Finite Group Databasebeta

← #11789728

Subgroups — #11789728

Order 1152.

483 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592823C211yesmaximal, characteristic, complemented
2C3×#5139C211yesmaximal, characteristic
3C3×Dic3×M16C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591076C211yesmaximal, characteristic
6#10589170C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70401—31nomaximal
9#69874—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63649—22no—
18C3×#825—22no—
19C3×#815—21no—
20C3×C8×Dic3—21no—
21#63569—21no—
22#63569—21no—
23#63560C412yescomplemented
24#63558C412yescomplemented
25C3×#421—31no—
26C3×C4×M16—31no—
27#5237—31no—
28C2×#837—31no—
29#5139D311yescharacteristic
30#5132—31no—
31#5124—31no—
32#5124—31no—
33#5124—61no—
34Dic3×M16D311yescharacteristic, complemented
35C2×#805—31no—
36#4559—31no—
37#4533—31no—
38#4532—31no—
39#4523—31no—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
42C22×C3×Dic3—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×M16—21no—
51C32×M16D412yes—
52C2×C32×C8—21no—
53#3748—21no—
54#3748—21no—
55#3748—21no—
56#3748C2×C412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3D411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×#208—21no—
66C3×#208C2×C412yes—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C3×#117—31no—
76C2×C3×C42—31no—
77#926C2×D311yescharacteristic
78C2×C4×Dic3C2×D311yescharacteristic
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208—61no—
85C2×#208C2×D311yescharacteristic
86C3×#104—62no—
87C3×#97—61no—
88C3×C4×C8—61no—
89#837—61no—
90#837—61no—
91#836—32no—
92#833—32no—
93#825—22no—
94#824—32no—
95#823—32no—
96#822—64no—
97#822—62no—
98#822—62no—
99#815—21no—
100C8×Dic3—21no—
101#805—61no—
102#805—61no—
103C23×C32#4111yescharacteristic
104C22×C3×D3—21no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C3×#67—41no—
112C3×#67—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—41no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—21no—
123C3×Dic6—21no—
124C32×C8—22no—
125C3⋊(C3⋊C8)—22no—
126C3⋊(C3⋊C8)—41no—
127C3×C3⋊C8—22no—
128#430—91no—
129#421—31no—
130C2×#104—91no—
131#413—91no—
132C4×M16—31no—
133#344—91no—
134#339—91no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C3×#41—61no—
139C2×C3×Q8—31no—
140C2×C3×D4—31no—
141C2×C3×D4—61no—
142C22×C3×C4—21no—
143C22×C3×C4—61no—
144C22×C3×C4—61no—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C2×#67—21no—
148C22×Dic3—21no—
149#235—21no—
150#235—21no—
151#235—21no—
152#235—21no—
153C2×D12C4×D311yescharacteristic
154C2×C4×D3—21no—
155C2×Dic6C4×D311yescharacteristic
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—22no—
159C3×M16—32no—
160C3×M16—41no—
161C3×M16—61no—
162C3×M16D1212yes—
163C3×M16#6712yes—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—61no—
173C3×C42—61no—
174#217—21no—
175C4⋊Dic3—21no—
176C4×Dic3—21no—
177C4×Dic3—21no—
178C4×Dic3#6711yescharacteristic
179C4×Dic3#6711yescharacteristic
180#208—21no—
181#208—32no—
182#208—32no—
183#208—62no—
184#208—62no—
185#208—61no—
186#208—61no—
187#208—62no—
188#208—61no—
189#208—61no—
190#208—61no—
191#208—61no—
192#208—121no—
193#208C4×D312yes—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—121no—
201C22×C32—41no—
202C22×C32#11711yescharacteristic
203C22×C32#12311yescharacteristic
204C22×C32#12411yescharacteristic
205C2×C3×D3—41no—
206C2×C3×D3—81no—
207C32×C4C4×D411yescharacteristic
208C32×C4C4×D411yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12611yescharacteristic
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—81no—
215C2×#41—31no—
216C2×M16—31no—
217C2×M16—91no—
218C2×M16—91no—
219C2×M16D3211yescharacteristic
220#117—31no—
221C2×C42—31no—
222#108—182no—
223#104—62no—
224#104—181no—
225#104—181no—
226#101—92no—
227#100—92no—
228#97—61no—
229C4×C8—61no—
230C23×C3—21no—
231C23×C3—61no—
