Finite Group Databasebeta

← #11876920

Subgroups — #11876920

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#10593875C212yesmaximal, complemented
2#10592406C211yesmaximal, characteristic, complemented
3C3×#4716C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5#10590874C211yesmaximal, characteristic, complemented
6#10590869C211yesmaximal, characteristic, complemented
7#10590868C212yesmaximal, complemented
8#10590858C211yesmaximal, characteristic, complemented
9#10590846C211yesmaximal, characteristic
10#10590842C212yesmaximal, complemented
11#10590358C212yesmaximal, complemented
12#79862—31nomaximal
13#79826—31nomaximal
14C2×#3743C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic
19C3×C4×D12C2212yes—
20C3×C4×Dic6C2212yes—
21#63916C2212yes—
22C4×#626—22no—
23#63872C2212yes—
24#63871C2212yes—
25#63863C2212yes—
26#63862—22no—
27#63855—22no—
28#63853—22no—
29C2×#3715C2212yes—
30C32×#97C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63630C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2212yes—
38#63576C2212yes—
39#63565C2212yes—
40#63562C2212yes—
41#5580—32no—
42#5557—32no—
43C3×#442—31no—
44C3×#441—31no—
45#5191—31no—
46#5189—31no—
47#5159—31no—
48#5155—31no—
49#5026—32no—
50#5018—32no—
51#4867—31no—
52#4865—31no—
53#4858—31no—
54#4858—31no—
55#4812—32no—
56#4800—32no—
57#4780—32no—
58#4768—32no—
59#4716D311yescharacteristic, complemented
60#4711D311yescharacteristic, complemented
61#4707—31no—
62#4707—31no—
63#4707—61no—
64C2×C4×C3⋊D3D412yes—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×Dic6C2312yes—
69C2×#626—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×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×Dic12—22no—
85C3×D24—22no—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89#3722—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93#3715—24no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×D8—31no—
97C3×C4×Q8—32no—
98C3×C4×D4—32no—
99#947—32no—
100#946—32no—
101C2×#215—32no—
102#938—32no—
103#936—32no—
104C2×#214—32no—
105C4×#67—62no—
106#926—62no—
107C2×Dic12C2×D311yescharacteristic
108C2×D24C2×D311yescharacteristic
109C2×ΓL(1,𝔽25)—31no—
110C2×ΓL(1,𝔽25)—31no—
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)—61no—
114C2×ΓL(1,𝔽25)—61no—
115#898—62no—
116#897—32no—
117#895—32no—
118#894—62no—
119#890—32no—
120#890—32no—
121#883—62no—
122#879—62no—
123C4×D12—62no—
124C4×D12C2×D312yes—
125#872—62no—
126C42×D3—31no—
127C42×D3—31no—
128C42×D3—61no—
129C4×Dic6C2×D312yes—
130C3×#106—31no—
131C3×#106—31no—
132C3×#103—32no—
133C3×#102—32no—
134C3×#97—21no—
135C3×#97C2×D311yescharacteristic
136C3×#97C2×D311yescharacteristic
137#835—32no—
138#832—32no—
139#821C2×D312yes—
140#817C2×D311yescharacteristic
141#817C2×D311yescharacteristic
142#816C2×D312yes—
143C8×Dic3—31no—
144C8×Dic3—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—61no—
148C8×Dic3—61no—
149#810—32no—
150#809—32no—
151#807—32no—
152#807—32no—
153#803—31no—
154#803—31no—
155#803—61no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C2×D411yescharacteristic
161C2×C3⋊Dic3C2×D412yes—
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×C4×D3—44no—
171C3×Dic6—22no—
172C3×Dic6—22no—
173#626—44no—
174C32×C8—21no—
175C32×C8#4112yes—
176C3⋊(C3⋊C8)—21no—
177C3⋊(C3⋊C8)#4112yes—
178#529—92no—
179#499—91no—
180#495—91no—
181#488—92no—
182#470—91no—
183#469—91no—
184#468—92no—
185#442—31no—
186#441—31no—
187#440—92no—
188C4×M16—91no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C22×C3×C4—62no—
192C2×#67—62no—
193C2×D12—62no—
194C2×D12C22×D312yes—
195C2×C4×D3—22no—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—61no—
201C2×C4×D3—62no—
202C2×Dic6C22×D312yes—
203C3×Q16—62no—
204C3×D8—62no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8C22×D311yescharacteristic
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C42—21no—
216C3×C42—62no—
217C3×C42C22×D311yescharacteristic
218C3×C42C22×D311yescharacteristic
219#217—62no—
220#217—62no—
221#217—62no—
