Finite Group Databasebeta

← #11785549

Subgroups — #11785549

Order 1152.

569 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×#63815C211yesmaximal, characteristic
2#10592697C211yesmaximal, characteristic, complemented
3C3×#5005C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic
6C3×#4533C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70396—31nomaximal
9#69032—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—21no—
19#63815—21no—
20#63815C412yescomplemented
21#63815C412yescomplemented
22C2×D3×C3⋊C8—21no—
23#63635—21no—
24#63634—21no—
25C3×#805—22no—
26#63578—21no—
27#63578—21no—
28#63568—22no—
29C2×#948—31no—
30C2×#907—31no—
31C3×#421—31no—
32#5236—31no—
33#5139—31no—
34C2×#822—31no—
35C2×#822—31no—
36#5005D311yescharacteristic
37#4998—31no—
38#4998—31no—
39#4998—61no—
40C3×#344—31no—
41#4559—31no—
42#4556—31no—
43#4533D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235C2×C412yes—
49C3×#235D412yes—
50C2×C3×D12Q811yescharacteristic
51C2×C3×C4×D3—21no—
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×#208—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208C2×C412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3711—22no—
75#3711—22no—
76D3×C3⋊C8—22no—
77D3×C3⋊C8—22no—
78#1814—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C3×#117—21no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87#948—32no—
88#948—32no—
89#948—61no—
90#948—61no—
91#926—31no—
92#926—31no—
93#926—61no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C22×C3⋊C8—61no—
102#907—32no—
103#907—32no—
104#907—61no—
105#907—61no—
106C2×ΓL(1,𝔽25)—61no—
107C2×D3×C8—61no—
108C3×#104—62no—
109#837—62no—
110#825—62no—
111#822—61no—
112#822—61no—
113#822—61no—
114#822—61no—
115#808—61no—
116#808—61no—
117#808—62no—
118#807—61no—
119#807—61no—
120#807—62no—
121#805—22no—
122C23×C32#4111yescharacteristic
123C22×C3×D3—21no—
124C2×C32×C4—41no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q811yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—41no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—21no—
135C3×D12—21no—
136C3×D12C4⋊C412yes—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×Dic6—21no—
140C3×Dic6C4⋊C412yes—
141C3⋊(C3⋊C8)C22⋊C411yescharacteristic
142C3⋊(C3⋊C8)C22⋊C411yescharacteristic
143C3⋊(C3⋊C8)C22⋊C411yescharacteristic
144C3⋊(C3⋊C8)C22⋊C411yescharacteristic
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C3×C3⋊C8—41no—
148C2×#131—91no—
149C2×#108—91no—
150#427—91no—
151#421—31no—
152#421—91no—
153#344—31no—
154#344—91no—
155C3×#41—32no—
156C3×#41—32no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—21no—
167#235—21no—
168#235—21no—
169#235C4×D312yes—
170#235#6712yes—
171C2×D12Dic611yescharacteristic
172C2×C4×D3—21no—
173C2×Dic6Dic611yescharacteristic
174C3×M16—32no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16—61no—
178C3×M16—61no—
179C3×M16—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—41no—
192#217—61no—
193#217—61no—
194#217—121no—
195C4⋊Dic3—62no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—121no—
201#208—21no—
202#208—21no—
203#208—21no—
204#208—21no—
205#208—21no—
206#208—62no—
207#208—62no—
208#208C4×D312yes—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
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—31no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232ΓL(1,𝔽25)—62no—
233ΓL(1,𝔽25)—62no—
234D3×C8—62no—
235D3×C8—62no—
236C22×C32—41no—
237C22×C32#11711yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C32×C4—81no—
243C32×C4C2×C22⋊C411yescharacteristic
244C32×C4C2×C4⋊C411yescharacteristic
245C32×C4#12111yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C3⋊Dic3—81no—
248C3×Dic3—22no—
249C2×#41—31no—
250#131—92no—
251#131—92no—
252#131—181no—
253#131—181no—
254C2×M16—31no—
255C2×M16—31no—
256C2×M16—31no—
257C2×M16—181no—
258C22×C8—91no—
259C22×C8—181no—
260#117—91no—
261#117D3211yescharacteristic
262#108—181no—
263#108—181no—
264#107—181no—
265#106—181no—
266#104—62no—
267#104—182no—
268C23×C3—21no—
269C23×C3—61no—
