Finite Group Databasebeta

← #29834608

Subgroups — #29834608

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840205C211yesmaximal, characteristic, complemented
2#21455539C211yesmaximal, characteristic
3C2×#16840037C211yesmaximal, characteristic, complemented
4#21447949C214yesmaximal, complemented
5#21447944C214yesmaximal, complemented
6#21447614C211yesmaximal, characteristic, complemented
7#21447569C211yesmaximal, characteristic, complemented
8C2×#16839579C211yesmaximal, characteristic, complemented
9C61×#3407C211yesmaximal, characteristic, complemented
10#16840560—21no—
11C2×#14519807—21no—
12C2×#14519799C2211yescharacteristic
13C22×Dic244C2211yescharacteristic
14#16840205—22no—
15#16840205—22no—
16C2×Dic488C2212yescomplemented
17C2×#14519722C2212yescomplemented
18#16840037—22no—
19#16840037C2212yes—
20#16840037C2214yes—
21#16840032C2212yes—
22#16840025—22no—
23C2×#14519713C2211yescharacteristic
24C2×#14519713C2211yescharacteristic
25#16839744—21no—
26C2×#14519695—21no—
27#16839592C2214yescomplemented
28#16839579C2212yescomplemented
29#16839579C2214yescomplemented
30#16839576C2212yescomplemented
31C2×#131×C61C2211yescharacteristic
32C61×#504—22no—
33C61×#504C2214yes—
34C2×M32×C61—22no—
35C2×M32×C61C2211yescharacteristic
36C2×M32×C61C2211yescharacteristic
37C2×#11758222—21no—
38C22×Dic122—21no—
39#14519808—41no—
40#14519807—22no—
41#14519807—24no—
42#14519807—42no—
43#14519803—41no—
44#14519802—22no—
45#14519799—21no—
46#14519799—21no—
47#14519799—21no—
48#14519799—21no—
49#14519797—42no—
50C2×Dic244—21no—
51C2×Dic244—21no—
52C2×Dic244—21no—
53C2×Dic244—21no—
54C2×Dic244—21no—
55C2×Dic244C2312yes—
56C2×Dic244C2311yescharacteristic
57C2×#11758202—41no—
58C2×#11758190—21no—
59C2×#11758200—41no—
60C2×D488C2311yescharacteristic
61C2×#11758194—21no—
62C2×#11758194—21no—
63Dic488—24no—
64#14519722—24no—
65#14519713—21no—
66#14519713—21no—
67#14519713C2312yes—
68#14519713C2312yes—
69#14519695—24no—
70#14519695—22no—
71#14519693—22no—
72C2×#41×C61D411yescharacteristic
73#131×C61—21no—
74#131×C61—21no—
75#131×C61D412yes—
76#131×C61C2312yes—
77C2×M16×C61—21no—
78C2×M16×C61D411yescharacteristic
79C22×C8×C61—21no—
80C22×C8×C61C2311yescharacteristic
81M32×C61—21no—
82M32×C61—24no—
83M32×C61D412yes—
84M32×C61D412yes—
85M32×C61C2312yes—
86C2×C16×C61—21no—
87C2×C16×C61—24no—
88C2×C16×C61C2312yes—
89#41×C61—21no—
90#41×C61—21no—
91#41×C61D812yes—
92#41×C61C2×D412yes—
93C2×Q8×C61D811yescharacteristic
94C2×D4×C61—21no—
95C2×D4×C61D811yescharacteristic
96C22×C4×C61—21no—
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—41no—
99C22×Dic61—41no—
100#11758222—41no—
101#11758222—41no—
102#11758222—41no—
103#11758222—41no—
104C2×D244—21no—
105C2×C4×D61—41no—
106C2×Dic122—22no—
107C2×Dic122—21no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122—41no—
112C2×Dic122—41no—
113M16×C61—21no—
114M16×C61—22no—
115M16×C61—22no—
116M16×C61C2×D412yes—
117C2×C8×C61—21no—
118C2×C8×C61—22no—
119C2×C8×C61—22no—
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61#4111yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61C2411yescharacteristic
126#11758202—42no—
127#11758202—44no—
128#11758201—42no—
129#11758200—44no—
130#11758200—42no—
