Finite Group Databasebeta

← #16857260

Subgroups — #16857260

Order 3968.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758493C211yesmaximal, characteristic, complemented
2#14521710C211yesmaximal, characteristic, complemented
3#14521698C211yesmaximal, characteristic, complemented
4#14521442C211yesmaximal, characteristic, complemented
5#14521295C211yesmaximal, characteristic, complemented
6#14521287C211yesmaximal, characteristic, complemented
7#14521266C211yesmaximal, characteristic, complemented
8#14521257C211yesmaximal, characteristic, complemented
9#14521210C211yesmaximal, characteristic, complemented
10#14521208C211yesmaximal, characteristic, complemented
11#14521205C211yesmaximal, characteristic, complemented
12#14521194C211yesmaximal, characteristic, complemented
13#14521150C211yesmaximal, characteristic, complemented
14#14521118C211yesmaximal, characteristic, complemented
15C2×C31×#137C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C22×Q8×C31C2211yescharacteristic
18C2×#92499C2211yescharacteristic
19C2×#92497C2211yescharacteristic
20C31×#137—24no—
21C2×Q16×C31C2211yescharacteristic
22C2×Q16×C31C2211yescharacteristic
23C2×SD16×C31C2211yescharacteristic
24C2×SD16×C31C2211yescharacteristic
25C2×M16×C31C2211yescharacteristic
26#11758524—21no—
27#11758524C2211yescharacteristic
28#11758523—21no—
29#11758523C2211yescharacteristic
30#11758523C2211yescharacteristic
31Q8×Dic31C2211yescharacteristic
32#11758521C2211yescharacteristic
33C2×#92482C2211yescharacteristic
34C2×#92482C2211yescharacteristic
35C2×#92481C2211yescharacteristic
36#11758516—21no—
37#11758512—21no—
38D4×Dic31C2211yescharacteristic
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#11758423C2211yescharacteristic
53#11758420C2211yescharacteristic
54C22⋊(C31⋊C8)C2211yescharacteristic
55#11758409C2211yescharacteristic
56(C2×D31)⋊C8C2211yescharacteristic
57#11758406C2211yescharacteristic
58#11758404C2211yescharacteristic
59#11758403C2211yescharacteristic
60Dic31⋊C8C2211yescharacteristic
61#41×C31—22no—
62#41×C31—41no—
63C2×Q8×C31—21no—
64C2×Q8×C31—22no—
65C2×Q8×C31—41no—
66C2×Q8×C31C2311yescharacteristic
67C2×Q8×C31C2311yescharacteristic
68C2×Q8×C31C2311yescharacteristic
69C2×D4×C31—21no—
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C2×C22⋊D31D411yescharacteristic
77C22×Dic31—21no—
78C22×Dic31—21no—
79#92499—22no—
80#92499—41no—
81#92497—22no—
82#92497—41no—
83C2×D124—21no—
84C2×D124C2311yescharacteristic
85C2×C4×D31—21no—
86C2×C4×D31C2311yescharacteristic
87C2×Dic62C2311yescharacteristic
88Q16×C31—22no—
89Q16×C31—22no—
90SD16×C31—22no—
91SD16×C31D414yescomplemented
92M16×C31—22no—
93C2×C8×C31C2311yescharacteristic
94C2×C8×C31C2311yescharacteristic
95C22⋊Dic31—21no—
96C22⋊Dic31—21no—
97C22⋊Dic31D411yescharacteristic
98#92482—22no—
99#92482—41no—
100#92481—41no—
101#92479—22no—
102(C2×D31)⋊C4—21no—
103(C2×D31)⋊C4—21no—
104(C2×D31)⋊C4—21no—
