Finite Group Databasebeta

← #11876945

Subgroups — #11876945

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595172C212yesmaximal, complemented
2#10592854C211yesmaximal, characteristic, complemented
3C3×#5159C211yesmaximal, characteristic
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591462C212yesmaximal, complemented
6#10591405C212yesmaximal, complemented
7#10591403C212yesmaximal, complemented
8#10590874C211yesmaximal, characteristic, complemented
9#10590853C211yesmaximal, characteristic, complemented
10#10590810C211yesmaximal, characteristic, complemented
11#10590667C211yesmaximal, characteristic, complemented
12#80852—31nomaximal
13#79862—31nomaximal
14C2×C32×D8C2211yescharacteristic
15#64145C2212yes—
16C2×#3754C2212yes—
17C2×#3746C2211yescharacteristic
18C3×#938C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21Dic3×#67—22no—
22#63969—22no—
23#63956—22no—
24#63955—22no—
25C4×D3×Dic3C2211yescharacteristic
26#63872C2212yes—
27#63857C2212yes—
28#63844C2212yes—
29C2×#3711C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#817C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36#63576C2212yes—
37#63567C2212yes—
38#63567C2212yes—
39#63554C2211yescharacteristic
40#63553C2211yescharacteristic
41#5600—32no—
42#5557—32no—
43C3×#469—31no—
44C3×#442—31no—
45#5159D311yescharacteristic
46#5155—31no—
47#5155—31no—
48#5155—61no—
49#5152D311yescharacteristic, complemented
50#5137—31no—
51Dic3×M16—31no—
52#5042—32no—
53#5018—32no—
54#4867—31no—
55#4858—31no—
56#4858—31no—
57#4853—31no—
58#4780—32no—
59#4768—32no—
60#4768—32no—
61#4757—32no—
62#4716—31no—
63#4707—31no—
64C2×C32×D4C2312yes—
65C2×#634C2312yes—
66C2×C3×#67—22no—
67C22×C3×Dic3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×D3×Dic3D412yes—
70C32×D8—22no—
71C2×C32×C8C2311yescharacteristic
72#3757—22no—
73#3757—22no—
74#3754—24no—
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77#3746—22no—
78C3×#217—22no—
79C3×#217—22no—
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×ΓL(1,𝔽25)—22no—
86#3724—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92Dic32D412yes—
93#3711—22no—
94#3183—91noSylow
95C2×C3×D8—21no—
96C2×C3×D8C2×D311yescharacteristic
97C2×C3×D8C2×D311yescharacteristic
98C2×C3×M16—31no—
99C3×#121—32no—
100C3×C4×D4—32no—
101#938C2×D312yes—
102#936—32no—
103#936—32no—
104#936—62no—
105#935—62no—
106D4×Dic3—62no—
107D4×Dic3C2×D312yes—
108C2×#214—32no—
109C2×#214—32no—
110C2×#214—62no—
111C4×#67—62no—
112#926—62no—
113#924—32no—
114C2×C4×Dic3—31no—
115C2×#208—31no—
116C2×Dic12—31no—
117C2×Dic12—31no—
118C2×Dic12—61no—
119C2×ΓL(1,𝔽25)—31no—
120C2×ΓL(1,𝔽25)C2×D311yescharacteristic
121#897—32no—
122#890—32no—
123#890—32no—
124#887—32no—
125#883—62no—
126#879—62no—
127#879—62no—
128#877—62no—
129C42×D3—31no—
130C4×Dic6—32no—
131C3×#106—31no—
132C3×#106—31no—
133C3×#102—32no—
134C3×#102—32no—
135C3×#97—31no—
136#832C2×D312yes—
137#832C2×D312yes—
138#817C2×D311yescharacteristic
139#817C2×D311yescharacteristic
140#816—32no—
141#816—32no—
142#815—31no—
143#815C2×D311yescharacteristic
144C8×Dic3—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—61no—
149#810—32no—
150#810—32no—
151#807—32no—
152#807—32no—
153#803—31no—
154C23×C32—22no—
155C22×C3×D3C2×D411yescharacteristic
156C32×D4—22no—
157C32×D4—22no—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D412yes—
161#634—22no—
162#634—22no—
163C3×#67—44no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—44no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D411yescharacteristic
169C3×C4×D3—21no—
170C3×C4×D3—21no—
171D3×Dic3—42no—
172C32×C8#4112yes—
173C3⋊(C3⋊C8)#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8—21no—
176#529—92no—
177#499—91no—
178#495—91no—
179#488—92no—
180#470—91no—
181#469—31no—
182#468—92no—
183#442—31no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×D4—22no—
188C2×C3×D4—62no—
189C2×C3×D4C22×D312yes—
190C2×C3×D4C22×D312yes—
191C22×C3×C4—31no—
192C22×C3×C4—62no—
193C2×#67—22no—
194C22×Dic3—22no—
195C22×Dic3—32no—
196C2×C4×D3—32no—
197C2×C4×D3C22×D311yescharacteristic
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C3×D8—22no—
202C3×D8—22no—
203C3×D8—42no—
204C3×M16—62no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C3×C4⋊C4—32no—
211C3×C4⋊C4—32no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C42—31no—
215#217—22no—
216#217—22no—
217#217—62no—
218#217—62no—
219#217—62no—
220#217—62no—
221#217—62no—
222#217—122no—
223#217—122no—
224#214—64no—
225#214—64no—
226#214—124no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3C22×D312yes—
232C4⋊Dic3C22×D312yes—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—31no—