222#215—64no—
223#214—64no—
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—
229(C2×D3)⋊C4—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—22no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—22no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—61no—
245C4×Dic3—62no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—31no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252Dic12—22no—
253D24—22no—
254ΓL(1,𝔽25)—62no—
255ΓL(1,𝔽25)—62no—
256ΓL(1,𝔽25)—64no—
257ΓL(1,𝔽25)—64no—
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—92no—
276C2×D8—31no—
277C2×M16—91no—
278C2×M16—91no—
279#126—182no—
280#125—92no—
281#124—92no—
282#123—182no—
283C22⋊Q8—92no—
284#121—92no—
285C4×Q8—32no—
286C4×D4—32no—
287C4×D4—182no—
288#117—182no—
289C2×C42—91no—
290#107—92no—
291#106—31no—
292#106—31no—
293#103—32no—
294#103—92no—
295#102—32no—
296#102—92no—
297#97—91no—
298#97D3211yescharacteristic
299C4×C8—91no—
300C4×C8—91no—
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×C4—124no—
316C2×C3×C4D3×D412yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320#67—124no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—31no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—31no—
328C2×Dic3—61no—
329C2×Dic3—62no—
330D12—22no—
331D12—22no—
332D12—124no—
333C4×D3—44no—
334C4×D3—62no—
335C4×D3—62no—
336C4×D3—61no—
337C4×D3—61no—
338C4×D3—61no—
339C4×D3—61no—
340C4×D3—122no—
341C4×D3—122no—
342C4×D3—124no—
343Dic6—22no—
344Dic6—22no—
345C3×C8—22no—
346C3×C8—21no—
347C3×C8—21no—
348C3×C8—22no—
349C3×C8#23512yes—
350C3×C8#23512yes—
351C3⋊C8—32no—
352C3⋊C8—32no—
353C3⋊C8—62no—
354C3⋊C8—62no—
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—62no—
365C22×C4—91no—
366C22×C4—92no—
367Q16—62no—
368SD16—184no—
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—182no—
380C4⋊C4—182no—
381C4⋊C4—182no—
382C22⋊C4—62no—
383C22⋊C4—182no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—182no—
387C42—62no—
388C42—91no—
389C42—92no—
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—62no—
402C2×D3—62no—
403C2×D3—61no—
404C2×D3—61no—
405C2×D3—122no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—42no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4D3×#4111yescharacteristic
417C3×C4D3×#4111yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—42no—
421Dic3—62no—
422Dic3—64no—
423Dic3—62no—
424Dic3—62no—
425Dic3—61no—
426Dic3—61no—
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—124no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—362no—
444C2×C4#380212yes—
445C2×C4C22×D3211yescharacteristic
446C8—21no—
447C8—92no—
448C8—181no—
449C8#379812yes—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—242no—
453C2×C3#554811yescharacteristic
454C2×C3#554811yescharacteristic
455C2×C3#577312yes—
456C2×C3#577712yes—
457D3—82no—
458D3—122no—
459D3—121no—
460D3—121no—
461C22—122no—
462C22—122no—
463C22—122no—
464C22—182no—
465C22—181no—
466C22C2×#380211yescharacteristic
467C4—22no—
468C4—122no—
469C4—122no—
470C4—122no—
471C4—182no—
472C4—181no—
473C4C2×#379811yescharacteristic
474C4#6430611yescharacteristic
475C3—21no—
476C3#7982611yescharacteristic, complemented
477C3#7986211yescharacteristic, complemented
478C2—242no—
479C2—361no—
480C2#1059397211yescharacteristic
481C2#1059471812yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10590846C2
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. #10593875C2semidirect
2. #10592406C2semidirect
3. C3×#4716C2semidirect
4. C3×#4711C2semidirect
5. #10590874C2semidirect
6. #10590869C2semidirect
7. #10590868C2semidirect
8. #10590858C2semidirect
10. #10590842C2semidirect
11. #10590358C2semidirect
59. #4716D3semidirect
60. #4711D3semidirect
427. C32#3183semidirect
476. C3#79826semidirect
477. C3#79862semidirect

Maximal subgroups

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

subgroupindex
#105938752
#105924062
C3×#47162
C3×#47112
#105908742
#105908692
#105908682
#105908582
#105908462
#105908422
#105903582
#798623
#798263