Finite Group Databasebeta

← #11789732

Subgroups — #11789732

Order 1152.

507 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592831C211yesmaximal, characteristic
2C3×#5125C211yesmaximal, characteristic, complemented
3#10591113C211yesmaximal, characteristic
4C2×#63570C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70727—31nomaximal
9#68750—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63651C412yescomplemented
18#63650C412yescomplemented
19C3×#819—22no—
20#63570—21no—
21#63570—21no—
22#63570—22no—
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C3×#430—31no—
26#5139—31no—
27C2×#825—31no—
28#5132—31no—
29#5132—31no—
30#5132—61no—
31#5125D311yescharacteristic, complemented
32Dic3×M16—31no—
33#5005—31no—
34C2×#805—31no—
35C4×#208—31no—
36C3×#339—31no—
37#4556—31no—
38#4555D311yescharacteristic, complemented
39#4533—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×#634C2×C411yescharacteristic
49C22×C3×Dic3—21no—
50C32×M16—21no—
51C32×M16C2×C412yes—
52C2×C32×C8—21no—
53#3748—21no—
54#3748C2×C412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208D412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77C3×#117—31no—
78C2×C3×C42—31no—
79#926C2×D311yescharacteristic
80C2×C4×Dic3C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#108—62no—
87#825—62no—
88#825—61no—
89#825—61no—
90#824—32no—
91#824—32no—
92#824—62no—
93#823—32no—
94#823—32no—
95#823—62no—
96#819—22no—
97#815—61no—
98C8×Dic3—61no—
99#805—61no—
100#805—61no—
101#805—62no—
102#803—61no—
103C4×C3⋊C8—61no—
104C23×C32#4111yescharacteristic
105C22×C3⋊D3—21no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—41no—
113#638—41no—
114C2×C3⋊Dic3—21no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—21no—
117C4×C3⋊D3—41no—
118C4×C3⋊D3—41no—
119#634—21no—
120#634—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—41no—
125C32×C8—22no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#430—31no—
130#421—91no—
131C2×#104—91no—
132#413—91no—
133C4×M16—91no—
134#344—91no—
135#339—31no—
136C22×C3×C4—21no—
137C22×C3×C4—61no—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C2×#67—62no—
141C2×#67—61no—
142C2×#67—61no—
143C22×Dic3—21no—
144#235—61no—
145#235—61no—
146#235—61no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—121no—
153#235—121no—
154#235—121no—
155#235—121no—
156C2×D12—31no—
157C2×D12—31no—
158C2×D12—61no—
159C2×C4×D3—62no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×Dic6—31no—
163C2×Dic6—31no—
164C2×Dic6—61no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—22no—
168C3×M16—32no—
169C3×M16—41no—
170C3×M16—61no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16C4×D312yes—
174C3×M16C4×D312yes—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—41no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C42—31no—
183C3×C42—31no—
184C3×C42—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3—21no—
188C4×Dic3—21no—
189C4×Dic3—21no—
190C4×Dic3D1211yescharacteristic
191C4×Dic3D1211yescharacteristic
192#208—21no—
193#208—21no—
194#208—21no—
195#208—32no—
196#208—32no—
197#208—62no—
198#208—61no—
199#208—61no—
200#208—121no—
201#208#6712yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—121no—
207C22×C32—41no—
208C22×C32#11711yescharacteristic
209C22×C32#12311yescharacteristic
210C22×C32#12411yescharacteristic
211C2×C3⋊D3—41no—
212C2×C3⋊D3—81no—
213C32×C4C4×D411yescharacteristic
214C32×C4C4×D411yescharacteristic
215C32×C4#12111yescharacteristic
216C32×C4#12611yescharacteristic
217C3⋊Dic3—41no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—81no—
221C2×#41—91no—
222C2×M16—31no—
223C2×M16—31no—
224C2×M16—91no—
225C2×M16D3211yescharacteristic
226#117—31no—
227C2×C42—31no—
228#108—62no—
229#104—181no—
230#104—181no—
231#104—182no—
232#101—92no—
233#100—92no—
234#97—181no—
235C4×C8—181no—
236C23×C3—21no—
237C23×C3#23711yescharacteristic
238C23×C3#23911yescharacteristic
239C22×D3—62no—
240C22×D3—61no—
241C22×D3—61no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—122no—
251C2×C3×C4—121no—