239C4×Dic3—31no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—61no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3C22×D311yescharacteristic
246#208—62no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8C22×D311yescharacteristic
251C2×C3⋊C8C22×D311yescharacteristic
252Dic12—62no—
253Dic12—62no—
254Dic12—122no—
255ΓL(1,𝔽25)—22no—
256ΓL(1,𝔽25)—62no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32C22×D411yescharacteristic
261C2×C3×D3—21no—
262C2×C3×D3—22no—
263C32×C4C2×#4111yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—22no—
266C3⋊Dic3—42no—
267C3×Dic3—21no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C2×Q16—91no—
272C2×SD16—92no—
273C2×D8D3211yescharacteristic
274C2×M16—31no—
275C2×M16—91no—
276#126—182no—
277#125—92no—
278#124—92no—
279#123—182no—
280C22⋊Q8—92no—
281#121—32no—
282C4×Q8—92no—
283C4×D4—32no—
284C4×D4—182no—
285#117—182no—
286C2×C42—91no—
287#107—92no—
288#106—31no—
289#106—31no—
290#103—92no—
291#103—92no—
292#102—32no—
293#102—32no—
294#97—31no—
295#97—91no—
296C4×C8—91no—
297C4×C8—91no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—31no—
301C23×C3—42no—
302C22×D3D3×D411yescharacteristic
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—42no—
308C3×D4—42no—
309C3×D4—124no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—32no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—124no—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320#67—44no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—44no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3D3×D411yescharacteristic
332C2×Dic3D3×D412yes—
333C4×D3—21no—
334C4×D3—21no—
335C4×D3—122no—
336Dic6—62no—
337Dic6—62no—
338Dic6—62no—
339Dic6—62no—
340Dic6—122no—
341Dic6—122no—
342C3×C8—22no—
343C3×C8—61no—
344C3×C8—61no—
345C3×C8#23512yes—
346C3×C8#23712yes—
347C3⋊C8—21no—
348C3⋊C8—21no—
349C3⋊C8—32no—
350C3⋊C8—32no—
351C3⋊C8—62no—
352C2×C32—82no—
353C2×C32#53211yescharacteristic
354C2×C32#57512yes—
355C3×D3—41no—
356C2×Q8—92no—
357C2×D4—62no—
358C2×D4C2×D3212yes—
359C22×C4—31no—
360C22×C4—62no—
361C22×C4—92no—
362Q16—182no—
363SD16—184no—
364D8—22no—
365M16—62no—
366M16—182no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—91no—
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—32no—
373C4⋊C4—182no—
374C4⋊C4—182no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C22⋊C4—62no—
378C22⋊C4—62no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—31no—
383C42—92no—
384C42—91no—
385C42—182no—
386C22×C3—21no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—62no—
394C22×C3—61no—
395C22×C3—82no—
396C22×C3—82no—
397C22×C3—82no—
398C22×C3C2×D3×D411yescharacteristic
399C22×C3C2×D3×D411yescharacteristic
400C2×D3—22no—
401C2×D3—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—62no—
405C3×C4—61no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4C2×#23511yescharacteristic
409C3×C4C2×#23711yescharacteristic
410C3×C4D3×#4111yescharacteristic
411C3×C4D3×#4111yescharacteristic
412Dic3—22no—
413Dic3—21no—
414Dic3—42no—
415Dic3—42no—
416Dic3—62no—
417Dic3—62no—
418Dic3—122no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—22no—
424C23—31no—
425Q8—182no—
426Q8—182no—
427D4—22no—
428D4—22no—
429D4—124no—
430C2×C4—32no—
431C2×C4—31no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—92no—
437C2×C4—124no—
438C2×C4—182no—
439C2×C4—362no—
440C2×C4C22×D3211yescharacteristic
441C8—61no—
442C8—61no—
443C8—92no—
444C8#380412yes—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—82no—
448C2×C3—82no—
449C2×C3—121no—
450C2×C3—162no—
451C2×C3#554811yescharacteristic
452C2×C3#559611yescharacteristic
453C2×C3#577312yes—
454C2×C3#577312yes—
455D3—41no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—61no—
460C22—62no—
461C22D32×D411yescharacteristic
462C4—61no—
463C4—62no—
464C4—122no—
465C4—122no—
466C4—182no—
467C4—362no—
468C4#6431211yescharacteristic
469C4C2×#380411yescharacteristic
470C3—21no—
471C3#7986211yescharacteristic, complemented
472C3#8085211yescharacteristic, complemented
473C2—82no—
474C2—121no—
475C2#1059472812yes—
476C2#1059513111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC3×#5159C2
hypercenterC2×D8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595172C2semidirect
2. #10592854C2semidirect
4. C3×#5152C2semidirect
5. #10591462C2semidirect
6. #10591405C2semidirect
7. #10591403C2semidirect
8. #10590874C2semidirect
9. #10590853C2semidirect
10. #10590810C2semidirect
11. #10590667C2semidirect
49. #5152D3semidirect
422. C32#3183semidirect
471. C3#79862semidirect
472. C3#80852semidirect

Maximal subgroups

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

subgroupindex
#105951722
#105928542
C3×#51592
C3×#51522
#105914622
#105914052
#105914032
#105908742
#105908532
#105908102
#105906672
#808523
#798623