Finite Group Databasebeta

← #11876950

Subgroups — #11876950

Order 1152.

795 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#10595382C212yesmaximal, complemented
2#10592888C211yesmaximal, characteristic, complemented
3C3×#5191C211yesmaximal, characteristic, complemented
4C3×#5184C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591590C212yesmaximal, complemented
7#10591566C212yesmaximal, complemented
8#10590871C211yesmaximal, characteristic, complemented
9#10590846C211yesmaximal, characteristic
10#10590771C211yesmaximal, characteristic, complemented
11#10590664C211yesmaximal, characteristic, complemented
12#81812—31nomaximal
13#79826—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64155C2212yes—
16C2×#3743C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C2×C3×D24C2211yescharacteristic
21#63916C2212yes—
22Dic3×D12C2212yes—
23C4×#624C2211yescharacteristic
24#63880—22no—
25#63877—22no—
26#63869C2212yes—
27#63858—22no—
28#63854—22no—
29C2×#3712C2211yescharacteristic
30#63662C2212yes—
31#63644C2211yescharacteristic
32C3×#835C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63575C2212yes—
37#63563C2212yes—
38#63562C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5680—32no—
42#5580—32no—
43C3×#495—31no—
44C3×#441—31no—
45#5191D311yescharacteristic, complemented
46#5189—31no—
47#5189—31no—
48#5189—61no—
49#5184D311yescharacteristic, complemented
50#5174—32no—
51#5164—32no—
52#5159—31no—
53#5152—31no—
54#5056—32no—
55#5026—32no—
56#4865—31no—
57#4858—31no—
58#4812—32no—
59#4800—32no—
60#4711—31no—
61#4707—31no—
62C4×ΓL(1,𝔽25)—31no—
63#4683—31no—
64C2×C32×Q8C2312yes—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×#626—22no—
68C2×#624D412yes—
69C2×D3×Dic3—22no—
70C32×Q16—22no—
71C2×C32×C8C2311yescharacteristic
72#3752—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—22no—
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3743—22no—
77C3×#215—24no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×D24—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3712—22no—
94#3183—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16C2×D311yescharacteristic
97C2×C3×Q16C2×D311yescharacteristic
98C2×C3×SD16—32no—
99C2×C3×D8—31no—
100C3×#124—32no—
101C3×C4×Q8—32no—
102#947C2×D312yes—
103#946—32no—
104#946—32no—
105#946—62no—
106Q8×Dic3C2×D312yes—
107C2×#215C2×D312yes—
108#938—32no—
109D4×Dic3—32no—
110C2×D24C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)—31no—
114C2×ΓL(1,𝔽25)—31no—
115C2×ΓL(1,𝔽25)—61no—
116#898—62no—
117#895—32no—
118#894—62no—
119#890—32no—
120#883—62no—
121#67⋊C4—62no—
122#879—62no—
123#877—62no—
124C4×D12—32no—
125C4×D12—62no—
126#872—62no—
127C42×D3—31no—
128C42×D3—31no—
129#870—32no—
130C3×#106—31no—
131C3×#103—32no—
132C3×#97—31no—
133C3×C4×C8—31no—
134#835—32no—
135#835—32no—
136#835—62no—
137#835C2×D312yes—
138#832—32no—
139#832—32no—
140#821—32no—
141#818—32no—
142#817—31no—
143#817—31no—
144#817—61no—
145#817C2×D311yescharacteristic
146#815—31no—
147#815C2×D311yescharacteristic
148C8×Dic3—31no—
149C8×Dic3C2×D311yescharacteristic
150#809—32no—
151#807—32no—
152#803—31no—
153C4×C3⋊C8—31no—
154C22×C3⋊D3C2×D411yescharacteristic
155C22×C3×D3—22no—
156C32×Q8—22no—
157C32×Q8—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169#626—44no—
170#624—42no—
171D3×Dic3—44no—
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—91no—
184#441—31no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—22no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
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—
201C3×Q16—22no—
202C3×Q16—22no—
203C3×Q16—42no—
204C3×SD16—64no—
205C3×D8—62no—
206C2×C3×C8—21no—
207C2×C3×C8—31no—
208C2×C3×C8—31no—
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C3×C4⋊C4—32no—
212C3×C4⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42—62no—
218#217—62no—
219#217—62no—
220#215—24no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—122no—
228C4⋊Dic3—22no—
229C4⋊Dic3—32no—
230C4⋊Dic3—32no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—122no—
240C4×Dic3—22no—
241C4×Dic3—32no—
242C4×Dic3—32no—
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
250D24—22no—
251ΓL(1,𝔽25)—62no—
252ΓL(1,𝔽25)—62no—
253ΓL(1,𝔽25)—62no—
254ΓL(1,𝔽25)—62no—
