Finite Group Databasebeta

← #11877037

Subgroups — #11877037

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595367C212yesmaximal
2#10592882C211yesmaximal, characteristic, complemented
3C3×#5189C211yesmaximal, characteristic
4C3×#5184C211yesmaximal, characteristic, complemented
5#10591598C212yesmaximal
6#10591541C212yesmaximal, complemented
7#10591538C212yesmaximal, complemented
8#10590900C211yesmaximal, characteristic, complemented
9#10590853C211yesmaximal, characteristic
10#10590810C211yesmaximal, characteristic, complemented
11#10590667C211yesmaximal, characteristic
12#80893—31nomaximal
13#79838—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64153C2212yes—
16C2×#3756C2212yes—
17C2×#3746C2211yescharacteristic
18C3×#946C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#63919C2212yes—
22#63899—22no—
23#63877—22no—
24C4×D3×Dic3C2211yescharacteristic
25#63857C2212yes—
26#63847—22no—
27#63844C2212yes—
28#63837—22no—
29C2×#3711C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#817C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36#63574C2212yes—
37#63567C2212yes—
38#63567C2212yes—
39#63554C2211yescharacteristic
40#63553C2211yescharacteristic
41#5622—32no—
42#5578—32no—
43C3×#470—31no—
44C3×#441—31no—
45#5189D311yescharacteristic
46#5184D311yescharacteristic, complemented
47#5183—31no—
48#5183—31no—
49#5183—61no—
50#5137—31no—
51Dic3×M16—31no—
52#5052—32no—
53#5030—32no—
54#4867—31no—
55#4855—31no—
56#4855—31no—
57#4853—31no—
58#4816—32no—
59#4792—32no—
60#4792—32no—
61#4789—32no—
62#4716—31no—
63#4707—31no—
64C2×C32×Q8C2312yes—
65C2×#634C2312yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×#627—22no—
68C2×D3×Dic3D412yes—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71#3756—24no—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3746—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×ΓL(1,𝔽25)—22no—
87#3724—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92Dic32D412yes—
93#3711—22no—
94#3185—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16C2×D311yescharacteristic
97C2×C3×Q16C2×D311yescharacteristic
98C2×C3×M16—31no—
99C3×C22⋊Q8—32no—
100C3×C4×Q8—32no—
101#946C2×D312yes—
102Q8×Dic3C2×D312yes—
103#944—32no—
104#944—32no—
105#944—62no—
106C2×#216—32no—
107C2×#216—32no—
108C2×#216—62no—
109#924—32no—
110C2×C4×Dic3—31no—
111C2×#208—31no—
112C2×Dic12—31no—
113C2×Dic12—31no—
114C2×Dic12—61no—
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#897—32no—
118#896—62no—
119#889—62no—
120#889—62no—
121#888—32no—
122#888—32no—
123#887—32no—
124#887—62no—
125#878—62no—
126#877—62no—
127#872—62no—
128C42×D3—31no—
129C4×Dic6—32no—
130C4×Dic6—62no—
131C3×#106—31no—
132C3×#106—31no—
133C3×#103—32no—
134C3×#103—32no—
135C3×#97—31no—
136#835C2×D312yes—
137#835C2×D312yes—
138#817C2×D311yescharacteristic
139#817C2×D311yescharacteristic
140#816—32no—
141#816—32no—
142#815—31no—
143#815C2×D311yescharacteristic
144C8×Dic3—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—61no—
149#810—32no—
150#810—32no—
151#808—32no—
152#808—32no—
153#803—31no—
154C22×C3×D3C2×D411yescharacteristic
155C32×Q8—22no—
156C32×Q8—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D412yes—
161#634—22no—
162#634—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D411yescharacteristic
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169#627—44no—
170D3×Dic3—24no—
171C32×C8#4112yes—
172C3⋊(C3⋊C8)#4112yes—
173C3×C3⋊C8—21no—
174C3×C3⋊C8—21no—
175#533—92no—
176#498—91no—
177#494—91no—
178#487—92no—
179#470—31no—
180#470—92no—
181#470—91no—
182#441—31no—
183#441—91no—
184#441—92no—
185C4×M16—91no—
186C2×C3×Q8—22no—
187C2×C3×Q8C22×D312yes—
188C2×C3×Q8C22×D312yes—
189C22×C3×C4—31no—
190C22×Dic3—32no—
191C2×C4×D3—32no—
192C2×C4×D3C22×D311yescharacteristic
193C2×Dic6—32no—
194C2×Dic6—32no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C3×Q16—22no—
199C3×Q16—22no—
200C3×Q16—42no—
201C3×M16—62no—
202C2×C3×C8—21no—
203C2×C3×C8—31no—
204C2×C3×C8—31no—
205C2×C3×C8C22×D311yescharacteristic
206C2×C3×C8C22×D311yescharacteristic
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4—62no—
211C3×C22⋊C4—62no—
212C3×C42—31no—
213C3×C42—62no—
214#217—62no—
215#216—64no—
216#216—64no—
217#216—124no—
218(C2×D3)⋊C4—22no—
219(C2×D3)⋊C4—62no—
220C4⋊Dic3—22no—
221C4⋊Dic3—62no—
222C4⋊Dic3C22×D312yes—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—22no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—122no—
