Finite Group Databasebeta

← #11774845

Subgroups — #11774845

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4#10589085C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#70764—31nomaximal
7#70499—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
19C2×C3×#208—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)—21no—
23C3×C4⋊(C3⋊C8)C2212yes—
24C3×C4×C3⋊C8C2212yes—
25#5479—31no—
26#5479—31no—
27#5479—61no—
28C3×#431—31no—
29C3×#423—31no—
30#4925D311yescharacteristic, complemented
31#4924D311yescharacteristic, 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—
59C3×#208—42no—
60C2×C3×C3⋊C8—22no—
61C2×C3×C3⋊C8—22no—
62#1495—91noSylow
63C2×C3×M16—61no—
64C2×C3×C42—21no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67#930—31no—
68#930—31no—
69#930—61no—
70#929—62no—
71#929—61no—
72#929—61no—
73C4×#67—62no—
74C4×#67—61no—
75C4×#67—61no—
76#924—31no—
77#924—31no—
78#924—61no—
79C2×#208—21no—
80#876—62no—
81#876—61no—
82#876—61no—
83#875—31no—
84#875—31no—
85#875—61no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89#872—62no—
90#872—61no—
91#872—61no—
92#870—31no—
93#870—31no—
94#870—61no—
95C4×Dic6—31no—
96C4×Dic6—31no—
97C4×Dic6—61no—
98C3×C4⋊C8—32no—
99C3×C4⋊C8—61no—
100C3×C4⋊C8—61no—
101C3×C22⋊C8—61no—
102C3×C4×C8—32no—
103#830—21no—
104C4⋊(C3⋊C8)—21no—
105C4⋊(C3⋊C8)—21no—
106C4⋊(C3⋊C8)C2×D312yes—
107C4×C3⋊C8C2×D312yes—
108C23×C32C22⋊C411yescharacteristic
109C22×C3⋊D3—21no—
110C2×C32×C4—22no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—42no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—22no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127#634—22no—
128C3×C3⋊C8—42no—
129C3×C3⋊C8—42no—
130#529—91no—
131#431—31no—
132#423—31no—
133Q8⋊C8—92no—
134D4⋊C8—92no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4D1211yescharacteristic
141C22×C3×C4D1211yescharacteristic
142C22×C3×C4#6711yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C2×#67—62no—
145C2×#67—61no—
146C2×#67—61no—
147C2×D12—31no—
148C2×D12—31no—
149C2×D12—61no—
150C2×C4×D3—62no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—61no—
156C3×M16—122no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42C4×D311yescharacteristic
164C3×C42C4×D311yescharacteristic
165C3×C42D1211yescharacteristic
166C3×C42D1211yescharacteristic
167C3×C42#6711yescharacteristic
168C3×C42#6711yescharacteristic
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172#217—61no—
173#217—61no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
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—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204C4×Dic3—62no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207#208—42no—
208C2×C3⋊C8—22no—
209C2×C3⋊C8—22no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32C2×C22⋊C411yescharacteristic
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4#13112yes—
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C32×C4#13711yescharacteristic
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C2×M16—61no—
228#126—181no—
229#125—91no—
230#124—91no—
231#123—181no—
232C22⋊Q8—91no—
233#121—91no—
234C4×Q8—91no—
235C4×D4—91no—
236C4×D4—181no—
237#117—181no—
238C2×C42D3211yescharacteristic
239C4⋊C8—32no—
240C4⋊C8—61no—
241C4⋊C8—61no—
242C22⋊C8—61no—
243C4×C8—32no—
244C23×C3—21no—
245C23×C3(C2×D3)⋊C411yescharacteristic
246C23×C3(C2×D3)⋊C411yescharacteristic
247C22×D3—62no—
248C22×D3—61no—
249C22×D3—61no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4(C2×D3)⋊C411yescharacteristic
269C2×C3×C4(C2×D3)⋊C411yescharacteristic
270C2×C3×C4(C2×D3)⋊C411yescharacteristic
271C2×C3×C4(C2×D3)⋊C411yescharacteristic
272C2×C3×C4(C2×D3)⋊C411yescharacteristic
273C2×C3×C4(C2×D3)⋊C411yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4C2×D1211yescharacteristic
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280#67—124no—
281#67—122no—
282#67—122no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292D12—62no—
293D12—62no—
294D12—122no—
295C4×D3—122no—
296C4×D3—122no—
297C4×D3—121no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—121no—
301Dic6—62no—
302Dic6—62no—
303Dic6—122no—
304C3×C8—122no—
305C3×C8—122no—
306C3⋊C8—42no—
307C3⋊C8—42no—
308C2×C32—41no—
309C2×C32#40811yescharacteristic
310C2×C32#41711yescharacteristic
311C2×C32#42111yescharacteristic
312C3⋊D3—81no—
313C2×Q8—91no—
314C2×D4—91no—
315C2×D4—181no—
316C22×C4—181no—
317C22×C4#62411yescharacteristic
318C22×C4#62611yescharacteristic
319C22×C4#62611yescharacteristic
320M16—122no—
321C2×C8—62no—
322C2×C8—62no—
323C4⋊C4—91no—
324C4⋊C4—91no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—181no—
335C42#62411yescharacteristic
336C42#62611yescharacteristic
337C42#62611yescharacteristic
338C42C2×D3211yescharacteristic
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3C2×(C2×D3)⋊C411yescharacteristic
350C22×C3C2×(C2×D3)⋊C411yescharacteristic
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4#90112yes—
376C3×C4#90712yes—
377C3×C4#90811yescharacteristic
378C3×C4#90911yescharacteristic
379C3×C4#93211yescharacteristic
380C3×C4#94211yescharacteristic
381Dic3—122no—
382Dic3—122no—
383Dic3—122no—
384Dic3—121no—
385Dic3—121no—
386Dic3—121no—
387Dic3—121no—
388Dic3—121no—
389Dic3—121no—
390C32#149511yescharacteristic, complemented, Sylow
391C23—181no—
392C23#372211yescharacteristic
393Q8—182no—
394D4—182no—
395D4—362no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—181no—
403C2×C4—361no—
404C2×C4—361no—
405C2×C4#372211yescharacteristic
406C2×C4#372211yescharacteristic
407C2×C4#372211yescharacteristic
408C2×C4C2×#62411yescharacteristic
409C2×C4C2×#62611yescharacteristic
410C2×C4C2×#62611yescharacteristic
411C8—122no—
412C8—122no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3#496611yescharacteristic
420C2×C3#500511yescharacteristic
421C2×C3#511011yescharacteristic
422C2×C3#512911yescharacteristic
423C2×C3#513311yescharacteristic
424C2×C3#513911yescharacteristic
425D3—242no—
426D3—241no—
427D3—241no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—361no—
432C22—361no—
433C22—361no—
434C22C2×#372211yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—361no—
440C4—361no—
441C4—361no—
442C4#6381712yes—
443C4#6383011yescharacteristic
444C4#6383311yescharacteristic
445C3—21no—
446C3#7049911yescharacteristic, complemented
447C3#7076411yescharacteristic, complemented
448C2—41no—
449C2—721no—
450C2#1059107311yescharacteristic
451C2#1059110611yescharacteristic
452C2#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#1495
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×#4924C2semidirect
4. #10589085C2semidirect
5. #10589082C2semidirect
30. #4925D3semidirect
31. #4924D3semidirect
390. C32#1495semidirect
446. C3#70499semidirect
447. C3#70764semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#49252
C3×#49242
#105890852
#105890822
#707643
#704993