252C2×C3×C4C2×C4×D311yescharacteristic
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4#23511yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4#23911yescharacteristic
262C2×C3×C4#23911yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264#67—122no—
265#67—122no—
266#67—121no—
267#67—121no—
268#67—121no—
269#67—121no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—42no—
273C2×Dic3—41no—
274C2×Dic3—62no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277D12—61no—
278D12—61no—
279D12—61no—
280D12—61no—
281D12—121no—
282D12—121no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—121no—
288C4×D3—121no—
289Dic6—61no—
290Dic6—61no—
291Dic6—61no—
292Dic6—61no—
293Dic6—121no—
294Dic6—121no—
295C3×C8—22no—
296C3×C8—22no—
297C3×C8—42no—
298C3×C8—62no—
299C3×C8—121no—
300C3⋊C8—22no—
301C3⋊C8—41no—
302C3⋊C8—62no—
303C3⋊C8—62no—
304C3⋊C8—122no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32#38811yescharacteristic
309C3⋊D3—81no—
310#41—181no—
311#41—181no—
312#41—181no—
313#41—181no—
314C2×Q8—91no—
315C2×D4—91no—
316C2×D4—181no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320M16—21no—
321M16—32no—
322M16—61no—
323M16—61no—
324M16—61no—
325M16—92no—
326M16—181no—
327M16#62412yes—
328C2×C8—21no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—181no—
332C4⋊C4—61no—
333C22⋊C4—61no—
334C42—31no—
335C42—31no—
336C42—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—81no—
344C22×C3#88511yescharacteristic
345C22×C3#88611yescharacteristic
346C22×C3#89211yescharacteristic
347C22×C3#89211yescharacteristic
348C22×C3#89411yescharacteristic
349C22×C3#94711yescharacteristic
350C2×D3—122no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—241no—
354C2×D3—241no—
355C2×D3—242no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—62no—
361C3×C4—121no—
362C3×C4—241no—
363C3×C4C4×D1211yescharacteristic
364C3×C4#67⋊C411yescharacteristic
365C3×C4#89311yescharacteristic
366C3×C4#89511yescharacteristic
367C3×C4#89811yescharacteristic
368C3×C4#89811yescharacteristic
369C3×C4C4×#6711yescharacteristic
370C3×C4#93911yescharacteristic
371Dic3—22no—
372Dic3—41no—
373Dic3—81no—
374Dic3—122no—
375Dic3—121no—
376Dic3—121no—
377C32#193211yescharacteristic, complemented, Sylow
378C23—181no—
379C23#379611yescharacteristic
380Q8—181no—
381Q8—181no—
382D4—181no—
383D4—181no—
384D4—361no—
385D4—361no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—122no—
389C2×C4—121no—
390C2×C4—181no—
391C2×C4—361no—
392C2×C4—361no—
393C2×C4#379611yescharacteristic
394C2×C4#379911yescharacteristic
395C2×C4D3×D1211yescharacteristic
396C2×C4#380411yescharacteristic
397C2×C4C2×#62411yescharacteristic
398C2×C4D3×#6711yescharacteristic
399C8—22no—
400C8—62no—
401C8—121no—
402C8—182no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3#467011yescharacteristic
414C2×C3#499011yescharacteristic
415D3—242no—
416D3—241no—
417D3—241no—
418C22—41no—
419C22—361no—
420C22—721no—
421C22#6384911yescharacteristic
422C22#6389011yescharacteristic
423C22#6390711yescharacteristic
424C4—62no—
425C4—121no—
426C4—241no—
427C4—361no—
428C4#6384811yescharacteristic
429C4#6388611yescharacteristic
430C4#6389411yescharacteristic
431C4#6395211yescharacteristic
432C3—21no—
433C3#6875011yescharacteristic, complemented
434C3#7072711yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—721no—
439C2#1059126611yescharacteristic
subgroupG/H
centerC4#63886
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#388
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1932
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. C3×#5125C2semidirect
5. Dic3×#208C2semidirect
6. C3×#4555C2semidirect
7. #10589169C2semidirect
17. #63651C4semidirect
18. #63650C4semidirect
31. #5125D3semidirect
38. #4555D3semidirect
377. C32#1932semidirect
433. C3#68750semidirect
434. C3#70727semidirect

Maximal subgroups

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

subgroupindex
#105928312
C3×#51252
#105911132
C2×#635702
Dic3×#2082
C3×#45552
#105891692
#707273
#687503