Finite Group Databasebeta

← #11876919

Subgroups — #11876919

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593870C212yesmaximal, complemented
2#10592410C211yesmaximal, characteristic, complemented
3C3×#4716C211yesmaximal, characteristic, complemented
4C3×#4707C211yesmaximal, characteristic, complemented
5#10590872C212yesmaximal, complemented
6#10590871C211yesmaximal, characteristic, complemented
7#10590865C211yesmaximal, characteristic, complemented
8#10590854C211yesmaximal, characteristic, complemented
9#10590850C212yesmaximal, complemented
10#10590835C211yesmaximal, characteristic
11#10590362C212yesmaximal, complemented
12#79826—31nomaximal
13#78534—31nomaximal
14C2×#3745C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2212yes—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C3×C42×D3C2211yescharacteristic
20C3×C4×Dic6C2212yes—
21#63909C2212yes—
22C4×#626—22no—
23#63874—22no—
24#63869C2212yes—
25#63868—22no—
26#63864C2212yes—
27#63856C2212yes—
28#63850—22no—
29C2×#3717C2212yes—
30C32×#97C2211yescharacteristic
31#63648C2212yes—
32#63644C2211yescharacteristic
33C3×#817C2211yescharacteristic
34C3×#816C2212yes—
35C3×C8×Dic3C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×#803C2211yescharacteristic
38#63575C2212yes—
39#63566C2212yes—
40#63564C2212yes—
41#5580—32no—
42#5479—32no—
43C3×#441—31no—
44C3×C4×M16—31no—
45#5191—31no—
46#5189—31no—
47#5137—31no—
48#5135—31no—
49#5134—32no—
50#5026—32no—
51#4865—31no—
52#4858—31no—
53#4812—32no—
54#4800—32no—
55#4716D311yescharacteristic, complemented
56#4711—31no—
57#4711—31no—
58#4711—61no—
59#4710—32no—
60#4707D311yescharacteristic, complemented
61#4697—32no—
62#4696—31no—
63#4683—31no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C3×C4×D3D412yes—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73#3752—22no—
74C4⋊(C3⋊Dic3)C2312yes—
75#3745—22no—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C3×Dic12—22no—
84C3×ΓL(1,𝔽25)—22no—
85C3×ΓL(1,𝔽25)—22no—
86#3724—22no—
87#3724—22no—
88Dic3⋊Dic3—22no—
89#3722—22no—
90#3722—22no—
91#3722—22no—
92(C2×D3)⋊Dic3—22no—
93#3717—24no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×M16—31no—
97C2×C3×M16—31no—
98C3×C4×Q8—32no—
99C2×C3×C42—31no—
100#947—32no—
101#946—32no—
102C2×#215—32no—
103#930—32no—
104#929—62no—
105C4×#67—62no—
106#924—32no—
107C2×Dic12C2×D311yescharacteristic
108C2×D24—31no—
109C2×D24—31no—
110C2×D24—61no—
111C2×#204—32no—
112C2×ΓL(1,𝔽25)C2×D311yescharacteristic
113C2×ΓL(1,𝔽25)C2×D311yescharacteristic
114#898—62no—
115#895—32no—
116#894—62no—
117#890—32no—
118#876—62no—
119#875—32no—
120C4×D12—32no—
121C4×D12—32no—
122C4×D12—62no—
123C4×D12—62no—
124#872—62no—
125#872—62no—
126C42×D3C2×D311yescharacteristic
127#870—32no—
128C4×Dic6C2×D312yes—
129C3×#106—31no—
130C3×#103—32no—
131C3×#97—21no—
132C3×#97—31no—
133C3×#97C2×D311yescharacteristic
134C3×#97C2×D311yescharacteristic
135C3×C4×C8—31no—
136C3×C4×C8—31no—
137#835—32no—
138#821—32no—
139#821—32no—
140#821—32no—
141#821—62no—
142#818—32no—
143#817—31no—
144#817—31no—
145#817—61no—
146#817C2×D311yescharacteristic
147#816—32no—
148#816C2×D312yes—
149C8×Dic3C2×D311yescharacteristic
150C8×Dic3C2×D311yescharacteristic
151#809—32no—
152#807—32no—
153#803C2×D311yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4×C3⋊D3—44no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3C2×D412yes—
165C2×C3×Dic3C2×D411yescharacteristic
166C3×C4×D3—21no—
167C3×C4×D3—21no—
168C3×C4×D3—42no—
169C3×Dic6—22no—
170C3×Dic6—22no—
171#626—44no—
172C32×C8—21no—
173C32×C8#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—91no—
178#495—91no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—31no—
185#440—92no—
186C4×M16—31no—
187C2×C3×Q8—32no—
188C22×C3×C4—31no—
189C22×C3×C4—32no—
190C2×#67—62no—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—62no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—122no—
198C2×C4×D3D1212yes—
199C2×C4×D3C22×D311yescharacteristic
200C2×Dic6C22×D312yes—
201C3×Q16—62no—
202C3×M16—62no—
203C3×M16—62no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C42—21no—
215C3×C42—32no—
216C3×C42—31no—
217C3×C42—62no—
218C3×C42C22×D311yescharacteristic
219C3×C42C22×D311yescharacteristic
220#217—62no—
221#215—64no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3—62no—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—22no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243C4×Dic3—22no—
244C4×Dic3D1212yes—
245C4×Dic3C22×D311yescharacteristic
246C2×C3⋊C8C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248Dic12—22no—
249D24—64no—