105(C2×D31)⋊C4—21no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4D411yescharacteristic
108C4⋊Dic31—21no—
109C4⋊Dic31C2311yescharacteristic
110C4⋊Dic31C2311yescharacteristic
111Dic31⋊C4—21no—
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×C31C2×D411yescharacteristic
125C22×D31—21no—
126C22×D31C2×D411yescharacteristic
127Q8×C31—21no—
128Q8×C31—21no—
129Q8×C31—21no—
130Q8×C31—21no—
131Q8×C31—21no—
132Q8×C31—42no—
133Q8×C31C2×D412yes—
134D4×C31—21no—
135D4×C31—42no—
136D4×C31C2×D412yes—
137C2×C4×C31—21no—
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—41no—
147C22⋊D31—42no—
148C22⋊D31—42no—
149C2×Dic31—21no—
150C2×Dic31—21no—
151C2×Dic31—21no—
152C2×Dic31—42no—
153C2×Dic31—42no—
154C2×Dic31C2×D411yescharacteristic
155C2×Dic31C2×D411yescharacteristic
156C2×Dic31C2×D411yescharacteristic
157D124—21no—
158D124—21no—
159D124—42no—
160C4×D31—21no—
161C4×D31—21no—
162C4×D31—42no—
163Dic62—21no—
164Dic62—21no—
165C8×C31—21no—
166C8×C31C2×D412yes—
167C31⋊C8—21no—
168C31⋊C8—21no—
169#3269—311nomaximal, Sylow
170C22×C31—22no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—41no—
175C22×C31—41no—
176C22×C31C22×D411yescharacteristic
177C2×D31—21no—
178C2×D31—21no—
179C2×D31—21no—
180C2×D31—41no—
181C2×D31—41no—
182C2×D31—41no—
183C4×C31—22no—
184C4×C31—21no—
185C4×C31—41no—
186C4×C31—41no—
187C4×C31C22×D411yescharacteristic
188C4×C31H(5,𝔽2)11yescharacteristic
189Dic31—21no—
190Dic31—21no—
191Dic31—21no—
192Dic31—41no—
193Dic31—41no—
194Dic31—41no—
195C2×#137D3111yescharacteristic, complemented
196C2×#135—311no—
197#548—311no—
198#547—311no—
199#497—311no—
200#468—311no—
201#467—311no—
202#463—311no—
203#462—311no—
204#452—311no—
205#452—311no—
206#451—311no—
207#449—311no—
208#440—311no—
209#435—311no—
210C2×C31—41no—
211C2×C31—42no—
212C2×C31D4211yescharacteristic
213C2×C31#57511yescharacteristic
214C2×C31#57811yescharacteristic
215D31—41no—
216D31—81no—
217C2×#41—311no—
218C2×#41—311no—
219C2×#41C2×D3111yescharacteristic
220C22×Q8C2×D3111yescharacteristic
221#137—24no—
222#135—624no—
223C2×Q16—311no—
224C2×Q16—311no—
225C2×Q16C2×D3111yescharacteristic
226C2×Q16C2×D3111yescharacteristic
227C2×SD16—311no—
228C2×SD16—311no—
229C2×SD16C2×D3111yescharacteristic
230C2×SD16C2×D3111yescharacteristic
231C2×D8—311no—
232C2×M16C2×D3111yescharacteristic
233C22×C8—311no—
234C4⋊Q8—311no—
235#124—311no—
236#124—621no—
237#123—621no—
238#123—621no—
239C22⋊Q8—311no—
240C22⋊Q8—311no—
241C22⋊Q8—311no—
242C22⋊Q8—621no—
243#121—311no—
244#121—621no—
245#121—621no—
246C4×Q8—311no—
247C4×D4—311no—
248C4×D4—311no—
249C4×D4—621no—
250C2×C4⋊C4—621no—
251#107—311no—
252C4⋊C8—311no—
253#103—311no—
254#103—311no—
255#103—311no—
256#103—311no—
257#102—311no—
258#102—311no—
259C22⋊C8—311no—
260C22⋊C8—311no—
261#97—311no—
262C31#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—41no—
265#41—622no—
266#41—622no—
267#41—1241no—
268#41—1241no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—311no—
273C2×Q8C22×D3111yescharacteristic
