Finite Group Databasebeta

← #11785560

Subgroups — #11785560

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2C2×#63577C211yesmaximal, characteristic, complemented
3#10591122C211yesmaximal, characteristic, complemented
4#10591111C211yesmaximal, characteristic
5#10591110C211yesmaximal, characteristic
6#10589425C211yesmaximal, characteristic, complemented
7C3×#4559C211yesmaximal, characteristic, complemented
8#72013—31nomaximal
9#69032—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—21no—
18C3×#907—21no—
19C3×#907C412yescomplemented
20C3×#907C412yescomplemented
21C2×C3×ΓL(1,𝔽25)—21no—
22C2×C3×D3×C8—21no—
23#63577—21no—
24#63577—21no—
25#63575—21no—
26#63573—21no—
27#63569—22no—
28#63568—22no—
29C2×C3×#131—31no—
30C2×#907D311yescharacteristic
31#5236—31no—
32#5236—31no—
33#5139—31no—
34C2×#822—31no—
35C2×#819—31no—
36#5106—31no—
37#5005—31no—
38#4998—31no—
39C3×#344—31no—
40#4559—31no—
41#4559—31no—
42#4559—61no—
43#4559D311yescharacteristic, 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×M16—21no—
54C32×M16C2×C412yes—
55C2×C32×C8—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4×C3⋊Dic3—21no—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×#208—21no—
66C3×#208—21no—
67C2×C3×C3⋊C8—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
74C3×ΓL(1,𝔽25)—22no—
75C3×ΓL(1,𝔽25)—22no—
76C3×D3×C8—22no—
77C3×D3×C8—22no—
78#1814—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C3×#131—32no—
82C3×#131—32no—
83C3×#131—61no—
84C3×#131—61no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16—61no—
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C2×D311yescharacteristic
90C22×C3×C8—31no—
91C22×C3×C8—61no—
92C3×#117—31no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C22×C3⋊C8C2×D311yescharacteristic
102#907—21no—
103#907—21no—
104#907Dic312yescomplemented
105#907Dic312yescomplemented
106C2×ΓL(1,𝔽25)—21no—
107C2×D3×C8—21no—
108#837—62no—
109#837—62no—
110#825—62no—
111#822—61no—
112#822—61no—
113#819—61no—
114#819—61no—
115#818—61no—
116#817—61no—
117#808—61no—
118#807—61no—
119#805—62no—
120C23×C32#4111yescharacteristic
121C22×C3×D3—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C3×D12—21no—
134C3×D12C4⋊C412yes—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×Dic6—21no—
138C3×Dic6C4⋊C412yes—
139C32×C8—22no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142C3×C3⋊C8C22⋊C411yescharacteristic
143C3×C3⋊C8C22⋊C411yescharacteristic
144C3×C3⋊C8C22⋊C411yescharacteristic
145C3×C3⋊C8C22⋊C411yescharacteristic
146C2×#131—31no—
147C2×#108—91no—
148#427—91no—
149#421—91no—
150#421—91no—
151#344—31no—
152#344—91no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—21no—
165#235—21no—
166#235—21no—
167#235D1212yes—
168#235C2×Dic312yes—
169C2×D12Dic611yescharacteristic
170C2×C4×D3—21no—
171C2×Dic6Dic611yescharacteristic
172C3×M16—21no—
173C3×M16—21no—
174C3×M16—22no—
175C3×M16—41no—
176C3×M16—62no—
177C3×M16—62no—
178C3×M16—61no—
179C3×M16—61no—
180C3×M16C4×D312yes—
181C3×M16C2×Dic312yes—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—31no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—41no—
191C2×C3×C8—62no—
192C2×C3×C8—62no—
193C2×C3×C8—61no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197#217—21no—
198#217—62no—
199#217—61no—
200#217—61no—
201C4⋊Dic3—21no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205C4×Dic3—21no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—121no—
209#208—21no—
210#208—21no—
211#208—61no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—121no—
216#208—121no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8C2×Dic311yescharacteristic
222C2×C3⋊C8C2×Dic311yescharacteristic
223C2×C3⋊C8#6711yescharacteristic
224C2×C3⋊C8#6711yescharacteristic
225C2×C3⋊C8#6711yescharacteristic
226C2×C3⋊C8#6711yescharacteristic
227ΓL(1,𝔽25)—22no—
228ΓL(1,𝔽25)—22no—
229D3×C8—22no—
230D3×C8—22no—
231C22×C32—41no—
232C22×C32#11711yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C2×C3×D3—22no—
236C2×C3×D3—42no—
237C32×C4C2×C22⋊C411yescharacteristic
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4#12111yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C3⋊Dic3—81no—
242C3×Dic3—22no—
243C3×Dic3—81no—
244C2×#41—31no—
245#131—32no—
246#131—32no—
247#131—61no—
248#131—61no—
249C2×M16—31no—
250C2×M16—61no—
251C2×M16—91no—