255ΓL(1,𝔽25)—122no—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—21no—
258C2×C3⋊D3—22no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C32×C4—42no—
263C32×C4C2×#4111yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—21no—
266C3⋊Dic3—42no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C2×Q16D3211yescharacteristic
271C2×SD16—32no—
272C2×D8—31no—
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—32no—
282C4×D4—92no—
283C4×D4—182no—
284#117—182no—
285C2×C42—91no—
286#107—92no—
287#106—31no—
288#106—91no—
289#103—32no—
290#103—92no—
291#102—92no—
292#102—92no—
293#97—31no—
294#97—91no—
295C4×C8—31no—
296C4×C8—91no—
297C23×C3—62no—
298C22×D3—22no—
299C22×D3—31no—
300C22×D3—31no—
301C22×D3—61no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×D4—62no—
309C3×D4—62no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—32no—
314C2×C3×C4—32no—
315C2×C3×C4—42no—
316C2×C3×C4—62no—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—124no—
320C2×Dic3—22no—
321C2×Dic3—31no—
322C2×Dic3—31no—
323C2×Dic3—61no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—122no—
327C2×Dic3—124no—
328C2×Dic3D3×D412yes—
329C2×Dic3D3×D412yes—
330D12—22no—
331D12—22no—
332D12—124no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—61no—
336C4×D3—61no—
337C4×D3—121no—
338C4×D3—121no—
339C4×D3—122no—
340C4×D3—122no—
341C4×D3—124no—
342C3×C8—22no—
343C3×C8—32no—
344C3×C8—61no—
345C3×C8#23512yes—
346C3×C8#23712yes—
347C3⋊C8—21no—
348C3⋊C8—61no—
349C3⋊C8—61no—
350C3⋊C8—121no—
351C3⋊C8#23712yes—
352C2×C32#53211yescharacteristic
353C2×C32#57512yes—
354C3⋊D3—41no—
355C3×D3—82no—
356C2×Q8C2×D3212yes—
357C2×D4—32no—
358C2×D4—182no—
359C22×C4—92no—
360C22×C4—91no—
361C22×C4—182no—
362Q16—22no—
363SD16—64no—
364D8—62no—
365M16—182no—
366M16—182no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—91no—
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4—92no—
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—31no—
384C42—62no—
385C42—92no—
386C22×C3—21no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C2×D3×D411yescharacteristic
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—42no—
395C2×D3—61no—
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—61no—
399C2×D3—121no—
400C2×D3—122no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—62no—
406C3×C4—62no—
407C3×C4—82no—
408C3×C4—122no—
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23711yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4D3×#4111yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—61no—
417Dic3—61no—
418Dic3—121no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—62no—
424C23—91no—
425Q8—22no—
426Q8—22no—
427D4—62no—
428D4—62no—
429D4—364no—
430C2×C4—22no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—62no—
434C2×C4—91no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—182no—
438C2×C4—362no—
439C2×C4—364no—
440C2×C4C22×D3211yescharacteristic
441C8—32no—
442C8—61no—
443C8—181no—
444C8#380412yes—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—242no—
448C2×C3#554811yescharacteristic
449C2×C3#571611yescharacteristic
450C2×C3#576812yes—
451C2×C3#577712yes—
452D3—82no—
453D3—121no—
454D3—121no—
455D3—241no—
456C22—122no—
457C22—122no—
458C22—122no—
459C22—181no—
460C22—182no—
461C22D32×D411yescharacteristic
462C4—42no—
463C4—62no—
464C4—62no—
465C4—122no—
466C4—181no—
467C4—362no—
468C4D3×#23711yescharacteristic
469C4C2×#380411yescharacteristic
470C3—21no—
471C3#7982611yescharacteristic, complemented
472C3#8181211yescharacteristic, complemented
473C2—242no—
474C2—361no—
475C2#1059476312yes—
476C2#1059513911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10590846C2
hypercenterC2×Q16D32
hypocenterC32#3183
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
1. #10595382C2semidirect
2. #10592888C2semidirect
3. C3×#5191C2semidirect
4. C3×#5184C2semidirect
5. #10591614C2semidirect
6. #10591590C2semidirect
7. #10591566C2semidirect
8. #10590871C2semidirect
10. #10590771C2semidirect
11. #10590664C2semidirect
45. #5191D3semidirect
49. #5184D3semidirect
422. C32#3183semidirect
471. C3#79826semidirect
472. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105953822
#105928882
C3×#51912
C3×#51842
#105916142
#105915902
#105915662
#105908712
#105908462
#105907712
#105906642
#818123
#798263