Finite Group Databasebeta

← #11876947

Subgroups — #11876947

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595191C212yesmaximal, complemented
2#10592858C211yesmaximal, characteristic
3C3×#5155C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591478C212yesmaximal, complemented
6#10591464C212yesmaximal, complemented
7#10591440C212yesmaximal, complemented
8#10590871C211yesmaximal, characteristic, complemented
9#10590858C211yesmaximal, characteristic, complemented
10#10590812C211yesmaximal, characteristic, complemented
11#10590664C211yesmaximal, characteristic, complemented
12#81812—31nomaximal
13#79862—31nomaximal
14C2×C32×D8C2211yescharacteristic
15#64147C2212yes—
16C2×#3743C2211yescharacteristic
17C3×#936C2212yes—
18C3×D4×Dic3C2212yes—
19C2×C3×#214C2212yes—
20C2×C3×Dic12C2211yescharacteristic
21#63975—22no—
22#63956—22no—
23#63955—22no—
24#63952—22no—
25C4×#624C2211yescharacteristic
26#63871C2212yes—
27#63869C2212yes—
28Dic3×Dic6C2212yes—
29C2×#3712C2211yescharacteristic
30#63659C2212yes—
31#63644C2211yescharacteristic
32C3×#832C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63575C2212yes—
37#63566C2212yes—
38#63565C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5680—32no—
42#5557—32no—
43C3×#495—31no—
44C3×#442—31no—
45#5189—31no—
46#5184—31no—
47#5174—32no—
48#5164—32no—
49#5159—31no—
50#5159—31no—
51#5159—61no—
52#5155D311yescharacteristic, complemented
53#5152D311yescharacteristic, complemented
54#5056—32no—
55#5018—32no—
56#4867—31no—
57#4858—31no—
58#4780—32no—
59#4768—32no—
60#4716—31no—
61#4707—31no—
62C4×ΓL(1,𝔽25)—31no—
63#4683—31no—
64C2×C32×D4C2312yes—
65C2×#638—22no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C22×C3×Dic3—22no—
68C2×C3×Dic6C2312yes—
69C2×#624D412yes—
70C32×D8—22no—
71C2×C32×C8C2311yescharacteristic
72#3757—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3743—22no—
76C3×#217—22no—
77C3×#217—22no—
78C3×#217—22no—
79C3×#214—24no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3C2311yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×Dic12—22no—
86#3724—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91Dic32—22no—
92Dic32D412yes—
93#3712—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×SD16—32no—
97C2×C3×D8—21no—
98C2×C3×D8C2×D311yescharacteristic
99C2×C3×D8C2×D311yescharacteristic
100C3×#124—32no—
101C3×C4×D4—32no—
102#946—32no—
103Q8×Dic3—32no—
104#938—32no—
105#938—32no—
106#938—62no—
107#936C2×D312yes—
108D4×Dic3C2×D312yes—
109C2×#214C2×D312yes—
110C4×#67—62no—
111#926—62no—
112C2×Dic12C2×D311yescharacteristic
113C2×ΓL(1,𝔽25)—31no—
114C2×ΓL(1,𝔽25)—31no—
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)—31no—
117C2×ΓL(1,𝔽25)—61no—
118#897—32no—
119#890—32no—
120#883—62no—
121#883—62no—
122#67⋊C4—62no—
123#879—62no—
124#879—62no—
125#877—62no—
126C42×D3—31no—
127C42×D3—31no—
128#870—32no—
129C4×Dic6—32no—
130C3×#106—31no—
131C3×#102—32no—
132C3×#97—31no—
133C3×C4×C8—31no—
134#835—32no—
135#835—32no—
136#832—32no—
137#832—32no—
138#832—62no—
139#832C2×D312yes—
140#818—32no—
141#817—31no—
142#817—31no—
143#817—61no—
144#817C2×D311yescharacteristic
145#816—32no—
146#815—31no—
147#815C2×D311yescharacteristic
148C8×Dic3—31no—
149C8×Dic3C2×D311yescharacteristic
150#810—32no—
151#807—32no—
152#803—31no—
153C4×C3⋊C8—31no—
154C23×C32—22no—
155C22×C3⋊D3C2×D411yescharacteristic
156C32×D4—22no—
157C32×D4—22no—
158C2×C32×C4C2411yescharacteristic
159#638—44no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—44no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×Dic6—22no—
170C3×Dic6—22no—
171#624—42no—
172C32×C8#4112yes—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—91no—
178#495—31no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—31no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—32no—
188C2×C3×D4—22no—
189C2×C3×D4C22×D312yes—
190C2×C3×D4C22×D312yes—
191C22×C3×C4—62no—
192C2×#67—62no—
193C2×#67—62no—
194C2×#67—122no—
195C22×Dic3—22no—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—61no—
201C2×Dic6C22×D312yes—
202C3×Q16—62no—
203C3×SD16—64no—
204C3×D8—22no—
205C3×D8—22no—
206C3×D8—42no—
207C2×C3×C8—21no—
208C2×C3×C8—31no—
209C2×C3×C8—31no—
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C4⋊C4—32no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C42—31no—
217C3×C42—31no—
218#217—22no—
219#217—22no—
220#217—22no—
221#217—62no—
222#217—62no—
223#217—122no—
224#214—24no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—62no—
242C4×Dic3—62no—
243C4×Dic3C22×D311yescharacteristic
244C4×Dic3C22×D311yescharacteristic
245C2×C3⋊C8—31no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8C22×D311yescharacteristic