131#11758199—42no—
132#11758194—22no—
133#11758194—22no—
134#11758194—41no—
135#11758194—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138Dic244—22no—
139Dic244—21no—
140Dic244—22no—
141Dic244—21no—
142Dic244—41no—
143Dic244—41no—
144D488—21no—
145D488—21no—
146#11758190—41no—
147#11758190—41no—
148C16×C61—22no—
149C16×C61C2×D414yes—
150C23×C61—21no—
151C23×C61#13511yescharacteristic
152C22×D61—41no—
153Q8×C61—21no—
154Q8×C61C2×D812yes—
155D4×C61—22no—
156D4×C61—22no—
157D4×C61—21no—
158D4×C61C2×D812yes—
159C2×C4×C61—21no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61C22×D411yescharacteristic
168C22⋊D61—81no—
169C22⋊D61—81no—
170C2×Dic61—42no—
171C2×Dic61—41no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174D244—41no—
175D244—41no—
176C4×D61—81no—
177C4×D61—81no—
178Dic122—41no—
179Dic122—42no—
180Dic122—42no—
181Dic122—41no—
182Dic122—81no—
183Dic122—81no—
184C8×C61—22no—
185C8×C61#12111yescharacteristic
186C8×C61#12111yescharacteristic
187C8×C61C22×D411yescharacteristic
188C8×C61C2×#4111yescharacteristic
189#92418—42no—
190#92418—42no—
191#33619—611nomaximal, Sylow
192C22×C61—22no—
193C22×C61—41no—
194C22×C61—81no—
195C22×C61#46611yescharacteristic
196C22×C61#46611yescharacteristic
197C22×C61C2×#13511yescharacteristic
198C2×D61—81no—
199C2×D61—161no—
200C4×C61—22no—
201C4×C61#46611yescharacteristic
202C4×C61#46611yescharacteristic
203C4×C61C2×#12111yescharacteristic
204C4×C61C22×D811yescharacteristic
205Dic61—82no—
206Dic61—81no—
207C2×#510—611no—
208#3407D6111yescharacteristic, complemented
209#3067—611no—
210C2×#473—611no—
211#2223—614no—
212#2222—614no—
213#2161—611no—
214#2148—611no—
215C2×#362—611no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—42no—
220C2×C61C2×#46611yescharacteristic
221D61—161no—
222#575—1221no—
223C2×#137—1221no—
224C2×#135—611no—
225C22×Q16—611no—
226C2×#131C2×D6111yescharacteristic
227#510—1222no—
228#510—1222no—
229C2×Q32—612no—
230C2×SD32—612no—
231#504—22no—
232#504C2×D6114yes—
233C2×M32—22no—
234C2×M32C2×D6111yescharacteristic
235C2×M32C2×D6111yescharacteristic
236#473—612no—
237#473—614no—
238#473—1222no—
239#472—612no—
240#471—1222no—
241C2×#108—611no—
242C2×#108—611no—
243#413—1221no—
244C2×#101—1221no—
245#368—614no—
246#362—614no—
247#362—612no—
248#361—612no—
249C61#3361911yescharacteristic, complemented, Sylow
250C2×#41—1221no—
251C2×#41D24411yescharacteristic
252C22×Q8—1221no—
253#137—1224no—
254#137—1222no—
255#137—2442no—
256#137—2441no—
257AGL(1,ℤ/8)—1222no—
258AGL(1,ℤ/8)—2441no—
259#135—1221no—
260#135—1221no—
261#135—1221no—
262#135—1221no—
263#135—2442no—
264C2×Q16—612no—
265C2×Q16—611no—
266C2×Q16—1221no—
267C2×Q16—1221no—
268C2×Q16—1221no—
269C2×Q16—1221no—
270C2×Q16—1221no—
271C2×Q16—2441no—
272C2×SD16—1221no—
273C2×SD16—2441no—
274C2×D8—611no—
275#131—21no—
276#131—21no—
277#131D24412yes—
278#131C22×D6112yes—
279C2×M16—21no—
280C2×M16—1221no—
281C2×M16—1221no—
282C2×M16D24411yescharacteristic
283C22×C8—21no—
284C22×C8C22×D6111yescharacteristic
285Q32—1224no—
286SD32—1224no—
287M32—21no—
288M32—24no—
289M32C22⋊D6112yes—
290M32C22⋊D6112yes—
291M32C22×D6112yes—
292C2×C16—21no—
293C2×C16—24no—
294C2×C16C22×D6112yes—
295#108—612no—
296#108—612no—
297#108—1221no—
