Finite Group Databasebeta

← #11876907

Subgroups — #11876907

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593943C212yesmaximal, complemented
2C4×#3743C211yesmaximal, characteristic, complemented
3C3×#4696C211yesmaximal, characteristic, complemented
4C3×#4683C211yesmaximal, characteristic, complemented
5#10590858C211yesmaximal, characteristic, complemented
6#10590846C211yesmaximal, characteristic
7#10590845C212yesmaximal, complemented
8#10590819C211yesmaximal, characteristic, complemented
9#10590781C211yesmaximal, characteristic, complemented
10#10590779C212yesmaximal, complemented
11#10590278C212yesmaximal, complemented
12#81911—31nomaximal
13#81812—31nomaximal
14C2×#3743C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic
19C2×C3×#204C2212yes—
20C3×#875C2212yes—
21C3×#870C2212yes—
22#63916C2212yes—
23#63898C2212yes—
24#63881—22no—
25#63878—22no—
26#63871C2212yes—
27#63862—22no—
28#63853—22no—
29#63843C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63642C2211yescharacteristic
32#63642C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#818C2212yes—
35C3×#817C2211yescharacteristic
36C3×#817C2211yescharacteristic
37#63565C2212yes—
38#63565C2212yes—
39#63562C2212yes—
40#63562C2212yes—
41#5691—32no—
42#5680—32no—
43C3×#499—31no—
44C3×#495—31no—
45#5189—31no—
46#5184—31no—
47#5174—32no—
48#5164—32no—
49#5159—31no—
50#5152—31no—
51#5068—32no—
52#5056—32no—
53#4889—32no—
54#4886—32no—
55#4869—31no—
56#4867—31no—
57#4865—31no—
58#4853—31no—
59#4696D311yescharacteristic, complemented
60C4×ΓL(1,𝔽25)—31no—
61C4×ΓL(1,𝔽25)—31no—
62C4×ΓL(1,𝔽25)—61no—
63#4683D311yescharacteristic, complemented
64C2×C4×C3⋊D3D412yes—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×C3×Dic6C2312yes—
68C2×#626—22no—
69C2×D3×Dic3—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77#3743—22no—
78#3743—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×Dic12—22no—
86C3×D24—22no—
87C3×#204—24no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×SD16—32no—
97C2×C3×D8—31no—
98C3×#125—32no—
99C3×#124—32no—
100#946—32no—
101Q8×Dic3—32no—
102#938—32no—
103D4×Dic3—32no—
104C2×Dic12C2×D311yescharacteristic
105C2×D24C2×D311yescharacteristic
106C2×#204C2×D312yes—
107C2×ΓL(1,𝔽25)—31no—
108C2×ΓL(1,𝔽25)—31no—
109C2×ΓL(1,𝔽25)—31no—
110C2×ΓL(1,𝔽25)—31no—
111C2×ΓL(1,𝔽25)—61no—
112C2×ΓL(1,𝔽25)—61no—
113#898—62no—
114#897—32no—
115#895—32no—
116#894—62no—
117#893—32no—
118#893—62no—
119#892—62no—
120#887—32no—
121#883—62no—
122#67⋊C4—62no—
123#879—62no—
124#877—62no—
125#875C2×D312yes—
126C42×D3—31no—
127C42×D3—31no—
128C42×D3—61no—
129#870C2×D312yes—
130C3×#107—32no—
131C3×#106—31no—
132C3×#106—31no—
133C3×C4×C8—21no—
134C3×C4×C8C2×D311yescharacteristic
135C3×C4×C8C2×D311yescharacteristic
136#835—32no—
137#835—32no—
138#832—32no—
139#832—32no—
140#818C2×D312yes—
141#817C2×D311yescharacteristic
142#817C2×D311yescharacteristic
143#815—31no—
144#815—31no—
145#815—31no—
146#815—31no—
147#815—61no—
148#815—61no—
149#810—32no—
150#810—32no—
151#809—32no—
152#809—32no—
153C4×C3⋊C8—31no—
154C4×C3⋊C8—31no—
155C4×C3⋊C8—61no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C2×D412yes—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C4×C3⋊D3—42no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C3×D12—22no—
169C3×D12—22no—
170C3×Dic6—22no—
171C3×Dic6—22no—
172#626—44no—
173D3×Dic3—44no—
174C32×C8#4112yes—
175C32×C8#4112yes—
176C3⋊(C3⋊C8)—21no—
177C3⋊(C3⋊C8)—21no—
178#529—92no—
179#499—31no—
180#495—31no—
181#488—92no—
182#470—91no—
183#469—91no—
184#468—92no—
185#442—91no—
186#441—91no—
187#440—92no—
188C4×M16—91no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C2×#67—62no—
192C22×Dic3—62no—
193C2×D12—62no—
194C2×D12C22×D312yes—
195C2×C4×D3—31no—
196C2×C4×D3—31no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—61no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×Dic6C22×D312yes—
203C3×Q16—62no—
204C3×SD16—64no—
205C3×D8—62no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C4⋊C4—32no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4—62no—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—21no—
219C3×C42C22×D311yescharacteristic
220C3×C42C22×D311yescharacteristic
221#217—62no—
222#217—62no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3C22×D312yes—
232C4⋊Dic3C22×D312yes—
233Dic3⋊C4—22no—
234Dic3⋊C4—22no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237C4×Dic3—32no—
238C4×Dic3—32no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—61no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C2×C3⋊C8—31no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251Dic12—22no—
252D24—22no—