249C2×C3⋊C8C22×D311yescharacteristic
250Dic12—22no—
251ΓL(1,𝔽25)—62no—
252ΓL(1,𝔽25)—62no—
253ΓL(1,𝔽25)—62no—
254ΓL(1,𝔽25)—62no—
255ΓL(1,𝔽25)—122no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—21no—
261C2×C3⋊D3—22no—
262C32×C4C2×#4111yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—21no—
265C3⋊Dic3—42no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C2×Q16—31no—
271C2×SD16—32no—
272C2×D8D3211yescharacteristic
273C2×M16—91no—
274C2×M16—91no—
275#126—182no—
276#125—92no—
277#124—32no—
278#123—182no—
279C22⋊Q8—92no—
280#121—92no—
281C4×Q8—92no—
282C4×D4—32no—
283C4×D4—182no—
284#117—182no—
285C2×C42—91no—
286#107—92no—
287#106—31no—
288#106—91no—
289#103—92no—
290#103—92no—
291#102—32no—
292#102—92no—
293#97—31no—
294#97—91no—
295C4×C8—31no—
296C4×C8—91no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—42no—
300C22×D3—31no—
301C22×D3—31no—
302C22×D3—61no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—42no—
310C3×D4—42no—
311C2×C3×C4—21no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—124no—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—124no—
320#67—124no—
321#67—244no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—31no—
325C2×Dic3—31no—
326C2×Dic3—44no—
327C2×Dic3—61no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3D3×D412yes—
332C2×Dic3D3×D412yes—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—61no—
336C4×D3—61no—
337C4×D3—121no—
338C4×D3—121no—
339C4×D3—122no—
340C4×D3—122no—
341Dic6—22no—
342Dic6—22no—
343C3×C8—22no—
344C3×C8—32no—
345C3×C8—61no—
346C3×C8#23512yes—
347C3×C8#23712yes—
348C3⋊C8—21no—
349C3⋊C8—61no—
350C3⋊C8—61no—
351C3⋊C8—121no—
352C3⋊C8#23712yes—
353C2×C32—82no—
354C2×C32#53211yescharacteristic
355C2×C32#57512yes—
356C3⋊D3—41no—
357C2×Q8—32no—
358C2×D4—182no—
359C2×D4C2×D3212yes—
360C22×C4—62no—
361C22×C4—92no—
362C22×C4—91no—
363Q16—62no—
364SD16—64no—
365D8—22no—
366M16—182no—
367M16—182no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—91no—
371C2×C8C2×D3211yescharacteristic
372C4⋊C4—32no—
373C4⋊C4—92no—
374C4⋊C4—182no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C4⋊C4—182no—
378C22⋊C4—62no—
379C22⋊C4—62no—
380C22⋊C4—62no—
381C22⋊C4—182no—
382C22⋊C4—182no—
383C42—31no—
384C42—31no—
385C42—92no—
386C42—182no—
387C22×C3—21no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—82no—
395C22×C3—82no—
396C22×C3—82no—
397C22×C3C2×D3×D411yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3—61no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—61no—
403C2×D3—121no—
404C2×D3—122no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—62no—
408C3×C4—62no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4C2×#23511yescharacteristic
412C3×C4C2×#23711yescharacteristic
413C3×C4C2×#23711yescharacteristic
414C3×C4D3×#4111yescharacteristic
415Dic3—22no—
416Dic3—22no—
417Dic3—42no—
418Dic3—42no—
419Dic3—61no—
420Dic3—61no—
421Dic3—121no—
422Dic3—122no—
423Dic3—122no—
424Dic3—242no—
425C32#318311yescharacteristic, complemented, Sylow
426C23—22no—
427C23—91no—
428Q8—62no—
429Q8—62no—
430D4—22no—
431D4—22no—
432D4—364no—
433C2×C4—32no—
434C2×C4—32no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—91no—
438C2×C4—124no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—182no—
442C2×C4—362no—
443C2×C4C22×D3211yescharacteristic
444C8—32no—
445C8—61no—
446C8—181no—
447C8#380412yes—
448C2×C3—21no—
449C2×C3—22no—
450C2×C3—82no—
451C2×C3—82no—
452C2×C3—162no—
453C2×C3#554811yescharacteristic
454C2×C3#571611yescharacteristic
455C2×C3#576812yes—
456C2×C3#577312yes—
457D3—121no—
458D3—121no—
459D3—241no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—181no—
464C22—182no—
465C22D32×D411yescharacteristic
466C4—62no—
467C4—62no—
468C4—122no—
469C4—122no—
470C4—181no—
471C4—362no—
472C4D3×#23711yescharacteristic
473C4C2×#380411yescharacteristic
474C3—21no—
475C3#7986211yescharacteristic, complemented
476C3#8181211yescharacteristic, complemented
477C2—82no—
478C2—361no—
479C2#1059472912yes—
480C2#1059513911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radical#10592858C2
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. #10595191C2semidirect
3. C3×#5155C2semidirect
4. C3×#5152C2semidirect
5. #10591478C2semidirect
6. #10591464C2semidirect
7. #10591440C2semidirect
8. #10590871C2semidirect
9. #10590858C2semidirect
10. #10590812C2semidirect
11. #10590664C2semidirect
52. #5155D3semidirect
53. #5152D3semidirect
425. C32#3183semidirect
475. C3#79862semidirect
476. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105951912
#105928582
C3×#51552
C3×#51522
#105914782
#105914642
#105914402
#105908712
#105908582
#105908122
#105906642
#818123
#798623