Finite Group Databasebeta

← #29575893

Subgroups — #29575893

Order 15616.

510 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
1#21455307C211yesmaximal, characteristic
2#21454388C211yesmaximal, characteristic
3#21444492C211yesmaximal, characteristic, complemented
4C2×#16839507C211yesmaximal, characteristic, complemented
5#21444204C211yesmaximal, characteristic
6#21443714C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×#14519810—21no—
9C2×#14519785—21no—
10C2×#14519777C2211yescharacteristic
11C4×#11758222C2211yescharacteristic
12#16839973—21no—
13#16839973C412yes—
14#16839968—21no—
15#16839968C412yes—
16#16839815C2211yescharacteristic
17#16839790—21no—
18#16839787—22no—
19#16839784—21no—
20C2×C4⋊#92418C2211yescharacteristic
21C4⋊C8×D61—21no—
22#16839772—21no—
23#16839509—22no—
24#16839507—21no—
25#16839507—21no—
26#16839492—21no—
27#16839489—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33#14519810—42no—
34#14519810—42no—
35C2×Dic244—22no—
36C2×#11758190—22no—
37#14519785—42no—
38#14519785—42no—
39C2×#11758189—22no—
40C22×#92418—21no—
41C2×C8×D61—22no—
42#14519777—21no—
43#14519777—21no—
44#14519777—21no—
45#14519777C2×C412yes—
46C4×Dic122C2×C411yescharacteristic
47C4×Dic122D411yescharacteristic
48C4×D244C2×C411yescharacteristic
49C4×D244D411yescharacteristic
50C4×C22⋊D61—21no—
51C4×C22⋊D61—21no—
52#14519736D411yescharacteristic
53#14519734—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C42×D61—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59C4⋊#92418D411yescharacteristic
60C4⋊#92418D411yescharacteristic
61#14519706—22no—
62#14519706—22no—
63#14519702—22no—
64#14519702—22no—
65C22⋊#92418—21no—
66C4×#92418—21no—
67C2×M16×C61—21no—
68C2×M16×C61—21no—
69C22×C8×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61C2×C412yes—
76C4⋊C8×C61D412yes—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—21no—
81C22×Dic61—41no—
82#11758222—21no—
83#11758222—21no—
84#11758222D812yes—
85#11758222SD1612yes—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122C22⋊C411yescharacteristic
97M16×C61—41no—
98M16×C61—41no—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—22no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—81no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C22⋊Dic61—21no—
110#11758198—21no—
111#11758198—21no—
112C4⋊Dic61—22no—
113C4⋊Dic61—22no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61C22⋊C411yescharacteristic
117C4⋊Dic61C22⋊C411yescharacteristic
118#11758196—21no—
119#11758196—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128Dic244—44no—
129#11758190—44no—
130#11758189—44no—
131C8×D61—44no—
132C23×C61#12311yescharacteristic
133C22×D61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C22⋊D61—22no—
148C22⋊D61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155D244—21no—
156D244#10212yes—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—81no—
162Dic122—21no—
163Dic122—42no—
164Dic122—42no—
165Dic122—81no—
166Dic122—81no—
167Dic122#10212yes—
168C8×C61—42no—
169C8×C61—42no—
170C8×C61—81no—
171#92418—41no—
172#92418—41no—
173#92418—81no—
174#9171—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61#38611yescharacteristic
178C22×C61#48011yescharacteristic
179C22×C61#48111yescharacteristic
180C2×D61—22no—
181C2×D61—41no—
182C2×D61—41no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61C2×#10211yescharacteristic
187C4×C61#41711yescharacteristic
188C4×C61#44711yescharacteristic
189C4×C61#44811yescharacteristic
190C4×C61#47111yescharacteristic
191C4×C61#47311yescharacteristic
192Dic61—22no—
193Dic61—41no—
194Dic61—41no—
195Dic61—82no—
196#3039—611no—
197#2906—611no—
198#1546—611no—
199C2×#332—611no—
200#1477—611no—
201#1301—611no—
202#1292D6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61#187411yescharacteristic
206C2×C61#190211yescharacteristic
207C2×C61#190811yescharacteristic
208D61—42no—
209C2×#137—1221no—
