Finite Group Databasebeta

← #11789723

Subgroups — #11789723

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#10592936C211yesmaximal, characteristic
2C3×#5236C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4#10591143C211yesmaximal, characteristic, complemented
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589169C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70401—31nomaximal
9#70378—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63663C412yescomplemented
18#63660C412yescomplemented
19C3×#837—21no—
20C3×#837—21no—
21C3×#837—22no—
22#63578—22no—
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C3×#421—31no—
26C2×C3×#104—31no—
27#5237—31no—
28#5237—31no—
29#5237—61no—
30#5236D311yescharacteristic
31C2×#837D311yescharacteristic
32#5124—31no—
33#5124—31no—
34Dic3×M16—31no—
35C4×#208—31no—
36#4556—31no—
37#4533—31no—
38#4532—31no—
39#4523—31no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4C2×C411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50#3748—21no—
51#3748—21no—
52#3748C2×C412yes—
53#3748C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
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×C3×#41—21no—
70C2×C3×#41C2×D311yescharacteristic
71C2×C3×#41C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C3×#117—31no—
75C2×C3×C42—31no—
76#926C2×D311yescharacteristic
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—61no—
87C3×#104—61no—
88C3×#104—62no—
89#837—21no—
90#837—21no—
91#837—22no—
92#836—32no—
93#836—32no—
94#836—62no—
95#833—32no—
96#833—32no—
97#833—62no—
98#822—62no—
99#822—62no—
100#815—61no—
101C8×Dic3—61no—
102#803—61no—
103C4×C3⋊C8—61no—
104C23×C32—21no—
105C23×C32#4111yescharacteristic
106C32×Q8—21no—
107C32×Q8—21no—
108C32×D4—21no—
109C32×D4—21no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—41no—
125C3⋊(C3⋊C8)—22no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#430—91no—
130#421—31no—
131C2×#104—31no—
132#413—91no—
133C4×M16—91no—
134#344—91no—
135#339—91no—
136C3×#41—21no—
137C3×#41—21no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—41no—
145C3×#41—41no—
146C3×#41—41no—
147C3×#41—41no—
148C2×C3×Q8—21no—
149C2×C3×Q8C4×D311yescharacteristic
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4C4×D311yescharacteristic
156C2×C3×D4C4×D311yescharacteristic
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C3×M16—32no—
166C3×M16—61no—
167C3×M16—61no—
168C3×M16—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42—61no—
176C3×C42—61no—
177#217—21no—
178C4⋊Dic3—21no—
179C4×Dic3—21no—
180C4×Dic3—21no—
181C4×Dic3#6711yescharacteristic
182C4×Dic3#6711yescharacteristic
183#208—21no—
184#208—21no—
185#208—21no—
186#208—32no—
187#208—32no—
188#208—32no—
189#208—32no—
190#208—62no—
191#208—62no—
192#208—61no—
193#208—61no—
194#208—61no—
195#208—61no—
196#208—121no—
197#208—121no—
198#208#6712yes—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C2×C3⋊C8—121no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32—81no—
210C22×C32#11711yescharacteristic
211C22×C32#12311yescharacteristic
212C22×C32#12411yescharacteristic
213C32×C4—41no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4#12611yescharacteristic
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—81no—
221C2×#41D3211yescharacteristic
222C2×M16—31no—
223C2×M16—31no—
224C2×M16—91no—
225C2×M16—91no—
226#117—31no—
227C2×C42—31no—
228#108—182no—
229#104—61no—
230#104—61no—
231#104—62no—
232#101—92no—
233#100—92no—
234#97—181no—
235C4×C8—181no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3#23711yescharacteristic
241C23×C3#23711yescharacteristic
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—21no—
245C3×Q8—21no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—21no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—122no—
278C2×C3×C4—121no—
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—42no—
294C2×Dic3—41no—
295C3×C8—62no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—62no—
300C3⋊C8—62no—
301C3⋊C8—62no—
302C3⋊C8—62no—
303C3⋊C8—122no—
304C3⋊C8—122no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32—81no—
309C2×C32#38811yescharacteristic
310#41—21no—
311#41—21no—
312#41—21no—
313#41—21no—
314C2×Q8#62411yescharacteristic
315C2×D4—21no—
316C2×D4#62411yescharacteristic
317C22×C4—21no—
318C22×C4—61no—
319C22×C4C2×D3211yescharacteristic
320M16—32no—
321M16—61no—
322M16—61no—
323M16—61no—
324M16—92no—
325M16—92no—
326M16—181no—
327M16—181no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—181no—
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—42no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—82no—
350C22×C3#87711yescharacteristic
351C22×C3#87711yescharacteristic
352C22×C3#88311yescharacteristic
353C22×C3#88511yescharacteristic
354C22×C3#93511yescharacteristic
355C22×C3#93611yescharacteristic
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—42no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—62no—
364C3×C4—121no—
365C3×C4—241no—
366C3×C4#87911yescharacteristic
367C3×C4#87911yescharacteristic
368C3×C4#67⋊C411yescharacteristic
369C3×C4#67⋊C411yescharacteristic
370C3×C4C4×#6711yescharacteristic
371C3×C4C4×#6711yescharacteristic
372C3×C4#93811yescharacteristic
373C3×C4#93911yescharacteristic
374Dic3—22no—
375Dic3—41no—
376Dic3—81no—
377C32#193211yescharacteristic, complemented, Sylow
378C23—21no—
379C23#380511yescharacteristic
380Q8—21no—
381Q8—21no—
382D4—21no—
383D4—21no—
384D4—41no—
385D4—41no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—122no—
392C2×C4—121no—
393C2×C4#380411yescharacteristic
394C2×C4#380411yescharacteristic
395C2×C4#380511yescharacteristic
396C2×C4C2×#62411yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C2×C4D3×#6711yescharacteristic
399C8—62no—
400C8—121no—
401C8—182no—
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—82no—
414C2×C3—81no—
415C2×C3—81no—
416C2×C3#494411yescharacteristic
417C2×C3#494511yescharacteristic
418C22—41no—
419C22—41no—
420C22—81no—
421C22#6395711yescharacteristic
422C22#6395911yescharacteristic
423C22#6396911yescharacteristic
424C4—41no—
425C4—62no—
426C4—121no—
427C4—241no—
428C4#6395211yescharacteristic
429C4#6395211yescharacteristic
430C4#6395611yescharacteristic
431C4#6397011yescharacteristic
432C3—21no—
433C3#7037811yescharacteristic, complemented
434C3#7040111yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—81no—
439C2#1059170311yescharacteristic
subgroupG/H
centerC4#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#388
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591143C2semidirect
5. Dic3×#208C2semidirect
6. #10589169C2semidirect
7. #10589161C2semidirect
17. #63663C4semidirect
18. #63660C4semidirect
377. C32#1932semidirect
433. C3#70378semidirect
434. C3#70401semidirect

Maximal subgroups

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

subgroupindex
#105929362
C3×#52362
C2×C3×#8372
#105911432
Dic3×#2082
#105891692
#105891612
#704013
#703783