Finite Group Databasebeta

← #11860770

Subgroups — #11860770

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic
5#10591405C214yesmaximal, complemented
6#10591401C214yesmaximal, complemented
7#10591138C211yesmaximal, characteristic, complemented
8#10591107C211yesmaximal, characteristic, complemented
9#10591057C211yesmaximal, characteristic, complemented
10#82543—31nomaximal
11#78916—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×#3754C418yescomplemented
15C2×#3754C2212yes—
16C2×#3754C2212yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yes—
21C3×#926C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63957—22no—
26#63844—22no—
27#63844C2214yescomplemented
28C3×#832C2214yes—
29#63576C2212yescomplemented
30#63574C2212yescomplemented
31#63567C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35#5798D311yescharacteristic
36C22×#214—31no—
37C22×#214—31no—
38C22×#214—61no—
39#5516—31no—
40#5516—31no—
41C3×#418—31no—
42#5215D311yescharacteristic
43#5122—31no—
44#5120—31no—
45#5018—34no—
46C4×#214—34no—
47#5004—31no—
48#4998—31no—
49#4998—31no—
50#4997—31no—
51#4758—34no—
52#4757—34no—
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634C2×C414yescomplemented
63C2×#634C2312yes—
64C22×C3×Dic3—24no—
65#3754C2×C418yescomplemented
66#3754C2×C418yescomplemented
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2311yescharacteristic
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70C3×#217—21no—
71C3×#217—21no—
72C3×#217—24no—
73C3×#217D412yes—
74C3×C4⋊Dic3D412yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3C2312yes—
80C3×#208—22no—
81C2×C3×C3⋊C8C2312yes—
82#3724—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C2×C3×M16—31no—
92C3×C4×D4—34no—
93C3×C4×D4—62no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117—31no—
97C2×C3×C22⋊C4—62no—
98C2×#217—22no—
99D4×Dic3—22no—
100D4×Dic3C2×D314yes—
101C2×#214—38no—
102C2×#214—38no—
103C2×#214—32no—
104C2×#214—32no—
105C2×#214—32no—
106C2×#214—32no—
107C2×#214—68no—
108C2×#214—62no—
109C2×#214—62no—
110#926C2×D311yescharacteristic
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117#887—34no—
118#887—62no—
119#877—62no—
120#877—62no—
121C4×Dic6—34no—
122C4×Dic6—62no—
123C3×#102—34no—
124#832C2×D314yes—
125#816—34no—
126#815—32no—
127C8×Dic3—32no—
128#810—34no—
129#808—32no—
130#808—32no—
131#807—32no—
132#807—32no—
133#803—32no—
134C4×C3⋊C8—32no—
135C23×C32—22no—
136C23×C32—24no—
137C23×C32—82no—
138C23×C32C2×D411yescharacteristic
139C32×D4—24no—
140C32×D4—22no—
141C32×D4C22×C414yes—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—24no—
147C2×C3⋊Dic3—22no—
148#634—24no—
149#634—22no—
150#634C22×C414yes—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—84no—
154C2×C3×Dic3C2×D414yes—
155C3⋊(C3⋊C8)C22×C412yes—
156C3⋊(C3⋊C8)C22×C412yes—
157C3×C3⋊C8—22no—
158C22×SD16—91no—
159#519—91no—
160#518—31no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—91no—
165#418—31no—
166#405—91no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—24no—
175C2×C3×D4—22no—
176C2×C3×D4—42no—
177C2×C3×D4—41no—
178C2×C3×D4C4×D314yes—
179C2×C3×D4C4×D314yes—
180C2×C3×D4C22×D312yes—
181C2×C3×D4C22×D312yes—
182C22×C3×C4—21no—
183C22×C3×C4—64no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—24no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C2×Dic6—34no—
191C2×Dic6—34no—
192C2×Dic6—32no—
193C2×Dic6—32no—
194C2×Dic6—64no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—61no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—122no—
201C2×Dic6—121no—
202C3×M16—62no—
203C2×C3×C8—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C22⋊C4—32no—
208C3×C22⋊C4—64no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C42—32no—
212C3×C42—61no—
213C3×C42—61no—
214#217—21no—
215#217—21no—
216#217—24no—
217#217#6712yes—
218#214—38no—
219#214—38no—
220#214—38no—
221#214—38no—
222#214—68no—
223#214—68no—
224C4⋊Dic3#6712yes—
225C4⋊Dic3C22×D312yes—
226C4⋊Dic3C22×D312yes—
227Dic3⋊C4—64no—
228Dic3⋊C4—64no—
229C4×Dic3—21no—
230C4×Dic3—21no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3C22×D312yes—
234#208—22no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D312yes—
245C22×C32—22no—
246C22×C32—24no—
247C22×C32—44no—
248C22×C32—84no—
249C22×C32C4×D412yes—
250C22×C32C22×D411yescharacteristic
251C32×C4C4×D412yes—
252C32×C4C23×C411yescharacteristic
253C32×C4C2×#4111yescharacteristic
254C3⋊Dic3—24no—
255C3×Dic3—24no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C22×Q8—91no—
259C22×D4D3211yescharacteristic
