Finite Group Databasebeta

← #11877036

Subgroups — #11877036

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595368C212yesmaximal
2#10592883C211yesmaximal, characteristic, complemented
3C3×#5189C211yesmaximal, characteristic
4C3×#5183C211yesmaximal, characteristic, complemented
5#10591638C212yesmaximal
6#10591623C212yesmaximal, complemented
7#10591582C212yesmaximal, complemented
8#10590889C211yesmaximal, characteristic, complemented
9#10590854C211yesmaximal, characteristic
10#10590819C211yesmaximal, characteristic, complemented
11Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic
12#81794—31nomaximal
13#80893—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16C3×#946C2212yes—
17C3×#944C2212yes—
18C2×C3×#216C2212yes—
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#63918C2212yes—
22#63893—22no—
23#63878—22no—
24C4×D3×Dic3C2211yescharacteristic
25#63856C2212yes—
26#63845—22no—
27#63843C2212yes—
28#63838—22no—
29C2×#3711C2211yescharacteristic
30#63662C2212yes—
31#63644C2211yescharacteristic
32#63642C2211yescharacteristic
33C3×#835C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63573C2212yes—
37#63566C2212yes—
38#63565C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5622—32no—
43C3×#494—31no—
44C3×#470—31no—
45#5189—32no—
46#5189—31no—
47#5189D311yescharacteristic
48#5184—31no—
49#5184—31no—
50#5184—32no—
51#5184—31no—
52#5184—61no—
53#5183D311yescharacteristic, complemented
54#5137—31no—
55Dic3×M16—31no—
56#5079—32no—
57#5052—32no—
58#4855—31no—
59#4853—31no—
60#4792—32no—
61#4789—32no—
62C4×ΓL(1,𝔽25)—31no—
63#4680—31no—
64C2×C32×Q8C2312yes—
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×Dic6C2312yes—
67C2×#627—22no—
68C2×D3×Dic3D412yes—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73C4×C3⋊Dic3—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×#216—24no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×Dic12—22no—
86C3×ΓL(1,𝔽25)—22no—
87#3724—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92Dic32D412yes—
93#3711—22no—
94#3185—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16—32no—
97C2×C3×Q16—31no—
98C2×C3×Q16C2×D311yescharacteristic
99C2×C3×Q16C2×D311yescharacteristic
100C2×C3×M16—31no—
101C3×C4⋊Q8—32no—
102C3×C22⋊Q8—32no—
103#946—32no—
104#946C2×D312yes—
105Q8×Dic3—32no—
106Q8×Dic3—32no—
107Q8×Dic3—32no—
108Q8×Dic3—62no—
109#944C2×D312yes—
110C2×#216C2×D312yes—
111#924—32no—
112C2×C4×Dic3—31no—
113C2×#208—31no—
114C2×Dic12C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#897—62no—
118#892—62no—
119#890—62no—
120#889—62no—
121#888—32no—
122#887—32no—
123#887—62no—
124#887—62no—
125#878—62no—
126#877—62no—
127C42×D3—31no—
128#869—32no—
129C3×#106—31no—
130C3×#103—32no—
131C3×C4×C8—31no—
132#835—32no—
133#835—32no—
134#835—32no—
135#835—32no—
136#835—62no—
137#835C2×D312yes—
138#817—31no—
139#817—31no—
140#817—32no—
141#817—61no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—31no—
147#815—31no—
148#815—61no—
149C8×Dic3—31no—
150C8×Dic3C2×D311yescharacteristic
151#810—32no—
152#808—32no—
153C4×C3⋊C8—31no—
154C22×C3×D3C2×D411yescharacteristic
155C32×Q8—22no—
156C32×Q8—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D412yes—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D412yes—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×Dic6—22no—
168C3×Dic6—22no—
169#627—44no—
170D3×Dic3—24no—
171C32×C8#4112yes—
172C3⋊(C3⋊C8)—21no—
173C3×C3⋊C8—21no—
174C3×C3⋊C8#4112yes—
175#533—92no—
176#498—91no—
177#494—31no—
178#487—92no—
179#470—31no—
180#470—92no—
181#470—91no—
182#441—92no—
183#441—91no—
184#441—91no—
185C4×M16—91no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C22×C3×C4—31no—
191C22×Dic3—32no—
192C2×C4×D3—32no—
193C2×C4×D3C22×D311yescharacteristic
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6C22×D312yes—
197C3×Q16—24no—
198C3×Q16—22no—
199C3×Q16—22no—
200C3×Q16—64no—
201C3×Q16—62no—
202C3×M16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8C22×D311yescharacteristic
207C2×C3×C8C22×D311yescharacteristic
208C3×C4⋊C4—32no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C22⋊C4—62no—
213C3×C42—31no—
214#217—62no—
215#216—24no—
216(C2×D3)⋊C4—22no—
217(C2×D3)⋊C4—62no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3—62no—
224C4⋊Dic3—62no—
225C4⋊Dic3—122no—
226C4⋊Dic3C22×D312yes—
227Dic3⋊C4—22no—
228Dic3⋊C4—22no—
