Finite Group Databasebeta

← #16857435

Subgroups — #16857435

Order 3968.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758493C211yesmaximal, characteristic, complemented
2#14521718C211yesmaximal, characteristic, complemented
3#14521698C211yesmaximal, characteristic, complemented
4#14521420C211yesmaximal, characteristic, complemented
5#14521278C211yesmaximal, characteristic, complemented
6#14521275C211yesmaximal, characteristic, complemented
7#14521257C211yesmaximal, characteristic, complemented
8#14521242C211yesmaximal, characteristic, complemented
9#14521211C211yesmaximal, characteristic, complemented
10#14521210C211yesmaximal, characteristic, complemented
11#14521194C211yesmaximal, characteristic, complemented
12#14521191C211yesmaximal, characteristic, complemented
13SD16×Dic31C211yesmaximal, characteristic, complemented
14C8×C22⋊D31C211yesmaximal, characteristic, complemented
15C2×C31×#135C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#41×C31C2211yescharacteristic
18C2×#92499C2211yescharacteristic
19C2×#92497C2211yescharacteristic
20C31×#135—24no—
21C2×Q16×C31C2211yescharacteristic
22C2×SD16×C31C2211yescharacteristic
23C2×SD16×C31C2211yescharacteristic
24C2×D8×C31C2211yescharacteristic
25C22×C8×C31C2211yescharacteristic
26#11758523C2211yescharacteristic
27Q8×Dic31C2211yescharacteristic
28#11758521C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30C2×#92481C2211yescharacteristic
31#11758517—21no—
32#11758517C2211yescharacteristic
33#11758516—21no—
34#11758515—21no—
35#11758515C2211yescharacteristic
36#11758512—21no—
37D4×Dic31C2211yescharacteristic
38C2×#92480C2211yescharacteristic
39C2×#92479C2211yescharacteristic
40#11758507—21no—
41#11758507C2211yescharacteristic
42#11758506—21no—
43C4×C22⋊D31—21no—
44C4×C22⋊D31C2211yescharacteristic
45#11758501C2211yescharacteristic
46C2×Dic31⋊C4—21no—
47#11758493—24no—
48C2×#92470C2211yescharacteristic
49C2×C8×D31C2211yescharacteristic
50#11758423C2211yescharacteristic
51#11758423C2211yescharacteristic
52#11758420C2211yescharacteristic
53#11758420C2211yescharacteristic
54C22⋊(C31⋊C8)C2211yescharacteristic
55#11758409C2211yescharacteristic
56(C2×D31)⋊C8C2211yescharacteristic
57#11758405C2211yescharacteristic
58#11758404C2211yescharacteristic
59Dic31⋊C8C2211yescharacteristic
60C8×Dic31C2211yescharacteristic
61#41×C31—22no—
62#41×C31—22no—
63#41×C31—41no—
64#41×C31—41no—
65C2×Q8×C31C2311yescharacteristic
66C2×Q8×C31C2311yescharacteristic
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31C2311yescharacteristic
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C2×C22⋊D31—21no—
77C2×C22⋊D31—21no—
78C2×C22⋊D31—21no—
79C2×C22⋊D31D411yescharacteristic
80C22×Dic31—21no—
81C22×Dic31—21no—
82#92499—22no—
83#92499—41no—
84#92497—22no—
85#92497—41no—
86C2×D124—21no—
87C2×D124C2311yescharacteristic
88C2×C4×D31—21no—
89C2×C4×D31C2311yescharacteristic
90C2×Dic62C2311yescharacteristic
91Q16×C31—22no—
92SD16×C31—22no—
93SD16×C31D414yescomplemented
94D8×C31—22no—
95C2×C8×C31—22no—
96C2×C8×C31C2311yescharacteristic
97C2×C8×C31C2311yescharacteristic
98C22⋊Dic31—21no—
99C22⋊Dic31—21no—
100C22⋊Dic31—21no—
101C22⋊Dic31D411yescharacteristic
102#92482—22no—
103#92481—41no—
