Finite Group Databasebeta

← #11783850

Subgroups — #11783850

Order 1152.

643 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2#10592831C211yesmaximal, characteristic
3C3×#5122C211yesmaximal, characteristic, complemented
4#10591232C211yesmaximal, characteristic
5#10591055C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#69898—31nomaximal
9#69014—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712C412yescomplemented
18#63817—21no—
19#63817—21no—
20#63817—21no—
21#63817—21no—
22C2×#3710C412yescomplemented
23#63651C412yescomplemented
24#63650C412yescomplemented
25C3×#815—21no—
26C3×C8×Dic3—21no—
27#63581C414yes—
28#63554—21no—
29Dic3×C3⋊C8—21no—
30C2×#907—31no—
31C2×#901—31no—
32C3×#405—31no—
33#5132—31no—
34#5132—31no—
35#5132—61no—
36#5122D311yescharacteristic, complemented
37#5101—31no—
38#5006—31no—
39#5006—31no—
40#4997—31no—
41C3×#344—31no—
42#4559D311yescharacteristic, complemented
43#4556—31no—
44#4533—31no—
45C22×C32×C4C2311yescharacteristic
46C2×#638C2×C412yes—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
52C2×C4×C3⋊D3C2×C412yes—
53C2×#634C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16C2×C412yes—
56C2×C32×C8—21no—
57#3748—21no—
58#3748C2×C412yes—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217C2×C412yes—
61C3×#217C2×C412yes—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8C2×C411yescharacteristic
70C2×C3×C3⋊C8C2×C411yescharacteristic
71C2×C3×C3⋊C8D411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75#3712—22no—
76#3712—22no—
77#3710—22no—
78#3710—22no—
79#1757—91noSylow
80C2×#235—31no—
81C2×#235—31no—
82C2×#235—61no—
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C2×D311yescharacteristic
87C22×C3×C8—31no—
88C3×#117—31no—
89C3×#117—31no—
90#926C2×D311yescharacteristic
91#926C2×D311yescharacteristic
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#907—61no—
98#907—61no—
99#907—61no—
100#907—61no—
101#901—61no—
102#901—61no—
103#901—61no—
104#901—61no—
105C2×ΓL(1,𝔽25)—32no—
106C2×ΓL(1,𝔽25)—32no—
107C2×D3×C8—32no—
108C2×D3×C8—32no—
109C3×#97—61no—
110C3×C4×C8—61no—
111#824—32no—
112#824—32no—
113#824—62no—
114#823—32no—
115#823—32no—
116#823—62no—
117#815—21no—
118#815—61no—
119C8×Dic3—21no—
120C8×Dic3—61no—
121#806—34no—
122#806—34no—
123#803—61no—
124C4×C3⋊C8—61no—
125C23×C32C22×C411yescharacteristic
126C22×C3⋊D3C4212yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—22no—
134#638—22no—
135C2×C3⋊Dic3C4212yes—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—21no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140#634—21no—
141#634—21no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8C22⋊C411yescharacteristic
148C3×C3⋊C8C22⋊C411yescharacteristic
149C3×C3⋊C8C22⋊C411yescharacteristic
150C3×C3⋊C8C22⋊C411yescharacteristic
151C2×#131—91no—
152#413—91no—
153#410—91no—
154#405—31no—
155#405—91no—
156#344—31no—
157#344—91no—
158C22×C3×C4—21no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—32no—
162C2×#67—32no—
163C2×#67—62no—
164#235—61no—
165#235—61no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—121no—
173#235—121no—
174#235—121no—
175#235—121no—
176C2×D12—31no—
177C2×D12—31no—
178C2×D12—61no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—62no—
182C2×Dic6—31no—
183C2×Dic6—31no—
184C2×Dic6—61no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—22no—
188C3×M16—41no—
189C3×M16—61no—
190C3×M16—61no—
191C3×M16C4×D312yes—
192C3×M16C4×D312yes—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C2×C3×C8—31no—
201C2×C3×C8—32no—
202C2×C3×C8—41no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C22⋊C4—32no—
206C3×C22⋊C4—32no—
207C3×C42—61no—
208C3×C42—61no—
209#217C4×D312yes—
210#217C4×D312yes—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4×Dic3—21no—
214C4×Dic3—21no—
215#208—21no—
216#208—21no—
217#208—32no—
218#208—32no—
219#208—62no—
220#208—61no—
221#208—61no—
222#208—121no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8C4×D312yes—
227C2×C3⋊C8C4×D311yescharacteristic
228C2×C3⋊C8C4×D311yescharacteristic
229C2×C3⋊C8D1211yescharacteristic
230C2×C3⋊C8D1211yescharacteristic
231C2×C3⋊C8#6711yescharacteristic
232C2×C3⋊C8#6711yescharacteristic
233ΓL(1,𝔽25)—62no—
234ΓL(1,𝔽25)—62no—
235ΓL(1,𝔽25)—62no—
236ΓL(1,𝔽25)—62no—
237D3×C8—62no—
238D3×C8—62no—
239D3×C8—62no—
240D3×C8—62no—
241C22×C32—41no—
242C22×C32C2×C4211yescharacteristic
243C22×C32C4×D411yescharacteristic
244C22×C32C4×D411yescharacteristic
245C2×C3⋊D3—22no—
246C2×C3⋊D3—42no—
247C32×C4C2×C22⋊C411yescharacteristic
248C32×C4#11711yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C3⋊Dic3—22no—
