Finite Group Databasebeta

← #16855024

Subgroups — #16855024

Order 3968.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758567C211yesmaximal, characteristic, complemented
2C2×#11758492C211yesmaximal, characteristic, complemented
3C2×#11758489C211yesmaximal, characteristic, complemented
4#14521628C211yesmaximal, characteristic, complemented
5#14521212C211yesmaximal, characteristic, complemented
6#14521211C211yesmaximal, characteristic, complemented
7#14521207C211yesmaximal, characteristic, complemented
8#14521206C211yesmaximal, characteristic, complemented
9#14521191C211yesmaximal, characteristic, complemented
10#14521187C211yesmaximal, characteristic, complemented
11#14521186C211yesmaximal, characteristic, complemented
12#14521047C211yesmaximal, characteristic, complemented
13#103×D31C211yesmaximal, characteristic, complemented
14#14521014C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17#11758567—24no—
18#11758567—24no—
19C2×Q8×D31C2211yescharacteristic
20C2×Q8×D31C2211yescharacteristic
21C2×#92497—21no—
22C2×#92497—21no—
23C2×#92497C2211yescharacteristic
24C2×#92497C2211yescharacteristic
25C2×#92497C2211yescharacteristic
26C2×#92495—21no—
27C2×#92495C2211yescharacteristic
28C22×Dic62—21no—
29C22×Dic62C2211yescharacteristic
30C2×SD16×C31C2211yescharacteristic
31C2×D8×C31C2211yescharacteristic
32C31×#121C2211yescharacteristic
33C2×#92482C2211yescharacteristic
34#11758516—21no—
35#11758515—21no—
36#11758515C2211yescharacteristic
37C2×#92480C2211yescharacteristic
38C2×#92480C2211yescharacteristic
39C2×#92480C2211yescharacteristic
40#11758501C2211yescharacteristic
41#11758492—24no—
42#11758489—24no—
43C2×Dic124C2211yescharacteristic
44C2×Dic124C2211yescharacteristic
45C2×#92469C2211yescharacteristic
46C2×C8×D31C2211yescharacteristic
47#11758474C2211yescharacteristic
48C4⋊C4×D31C2211yescharacteristic
49#11758461—21no—
50#11758455—21no—
51C31×#103C2211yescharacteristic
52C31×#102C2211yescharacteristic
53C31×C22⋊C8C2211yescharacteristic
54#11758423C2211yescharacteristic
55#11758420C2211yescharacteristic
56C22⋊(C31⋊C8)C2211yescharacteristic
57(C2×D31)⋊C8C2211yescharacteristic
58(C2×D31)⋊C8C2211yescharacteristic
59#11758404C2211yescharacteristic
60#11758404C2211yescharacteristic
61#11758398C2211yescharacteristic
62#11758398C2211yescharacteristic
63#41×C31—22no—
64#41×C31—22no—
65C2×Q8×C31C2311yescharacteristic
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31C2311yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C22×C4×C31—21no—
71C22×C4×C31C2311yescharacteristic
72C2×C22⋊D31—21no—
73C2×C22⋊D31—21no—
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C2×C22⋊D31D411yescharacteristic
77C2×C22⋊D31D411yescharacteristic
78C22×Dic31—21no—
79C22×Dic31—21no—
80C22×Dic31—21no—
81C22×Dic31—21no—
82Q8×D31—22no—
83Q8×D31—22no—
84Q8×D31—22no—
85Q8×D31D414yescomplemented
86#92497—28no—
87#92497—28no—
88#92497—22no—
89#92497—22no—
90#92497—22no—
91#92497—22no—
92#92497—22no—
93#92497D414yescomplemented
94#92495—28no—
95#92495—22no—
96#92495—22no—
97C2×D124D411yescharacteristic
98C2×C4×D31—21no—
99C2×C4×D31—21no—
100C2×C4×D31—21no—
101C2×C4×D31C2311yescharacteristic
102C2×C4×D31C2311yescharacteristic
103C2×Dic62—28no—
104C2×Dic62—21no—
105C2×Dic62—21no—
106C2×Dic62—21no—
107C2×Dic62—22no—
108C2×Dic62—22no—
109C2×Dic62D411yescharacteristic
110C2×Dic62C2311yescharacteristic
111C2×Dic62C2311yescharacteristic
112C2×Dic62C2311yescharacteristic
113SD16×C31—22no—
114D8×C31—22no—
115C2×C8×C31C2311yescharacteristic