210C2×#131—1221no—
211C2×C4⋊Q8—611no—
212C4×#41—611no—
213#462—612no—
214#462—1221no—
215#461—612no—
216#461—1221no—
217#431—611no—
218#424—1221no—
219#424—1222no—
220#423—1221no—
221#423C2×D6111yescharacteristic
222#423C2×D6111yescharacteristic
223C2×C4⋊C8—611no—
224C2×C4⋊C8—1221no—
225C2×C4⋊C8C2×D6111yescharacteristic
226#419—1221no—
227#332—1221no—
228#332—1221no—
229#332—1222no—
230Q8⋊C8—1221no—
231D4⋊C8—1221no—
232C61#917111yescharacteristic, complemented, Sylow
233C2×#41—611no—
234C22×Q8—1221no—
235#137—2442no—
236#137—2442no—
237C2×Q16—1222no—
238C2×SD16—1222no—
239#131—2442no—
240#131—2442no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—1222no—
244C22×C8—21no—
245C22×C8—1222no—
246C22×C8—1221no—
247C4⋊Q8—612no—
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250C4⋊Q8—1221no—
251C4×Q8—611no—
252C4×Q8—611no—
253C4×D4—611no—
254C4×D4—611no—
255C4×D4—1221no—
256C4×D4—1221no—
257#117—611no—
258#117—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—611no—
268C4⋊C8—611no—
269C4⋊C8—1222no—
270C4⋊C8—1222no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8C4×D6112yes—
274C4⋊C8D24412yes—
275#103—1222no—
276#103—1222no—
277C22⋊C8—1221no—
278C4×C8—1221no—
279#41—612no—
280#41—612no—
281#41—1221no—
282#41—1221no—
283C2×Q8—611no—
284C2×Q8—1222no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×D4—611no—
291C2×D4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—2441no—
296C22×C4#1175822211yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4#1175822611yescharacteristic
299Q16—2444no—
300SD16—2444no—
301M16—41no—
302M16—41no—
303M16—41no—
304M16—41no—
305M16—2444no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—81no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—2444no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C4⋊C4—611no—
317C4⋊C4—611no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1222no—
321C4⋊C4—1222no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C42—1221no—
328C42—1221no—
329C42—1221no—
330C42C2×C4×D6111yescharacteristic
331C42C2×D24411yescharacteristic
332C42D4×D6111yescharacteristic
333C42D4×D6111yescharacteristic
334C23—1221no—
335C23#1451976211yescharacteristic
336Q8—612no—
337Q8—1221no—
338Q8—4881no—
339Q8—4881no—
340Q8—2442no—
341Q8—2442no—
342D4—612no—
343D4—1222no—
344D4—1222no—
345D4—1221no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—1221no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4C22⋊C4×D6111yescharacteristic
361C2×C4#1451973911yescharacteristic
362C2×C4C4×D24411yescharacteristic
363C2×C4#1451974711yescharacteristic
364C2×C4#1451975011yescharacteristic
365C2×C4#1451975211yescharacteristic
366C2×C4D8×D6111yescharacteristic
367C2×C4SD16×D6111yescharacteristic
368C2×C4#1451980411yescharacteristic
369C2×C4#1451980911yescharacteristic
370C8—42no—
371C8—42no—
372C8—81no—
373C8—4881no—
374C8—2441no—
375C8—2441no—
376C22—21no—
377C22—21no—
378C22—1222no—
379C22—2441no—
380C22—2441no—
381C22#1683964011yescharacteristic
382C22#1684007711yescharacteristic
383C22#1684008211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—1222no—
388C4—4882no—
389C4—2441no—
390C4—2441no—
391C4#102×D6111yescharacteristic
392C4#1683976211yescharacteristic
393C4#1683989711yescharacteristic
394C4#1683990211yescharacteristic
395C4#1684002411yescharacteristic
396C4#1684003611yescharacteristic
397C2—21no—
398C2—21no—
399C2—2442no—
400C2#2144613511yescharacteristic
401C2#2144629311yescharacteristic
402C2#2144633511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9171
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #21444492C2semidirect
4. C2×#16839507C2semidirect
6. #21443714C2semidirect
7. C61×#1292C2semidirect
202. #1292D61semidirect
232. C61#9171semidirect

Maximal subgroups

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

subgroupindex
#214553072
#214543882
#214444922
C2×#168395072
#214442042
#214437142
C61×#12922
#917161