252C3×Dic3—42no—
253C3×Dic3—42no—
254C2×#41—91no—
255#131—181no—
256#131—181no—
257#131—181no—
258#131—181no—
259C2×M16—31no—
260C2×M16—92no—
261C2×M16—91no—
262C2×M16D3211yescharacteristic
263C22×C8—31no—
264C22×C8—92no—
265#117—31no—
266#117—31no—
267#101—92no—
268#100—92no—
269#99—94no—
270#97—61no—
271#97—181no—
272C4×C8—61no—
273C4×C8—181no—
274C23×C3—21no—
275C23×C3C2×C4×D311yescharacteristic
276C23×C3C2×C4×D311yescharacteristic
277C22×D3—32no—
278C22×D3—32no—
279C22×D3—62no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—62no—
301#67—62no—
302#67—62no—
303#67—62no—
304#67—122no—
305#67—122no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—62no—
311D12—61no—
312D12—61no—
313D12—61no—
314D12—61no—
315D12—121no—
316D12—121no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—122no—
322C4×D3—122no—
323Dic6—61no—
324Dic6—61no—
325Dic6—61no—
326Dic6—61no—
327Dic6—121no—
328Dic6—121no—
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—31no—
332C3×C8—31no—
333C3×C8—31no—
334C3×C8—31no—
335C3×C8—42no—
336C3×C8—62no—
337C3⋊C8—22no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
341C3⋊C8(C2×D3)⋊C411yescharacteristic
342C3⋊C8(C2×D3)⋊C411yescharacteristic
343C3⋊C8(C2×D3)⋊C411yescharacteristic
344C3⋊C8(C2×D3)⋊C411yescharacteristic
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32C4×C22⋊C411yescharacteristic
349C3⋊D3—42no—
350#41—181no—
351#41—181no—
352#41—181no—
353#41—181no—
354C2×Q8—91no—
355C2×D4—92no—
356C2×D4—91no—
357C22×C4—92no—
358C22×C4C2×D3211yescharacteristic
359M16—21no—
360M16—61no—
361M16—61no—
362M16—92no—
363M16—182no—
364M16—182no—
365M16—181no—
366M16#62412yes—
367C2×C8—21no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—31no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—31no—
374C2×C8—32no—
375C2×C8—182no—
376C2×C8—182no—
377C2×C8—181no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C22⋊C4—32no—
381C22⋊C4—32no—
382C42—61no—
383C42—61no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—81no—
390C22×C3C42×D311yescharacteristic
391C22×C3C42×D311yescharacteristic
392C22×C3C4×D1211yescharacteristic
393C22×C3#67⋊C411yescharacteristic
394C22×C3#89311yescharacteristic
395C22×C3C4×#6711yescharacteristic
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—242no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4#87211yescharacteristic
409C3×C4C4×D1211yescharacteristic
410C3×C4D3×C22⋊C411yescharacteristic
411C3×C4#67⋊C411yescharacteristic
412C3×C4#89211yescharacteristic
413C3×C4#89311yescharacteristic
414C3×C4C2×(C2×D3)⋊C411yescharacteristic
415C3×C4C4×#6711yescharacteristic
416Dic3—42no—
417Dic3—42no—
418Dic3—62no—
419Dic3—62no—
420Dic3—122no—
421C32#175711yescharacteristic, complemented, Sylow
422C23—92no—
423C23C4×D3211yescharacteristic
424Q8—181no—
425Q8—181no—
426D4—182no—
427D4—182no—
428D4—181no—
429D4—181no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—92no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4#379911yescharacteristic
436C2×C4C4×D3211yescharacteristic
437C2×C4D3×D1211yescharacteristic
438C2×C4#380411yescharacteristic
439C2×C4C2×#62411yescharacteristic
440C2×C4D3×#6711yescharacteristic
441C8—22no—
442C8—31no—
443C8—31no—
444C8—31no—
445C8—31no—
446C8—62no—
447C8—182no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—41no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3#466611yescharacteristic
459C2×C3C4×(C2×D3)⋊C411yescharacteristic
460D3—122no—
461D3—122no—
462D3—242no—
463C22—41no—
464C22—182no—
465C22—362no—
466C22#6388011yescharacteristic
467C22C4×#62411yescharacteristic
468C22#6390411yescharacteristic
469C4—122no—
470C4—122no—
471C4—182no—
472C4#6383611yescharacteristic
473C4#6389411yescharacteristic
474C4D3×(C2×D3)⋊C411yescharacteristic
475C4#6395211yescharacteristic
476C3—21no—
477C3#6901411yescharacteristic, complemented
478C3#6989811yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—21no—
482C2—362no—
483C2#1059123311yescharacteristic
subgroupG/H
centerC4D3×(C2×D3)⋊C4
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32C4×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5122C2semidirect
5. #10591055C2semidirect
6. C3×#4559C2semidirect
7. #10589169C2semidirect
17. C2×#3712C4semidirect
22. C2×#3710C4semidirect
23. #63651C4semidirect
24. #63650C4semidirect
36. #5122D3semidirect
42. #4559D3semidirect
421. C32#1757semidirect
477. C3#69014semidirect
478. C3#69898semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105928312
C3×#51222
#105912322
#105910552
C3×#45592
#105891692
#698983
#690143