Finite Group Databasebeta

← #11774439

Subgroups — #11774439

Order 1152.

465 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593870C211yesmaximal, characteristic
2C3×#4685C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589325C211yesmaximal, characteristic, complemented
5C3×#4456C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#70760—31nomaximal
9#68233—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C3×C42×D3C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13#63909C411yescharacteristic
14C4×#626—21no—
15#63874—21no—
16#63869C411yescharacteristic
17#63868—21no—
18#63864C411yescharacteristic
19#63856C411yescharacteristic
20#63850—21no—
21C32×C4×C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×(C2×D3)⋊C8—21no—
24C3×Dic3⋊C8—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27(C2×D3)⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29#5580—31no—
30#5479—31no—
31C3×#431—31no—
32#4925—31no—
33#4833—31no—
34#4685D311yescharacteristic, complemented
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4483—31no—
38#4459—31no—
39#4459—31no—
40#4459—31no—
41#4459—61no—
42#4456—31no—
43#4456D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71#1482—91noSylow
72C3×C4×Q8—31no—
73C2×C3×C42—31no—
74#947—31no—
75#946—31no—
76#930—31no—
77#929—61no—
78C4×#67—61no—
79#924—31no—
80#898—61no—
81#895—31no—
82#894—61no—
83#890—31no—
84#876—61no—
85#875—31no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89C4×D12—61no—
90#872—61no—
91#872—61no—
92C42×D3C2×D311yescharacteristic
93#870—31no—
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—31no—
96C3×C4⋊C8—61no—
97C3×C22⋊C8—61no—
98C3×C4×C8—21no—
99C3×C4×C8—31no—
100C3×C4×C8C2×D311yescharacteristic
101C3×C4×C8C2×D311yescharacteristic
102#830—61no—
103(C2×D3)⋊C8—21no—
104(C2×D3)⋊C8—61no—
105Dic3⋊C8—21no—
106C8×Dic3—61no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111C4×C3⋊C8—61no—
112C4×C3⋊C8C2×D311yescharacteristic
113C22×C3⋊D3—21no—
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C4⋊(C3⋊D3)—21no—
120C4⋊(C3⋊D3)—21no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—41no—
133C3×Dic6—21no—
134C3×Dic6—21no—
135#626—42no—
136C32×C8—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140#529—91no—
141#431—31no—
142#431—91no—
143Q8⋊C8—31no—
144Q8⋊C8—91no—
145D4⋊C8—91no—
146D4⋊C8—91no—
147C2×C3×Q8—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C2×#67—61no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—61no—
155C2×D12—61no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—121no—
159C2×C4×D3C4×D311yescharacteristic
160C2×C4×D3D1211yescharacteristic
161C2×C4×D3#6711yescharacteristic
162C2×Dic6C4×D311yescharacteristic
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C42—21no—
171C3×C42—31no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—61no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3C4×D311yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199C4×Dic3—21no—
200C4×Dic3C4×D311yescharacteristic
201C4×Dic3D1211yescharacteristic
202C4×Dic3#6711yescharacteristic
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32C2×C22⋊C411yescharacteristic
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C32×C4—21no—
216C32×C4#13111yescharacteristic
217C32×C4#13111yescharacteristic
218C32×C4#13511yescharacteristic
219C32×C4#13511yescharacteristic
220C3⋊Dic3—41no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—21no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226#126—181no—
227#125—91no—
228#124—91no—
229#123—181no—
230C22⋊Q8—91no—
231#121—91no—
232C4×Q8—31no—
233C4×D4—91no—
234C4×D4—181no—
235#117—181no—
236C2×C42—31no—
237C4⋊C8—31no—
238C4⋊C8—61no—
239C4⋊C8—91no—
240C22⋊C8—61no—
241C22⋊C8—181no—
242C4×C8—31no—
243C4×C8—181no—
244C4×C8D3211yescharacteristic
245C23×C3—31no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—121no—
249C22×D3(C2×D3)⋊C411yescharacteristic