235Dic3⋊C4—122no—
236C4×Dic3—22no—
237C4×Dic3—31no—
238C4×Dic3—31no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—61no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C4×Dic3C22×D311yescharacteristic
245#208—62no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8C22×D311yescharacteristic
250C2×C3⋊C8C22×D311yescharacteristic
251Dic12—62no—
252Dic12—62no—
253Dic12—122no—
254ΓL(1,𝔽25)—22no—
255ΓL(1,𝔽25)—62no—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—21no—
258C2×C3×D3—22no—
259C32×C4—42no—
260C32×C4C2×#4111yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3⋊Dic3—42no—
263C3⋊Dic3#13714yes—
264C3×Dic3—21no—
265C3×Dic3—22no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C2×Q16—92no—
269C2×Q16—91no—
270C2×Q16D3211yescharacteristic
271C2×M16—31no—
272C2×M16—91no—
273C4⋊Q8—92no—
274C4⋊Q8—92no—
275#125—182no—
276C22⋊Q8—32no—
277C22⋊Q8—92no—
278C22⋊Q8—182no—
279C4×Q8—32no—
280C4×Q8—92no—
281C4×Q8—182no—
282#117—182no—
283C2×C42—91no—
284#106—31no—
285#106—31no—
286#106—92no—
287#103—32no—
288#103—32no—
289#103—92no—
290#103—92no—
291#97—31no—
292#97—91no—
293C4×C8—91no—
294C4×C8—91no—
295C23×C3—31no—
296C22×D3D3×D411yescharacteristic
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—42no—
302C3×Q8—42no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—31no—
307C2×C3×C4—32no—
308C2×C3×C4—42no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—62no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3D3×D412yes—
325C2×Dic3D3×D411yescharacteristic
326C4×D3—21no—
327C4×D3—21no—
328C4×D3—64no—
329Dic6—62no—
330Dic6—62no—
331Dic6—62no—
332Dic6—62no—
333Dic6—122no—
334Dic6—122no—
335Dic6—124no—
336Dic6—124no—
337C3×C8—22no—
338C3×C8—61no—
339C3×C8—61no—
340C3×C8#23512yes—
341C3×C8#23712yes—
342C3⋊C8—21no—
343C3⋊C8—21no—
344C3⋊C8—32no—
345C3⋊C8—32no—
346C3⋊C8—62no—
347C2×C32#53211yescharacteristic
348C2×C32C2×#13712yes—
349C3×D3—41no—
350C2×Q8—92no—
351C2×Q8—182no—
352C2×Q8C2×D3212yes—
353C22×C4—31no—
354C22×C4—92no—
355Q16—22no—
356Q16—184no—
357Q16—182no—
358M16—62no—
359M16—182no—
360C2×C8—31no—
361C2×C8—31no—
362C2×C8—91no—
363C2×C8C2×D3211yescharacteristic
364C4⋊C4—32no—
365C4⋊C4—32no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—182no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C22⋊C4—62no—
374C22⋊C4—182no—
375C42—31no—
376C42—62no—
377C42—92no—
378C42—91no—
379C42—182no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—61no—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C2×D3×D411yescharacteristic
385C2×D3—22no—
386C2×D3—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—62no—
392C3×C4—61no—
393C3×C4—82no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4C2×#23511yescharacteristic
397C3×C4C2×#23711yescharacteristic
398C3×C4D3×#4111yescharacteristic
399C3×C4D3×#4111yescharacteristic
400Dic3—22no—
401Dic3—21no—
402Dic3—34no—
403Dic3—34no—
404Dic3—42no—
405Dic3—42no—
406Dic3—64no—
407Dic3—122no—
408Dic3—122no—
409Dic3—242no—
410C32#318511yescharacteristic, complemented, Sylow
411C23—31no—
412Q8—22no—
413Q8—22no—
414Q8—182no—
415Q8—182no—
416Q8—364no—
417C2×C4—22no—
418C2×C4—32no—
419C2×C4—31no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—92no—
425C2×C4—184no—
426C2×C4—182no—
427C2×C4C22×D3211yescharacteristic
428C8—61no—
429C8—61no—
430C8—92no—
431C8#380412yes—
432C2×C3—21no—
433C2×C3—22no—
434C2×C3—121no—
435C2×C3#554811yescharacteristic
436C2×C3#559611yescharacteristic
437C2×C3D3×#13712yes—
438C2×C3D3×#13712yes—
439D3—41no—
440C22—61no—
441C22—62no—
442C22D32×D411yescharacteristic
443C4—42no—
444C4—61no—
445C4—62no—
446C4—94no—
447C4—122no—
448C4—122no—
449C4—362no—
450C4#6431211yescharacteristic
451C4C2×#380411yescharacteristic
452C3—21no—
453C3#7983811yescharacteristic, complemented
454C3#8089311yescharacteristic, complemented
455C2—121no—
456C2#1059476012yes—
457C2#1059513111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3185
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
2. #10592882C2semidirect
4. C3×#5184C2semidirect
6. #10591541C2semidirect
7. #10591538C2semidirect
8. #10590900C2semidirect
10. #10590810C2semidirect
46. #5184D3semidirect
410. C32#3185semidirect
453. C3#79838semidirect
454. C3#80893semidirect

Maximal subgroups

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

subgroupindex
#105953672
#105928822
C3×#51892
C3×#51842
#105915982
#105915412
#105915382
#105909002
#105908532
#105908102
#105906672
#808933
#798383