Finite Group Databasebeta

← #11785557

Subgroups — #11785557

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C3×#5139C211yesmaximal, characteristic
4#10591138C211yesmaximal, characteristic, complemented
5#10591111C211yesmaximal, characteristic
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70396—31nomaximal
9#69032—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—21no—
19#63815—21no—
20#63815C412yescomplemented
21#63815C412yescomplemented
22C2×D3×C3⋊C8—21no—
23#63649—21no—
24#63649—21no—
25C3×#825—22no—
26#63576—21no—
27#63574—21no—
28#63569—22no—
29C2×#948—31no—
30C2×#907—31no—
31C3×#421—31no—
32#5236—31no—
33#5139D311yescharacteristic
34C2×#822—31no—
35C2×#822—31no—
36C2×#822—61no—
37#5005—31no—
38#4998—31no—
39#4998—31no—
40C3×#344—31no—
41#4559—31no—
42#4556D311yescharacteristic, complemented
43#4533—31no—
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×M16—21no—
54C32×M16—21no—
55C2×C32×C8—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—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×#208C2×C412yes—
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—21no—
82C2×C3×M16—31no—
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×M16C2×D311yescharacteristic
85C3×#117—31no—
86C3×#117—31no—
87#948—32no—
88#948—32no—
89#948—61no—
90#948—61no—
91#926C2×D311yescharacteristic
92#926C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208—61no—
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—22no—
111#822—61no—
112#822—61no—
113#822—61no—
114#822—61no—
115#822—62no—
116#822—62no—
117#808—61no—
118#808—61no—
119#807—61no—
120#807—61no—
121#805—62no—
122C23×C32#4111yescharacteristic
123C22×C3×D3—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C3×#67—22no—
131C3×#67—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C3×D12—21no—
136C3×D12C4⋊C412yes—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×Dic6—21no—
140C3×Dic6C4⋊C412yes—
141C32×C8—41no—
142C3⋊(C3⋊C8)—41no—
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—
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—22no—
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—21no—
179C3×M16—32no—
180C3×M16—41no—
181C3×M16—61no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—41no—
185C2×C3×C8—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191C3×C42—61no—
192#217—21no—
193#217—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198#208—21no—
199#208—62no—
200#208—62no—
201#208—62no—
202#208—61no—
203#208—61no—
204#208—61no—
205#208—61no—
206#208—121no—
207#208C4×D312yes—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—31no—
210C2×C3⋊C8—31no—
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—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—121no—
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×C4C2×C22⋊C411yescharacteristic
243C32×C4C2×C4⋊C411yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3×Dic3—22no—
247C3×Dic3—81no—
248C3×Dic3—81no—
249C2×#41—31no—
250#131—92no—
251#131—92no—
252#131—181no—
253#131—181no—
254C2×M16—31no—
255C2×M16—91no—
256C2×M16—181no—
257C2×M16D3211yescharacteristic
258C22×C8—91no—
259C22×C8—181no—
260#117—31no—
261#117—31no—
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—61no—
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×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—22no—
303#67—22no—
304C2×Dic3—21no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307D12—21no—
308D12Dic3⋊C412yes—
309C4×D3—22no—
310C4×D3—22no—
311Dic6—21no—
312Dic6Dic3⋊C412yes—
313C3×C8—42no—
314C3×C8—41no—
315C3×C8—41no—
316C3×C8—62no—
317C3⋊C8—22no—
318C3⋊C8—31no—
319C3⋊C8—31no—
320C3⋊C8—31no—
321C3⋊C8—31no—
322C3⋊C8—31no—
323C3⋊C8—31no—
324C3⋊C8—31no—
325C3⋊C8—31no—
326C3⋊C8—61no—
327C3⋊C8—61no—
328C3⋊C8—61no—
329C3⋊C8—61no—
330C3⋊C8—122no—
331C3⋊C8—121no—
332C3⋊C8—121no—
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—21no—
348M16—21no—
349M16—32no—
350M16—61no—
351M16—182no—
352M16—182no—
353M16—181no—
354M16—181no—
355C2×C8—21no—
356C2×C8—61no—
357C2×C8—91no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—91no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8—182no—
364C2×C8—182no—
365C2×C8—181no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C42—61no—
371C42—61no—
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—241no—
394C3×C4—241no—
395C3×C4#87811yescharacteristic
396C3×C4D3×C22⋊C411yescharacteristic
397C3×C4D3×C22⋊C411yescharacteristic
398C3×C4#88411yescharacteristic
399C3×C4D3×C4⋊C411yescharacteristic
400C3×C4#89611yescharacteristic
401C3×C4C2×Dic3⋊C411yescharacteristic
402C3×C4#93911yescharacteristic
403Dic3—22no—
404Dic3—81no—
405Dic3—81no—
406C32#181411yescharacteristic, complemented, Sylow
407C23—61no—
408C23#379511yescharacteristic
409Q8—32no—
410Q8—61no—
411D4—32no—
412D4—62no—
413D4—62no—
414D4—61no—
415C2×C4—61no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4D3×Dic611yescharacteristic
421C2×C4C4×D3211yescharacteristic
422C2×C4#380211yescharacteristic
423C2×C4#380411yescharacteristic
424C2×C4D3×#6711yescharacteristic
425C2×C4#381111yescharacteristic
426C8—41no—
427C8—62no—
428C8—91no—
429C8—91no—
430C8—91no—
431C8—91no—
432C8—361no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3—122no—
444C2×C3#466711yescharacteristic
445C2×C3#494211yescharacteristic
446D3—42no—
447C22—41no—
448C22—62no—
449C22—122no—
450C22#6387711yescharacteristic
451C22#6388511yescharacteristic
452C22#6389611yescharacteristic
453C4—62no—
454C4—241no—
455C4—241no—
456C4D3×Dic3⋊C411yescharacteristic
457C4#6389911yescharacteristic
458C4#6392111yescharacteristic
459C4#6397111yescharacteristic
460C3—21no—
461C3#6903211yescharacteristic, complemented
462C3#7039611yescharacteristic, complemented
463C2—21no—
464C2—21no—
465C2—21no—
466C2—122no—
467C2#1059136911yescharacteristic
subgroupG/H
centerC4#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#380
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1814
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63649C2semidirect
4. #10591138C2semidirect
6. C3×#4556C2semidirect
7. #10589170C2semidirect
20. #63815C4semidirect
21. #63815C4semidirect
42. #4556D3semidirect
406. C32#1814semidirect
461. C3#69032semidirect
462. C3#70396semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×#636492
C3×#51392
#105911382
#105911112
C3×#45562
#105891702
#703963
#690323