Finite Group Databasebeta

← #11785492

Subgroups — #11785492

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C3×#5006C211yesmaximal, characteristic
3C3×#4998C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic
5#10591122C211yesmaximal, characteristic, complemented
6#10589397C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70664—31nomaximal
9#70041—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711C412yescomplemented
18#63814—21no—
19#63814—21no—
20#63814—21no—
21#63814—21no—
22C2×D3×C3⋊C8C412yescomplemented
23C3×#808—21no—
24C3×#807—21no—
25C3×#806—22no—
26#63580—22no—
27#63575—21no—
28#63573—21no—
29C2×#948—31no—
30C2×#901—31no—
31C3×#427—31no—
32C3×#410—31no—
33#5240—31no—
34#5106—31no—
35#5006—31no—
36#5006D311yescharacteristic
37#4998—31no—
38#4998D311yescharacteristic, complemented
39#4531—31no—
40#4531—31no—
41#4531—31no—
42#4531—31no—
43#4531—61no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67D412yes—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12Q811yescharacteristic
51C2×C3×C4×D3C2×C412yes—
52C2×C3×Dic6Q811yescharacteristic
53C32×C4⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4×C3⋊Dic3—21no—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)C2×C412yes—
62C3×#217—21no—
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C2×C3×C3⋊C8C2×C411yescharacteristic
69C2×C3×C3⋊C8C2×C411yescharacteristic
70C2×C3×C3⋊C8D411yescharacteristic
71C2×C3×C3⋊C8D411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74#3711—22no—
75#3711—22no—
76D3×C3⋊C8—22no—
77D3×C3⋊C8—22no—
78#1812—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C22×C3×C8—31no—
82C3×#117—21no—
83C3×#117—31no—
84C3×#117—31no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87#948—61no—
88#948—61no—
89#948—61no—
90#948—61no—
91#926—31no—
92#926—31no—
93#926—61no—
94#926C2×D311yescharacteristic
95#926C2×D311yescharacteristic
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—32no—
99C2×#208—61no—
100C22×C3⋊C8—32no—
101C22×C3⋊C8C2×D311yescharacteristic
102#901—61no—
103#901—61no—
104#901—61no—
105#901—61no—
106C2×ΓL(1,𝔽25)—32no—
107C2×D3×C8—32no—
108C3×#107—61no—
109C3×#106—61no—
110C3×#99—62no—
111#834—62no—
112#818—61no—
113#817—61no—
114#808—21no—
115#808—61no—
116#807—21no—
117#807—61no—
118#806—22no—
119#806—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3C4⋊C412yes—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—41no—
130C3×#67—22no—
131C3×#67—22no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C4⋊C412yes—
135C3×D12—21no—
136C3×D12—21no—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×Dic6—21no—
140C3×Dic6—21no—
141C3⋊(C3⋊C8)—22no—
142C3×C3⋊C8C22⋊C411yescharacteristic
143C3×C3⋊C8C22⋊C411yescharacteristic
144C3×C3⋊C8C22⋊C411yescharacteristic
145C3×C3⋊C8C22⋊C411yescharacteristic
146C2×#131—91no—
147#427—31no—
148#427—91no—
149#410—31no—
150#410—91no—
151H(3,ℤ/4)—91no—
152H(3,ℤ/4)—91no—
153C3×#41—61no—
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—32no—
159C2×C3×D4—31no—
160C22×C3×C4—21no—
161C22×C3×C4—32no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67#6712yes—
165#235—21no—
166#235—21no—
167#235—21no—
168#235—21no—
169C2×D12Dic611yescharacteristic
170C2×C4×D3C4×D312yes—
171C2×Dic6Dic611yescharacteristic
172C2×C3×C8—31no—
173C2×C3×C8—31no—
174C2×C3×C8—31no—
175C2×C3×C8—31no—
176C2×C3×C8—31no—
177C2×C3×C8—31no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—22no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—61no—
192C3×C42—61no—
193#217—21no—
194#217—21no—
195#217—61no—
196#217—61no—
197#217—121no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—121no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3—62no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208#208—61no—
209#208—61no—
210#208—61no—
211#208—61no—
212#208—62no—
213#208—62no—
214#208—121no—
215#208—121no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8C4×D311yescharacteristic
222C2×C3⋊C8C4×D311yescharacteristic
223C2×C3⋊C8D1211yescharacteristic
224C2×C3⋊C8D1211yescharacteristic
225C2×C3⋊C8#6711yescharacteristic
226C2×C3⋊C8#6711yescharacteristic
227ΓL(1,𝔽25)—62no—
228ΓL(1,𝔽25)—62no—
229D3×C8—62no—
230D3×C8—62no—
231C22×C32—41no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32#12111yescharacteristic
235C2×C3×D3—22no—
236C2×C3×D3—42no—
237C32×C4—81no—
238C32×C4C2×C22⋊C411yescharacteristic
239C32×C4#11711yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C3⋊Dic3—81no—
243C3×Dic3—22no—
244C3×Dic3—81no—
245C3×Dic3—81no—
246C2×#41—31no—