250D24—62no—
251D24—62no—
252#204—64no—
253ΓL(1,𝔽25)—22no—
254ΓL(1,𝔽25)—22no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3×D3—21no—
260C2×C3×D3—22no—
261C32×C4—22no—
262C32×C4C2×#4111yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—42no—
265C3×Dic3—21no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C2×Q16—31no—
270C2×SD16—92no—
271C2×D8—91no—
272C2×M16—31no—
273C2×M16—31no—
274#126—182no—
275#125—92no—
276#124—92no—
277#123—182no—
278C22⋊Q8—92no—
279#121—92no—
280C4×Q8—32no—
281C4×D4—92no—
282C4×D4—182no—
283#117—182no—
284C2×C42—31no—
285#107—92no—
286#106—31no—
287#106—91no—
288#103—32no—
289#103—92no—
290#102—92no—
291#102—92no—
292#97—31no—
293#97D3211yescharacteristic
294C4×C8—31no—
295C4×C8—31no—
296C23×C3—31no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3C2×D1211yescharacteristic
301C3×Q8—62no—
302C3×Q8—62no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—32no—
306C2×C3×C4—31no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—122no—
312C2×C3×C4C2×D1212yes—
313C2×C3×C4D3×D412yes—
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316#67—124no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3C2×D1211yescharacteristic
323C2×Dic3C2×D1212yes—
324D12—64no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—62no—
329D12—122no—
330D12—124no—
331C4×D3—21no—
332C4×D3—21no—
333C4×D3—42no—
334C4×D3—124no—
335C4×D3—124no—
336C4×D3—244no—
337Dic6—22no—
338Dic6—22no—
339C3×C8—21no—
340C3×C8—21no—
341C3×C8—22no—
342C3×C8—32no—
343C3×C8—41no—
344C3×C8—61no—
345C3×C8#23512yes—
346C3×C8#23512yes—
347C3⋊C8—21no—
348C3⋊C8#23512yes—
349C2×C32#53211yescharacteristic
350C2×C32#57512yes—
351C3⋊D3—82no—
352C3×D3—41no—
353C2×Q8—32no—
354C2×D4—92no—
355C2×D4—182no—
356C22×C4—31no—
357C22×C4—32no—
358C22×C4—182no—
359Q16—62no—
360SD16—184no—
361D8—182no—
362M16—62no—
363M16—62no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8C2×D3211yescharacteristic
367C2×C8C2×D3211yescharacteristic
368C4⋊C4—32no—
369C4⋊C4—62no—
370C4⋊C4—92no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C4⋊C4—182no—
374C22⋊C4—182no—
375C22⋊C4—182no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C22⋊C4—182no—
379C42—31no—
380C42—32no—
381C42—62no—
382C42C2×D3211yescharacteristic
383C22×C3—21no—
384C22×C3—62no—
385C22×C3—61no—
386C22×C3C22×D1211yescharacteristic
387C22×C3C2×D3×D411yescharacteristic
388C2×D3—21no—
389C2×D3—22no—
390C2×D3—124no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—242no—
398C2×D3—242no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—62no—
405C3×C4—61no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4C2×#23511yescharacteristic
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4D3×#4111yescharacteristic
412Dic3—21no—
413Dic3—22no—
414Dic3—42no—
415Dic3—42no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419C32#318311yescharacteristic, complemented, Sylow
420C23—31no—
421C23—182no—
422Q8—62no—
423Q8—62no—
424D4—182no—
425D4—182no—
426D4—364no—
427C2×C4—32no—
428C2×C4—31no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—122no—
434C2×C4—182no—
435C2×C4—364no—
436C2×C4D3×D1212yes—
437C2×C4C22×D3211yescharacteristic
438C8—21no—
439C8—32no—
440C8—61no—
441C8#379812yes—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—121no—
445C2×C3#547711yescharacteristic
446C2×C3#554811yescharacteristic
447C2×C3#574812yes—
448C2×C3#577712yes—
449D3—41no—
450D3—244no—
451D3—242no—
452D3—242no—
453C22—62no—
454C22—61no—
455C22—362no—
456C22—362no—
457C22—362no—
458C22C2×D3×D1211yescharacteristic
459C4—22no—
460C4—62no—
461C4—61no—
462C4—122no—
463C4—122no—
464C4—362no—
465C4C2×#379811yescharacteristic
466C4D3×#23511yescharacteristic
467C3—21no—
468C3#7853411yescharacteristic, complemented
469C3#7982611yescharacteristic, complemented
470C2—121no—
471C2—722no—
472C2#1059396811yescharacteristic
473C2#1059471112yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10590835C2
hypercenter#97D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593870C2semidirect
2. #10592410C2semidirect
3. C3×#4716C2semidirect
4. C3×#4707C2semidirect
5. #10590872C2semidirect
6. #10590871C2semidirect
7. #10590865C2semidirect
8. #10590854C2semidirect
9. #10590850C2semidirect
11. #10590362C2semidirect
55. #4716D3semidirect
60. #4707D3semidirect
419. C32#3183semidirect
468. C3#78534semidirect
469. C3#79826semidirect

Maximal subgroups

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

subgroupindex
#105938702
#105924102
C3×#47162
C3×#47072
#105908722
#105908712
#105908652
#105908542
#105908502
#105908352
#105903622
#798263
#785343