250C3×Q8—61no—
251C3×Q8—61no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—122no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—121no—
277C2×Dic3(C2×D3)⋊C411yescharacteristic
278C2×Dic3(C2×D3)⋊C411yescharacteristic
279C2×Dic3(C2×D3)⋊C411yescharacteristic
280D12—62no—
281D12—61no—
282D12—61no—
283D12—61no—
284D12—61no—
285D12—121no—
286D12—122no—
287C4×D3—21no—
288C4×D3—21no—
289C4×D3—21no—
290C4×D3—21no—
291C4×D3—41no—
292C4×D3—121no—
293C4×D3—121no—
294C4×D3—121no—
295C4×D3—121no—
296C4×D3—241no—
297C4×D3—241no—
298Dic6—21no—
299Dic6—21no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—42no—
303C3×C8—121no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—41no—
307C3⋊C8—121no—
308C3⋊C8—121no—
309C3⋊C8—241no—
310C2×C32#40811yescharacteristic
311C2×C32#41611yescharacteristic
312C2×C32#42111yescharacteristic
313C3⋊D3—81no—
314C3×D3—41no—
315C2×Q8—31no—
316C2×D4—91no—
317C2×D4—181no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—181no—
322C2×C8—21no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—181no—
326C4⋊C4—31no—
327C4⋊C4—61no—
328C4⋊C4—91no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C42—31no—
338C42—31no—
339C42—31no—
340C42—61no—
341C42C2×D3211yescharacteristic
342C22×C3—21no—
343C22×C3—61no—
344C22×C3—61no—
345C22×C3—61no—
346C22×C3D3×C22⋊C411yescharacteristic
347C22×C3C2×(C2×D3)⋊C411yescharacteristic
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—122no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—241no—
359C2×D3—241no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—61no—
368C3×C4—61no—
369C3×C4—61no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4#90111yescharacteristic
373C3×C4#90411yescharacteristic
374C3×C4#90411yescharacteristic
375C3×C4#90711yescharacteristic
376C3×C4#90711yescharacteristic
377C3×C4#90711yescharacteristic
378C3×C4#91611yescharacteristic
379C3×C4#91911yescharacteristic
380Dic3—21no—
381Dic3—21no—
382Dic3—21no—
383Dic3—41no—
384Dic3—41no—
385Dic3—121no—
386Dic3—121no—
387Dic3—241no—
388C32#148211yescharacteristic, complemented, Sylow
389C23—31no—
390C23—181no—
391Q8—61no—
392Q8—61no—
393D4—181no—
394D4—181no—
395D4—362no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—121no—
406C2×C4—181no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4C4×D3211yescharacteristic
410C2×C4D3×D1211yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—41no—
413C8—121no—
414C8—121no—
415C8—361no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—121no—
420C2×C3#472711yescharacteristic
421C2×C3#480411yescharacteristic
422C2×C3#482111yescharacteristic
423C2×C3#500511yescharacteristic
424C2×C3#511311yescharacteristic
425C2×C3#512911yescharacteristic
426D3—41no—
427D3—242no—
428D3—241no—
429D3—241no—
430C22—61no—
431C22—61no—
432C22—61no—
433C22—361no—
434C22—361no—
435C22—361no—
436C22D3×(C2×D3)⋊C411yescharacteristic
437C4—21no—
438C4—61no—
439C4—61no—
440C4—61no—
441C4—121no—
442C4—121no—
443C4—361no—
444C4#6380411yescharacteristic
445C4#6380511yescharacteristic
446C4#6380611yescharacteristic
447C4#6380811yescharacteristic
448C3—21no—
449C3#6823311yescharacteristic, complemented
450C3#7076011yescharacteristic, complemented
451C2—121no—
452C2—721no—
453C2#1059039211yescharacteristic
454C2#1059069011yescharacteristic
455C2#1059095511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radical#63909C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4685C2semidirect
3. #10590248C2semidirect
4. #10589325C2semidirect
5. C3×#4456C2semidirect
6. #10589084C2semidirect
7. #10589082C2semidirect
34. #4685D3semidirect
43. #4456D3semidirect
388. C32#1482semidirect
449. C3#68233semidirect
450. C3#70760semidirect

Maximal subgroups

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

subgroupindex
#105938702
C3×#46852
#105902482
#105893252
C3×#44562
#105890842
#105890822
#707603
#682333