104#92480—41no—
105#92479—22no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4—21no—
108(C2×D31)⋊C4D411yescharacteristic
109C4⋊Dic31—21no—
110C4⋊Dic31C2311yescharacteristic
111C4⋊Dic31C2311yescharacteristic
112Dic31⋊C4—21no—
113Dic31⋊C4—21no—
114Dic31⋊C4—21no—
115Dic31⋊C4—21no—
116Dic31⋊C4D411yescharacteristic
117C4×Dic31—21no—
118C4×Dic31C2311yescharacteristic
119C2×C31⋊C8C2311yescharacteristic
120C2×C31⋊C8C2311yescharacteristic
121#92470—22no—
122C8×D31—22no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31C2×D411yescharacteristic
126C22×D31—21no—
127C22×D31C2×D411yescharacteristic
128Q8×C31—21no—
129Q8×C31—21no—
130Q8×C31—21no—
131Q8×C31C2×D412yes—
132D4×C31—21no—
133D4×C31—21no—
134D4×C31—21no—
135D4×C31—42no—
136D4×C31—42no—
137D4×C31C2×D412yes—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31C2×D411yescharacteristic
145C2×C4×C31C2411yescharacteristic
146C22⋊D31—22no—
147C22⋊D31—42no—
148C22⋊D31—42no—
149C22⋊D31—81no—
150C22⋊D31—81no—
151C22⋊D31—81no—
152C2×Dic31—21no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—42no—
156C2×Dic31—42no—
157C2×Dic31C2×D411yescharacteristic
158C2×Dic31C2×D411yescharacteristic
159C2×Dic31C2×D411yescharacteristic
160D124—21no—
161D124—21no—
162D124—42no—
163C4×D31—21no—
164C4×D31—21no—
165C4×D31—42no—
166Dic62—21no—
167Dic62—21no—
168C8×C31—21no—
169C8×C31C2×D412yes—
170C31⋊C8—21no—
171C31⋊C8—21no—
172#3284—311nomaximal, Sylow
173C22×C31—22no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31C22×D411yescharacteristic
183C2×D31—21no—
184C2×D31—21no—
185C2×D31—21no—
186C2×D31—41no—
187C2×D31—41no—
188C2×D31—41no—
189C4×C31—22no—
190C4×C31—21no—
191C4×C31—41no—
192C4×C31C22×D411yescharacteristic
193C4×C31H(5,𝔽2)11yescharacteristic
194Dic31—21no—
195Dic31—21no—
196Dic31—41no—
197Dic31—41no—
198Dic31—41no—
199Dic31#13512yescomplemented
200C2×#135—311no—
201C2×#135D3111yescharacteristic, complemented
202#550—311no—
203#547—311no—
204#492—311no—
205#465—311no—
206#465—311no—
207#462—311no—
208#459—311no—
209#452—311no—
210#452—311no—
211#449—311no—
212#449—311no—
213C4×SD16—311no—
214C8×D4—311no—
215C2×C31—41no—
216C2×C31—42no—
217C2×C31—81no—
218C2×C31D4211yescharacteristic
219C2×C31C2×#13511yescharacteristic
220C2×C31#57711yescharacteristic
221D31—41no—
222D31—81no—
223C2×#41—311no—
224C2×#41—311no—
225C2×#41C2×D3111yescharacteristic
226C2×#41C2×D3111yescharacteristic
227#135—24no—
228#135—624no—
229C2×Q16—311no—
230C2×Q16C2×D3111yescharacteristic
231C2×SD16—311no—
232C2×SD16—311no—
233C2×SD16—311no—
234C2×SD16C2×D3111yescharacteristic
235C2×SD16C2×D3111yescharacteristic
236C2×D8—311no—
237C2×D8C2×D3111yescharacteristic
238C22×C8—311no—
239C22×C8C2×D3111yescharacteristic
240C4⋊Q8—311no—
241#127—311no—
242#127—621no—
243#123—621no—
244#123—621no—
245C22⋊Q8—311no—
246C22⋊Q8—311no—
247#121—311no—
248#121—311no—
249#121—621no—
250#121—621no—
251#121—621no—
252C4×Q8—311no—
253C4×D4—311no—
254C4×D4—311no—
255C4×D4—621no—
256C2×C4⋊C4—621no—
257#106—311no—
258C4⋊C8—311no—
259#103—311no—
260#103—311no—
261#103—311no—
262#102—311no—
263#102—311no—
264#102—311no—
265C22⋊C8—311no—
266C22⋊C8—311no—
267C4×C8—311no—
268C31#328411yescharacteristic, complemented, Sylow
