Finite Group Databasebeta

← #11774437

Subgroups — #11774437

Order 1152.

541 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10589085C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#70760—31nomaximal
7#70759—31nomaximal
8C2×C32×C42C2211yescharacteristic
9#64139C411yescharacteristic
10#64138—21no—
11C4×#638—21no—
12#64133C411yescharacteristic
13#64085—21no—
14#64084C411yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64081—21no—
17#64079C411yescharacteristic
18C4×#634C2211yescharacteristic
19C3×#830—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×C4×C3⋊C8—21no—
24C3×C4×C3⋊C8C2212yes—
25#5479—31no—
26#5479—31no—
27#5479—61no—
28C3×#431—31no—
29C3×#431—31no—
30#4925D311yescharacteristic, complemented
31#4925D311yescharacteristic, complemented
32#4484—32no—
33#4483—32no—
34#4459—32no—
35#4456—32no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×#638—21no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634C2×C411yescharacteristic
43C32×C42C2×C411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42C2311yescharacteristic
47#3757—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55#3750—21no—
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61#1482—91noSylow
62C2×C3×C42—21no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65#930—31no—
66#930—31no—
67#930—61no—
68#929—62no—
69#929—61no—
70#929—61no—
71C4×#67—62no—
72C4×#67—61no—
73C4×#67—61no—
74#924—31no—
75#924—31no—
76#924—61no—
77#876—62no—
78#876—61no—
79#876—61no—
80#875—31no—
81#875—31no—
82#875—61no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86#872—62no—
87#872—61no—
88#872—61no—
89#870—31no—
90#870—31no—
91#870—61no—
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—61no—
95C3×C4⋊C8—32no—
96C3×C4⋊C8—61no—
97C3×C22⋊C8—61no—
98C3×C22⋊C8—61no—
99C3×C4×C8—32no—
100C3×C4×C8—61no—
101#830—21no—
102#830—21no—
103C4⋊(C3⋊C8)—21no—
104C4⋊(C3⋊C8)C2×D312yes—
105C4×C3⋊C8—21no—
106C4×C3⋊C8C2×D312yes—
107C23×C32C22⋊C411yescharacteristic
108C22×C3⋊D3—21no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118#638—42no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C4⋊(C3⋊D3)—22no—
123C4×C3⋊D3—42no—
124#634—22no—
125C3×C3⋊C8—42no—
126C3×C3⋊C8—42no—
127#529—91no—
128#431—31no—
129#431—31no—
130Q8⋊C8—92no—
131D4⋊C8—92no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4C4×D311yescharacteristic
136C22×C3×C4C4×D311yescharacteristic
137C22×C3×C4D1211yescharacteristic
138C22×C3×C4D1211yescharacteristic
139C22×C3×C4#6711yescharacteristic
140C22×C3×C4#6711yescharacteristic
141C2×#67—62no—
142C2×#67—61no—
143C2×#67—61no—
144C2×D12—31no—
145C2×D12—31no—
146C2×D12—61no—
147C2×C4×D3—62no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×Dic6—31no—
151C2×Dic6—31no—
152C2×Dic6—61no—
153C2×C3×C8—62no—
154C2×C3×C8—62no—
155C3×C42—21no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42C4×D311yescharacteristic
160C3×C42C4×D311yescharacteristic
161C3×C42D1211yescharacteristic
162C3×C42D1211yescharacteristic
163C3×C42#6711yescharacteristic
164C3×C42#6711yescharacteristic
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167#217—62no—
168#217—61no—
169#217—61no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200C4×Dic3—62no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C2×C3⋊C8—22no—
204C2×C3⋊C8—22no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32C2×C22⋊C411yescharacteristic
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C32×C4—21no—
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4#13112yes—
217C32×C4#13512yes—
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3⋊Dic3—41no—