116C2×C8×C31C2311yescharacteristic
117C4⋊C4×C31C2311yescharacteristic
118C22⋊C4×C31—21no—
119C22⋊Dic31—21no—
120C22⋊Dic31—21no—
121#92482—22no—
122#92480—22no—
123#92480—22no—
124#92480—22no—
125(C2×D31)⋊C4—21no—
126C4⋊Dic31—21no—
127C4⋊Dic31C2311yescharacteristic
128Dic31⋊C4—21no—
129Dic31⋊C4—21no—
130C2×C31⋊C8C2311yescharacteristic
131C2×C31⋊C8C2311yescharacteristic
132Dic124—22no—
133Dic124—22no—
134#92469—22no—
135C8×D31—22no—
136C23×C31—21no—
137C23×C31—21no—
138C23×C31C2×D411yescharacteristic
139C22×D31C2×D411yescharacteristic
140C22×D31C2×D411yescharacteristic
141Q8×C31—21no—
142Q8×C31C2×D412yes—
143D4×C31—24no—
144D4×C31—21no—
145D4×C31—21no—
146D4×C31—21no—
147D4×C31—81no—
148D4×C31C2×D412yes—
149C2×C4×C31—24no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31C2×D411yescharacteristic
155C2×C4×C31C2411yescharacteristic
156C22⋊D31—24no—
157C22⋊D31—22no—
158C22⋊D31—24no—
159C22⋊D31—22no—
160C22⋊D31—42no—
161C22⋊D31—81no—
162C2×Dic31—24no—
163C2×Dic31—24no—
164C2×Dic31—21no—
165C2×Dic31—21no—
166C2×Dic31—24no—
167C2×Dic31—21no—
168C2×Dic31—21no—
169C2×Dic31—42no—
170C2×Dic31C2×D411yescharacteristic
171C2×Dic31C2×D411yescharacteristic
172D124—22no—
173C4×D31—24no—
174C4×D31—24no—
175C4×D31—21no—
176C4×D31—21no—
177C4×D31—81no—
178C4×D31C2×D412yes—
179C4×D31C2×D412yes—
180Dic62—24no—
181Dic62—24no—
182Dic62—21no—
183Dic62—21no—
184Dic62—22no—
185Dic62—24no—
186Dic62—21no—
187Dic62—21no—
188Dic62C2×D412yes—
189Dic62C2×D412yes—
190C8×C31—21no—
191C8×C31—21no—
192C31⋊C8—21no—
193C31⋊C8—21no—
194#3013—311nomaximal, Sylow
195C22×C31—21no—
196C22×C31—22no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—41no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—41no—
203C22×C31—41no—
204C22×C31C22×D411yescharacteristic
205C2×D31—21no—
206C2×D31—21no—
207C2×D31—21no—
208C2×D31—21no—
209C2×D31—21no—
210C2×D31#12012yes—
211C4×C31—21no—
212C4×C31—22no—
213C4×C31—41no—
214C4×C31C22×D411yescharacteristic
215C4×C31C22×D411yescharacteristic
216Dic31—21no—
217Dic31—22no—
218Dic31—22no—
219Dic31—41no—
220Dic31—41no—
221Dic31#12012yes—
222C2×2−1+4—311no—
223C2×#137—311no—
224C2×#135—311no—
225#537—311no—
226#452—311no—
227#452—311no—
228#451—311no—
229#451—311no—
230#449—311no—
231#449D3111yescharacteristic, complemented
232#448—311no—
233#448—311no—
234#417—311no—
235C2×#103—311no—
236#408—311no—
237C2×C31—41no—
238C2×C31—42no—
239C2×C31—81no—
240C2×C31C2×#12011yescharacteristic
241C2×C31#57711yescharacteristic
242C2×C31#57811yescharacteristic
243D31—22no—
244D31—41no—
2452−1+4—624no—
2462−1+4—624no—
247C2×#41—311no—
248C2×#41—311no—
249C2×#41—311no—
250C2×#41—311no—
251C2×#41—621no—
252C2×#41—621no—
253C2×#41—621no—
254C2×#41C2×D3111yescharacteristic
255C22×Q8—311no—
256C22×Q8—311no—
257C22×Q8—311no—
258C22×Q8—621no—
259#137—624no—
260#135—624no—
261C2×Q16—311no—
262C2×Q16—311no—
263C2×Q16—311no—
264C2×SD16—311no—
265C2×SD16—311no—
266C2×SD16—311no—
267C2×SD16C2×D3111yescharacteristic
268C2×D8C2×D3111yescharacteristic
269C2×M16—311no—
270C22×C8—311no—
271C22⋊Q8—311no—
272C22⋊Q8—311no—
273C22⋊Q8—621no—
274#121—311no—
275#121—621no—
276#121—621no—
277#121—621no—
278#121C2×D3111yescharacteristic
279C2×C4⋊C4—311no—
280#103—311no—
281#103—311no—
282#103—311no—
283#103—311no—
284#103—311no—
285#103C2×D3111yescharacteristic
286#102—311no—
287#102C2×D3111yescharacteristic
288C22⋊C8—311no—
289C22⋊C8—311no—
290C22⋊C8—311no—
291C22⋊C8C2×D3111yescharacteristic
292C31#301311yescharacteristic, complemented, Sylow
293#41—22no—
