Finite Group Databasebeta

← #11785490

Subgroups — #11785490

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2#10592697C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic
4#10591231C211yesmaximal, characteristic
5#10591138C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70041—31nomaximal
9#68710—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711C412yescomplemented
18#63815—21no—
19#63815—21no—
20#63815—21no—
21#63815—21no—
22C2×D3×C3⋊C8C412yescomplemented
23#63635—21no—
24#63634—21no—
25C3×#806—22no—
26#63580—22no—
27#63576—21no—
28#63574—21no—
29C2×#948—31no—
30C2×#907—31no—
31C3×#410—31no—
32#5240—31no—
33#5006—31no—
34#5006D311yescharacteristic
35#4998—31no—
36#4998—31no—
37#4998—31no—
38#4998—31no—
39#4998—61no—
40C3×H(3,ℤ/4)—31no—
41#4557—31no—
42#4531—31no—
43#4531D311yescharacteristic, complemented
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—
59C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
61C2×C3⋊(C3⋊C8)D411yescharacteristic
62C2×C3⋊(C3⋊C8)D411yescharacteristic
63C2×C3⋊(C3⋊C8)D411yescharacteristic
64C2×C3⋊(C3⋊C8)D411yescharacteristic
65C3×#217—21no—
66C3×#217—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8C2×C412yes—
74#3711—22no—
75#3711—22no—
76D3×C3⋊C8—22no—
77D3×C3⋊C8—22no—
78#1812—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C2×C3×M16—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—32no—
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—32no—
101C22×C3⋊C8—61no—
102#907—61no—
103#907—61no—
104#907—61no—
105#907—61no—
106C2×ΓL(1,𝔽25)—32no—
107C2×D3×C8—32no—
108C3×#99—62no—
109#834—62no—
110#808—61no—
111#808—61no—
112#808—61no—
113#808—61no—
114#808—62no—
115#807—61no—
116#807—61no—
117#807—61no—
118#807—61no—
119#807—62no—
120#806—22no—
121#806—62no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3C4⋊C412yes—
124C2×C32×C4—41no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—41no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C4⋊C412yes—
137C3×D12—21no—
138C3×D12—21no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×Dic6—21no—
142C3×Dic6—21no—
143C3⋊(C3⋊C8)C22⋊C411yescharacteristic
144C3⋊(C3⋊C8)C22⋊C411yescharacteristic
145C3⋊(C3⋊C8)C22⋊C411yescharacteristic
146C3⋊(C3⋊C8)C22⋊C411yescharacteristic
147C3×C3⋊C8—22no—
148C2×#131—91no—
149#427—91no—
150#427—91no—
151#410—31no—
152#410—91no—
153H(3,ℤ/4)—31no—
154H(3,ℤ/4)—91no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C22×C3×C4—21no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67#6712yes—
167#235—21no—
168#235—21no—
169#235—21no—
170#235—21no—
171C2×D12Dic611yescharacteristic
172C2×C4×D3C4×D312yes—
173C2×Dic6Dic611yescharacteristic
174C3×M16—61no—
175C3×M16—61no—
176C2×C3×C8—32no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—41no—
190C3×C42—61no—
191C3×C42—61no—
192#217—21no—
193#217—21no—
194#217—61no—
195#217—61no—
196#217—121no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—121no—
207#208—21no—
208#208—21no—
209#208—62no—
210#208—62no—
211C2×C3⋊C8—31no—
212C2×C3⋊C8—31no—
213C2×C3⋊C8—31no—
214C2×C3⋊C8—31no—
215C2×C3⋊C8—31no—
216C2×C3⋊C8—31no—
217C2×C3⋊C8—31no—
218C2×C3⋊C8—31no—
219C2×C3⋊C8—31no—
220C2×C3⋊C8—31no—
221C2×C3⋊C8—31no—
222C2×C3⋊C8—31no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8C4×D312yes—
232ΓL(1,𝔽25)—62no—
233ΓL(1,𝔽25)—62no—
234D3×C8—62no—
235D3×C8—62no—
236C22×C32—41no—
237C22×C32C2×C4⋊C411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C32×C4—81no—
243C32×C4C2×C22⋊C411yescharacteristic
244C32×C4#11711yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C3⋊Dic3—81no—
248C3×Dic3—22no—
249C3×Dic3—81no—
250C3×Dic3—81no—
251C2×#41—31no—
252#131—181no—
253#131—181no—
254#131—181no—
255#131—181no—
256C2×M16—31no—
257C2×M16—92no—
258C22×C8—92no—
259C22×C8—91no—
260#117—31no—
261#117—31no—
262#117—91no—
263#117D3211yescharacteristic
264#107—181no—
265#107—181no—
266#106—181no—
267#106—181no—