260C2×SD16—98no—
261C2×SD16—92no—
262C2×SD16—92no—
263C2×M16—31no—
264C22×C8—91no—
265C4×Q8—94no—
266C4×Q8—182no—
267C4×D4—34no—
268C4×D4—62no—
269#117—31no—
270#117—31no—
271#117—31no—
272#117—182no—
273C2×C22⋊C4—62no—
274#107—92no—
275#106—92no—
276#103—94no—
277#102—34no—
278#97—92no—
279C4×C8—92no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—21no—
285C23×C3—42no—
286C23×C3—44no—
287C23×C3—82no—
288C23×C3—82no—
289C23×C3—84no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C3×D4—24no—
293C3×D4—24no—
294C3×D4—22no—
295C3×D4—22no—
296C3×D4—24no—
297C3×D4—42no—
298C3×D4—44no—
299C3×D4C2×C4×D314yes—
300C3×D4C2×C4×D314yes—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—34no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—244no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4#23512yes—
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23712yes—
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—64no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—84no—
324C2×Dic3—122no—
325C2×Dic3—124no—
326C2×Dic3C2×#6714yes—
327Dic6—34no—
328Dic6—34no—
329Dic6—64no—
330Dic6—64no—
331Dic6—64no—
332Dic6—62no—
333Dic6—62no—
334Dic6—122no—
335Dic6—124no—
336C3×C8—62no—
337C3⋊C8—22no—
338C3⋊C8—32no—
339C3⋊C8—32no—
340C3⋊C8—32no—
341C3⋊C8—32no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C2×C32—22no—
345C2×C32—44no—
346C2×C32C2×C4×D411yescharacteristic
347C2×C32#57712yes—
348C24—21no—
349C2×Q8—92no—
350C2×Q8—94no—
351C2×Q8—182no—
352C2×Q8—181no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4#62414yes—
356C2×D4C2×D3212yes—
357C22×C4—64no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360SD16—98no—
361SD16—98no—
362M16—62no—
363C2×C8—32no—
364C2×C8—91no—
365C2×C8—91no—
366C2×C8—94no—
367C4⋊C4—32no—
368C4⋊C4—32no—
369C4⋊C4—32no—
370C4⋊C4—184no—
371C22⋊C4—32no—
372C22⋊C4—64no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C42—32no—
376C42—61no—
377C42—61no—
378C42—184no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—24no—
383C22×C3—24no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—44no—
387C22×C3—44no—
388C22×C3—44no—
389C22×C3—84no—
390C22×C3—84no—
391C22×C3—84no—
392C22×C3—88no—
393C22×C3#67⋊C412yes—
394C22×C3C4×#6712yes—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C22×#6711yescharacteristic
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—22no—
400C3×C4—64no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4#67⋊C412yes—
404C3×C4C4×#6712yes—
405C3×C4C22×C4×D311yescharacteristic
406C3×C4C22×C4×D311yescharacteristic
407C3×C4C2×#23511yescharacteristic
408C3×C4C2×#23711yescharacteristic
409Dic3—24no—
410Dic3—42no—
411Dic3—42no—
412Dic3—64no—
413Dic3—64no—
414Dic3—124no—
415C32#294911yescharacteristic, complemented, Sylow
416C23—22no—
417C23—24no—
418C23—82no—
419C23D3×#6711yescharacteristic
420Q8—94no—
421Q8—182no—
422Q8—184no—
423D4—22no—
424D4—24no—
425D4C2×#62414yes—
426C2×C4—34no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—182no—
430C2×C4—184no—
431C2×C4—244no—
432C2×C4#380412yes—
433C2×C4C2×#62412yes—
434C2×C4D3×#6711yescharacteristic
435C2×C4C22×D3211yescharacteristic
436C8—62no—
437C8—92no—
438C8—92no—
439C2×C3—24no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—44no—
445C2×C3—44no—
446C2×C3—84no—
447C2×C3C2×#67⋊C411yescharacteristic
448C2×C3#577512yes—
449C2×C3C2×C4×#6711yescharacteristic
450C2×C3#583612yes—
451C22—22no—
452C22—24no—
453C22—44no—
454C22—84no—
455C22#6395212yes—
456C22C2×D3×#6711yescharacteristic
457C4—64no—
458C4—122no—
459C4—122no—
460C4—184no—
461C4#6395212yes—
462C4C2×#380411yescharacteristic
463C4C22×#62411yescharacteristic
464C3—21no—
465C3#7891611yescharacteristic, complemented
466C3#8254311yescharacteristic, complemented
467C2—22no—
468C2—44no—
469C2#1059510612yes—
470C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10594828C2semidirect
5. #10591405C2semidirect
6. #10591401C2semidirect
7. #10591138C2semidirect
8. #10591107C2semidirect
9. #10591057C2semidirect
14. C2×#3754C4semidirect
27. #63844C22semidirect
29. #63576C22semidirect
30. #63574C22semidirect
31. #63567C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
62. C2×#634C2×C4semidirect
65. #3754C2×C4semidirect
66. #3754C2×C4semidirect
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
415. C32#2949semidirect
465. C3#78916semidirect
466. C3#82543semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C3×#57982
#105948282
C3×#52152
#105914052
#105914012
#105911382
#105911072
#105910572
#825433
#789163