232C23×C3#23511yescharacteristic
233C23×C3#23711yescharacteristic
234C22×D3—21no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×D4—61no—
238C3×D4—61no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—122no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4C2×C4×D311yescharacteristic
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4#23511yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4#23511yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—41no—
267#67—41no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—42no—
272C2×Dic3—41no—
273D12—21no—
274D12—21no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—21no—
278Dic6—21no—
279C3×C8—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—62no—
283C3⋊C8—22no—
284C3⋊C8—64no—
285C3⋊C8—62no—
286C3⋊C8—62no—
287C3⋊C8—122no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32#38811yescharacteristic
294C3×D3—81no—
295#41—61no—
296#41—61no—
297#41—61no—
298#41—61no—
299C2×Q8—31no—
300C2×D4—31no—
301C2×D4—61no—
302C22×C4—61no—
303C22×C4—61no—
304C22×C4C2×D3211yescharacteristic
305M16—21no—
306M16—32no—
307M16—61no—
308M16—92no—
309M16—181no—
310M16—181no—
311M16—181no—
312M16#62612yes—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—181no—
316C2×C8—181no—
317C4⋊C4—61no—
318C22⋊C4—61no—
319C42—31no—
320C42—31no—
321C42—61no—
322C42—61no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—81no—
329C22×C3—121no—
330C22×C3—241no—
331C22×C3#87211yescharacteristic
332C22×C3#87511yescharacteristic
333C22×C3#87711yescharacteristic
334C22×C3#88311yescharacteristic
335C22×C3#92911yescharacteristic
336C22×C3#93611yescharacteristic
337C2×D3—41no—
338C2×D3—81no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—62no—
344C3×C4—121no—
345C3×C4—121no—
346C3×C4—241no—
347C3×C4C4×D1211yescharacteristic
348C3×C4#87611yescharacteristic
349C3×C4#87911yescharacteristic
350C3×C4#67⋊C411yescharacteristic
351C3×C4C4×#6711yescharacteristic
352C3×C4C4×#6711yescharacteristic
353C3×C4#93011yescharacteristic
354C3×C4#93911yescharacteristic
355Dic3—22no—
356Dic3—41no—
357Dic3—41no—
358Dic3—81no—
359C32#193211yescharacteristic, complemented, Sylow
360C23—61no—
361C23#379511yescharacteristic
362Q8—61no—
363Q8—61no—
364D4—61no—
365D4—61no—
366D4—121no—
367D4—121no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—122no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4#379511yescharacteristic
376C2×C4#379811yescharacteristic
377C2×C4C4×D3211yescharacteristic
378C2×C4#380411yescharacteristic
379C2×C4C2×#62611yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—22no—
382C8—62no—
383C8—182no—
384C8—361no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—241no—
396C2×C3#494011yescharacteristic
397C2×C3#494511yescharacteristic
398D3—81no—
399C22—41no—
400C22—121no—
401C22—241no—
402C22#6386011yescharacteristic
403C22#6387711yescharacteristic
404C22#6390511yescharacteristic
405C4—62no—
406C4—121no—
407C4—121no—
408C4—241no—
409C4#6385911yescharacteristic
410C4#6387911yescharacteristic
411C4C4×#62611yescharacteristic
412C4#6397811yescharacteristic
413C3—21no—
414C3#6987411yescharacteristic, complemented
415C3#7040111yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—21no—
419C2—241no—
420C2#1059128011yescharacteristic
subgroupG/H
centerC4#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#388
prime radicalC2×C3×#235C22
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
1. #10592823C2semidirect
3. C3×Dic3×M16C2semidirect
6. #10589170C2semidirect
7. #10589161C2semidirect
23. #63560C4semidirect
24. #63558C4semidirect
34. Dic3×M16D3semidirect
359. C32#1932semidirect
414. C3#69874semidirect
415. C3#70401semidirect

Maximal subgroups

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

subgroupindex
#105928232
C3×#51392
C3×Dic3×M162
C2×#635692
#105910762
#105891702
#105891612
#704013
#698743