253#204—24no—
254ΓL(1,𝔽25)—64no—
255ΓL(1,𝔽25)—64no—
256ΓL(1,𝔽25)—62no—
257ΓL(1,𝔽25)—62no—
258ΓL(1,𝔽25)—62no—
259ΓL(1,𝔽25)—62no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—21no—
262C2×C3⋊D3—22no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—22no—
267C32×C4C2×#4111yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—21no—
270C3⋊Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C2×Q16—31no—
275C2×SD16—32no—
276C2×D8—31no—
277C2×M16—91no—
278C2×M16—91no—
279#126—182no—
280#125—32no—
281#124—32no—
282#123—182no—
283C22⋊Q8—92no—
284#121—92no—
285C4×Q8—92no—
286C4×D4—92no—
287C4×D4—182no—
288#117—182no—
289C2×C42—91no—
290#107—32no—
291#106—31no—
292#106—31no—
293#103—92no—
294#103—92no—
295#102—92no—
296#102—92no—
297#97—91no—
298#97—91no—
299C4×C8—91no—
300C4×C8D3211yescharacteristic
301C23×C3—62no—
302C22×D3—22no—
303C22×D3—31no—
304C22×D3—31no—
305C22×D3—61no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×D4—62no—
309C3×D4—62no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4D3×D412yes—
316C2×C3×C4D3×D412yes—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—124no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—31no—
326C2×Dic3—31no—
327C2×Dic3—61no—
328C2×Dic3—62no—
329C2×Dic3—124no—
330D12—22no—
331D12—22no—
332D12—124no—
333C4×D3—62no—
334C4×D3—62no—
335C4×D3—61no—
336C4×D3—61no—
337C4×D3—61no—
338C4×D3—61no—
339C4×D3—122no—
340C4×D3—122no—
341C4×D3—124no—
342C4×D3—124no—
343Dic6—22no—
344Dic6—22no—
345C3×C8—22no—
346C3×C8—22no—
347C3×C8#23712yes—
348C3×C8#23712yes—
349C3×C8#23912yes—
350C3×C8#23912yes—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C3⋊C8—61no—
354C3⋊C8—61no—
355C3⋊C8—61no—
356C3⋊C8—61no—
357C2×C32#53211yescharacteristic
358C2×C32#57512yes—
359C3⋊D3—41no—
360C3×D3—82no—
361C2×Q8—32no—
362C2×D4—32no—
363C2×D4—182no—
364C22×C4—91no—
365C22×C4—92no—
366C22×C4—182no—
367Q16—62no—
368SD16—64no—
369D8—62no—
370M16—182no—
371M16—182no—
372C2×C8—91no—
373C2×C8—91no—
374C2×C8C2×D3211yescharacteristic
375C2×C8C2×D3211yescharacteristic
376C4⋊C4—32no—
377C4⋊C4—32no—
378C4⋊C4—62no—
379C4⋊C4—62no—
380C4⋊C4—182no—
381C4⋊C4—182no—
382C22⋊C4—62no—
383C22⋊C4—62no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—182no—
387C42—91no—
388C42—92no—
389C42—182no—
390C42C2×D3211yescharacteristic
391C22×C3—21no—
392C22×C3—122no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C2×D3×D411yescharacteristic
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—62no—
401C2×D3—61no—
402C2×D3—61no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—122no—
406C3×C4—24no—
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4C2×#23711yescharacteristic
415C3×C4C2×#23711yescharacteristic
416C3×C4C2×#23911yescharacteristic
417C3×C4C2×#23911yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—42no—
421Dic3—62no—
422Dic3—61no—
423Dic3—61no—
424Dic3—62no—
425Dic3—62no—
426Dic3—122no—
427C32#318311yescharacteristic, complemented, Sylow
428C23—62no—
429C23—91no—
430Q8—62no—
431Q8—62no—
432D4—62no—
433D4—62no—
434D4—364no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—92no—
439C2×C4—91no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—362no—
443C2×C4—364no—
444C2×C4#380212yes—
445C2×C4C22×D3211yescharacteristic
446C8—181no—
447C8—181no—
448C8#379612yes—
449C8#379612yes—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—242no—
453C2×C3#571611yescharacteristic
454C2×C3#572511yescharacteristic
455C2×C3#576812yes—
456C2×C3#576812yes—
457D3—82no—
458D3—122no—
459D3—121no—
460D3—121no—
461C22—122no—
462C22—122no—
463C22—122no—
464C22—181no—
465C22—182no—
466C22C2×#380211yescharacteristic
467C4—22no—
468C4—122no—
469C4—122no—
470C4—122no—
471C4—181no—
472C4—182no—
473C4C2×#379611yescharacteristic
474C4C2×#379611yescharacteristic
475C3—21no—
476C3#8181211yescharacteristic, complemented
477C3#8191111yescharacteristic, complemented
478C2—242no—
479C2—361no—
480C2#1059390711yescharacteristic
481C2#1059468512yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590846C2
hypercenterC4×C8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593943C2semidirect
2. C4×#3743C2semidirect
3. C3×#4696C2semidirect
4. C3×#4683C2semidirect
5. #10590858C2semidirect
7. #10590845C2semidirect
8. #10590819C2semidirect
9. #10590781C2semidirect
10. #10590779C2semidirect
11. #10590278C2semidirect
59. #4696D3semidirect
63. #4683D3semidirect
427. C32#3183semidirect
476. C3#81812semidirect
477. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105939432
C4×#37432
C3×#46962
C3×#46832
#105908582
#105908462
#105908452
#105908192
#105907812
#105907792
#105902782
#819113
#818123