247#131—181no—
248#131—181no—
249#131—181no—
250#131—181no—
251C2×M16—92no—
252C2×M16—91no—
253C22×C8—31no—
254C22×C8—92no—
255#117—31no—
256#117—31no—
257#117—91no—
258#117D3211yescharacteristic
259#107—61no—
260#107—181no—
261#106—61no—
262#106—181no—
263#99—62no—
264#99—182no—
265C23×C3—21no—
266C23×C3—32no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3Dic3⋊C412yes—
270C3×Q8—61no—
271C3×Q8—61no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C3×D4—61no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—32no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4C2×Dic611yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23711yescharacteristic
299C2×C3×C4D3×Q811yescharacteristic
300C2×C3×C4#23911yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—22no—
303#67—22no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—122no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3Dic3⋊C412yes—
310D12—21no—
311D12—21no—
312C4×D3—22no—
313C4×D3—22no—
314Dic6—21no—
315Dic6—21no—
316C3×C8—31no—
317C3×C8—31no—
318C3×C8—31no—
319C3×C8—31no—
320C3⋊C8—62no—
321C3⋊C8—62no—
322C3⋊C8—122no—
323C3⋊C8(C2×D3)⋊C411yescharacteristic
324C3⋊C8(C2×D3)⋊C411yescharacteristic
325C3⋊C8(C2×D3)⋊C411yescharacteristic
326C3⋊C8(C2×D3)⋊C411yescharacteristic
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32#38011yescharacteristic
331C3×D3—42no—
332#41—61no—
333#41—61no—
334#41—61no—
335#41—61no—
336C2×Q8—31no—
337C2×D4—32no—
338C2×D4—31no—
339C22×C4—32no—
340C22×C4C2×D3211yescharacteristic
341M16—182no—
342M16—182no—
343M16—181no—
344M16—181no—
345C2×C8—31no—
346C2×C8—31no—
347C2×C8—31no—
348C2×C8—31no—
349C2×C8—31no—
350C2×C8—31no—
351C2×C8—92no—
352C2×C8—182no—
353C2×C8—182no—
354C4⋊C4—21no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—181no—
358C22⋊C4—21no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—181no—
362C42—21no—
363C42—61no—
364C42—61no—
365C42—181no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—62no—
372C22×C3—81no—
373C22×C3—122no—
374C22×C3D3×C4⋊C411yescharacteristic
375C22×C3#89511yescharacteristic
376C22×C3C2×Dic3⋊C411yescharacteristic
377C22×C3#93811yescharacteristic
378C22×C3#93911yescharacteristic
379C22×C3#93911yescharacteristic
380C2×D3—22no—
381C2×D3—42no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—62no—
387C3×C4—81no—
388C3×C4—81no—
389C3×C4—82no—
390C3×C4—241no—
391C3×C4—241no—
392C3×C4#87711yescharacteristic
393C3×C4#87811yescharacteristic
394C3×C4#87811yescharacteristic
395C3×C4D3×C22⋊C411yescharacteristic
396C3×C4#89211yescharacteristic
397C3×C4#89711yescharacteristic
398C3×C4C2×(C2×D3)⋊C411yescharacteristic
399C3×C4#94611yescharacteristic
400Dic3—22no—
401Dic3—81no—
402Dic3—81no—
403Dic3—241no—
404Dic3—241no—
405Dic3—242no—
406C32#181211yescharacteristic, complemented, Sylow
407C23—32no—
408C23D3×#6711yescharacteristic
409Q8—61no—
410Q8—61no—
411D4—62no—
412D4—62no—
413D4—61no—
414D4—61no—
415C2×C4—32no—
416C2×C4—41no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—361no—
422C2×C4D3×Dic611yescharacteristic
423C2×C4#379611yescharacteristic
424C2×C4C4×D3211yescharacteristic
425C2×C4D3×D1211yescharacteristic
426C2×C4#380511yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C8—31no—
429C8—31no—
430C8—31no—
431C8—31no—
432C8—182no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3—122no—
444C2×C3#494211yescharacteristic
445C2×C3#498711yescharacteristic
446D3—42no—
447C22—41no—
448C22—62no—
449C22—122no—
450C22D3×Dic3⋊C411yescharacteristic
451C22#6388611yescharacteristic
452C22#6397011yescharacteristic
453C4—62no—
454C4—81no—
455C4—241no—
456C4—241no—
457C4—721no—
458C4#6387811yescharacteristic
459C4#6388711yescharacteristic
460C4#6389311yescharacteristic
461C4D3×(C2×D3)⋊C411yescharacteristic
462C3—21no—
463C3#7004111yescharacteristic, complemented
464C3#7066411yescharacteristic, complemented
465C2—21no—
466C2—21no—
467C2—21no—
468C2—122no—
469C2#1059136611yescharacteristic
subgroupG/H
centerC4#63878
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#380
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1812
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#4998C2semidirect
5. #10591122C2semidirect
6. #10589397C2semidirect
7. #10589157C2semidirect
17. C2×#3711C4semidirect
22. C2×D3×C3⋊C8C4semidirect
38. #4998D3semidirect
406. C32#1812semidirect
463. C3#70041semidirect
464. C3#70664semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C3×#50062
C3×#49982
#105912312
#105911222
#105893972
#105891572
#706643
#700413