252C2×M16D3211yescharacteristic
253C22×C8—31no—
254C22×C8—61no—
255#117—31no—
256#117—91no—
257#108—181no—
258#108—181no—
259#107—181no—
260#106—181no—
261#104—182no—
262#104—182no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23511yescharacteristic
267C22×D3—21no—
268C3×Q8—32no—
269C3×Q8—61no—
270C3×D4—32no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—61no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—121no—
284C2×C3×C4C2×Dic611yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×D1211yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×Q811yescharacteristic
293C2×C3×C4C22×Dic311yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296#67—22no—
297#67—22no—
298C2×Dic3—21no—
299C2×Dic3—41no—
300C2×Dic3—122no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303D12—21no—
304D12C4⋊Dic312yes—
305C4×D3—22no—
306C4×D3—22no—
307Dic6—21no—
308Dic6C4⋊Dic312yes—
309C3×C8—22no—
310C3×C8—22no—
311C3×C8—31no—
312C3×C8—31no—
313C3×C8—31no—
314C3×C8—31no—
315C3×C8—42no—
316C3×C8—121no—
317C3⋊C8—41no—
318C3⋊C8—122no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C3⋊C8#21711yescharacteristic
322C3⋊C8#21711yescharacteristic
323C3⋊C8#21711yescharacteristic
324C3⋊C8#21711yescharacteristic
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32#38011yescharacteristic
329C3×D3—42no—
330#41—32no—
331#41—32no—
332#41—61no—
333#41—61no—
334C2×Q8—31no—
335C2×D4—31no—
336C2×D4—61no—
337C22×C4—61no—
338C22×C4C2×D3211yescharacteristic
339M16—21no—
340M16—62no—
341M16—62no—
342M16—61no—
343M16—61no—
344M16—181no—
345M16—181no—
346M16D3×Dic312yes—
347C2×C8—21no—
348C2×C8—31no—
349C2×C8—31no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—31no—
354C2×C8—62no—
355C2×C8—62no—
356C2×C8—61no—
357C2×C8—181no—
358C4⋊C4—61no—
359C4⋊C4—181no—
360C22⋊C4—61no—
361C22⋊C4—181no—
362C42—61no—
363C42—181no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—62no—
370C22×C3—81no—
371C22×C3—122no—
372C22×C3#87211yescharacteristic
373C22×C3#88411yescharacteristic
374C22×C3#89611yescharacteristic
375C22×C3#92411yescharacteristic
376C22×C3#92611yescharacteristic
377C22×C3#93011yescharacteristic
378C2×D3—22no—
379C2×D3—42no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—62no—
385C3×C4—241no—
386C3×C4D3×C22⋊C411yescharacteristic
387C3×C4#88411yescharacteristic
388C3×C4D3×C4⋊C411yescharacteristic
389C3×C4#89611yescharacteristic
390C3×C4#92411yescharacteristic
391C3×C4C2×C4⋊Dic311yescharacteristic
392C3×C4#93011yescharacteristic
393C3×C4C2×#21711yescharacteristic
394Dic3—22no—
395Dic3—81no—
396Dic3—241no—
397Dic3—241no—
398Dic3—242no—
399C32#181411yescharacteristic, complemented, Sylow
400C23—61no—
401C23#379811yescharacteristic
402Q8—32no—
403Q8—61no—
404D4—32no—
405D4—62no—
406D4—62no—
407D4—61no—
408C2×C4—61no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—121no—
412C2×C4—361no—
413C2×C4D3×Dic611yescharacteristic
414C2×C4#379811yescharacteristic
415C2×C4D3×D1211yescharacteristic
416C2×C4C2×D3×Dic311yescharacteristic
417C2×C4D3×#6711yescharacteristic
418C2×C4D3×#6711yescharacteristic
419C8—22no—
420C8—31no—
421C8—31no—
422C8—31no—
423C8—31no—
424C8—121no—
425C8—361no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—41no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3—122no—
437C2×C3#466711yescharacteristic
438C2×C3#521211yescharacteristic
439D3—42no—
440C22—41no—
441C22—62no—
442C22—122no—
443C22#6385111yescharacteristic
444C22#6385511yescharacteristic
445C22#6390611yescharacteristic
446C4—62no—
447C4—241no—
448C4—721no—
449C4#6385111yescharacteristic
450C4D3×C4⋊Dic311yescharacteristic
451C4#6390611yescharacteristic
452C4D3×#21711yescharacteristic
453C3—21no—
454C3#6903211yescharacteristic, complemented
455C3#7201311yescharacteristic, complemented
456C2—21no—
457C2—21no—
458C2—21no—
459C2—122no—
460C2#1059129511yescharacteristic
subgroupG/H
centerC4#63906
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×#63577C2semidirect
3. #10591122C2semidirect
6. #10589425C2semidirect
7. C3×#4559C2semidirect
19. C3×#907C4semidirect
20. C3×#907C4semidirect
43. #4559D3semidirect
104. #907Dic3semidirect
105. #907Dic3semidirect
399. C32#1814semidirect
454. C3#69032semidirect
455. C3#72013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×#635772
#105911222
#105911112
#105911102
#105894252
C3×#45592
#720133
#690323