270C23×C3#23511yescharacteristic
271C23×C3#23711yescharacteristic
272C22×D3—21no—
273C3×Q8—32no—
274C3×Q8—61no—
275C3×D4—32no—
276C3×D4—62no—
277C3×D4—62no—
278C3×D4—61no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—61no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4C2×Dic611yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4D3×Q811yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—22no—
304#67—22no—
305C2×Dic3—21no—
306C2×Dic3—122no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309D12—21no—
310D12Dic3⋊C412yes—
311C4×D3—22no—
312C4×D3—22no—
313Dic6—21no—
314Dic6Dic3⋊C412yes—
315C3×C8—62no—
316C3×C8—121no—
317C3×C8—121no—
318C3⋊C8—22no—
319C3⋊C8—31no—
320C3⋊C8—31no—
321C3⋊C8—31no—
322C3⋊C8—31no—
323C3⋊C8—31no—
324C3⋊C8—31no—
325C3⋊C8—31no—
326C3⋊C8—31no—
327C3⋊C8—41no—
328C3⋊C8—41no—
329C3⋊C8—61no—
330C3⋊C8—61no—
331C3⋊C8—61no—
332C3⋊C8—61no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38011yescharacteristic
337C3×D3—42no—
338#41—32no—
339#41—32no—
340#41—61no—
341#41—61no—
342C2×Q8—31no—
343C2×D4—31no—
344C2×D4—61no—
345C22×C4—61no—
346C22×C4C2×D3211yescharacteristic
347M16—32no—
348M16—61no—
349M16—61no—
350M16—61no—
351M16—61no—
352M16—61no—
353M16—182no—
354M16—182no—
355C2×C8—61no—
356C2×C8—61no—
357C2×C8—61no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—91no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8—91no—
364C2×C8—182no—
365C2×C8—182no—
366C4⋊C4—21no—
367C4⋊C4—181no—
368C22⋊C4—21no—
369C22⋊C4—181no—
370C42—21no—
371C42—181no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—42no—
378C22×C3—62no—
379C22×C3—122no—
380C22×C3#87211yescharacteristic
381C22×C3#87711yescharacteristic
382C22×C3#87811yescharacteristic
383C22×C3#88411yescharacteristic
384C22×C3#89611yescharacteristic
385C22×C3#93911yescharacteristic
386C2×D3—22no—
387C2×D3—42no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—62no—
393C3×C4—82no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4#87811yescharacteristic
397C3×C4D3×C22⋊C411yescharacteristic
398C3×C4D3×C22⋊C411yescharacteristic
399C3×C4#88411yescharacteristic
400C3×C4D3×C4⋊C411yescharacteristic
401C3×C4#89611yescharacteristic
402C3×C4C2×Dic3⋊C411yescharacteristic
403C3×C4#93911yescharacteristic
404Dic3—22no—
405Dic3—242no—
406Dic3—241no—
407Dic3—241no—
408C32#181411yescharacteristic, complemented, Sylow
409C23—61no—
410C23#380411yescharacteristic
411Q8—32no—
412Q8—61no—
413D4—32no—
414D4—62no—
415D4—62no—
416D4—61no—
417C2×C4—41no—
418C2×C4—61no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—361no—
422C2×C4D3×Dic611yescharacteristic
423C2×C4#379511yescharacteristic
424C2×C4C4×D3211yescharacteristic
425C2×C4#380211yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C2×C4#381111yescharacteristic
428C8—62no—
429C8—91no—
430C8—91no—
431C8—91no—
432C8—91no—
433C8—121no—
434C8—121no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—122no—
446C2×C3#466711yescharacteristic
447C2×C3#494211yescharacteristic
448D3—42no—
449C22—41no—
450C22—62no—
451C22—122no—
452C22#6387711yescharacteristic
453C22#6389911yescharacteristic
454C22#6397111yescharacteristic
455C4—62no—
456C4—81no—
457C4—721no—
458C4D3×Dic3⋊C411yescharacteristic
459C4#6388511yescharacteristic
460C4#6389611yescharacteristic
461C4#6392111yescharacteristic
462C3—21no—
463C3#6903211yescharacteristic, complemented
464C3#7039611yescharacteristic, complemented
465C2—21no—
466C2—21no—
467C2—21no—
468C2—122no—
469C2#1059136911yescharacteristic
subgroupG/H
centerC4#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#380
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1814
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
4. C2×#63578C2semidirect
6. C3×#4533C2semidirect
7. #10589171C2semidirect
20. #63815C4semidirect
21. #63815C4semidirect
43. #4533D3semidirect
408. C32#1814semidirect
463. C3#69032semidirect
464. C3#70396semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
#105926972
C3×#50052
C2×#635782
#105911102
C3×#45332
#105891712
#703963
#690323