221#126—181no—
222#125—91no—
223#124—91no—
224#123—181no—
225C22⋊Q8—91no—
226#121—91no—
227C4×Q8—91no—
228C4×D4—91no—
229C4×D4—181no—
230#117—181no—
231C2×C42D3211yescharacteristic
232C4⋊C8—32no—
233C4⋊C8—61no—
234C22⋊C8—61no—
235C22⋊C8—61no—
236C4×C8—32no—
237C4×C8—61no—
238C23×C3—21no—
239C23×C3(C2×D3)⋊C411yescharacteristic
240C23×C3(C2×D3)⋊C411yescharacteristic
241C22×D3—62no—
242C22×D3—61no—
243C22×D3—61no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—42no—
259C2×C3×C4(C2×D3)⋊C411yescharacteristic
260C2×C3×C4(C2×D3)⋊C411yescharacteristic
261C2×C3×C4(C2×D3)⋊C411yescharacteristic
262C2×C3×C4(C2×D3)⋊C411yescharacteristic
263C2×C3×C4(C2×D3)⋊C411yescharacteristic
264C2×C3×C4(C2×D3)⋊C411yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—124no—
272#67—122no—
273#67—122no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283D12—62no—
284D12—62no—
285D12—122no—
286C4×D3—124no—
287C4×D3—122no—
288C4×D3—122no—
289Dic6—62no—
290Dic6—62no—
291Dic6—122no—
292C3×C8—122no—
293C3×C8—122no—
294C3⋊C8—42no—
295C3⋊C8—42no—
296C2×C32—41no—
297C2×C32#40811yescharacteristic
298C2×C32#41611yescharacteristic
299C2×C32#42111yescharacteristic
300C3⋊D3—81no—
301C2×Q8—91no—
302C2×D4—91no—
303C2×D4—181no—
304C22×C4—181no—
305C22×C4#62411yescharacteristic
306C22×C4#62611yescharacteristic
307C22×C4#62611yescharacteristic
308C2×C8—62no—
309C2×C8—62no—
310C4⋊C4—91no—
311C4⋊C4—91no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C22⋊C4—181no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—181no—
321C42—181no—
322C42#62411yescharacteristic
323C42#62611yescharacteristic
324C42#62611yescharacteristic
325C42C2×D3211yescharacteristic
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3C2×(C2×D3)⋊C411yescharacteristic
337C22×C3C2×(C2×D3)⋊C411yescharacteristic
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4#90112yes—
362C3×C4#90412yes—
363C3×C4#90712yes—
364C3×C4#95012yes—
365Dic3—122no—
366Dic3—122no—
367Dic3—122no—
368Dic3—121no—
369Dic3—121no—
370Dic3—121no—
371Dic3—121no—
372Dic3—121no—
373Dic3—121no—
374C32#148211yescharacteristic, complemented, Sylow
375C23—181no—
376C23#372211yescharacteristic
377Q8—182no—
378D4—182no—
379D4—362no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—181no—
386C2×C4—362no—
387C2×C4#372211yescharacteristic
388C2×C4#372211yescharacteristic
389C2×C4#372211yescharacteristic
390C2×C4C2×#62411yescharacteristic
391C2×C4C2×#62611yescharacteristic
392C2×C4C2×#62611yescharacteristic
393C8—122no—
394C8—122no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—42no—
399C2×C3—41no—
400C2×C3—41no—
401C2×C3#500211yescharacteristic
402C2×C3#500511yescharacteristic
403C2×C3#511011yescharacteristic
404C2×C3#511311yescharacteristic
405C2×C3#512911yescharacteristic
406C2×C3#513911yescharacteristic
407D3—242no—
408D3—241no—
409D3—241no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—361no—
414C22—361no—
415C22—361no—
416C22C2×#372211yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—361no—
422C4—361no—
423C4—361no—
424C4#6381712yes—
425C4#6382912yes—
426C3—21no—
427C3#7075911yescharacteristic, complemented
428C3#7076011yescharacteristic, complemented
429C2—41no—
430C2—721no—
431C2#1059107311yescharacteristic
432C2#1059110511yescharacteristic
433C2#1059111311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×#4925C2semidirect
4. #10589085C2semidirect
5. #10589082C2semidirect
30. #4925D3semidirect
31. #4925D3semidirect
374. C32#1482semidirect
427. C3#70759semidirect
428. C3#70760semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#49252
#105890852
#105890822
#707603
#707593