yescharacteristic, complemented
399C2—21no—
400C2—21no—
401C2—21no—
402C2—122no—
403C2#1059127711yescharacteristic
subgroupG/H
centerC4#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1858
LCSG ▷ C2×C32×C4 ▷ 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×#5124C2semidirect
3. #10591143C2semidirect
6. #10589424C2semidirect
7. #10589165C2semidirect
34. #5124D3semidirect
347. C32#1858semidirect
397. C3#70734semidirect
398. C3#72027semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
C3×#51242
#105911432
#105910762
#105910712
#105894242
#105891652
#720273
#707343