268#99—62no—
269#99—182no—
270C23×C3—21no—
271C23×C3—32no—
272C23×C3D3×D411yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C22×D3Dic3⋊C412yes—
275C3×Q8—61no—
276C3×Q8—61no—
277C3×D4—62no—
278C3×D4—62no—
279C3×D4—61no—
280C3×D4—61no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—32no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×Dic611yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4D3×Q811yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3Dic3⋊C412yes—
315D12—21no—
316D12—21no—
317C4×D3—22no—
318C4×D3—22no—
319Dic6—21no—
320Dic6—21no—
321C3×C8—62no—
322C3⋊C8—22no—
323C3⋊C8—31no—
324C3⋊C8—31no—
325C3⋊C8—31no—
326C3⋊C8—31no—
327C3⋊C8—31no—
328C3⋊C8—31no—
329C3⋊C8—31no—
330C3⋊C8—31no—
331C3⋊C8—61no—
332C3⋊C8—61no—
333C3⋊C8—61no—
334C3⋊C8—61no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#38011yescharacteristic
339C3×D3—42no—
340#41—61no—
341#41—61no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—32no—
346C2×D4—31no—
347C22×C4—32no—
348C22×C4C2×D3211yescharacteristic
349M16—61no—
350M16—61no—
351M16—182no—
352M16—182no—
353C2×C8—32no—
354C2×C8—91no—
355C2×C8—91no—
356C2×C8—91no—
357C2×C8—91no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—182no—
361C2×C8—182no—
362C4⋊C4—21no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—181no—
366C22⋊C4—21no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—181no—
370C42—21no—
371C42—61no—
372C42—61no—
373C42—181no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—42no—
380C22×C3—62no—
381C22×C3—122no—
382C22×C3#88411yescharacteristic
383C22×C3#88411yescharacteristic
384C22×C3D3×C4⋊C411yescharacteristic
385C22×C3C2×Dic3⋊C411yescharacteristic
386C22×C3#93911yescharacteristic
387C22×C3#93911yescharacteristic
388C2×D3—22no—
389C2×D3—42no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—62no—
395C3×C4—82no—
396C3×C4—81no—
397C3×C4—81no—
398C3×C4—241no—
399C3×C4—241no—
400C3×C4#87211yescharacteristic
401C3×C4#87711yescharacteristic
402C3×C4#87811yescharacteristic
403C3×C4#87811yescharacteristic
404C3×C4D3×C22⋊C411yescharacteristic
405C3×C4D3×C22⋊C411yescharacteristic
406C3×C4#89611yescharacteristic
407C3×C4#89611yescharacteristic
408Dic3—22no—
409Dic3—81no—
410Dic3—81no—
411Dic3—242no—
412Dic3—241no—
413Dic3—241no—
414C32#181211yescharacteristic, complemented, Sylow
415C23—32no—
416C23D3×#6711yescharacteristic
417Q8—61no—
418Q8—61no—
419D4—62no—
420D4—62no—
421D4—61no—
422D4—61no—
423C2×C4—32no—
424C2×C4—41no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—361no—
430C2×C4D3×Dic611yescharacteristic
431C2×C4#379511yescharacteristic
432C2×C4C4×D3211yescharacteristic
433C2×C4#380211yescharacteristic
434C2×C4#380411yescharacteristic
435C2×C4#381111yescharacteristic
436C8—62no—
437C8—91no—
438C8—91no—
439C8—91no—
440C8—91no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—122no—
452C2×C3#466711yescharacteristic
453C2×C3#494211yescharacteristic
454D3—42no—
455C22—41no—
456C22—62no—
457C22—122no—
458C22D3×Dic3⋊C411yescharacteristic
459C22#6388511yescharacteristic
460C22#6397111yescharacteristic
461C4—62no—
462C4—81no—
463C4—241no—
464C4—241no—
465C4—721no—
466C4#6387711yescharacteristic
467C4#6389611yescharacteristic
468C4#6389911yescharacteristic
469C4#6392111yescharacteristic
470C3—21no—
471C3#6871011yescharacteristic, complemented
472C3#7004111yescharacteristic, complemented
473C2—21no—
474C2—21no—
475C2—21no—
476C2—122no—
477C2#1059136911yescharacteristic
subgroupG/H
centerC4#63877
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
2. #10592697C2semidirect
5. #10591138C2semidirect
6. C3×#4531C2semidirect
7. #10589158C2semidirect
17. C2×#3711C4semidirect
22. C2×D3×C3⋊C8C4semidirect
43. #4531D3semidirect
414. C32#1812semidirect
471. C3#68710semidirect
472. C3#70041semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
#105926972
C3×#50062
#105912312
#105911382
C3×#45312
#105891582
#700413
#687103