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—622no—
274#41—622no—
275#41—1241no—
276#41—1241no—
277C2×Q8—311no—
278C2×Q8C22×D3111yescharacteristic
279C2×Q8C22×D3111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—311no—
283C2×D4—311no—
284C2×D4—621no—
285C2×D4—621no—
286C2×D4—621no—
287C2×D4—621no—
288C2×D4—621no—
289C2×D4—621no—
290C2×D4C22×D3111yescharacteristic
291C2×D4C22×D3111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—311no—
295C22×C4—621no—
296C22×C4—621no—
297C22×C4—621no—
298C22×C4C22×D3111yescharacteristic
299Q16—22no—
300Q16—622no—
301SD16—22no—
302SD16—622no—
303SD16—1241no—
304SD16—1241no—
305SD16C22⋊D3114yescomplemented
306D8—22no—
307D8—622no—
308C2×C8—22no—
309C2×C8—311no—
310C2×C8—311no—
311C2×C8—622no—
312C2×C8C22×D3111yescharacteristic
313C2×C8C22×D3111yescharacteristic
314C4⋊C4—311no—
315C4⋊C4—311no—
316C4⋊C4—311no—
317C4⋊C4—621no—
318C4⋊C4—621no—
319C4⋊C4—621no—
320C4⋊C4—621no—
321C4⋊C4—621no—
322C22⋊C4—311no—
323C22⋊C4—311no—
324C22⋊C4—621no—
325C22⋊C4—621no—
326C22⋊C4—621no—
327C22⋊C4—621no—
328C22⋊C4—621no—
329C42—311no—
330C42—621no—
331C23—21no—
332C23—21no—
333C23—311no—
334C23—621no—
335C23D4×D3111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—621no—
340Q8—621no—
341Q8C2×C22⋊D3112yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—622no—
348D4—621no—
349D4—621no—
350D4—1242no—
351D4—1242no—
352D4—1242no—
353D4—2481no—
354D4—2481no—
355D4—2481no—
356D4C2×C22⋊D3112yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—311no—
364C2×C4—311no—
365C2×C4—311no—
366C2×C4—621no—
367C2×C4—621no—
368C2×C4—621no—
369C2×C4—621no—
370C2×C4—621no—
371C2×C4—1242no—
372C2×C4—1242no—
373C2×C4—1242no—
374C2×C4D4×D3111yescharacteristic
375C2×C4C23×D3111yescharacteristic
376C8—21no—
377C8—621no—
378C8—621no—
379C8C2×C22⋊D3112yes—
380C22—21no—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—621no—
390C22—621no—
391C22—621no—
392C22—1241no—
393C22—1241no—
394C22—1241no—
395C22C2×D4×D3111yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—312no—
400C4—621no—
401C4—621no—
402C4—1241no—
403C4—1241no—
404C4—1241no—
405C4#1175856111yescharacteristic
406C4C22×C22⋊D3111yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—1241no—
411C2—2481no—
412C2D4×C22⋊D3111yescharacteristic
413C2#135×D3111yescharacteristic
414C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#135C2
socleC22×C31C22×D4
hypercenterC2×#135D31
hypocenterC31#3284
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11758493C2semidirect
2. #14521718C2semidirect
3. #14521698C2semidirect
4. #14521420C2semidirect
5. #14521278C2semidirect
6. #14521275C2semidirect
7. #14521257C2semidirect
8. #14521242C2semidirect
9. #14521211C2semidirect
10. #14521210C2semidirect
11. #14521194C2semidirect
12. #14521191C2semidirect
13. SD16×Dic31C2semidirect
14. C8×C22⋊D31C2semidirect
15. C2×C31×#135C2semidirect
93. SD16×C31D4semidirect
199. Dic31#135semidirect
201. C2×#135D31semidirect
268. C31#3284semidirect
305. SD16C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584932
#145217182
#145216982
#145214202
#145212782
#145212752
#145212572
#145212422
#145212112
#145212102
#145211942
#145211912
SD16×Dic312
C8×C22⋊D312
C2×C31×#1352
#328431