294#41—22no—
295#41—314no—
296#41—622no—
297#41—622no—
298#41—628no—
299#41—622no—
300#41—622no—
301#41—622no—
302#41—622no—
303#41—628no—
304#41—628no—
305#41—622no—
306C2×Q8—311no—
307C2×Q8—314no—
308C2×Q8—311no—
309C2×Q8—311no—
310C2×Q8—311no—
311C2×Q8—621no—
312C2×Q8—621no—
313C2×Q8—622no—
314C2×Q8—622no—
315C2×Q8—628no—
316C2×Q8—622no—
317C2×Q8—622no—
318C2×Q8—622no—
319C2×Q8—621no—
320C2×Q8C22×D3111yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—311no—
324C2×D4—311no—
325C2×D4—311no—
326C2×D4—621no—
327C2×D4—621no—
328C2×D4—621no—
329C2×D4—621no—
330C2×D4C22×D3111yescharacteristic
331C2×D4C22×D3111yescharacteristic
332C22×C4—21no—
333C22×C4—311no—
334C22×C4—311no—
335C22×C4—621no—
336C22×C4—621no—
337C22×C4—621no—
338C22×C4—621no—
339C22×C4—621no—
340C22×C4—621no—
341C22×C4—621no—
342C22×C4C22×D3111yescharacteristic
343Q16—622no—
344Q16—622no—
345Q16—622no—
346SD16—22no—
347SD16—622no—
348SD16—622no—
349SD16—622no—
350D8—22no—
351M16—622no—
352C2×C8—311no—
353C2×C8—311no—
354C2×C8—622no—
355C2×C8C22×D3111yescharacteristic
356C2×C8C22×D3111yescharacteristic
357C4⋊C4—311no—
358C4⋊C4—621no—
359C4⋊C4—621no—
360C4⋊C4—621no—
361C4⋊C4C22×D3111yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—621no—
364C22⋊C4—621no—
365C22⋊C4—621no—
366C23—21no—
367C23—21no—
368C23—311no—
369C23—311no—
370C23D4×D3111yescharacteristic
371Q8—21no—
372Q8—312no—
373Q8—312no—
374Q8—622no—
375Q8—624no—
376Q8—624no—
377Q8—624no—
378Q8—621no—
379Q8—621no—
380Q8—621no—
381Q8—621no—
382Q8D4×D3112yes—
383D4—24no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—81no—
388D4—622no—
389D4—622no—
390D4—622no—
391D4—624no—
392D4—624no—
393D4—1242no—
394D4—2481no—
395D4D4×D3112yes—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—311no—
402C2×C4—312no—
403C2×C4—312no—
404C2×C4—311no—
405C2×C4—624no—
406C2×C4—624no—
407C2×C4—624no—
408C2×C4—624no—
409C2×C4—624no—
410C2×C4—621no—
411C2×C4—621no—
412C2×C4—621no—
413C2×C4—621no—
414C2×C4—621no—
415C2×C4—621no—
416C2×C4—1242no—
417C2×C4—2481no—
418C2×C4D4×D3111yescharacteristic
419C2×C4C23×D3111yescharacteristic
420C8—21no—
421C8—21no—
422C8—621no—
423C8—621no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—312no—
434C22—621no—
435C22—621no—
436C22—621no—
437C22—621no—
438C22—621no—
439C22C2×D4×D3111yescharacteristic
440C4—21no—
441C4—22no—
442C4—41no—
443C4—312no—
444C4—621no—
445C4—622no—
446C4—622no—
447C4—1241no—
448C4—1241no—
449C4C2×D4×D3111yescharacteristic
450C4C2×D4×D3111yescharacteristic
451C2—41no—
452C2—42no—
453C2—81no—
454C2—622no—
455C2—1241no—
456C2#120×D3111yescharacteristic
457C2#1452185911yescharacteristic
458C2#1452186311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3013
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11758567C2semidirect
2. C2×#11758492C2semidirect
3. C2×#11758489C2semidirect
4. #14521628C2semidirect
5. #14521212C2semidirect
6. #14521211C2semidirect
7. #14521207C2semidirect
8. #14521206C2semidirect
9. #14521191C2semidirect
10. #14521187C2semidirect
11. #14521186C2semidirect
12. #14521047C2semidirect
13. #103×D31C2semidirect
14. #14521014C2semidirect
15. C31×#449C2semidirect
85. Q8×D31D4semidirect
93. #92497D4semidirect
231. #449D31semidirect
292. C31#3013semidirect

Maximal subgroups

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

subgroupindex
C2×#117585672
C2×#117584922
C2×#117584892
#145216282
#145212122
#145212112
#145212072
#145212062
#145211912
#145211872
#145211862
#145210472
#103×D312
#145210142
C31×#4492
#301331