298#108—1221no—
299#101—1224no—
300#101—1222no—
301#100—1222no—
302#41—21no—
303#41—21no—
304#41—2441no—
305#41—2441no—
306#41—2441no—
307#41—2441no—
308#41D48812yes—
309#41C2×D24412yes—
310C2×Q8—1221no—
311C2×Q8—1222no—
312C2×Q8—2441no—
313C2×Q8—2441no—
314C2×Q8—2441no—
315C2×Q8—2441no—
316C2×Q8—2441no—
317C2×Q8D48811yescharacteristic
318C2×D4—21no—
319C2×D4—1221no—
320C2×D4—2441no—
321C2×D4D48811yescharacteristic
322C22×C4—21no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4C2×D24411yescharacteristic
326Q16—1222no—
327Q16—1221no—
328Q16—1222no—
329Q16—1221no—
330Q16—2444no—
331Q16—2442no—
332Q16—2441no—
333Q16—2441no—
334SD16—2442no—
335SD16—2444no—
336SD16—2442no—
337SD16—2441no—
338SD16—2441no—
339D8—1221no—
340D8—1221no—
341D8—2442no—
342M16—21no—
343M16—22no—
344M16—22no—
345M16—1222no—
346M16—1222no—
347M16—2441no—
348M16—2441no—
349M16C2×D24412yes—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8C2×D24411yescharacteristic
356C2×C8#1175822211yescharacteristic
357C2×C8#1175822211yescharacteristic
358C2×C8C2×C22⋊D6111yescharacteristic
359C2×C8C2×C22⋊D6111yescharacteristic
360C2×C8C23×D6111yescharacteristic
361C16—22no—
362C16C2×C22⋊D6114yes—
363C23—21no—
364C23—2441no—
365C23#1451979911yescharacteristic
366Q8—21no—
367Q8—4881no—
368Q8—4881no—
369Q8—2441no—
370Q8—2442no—
371Q8—2442no—
372Q8—2441no—
373Q8C2×D48812yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—4881no—
378D4—4881no—
379D4—2441no—
380D4—2441no—
381D4C2×D48812yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—2441no—
390C2×C4—2442no—
391C2×C4#1451975111yescharacteristic
392C2×C4#1451975111yescharacteristic
393C2×C4C2×D48811yescharacteristic
394C2×C4C2×D48811yescharacteristic
395C2×C4#1451979911yescharacteristic
396C2×C4C22×D24411yescharacteristic
397C8—22no—
398C8—2442no—
399C8—2442no—
400C8#1451975111yescharacteristic
401C8#1451975111yescharacteristic
402C8C22×C22⋊D6111yescharacteristic
403C8C2×#1175822211yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—9761no—
408C22—4881no—
409C22#1683999811yescharacteristic
410C22#1683999811yescharacteristic
411C22C2×#1451979911yescharacteristic
412C4—22no—
413C4—4881no—
414C4—4882no—
415C4#1683999811yescharacteristic
416C4#1683999811yescharacteristic
417C4C2×#1451975111yescharacteristic
418C4C22×D48811yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—9761no—
424C2C2×#1683999811yescharacteristic
subgroupG/H
centerC2C2×#16839998
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3407C2
socleC2×C61C2×#466
prime radical#21455539C2
hypercenter#3407D61
hypocenterC61#33619
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
1. C2×#16840205C2semidirect
3. C2×#16840037C2semidirect
4. #21447949C2semidirect
5. #21447944C2semidirect
6. #21447614C2semidirect
7. #21447569C2semidirect
8. C2×#16839579C2semidirect
9. C61×#3407C2semidirect
16. C2×Dic488C22semidirect
17. C2×#14519722C22semidirect
27. #16839592C22semidirect
28. #16839579C22semidirect
29. #16839579C22semidirect
30. #16839576C22semidirect
208. #3407D61semidirect
249. C61#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#168402052
#214555392
C2×#168400372
#214479492
#214479442
#214476142
#214475692
C2×#168395792
C61×#34072
#3361961