229Dic3⋊C4—22no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—61no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C4×Dic3—62no—
243C4×Dic3—122no—
244C4×Dic3C22×D311yescharacteristic
245#208—62no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8C22×D311yescharacteristic
250C2×C3⋊C8C22×D311yescharacteristic
251Dic12—22no—
252ΓL(1,𝔽25)—22no—
253ΓL(1,𝔽25)—62no—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—21no—
256C2×C3×D3—22no—
257C32×C4—42no—
258C32×C4C2×#4111yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3⋊Dic3—22no—
261C3⋊Dic3—42no—
262C3×Dic3—21no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C3×Dic3#13714yes—
266C2×Q16—32no—
267C2×Q16—31no—
268C2×Q16D3211yescharacteristic
269C2×M16—31no—
270C2×M16—91no—
271C4⋊Q8—32no—
272C4⋊Q8—92no—
273#125—182no—
274C22⋊Q8—32no—
275C22⋊Q8—92no—
276C22⋊Q8—182no—
277C4×Q8—92no—
278C4×Q8—92no—
279C4×Q8—182no—
280#117—182no—
281C2×C42—91no—
282#106—31no—
283#106—92no—
284#106—91no—
285#103—32no—
286#103—92no—
287#103—92no—
288#103—92no—
289#97—91no—
290#97—91no—
291C4×C8—31no—
292C4×C8—91no—
293C23×C3—31no—
294C22×D3D3×D411yescharacteristic
295C3×Q8—24no—
296C3×Q8—22no—
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—42no—
301C3×Q8—62no—
302C3×Q8—62no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—31no—
308C2×C3×C4—42no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—62no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3D3×D411yescharacteristic
325C2×Dic3D3×D412yes—
326C4×D3—21no—
327C4×D3—21no—
328C4×D3—64no—
329Dic6—22no—
330Dic6—22no—
331Dic6—124no—
332Dic6—124no—
333C3×C8—22no—
334C3×C8—32no—
335C3×C8—61no—
336C3×C8#23712yes—
337C3×C8#23712yes—
338C3⋊C8—21no—
339C3⋊C8—61no—
340C3⋊C8—61no—
341C3⋊C8—121no—
342C3⋊C8#23712yes—
343C2×C32#53211yescharacteristic
344C2×C32C2×#13712yes—
345C3×D3—41no—
346C2×Q8—32no—
347C2×Q8—182no—
348C2×Q8C2×D3212yes—
349C22×C4—31no—
350C22×C4—92no—
351Q16—22no—
352Q16—64no—
353Q16—62no—
354M16—62no—
355M16—182no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—91no—
359C2×C8C2×D3211yescharacteristic
360C4⋊C4—32no—
361C4⋊C4—62no—
362C4⋊C4—62no—
363C4⋊C4—62no—
364C4⋊C4—92no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4—182no—
369C22⋊C4—62no—
370C22⋊C4—182no—
371C42—31no—
372C42—92no—
373C42—91no—
374C42—182no—
375C42—182no—
376C22×C3—21no—
377C22×C3—61no—
378C22×C3—62no—
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C2×D3×D411yescharacteristic
381C2×D3—22no—
382C2×D3—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—34no—
386C3×C4—44no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—61no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4C2×#23711yescharacteristic
393C3×C4C2×#23711yescharacteristic
394C3×C4C2×#23711yescharacteristic
395C3×C4D3×#4111yescharacteristic
396Dic3—21no—
397Dic3—42no—
398Dic3—42no—
399Dic3—62no—
400Dic3—62no—
401Dic3—122no—
402Dic3—122no—
403Dic3—122no—
404Dic3—242no—
405Dic3#91814yes—
406C32#318511yescharacteristic, complemented, Sylow
407C23—31no—
408Q8—22no—
409Q8—22no—
410Q8—62no—
411Q8—62no—
412Q8—364no—
413C2×C4—22no—
414C2×C4—32no—
415C2×C4—31no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—92no—
421C2×C4—184no—
422C2×C4—182no—
423C2×C4C22×D3211yescharacteristic
424C8—32no—
425C8—61no—
426C8—181no—
427C8#380512yes—
428C2×C3—21no—
429C2×C3—22no—
430C2×C3—121no—
431C2×C3#559611yescharacteristic
432C2×C3#571611yescharacteristic
433C2×C3C2×#91812yes—
434C2×C3D3×#13712yes—
435D3—41no—
436C22—61no—
437C22—62no—
438C22D32×D411yescharacteristic
439C4—34no—
440C4—42no—
441C4—61no—
442C4—122no—
443C4—122no—
444C4—182no—
445C4—362no—
446C4D3×#23711yescharacteristic
447C4C2×#380511yescharacteristic
448C3—21no—
449C3#8089311yescharacteristic, complemented
450C3#8179411yescharacteristic, complemented
451C2—121no—
452C2D3×#91812yes—
453C2#1059513311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3185
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10592883C2semidirect
4. C3×#5183C2semidirect
6. #10591623C2semidirect
7. #10591582C2semidirect
8. #10590889C2semidirect
10. #10590819C2semidirect
53. #5183D3semidirect
406. C32#3185semidirect
449. C3#80893semidirect
450. C3#81794semidirect

Maximal subgroups

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

subgroupindex
#105953682
#105928832
C3×#51892
C3×#51832
#105916382
#105916232
#105915822
#105908892
#105908542
#105908192
Dic3×ΓL(1,𝔽25)2
#817943
#808933