274C2×Q8C22×D3111yescharacteristic
275C2×Q8C22×D3111yescharacteristic
276C2×D4—21no—
277C2×D4—311no—
278C2×D4—311no—
279C2×D4—621no—
280C2×D4—621no—
281C2×D4—621no—
282C2×D4C22×D3111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—311no—
286C22×C4—621no—
287C22×C4—621no—
288C22×C4—621no—
289C22×C4C22×D3111yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—622no—
293Q16—1241no—
294SD16—22no—
295SD16—622no—
296SD16—1241no—
297SD16C22⋊D3114yescomplemented
298D8—622no—
299M16—22no—
300C2×C8—311no—
301C2×C8—311no—
302C2×C8—622no—
303C2×C8C22×D3111yescharacteristic
304C2×C8C22×D3111yescharacteristic
305C4⋊C4—311no—
306C4⋊C4—311no—
307C4⋊C4—311no—
308C4⋊C4—621no—
309C4⋊C4—621no—
310C4⋊C4—621no—
311C4⋊C4—621no—
312C4⋊C4—621no—
313C4⋊C4—621no—
314C22⋊C4—311no—
315C22⋊C4—311no—
316C22⋊C4—621no—
317C22⋊C4—621no—
318C22⋊C4—621no—
319C22⋊C4—621no—
320C22⋊C4—621no—
321C22⋊C4—621no—
322C22⋊C4—621no—
323C42—311no—
324C42—621no—
325C23—21no—
326C23—311no—
327C23—621no—
328C23D4×D3111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—621no—
336Q8—621no—
337Q8C2×C22⋊D3112yes—
338D4—21no—
339D4—42no—
340D4—621no—
341D4—621no—
342D4—1242no—
343D4—1241no—
344D4—1242no—
345D4—1242no—
346D4C2×C22⋊D3112yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—311no—
355C2×C4—311no—
356C2×C4—311no—
357C2×C4—621no—
358C2×C4—621no—
359C2×C4—621no—
360C2×C4—621no—
361C2×C4—621no—
362C2×C4—1242no—
363C2×C4—1242no—
364C2×C4—1242no—
365C2×C4D4×D3111yescharacteristic
366C2×C4C23×D3111yescharacteristic
367C8—21no—
368C8—621no—
369C8—621no—
370C8C2×C22⋊D3112yes—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—621no—
378C22—621no—
379C22—621no—
380C22—1241no—
381C22—1241no—
382C22—1241no—
383C22C2×D4×D3111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—621no—
389C4—621no—
390C4—621no—
391C4—1241no—
392C4—1241no—
393C4—1241no—
394C4#1175856111yescharacteristic
395C4C22×C22⋊D3111yescharacteristic
396C2—41no—
397C2—42no—
398C2—1241no—
399C2—2481no—
400C2D4×C22⋊D3111yescharacteristic
401C2#1452184811yescharacteristic
402C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#137C2
socleC22×C31C22×D4
hypercenterC2×#137D31
hypocenterC31#3269
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11758493C2semidirect
2. #14521710C2semidirect
3. #14521698C2semidirect
4. #14521442C2semidirect
5. #14521295C2semidirect
6. #14521287C2semidirect
7. #14521266C2semidirect
8. #14521257C2semidirect
9. #14521210C2semidirect
10. #14521208C2semidirect
11. #14521205C2semidirect
12. #14521194C2semidirect
13. #14521150C2semidirect
14. #14521118C2semidirect
15. C2×C31×#137C2semidirect
91. SD16×C31D4semidirect
195. C2×#137D31semidirect
262. C31#3269semidirect
297. SD16C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584932
#145217102
#145216982
#145214422
#145212952
#145212872
#145212662
#145212572
#145212102
#145212082
#145212052
#145211942
#145211502
#145211182
C2×C31×#1372
#326931