Finite Group Databasebeta

← #29582568

Subgroups — #29582568

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840135C211yesmaximal, characteristic
2C2×#16840047C211yesmaximal, characteristic, complemented
3C2×#16839962C211yesmaximal, characteristic
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1984C211yesmaximal, characteristic, complemented
8C22×#11758190—22no—
9C22×#11758201—21no—
10C2×#14519777C2211yescharacteristic
11C2×#14519774C2211yescharacteristic
12#16840135—22no—
13#16840135—22no—
14#16840047—22no—
15#16840047—22no—
16#16839962—22no—
17#16839962—22no—
18C2×#14519708—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519701—21no—
22C2×#14519697—21no—
23#16839509—22no—
24#16839505—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#336—22no—
29C22×Dic122—21no—
30C22×D244—21no—
31C22×D244—21no—
32C22×D244—21no—
33C2×#11758190—28no—
34C2×#11758190—44no—
35C2×#11758190—44no—
36C2×#11758201—24no—
37C2×#11758201—42no—
38C2×#11758201—42no—
39C22×#92418—21no—
40C22×#92418—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777—21no—
44#14519777D412yes—
45#14519774—21no—
46#14519774—21no—
47#14519774—21no—
48#14519774D412yes—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51#14519708—24no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yes—
55C4⋊#92418D412yes—
56#14519701—24no—
57#14519697—24no—
58C22×Q8×C61D411yescharacteristic
59C22×C8×C61—21no—
60C22×C8×C61D412yes—
61C4×Q8×C61—21no—
62C4×Q8×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C23×D61—41no—
74C2×Q8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61SD1612yescomplemented
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×Dic61—41no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—41no—
90C2×D244—42no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—42no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—82no—
99C2×Dic122—22no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—41no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61—42no—
107C2×C8×C61SD1614yescomplemented
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C42×C61—41no—
113C42×C61—41no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118#11758201—48no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—41no—
129#11758190—416no—
130C23×C61#12111yescharacteristic
131C22×D61—42no—
132C22×D61—82no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61—82no—
136Q8×C61—22no—
137Q8×C61—22no—
138Q8×C61—41no—
139Q8×C61—41no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12711yescharacteristic
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61C2×SD1612yes—
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)12yes—
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—42no—
159C2×Dic61—82no—
160D244—44no—
161D244—42no—
162D244—42no—
163D244—82no—
164D244—82no—
165D244—81no—
166D244—81no—
167D244—81no—
168D244—81no—
169Dic122—44no—
170Dic122—81no—
171Dic122—81no—
172C8×C61—24no—
173C8×C61—81no—
174#92418—42no—
175#92418—42no—
176#10268—611nomaximal, Sylow
177C22×C61#39211yescharacteristic
178C22×C61#46012yes—
179C22×C61#46511yescharacteristic
180C22×C61#46811yescharacteristic
181C22×C61#47112yes—
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—162no—
186C2×D61—162no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—42no—
190C4×C61—81no—
191C4×C61#44811yescharacteristic
192C4×C61#44911yescharacteristic
193C4×C61#45012yes—
194C4×C61#45011yescharacteristic
195C4×C61#45211yescharacteristic
196C4×C61#49211yescharacteristic
197C4×C61#49611yescharacteristic
198Dic61—82no—
199C2×#492—611no—
200C2×#475—611no—
201C2×#460—611no—
202#1984D6111yescharacteristic, complemented
203C2×#332—611no—
204C2×#331—611no—
205#1277—611no—
206C2×C61#166612yes—
207C2×C61#168612yes—
208C2×C61#200011yescharacteristic
209C2×C61#201411yescharacteristic
210C2×C61#201911yescharacteristic
211D61—162no—
212C22×SD16—1221no—
213C22×SD16—1222no—
214C2×C4⋊Q8—611no—
215C2×#127—611no—
216C2×C4×Q8C2×D6111yescharacteristic
217#492—1222no—
218#492—1222no—
219#475—1222no—
220#475—1222no—
221#460—1222no—
222#460—1222no—
223C2×#106—1221no—
224C2×C4⋊C8—611no—
225C2×C4⋊C8—611no—
226C2×C4⋊C8C2×D6111yescharacteristic
227C2×#103—1221no—
228C2×#102—1221no—
229C2×C4×C8C2×D6111yescharacteristic
230#336—22no—
231#332—1222no—
232#331—1222no—
233C61#1026811yescharacteristic, complemented, Sylow
234C22×Q8—1221no—
235C22×Q8D24411yescharacteristic
236C22×D4—1221no—
237C22×D4—1221no—
238C22×D4—1221no—
239C2×SD16—1228no—
240C2×SD16—1224no—
241C2×SD16—2444no—
242C2×SD16—2442no—
243C2×SD16—2442no—
244C2×SD16—2444no—
245C22×C8—21no—
246C22×C8—1221no—
247C22×C8—1221no—
248C22×C8C22⋊D6112yes—
249C4⋊Q8—612no—
250C4⋊Q8—1221no—
251C4⋊Q8—1221no—
252C4⋊Q8—1221no—
253#127—612no—
254#127—1221no—
255#127—1221no—
256#127—1221no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4D24411yescharacteristic
265C2×C42—21no—
266C2×C42C22×D6111yescharacteristic
267#106—1224no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—612no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274#103—1224no—
275#102—1224no—
276C4×C8—21no—
277C4×C8—21no—
278C24—2441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—1222no—
285C2×Q8—2442no—
286C2×Q8—2442no—
287C2×Q8—2441no—
288C2×Q8#1175819012yescomplemented
289C2×D4—1222no—
290C2×D4—1222no—
291C2×D4—1222no—
292C2×D4—4882no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2442no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2442no—
301C2×D4—2441no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—2441no—
305C22×C4C2×D24411yescharacteristic
306C22×C4#1175822211yescharacteristic
307C22×C4C2×C22⋊D6111yescharacteristic
308SD16—24416no—
309SD16—2448no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—42no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8#1175820114yescomplemented
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—1222no—
326C4⋊C4—1222no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C42—41no—
330C42—41no—
331C42D4×D6111yescharacteristic
332C42D4×D6111yescharacteristic
333C42D4×D6111yescharacteristic
334C42D4×D6111yescharacteristic
335C23—4882no—
336C23—4881no—
337C23—4881no—
338C23—4882no—
339C23—2442no—
340C23#1451975111yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—4881no—
346Q8—4881no—
347Q8—2444no—
348D4—4882no—
349D4—4882no—
350D4—4881no—
351D4—4881no—
352D4—4881no—
353D4—4881no—
354D4—2444no—
355D4—2442no—
356D4—2442no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—4882no—
364C2×C4—2442no—
365C2×C4#1451974511yescharacteristic
366C2×C4#1451974711yescharacteristic
367C2×C4#1451974711yescharacteristic
368C2×C4#1451975011yescharacteristic
369C2×C4#1451975011yescharacteristic
370C2×C4#1451977311yescharacteristic
371C2×C4C2×#1175820112yes—
372C2×C4C2×#1175819011yescharacteristic
373C2×C4#1451979911yescharacteristic
374C2×C4#1451980212yes—
375C2×C4#1451980511yescharacteristic
376C2×C4#1451981011yescharacteristic
377C8—24no—
378C8—81no—
379C8—2442no—
380C8—2442no—
381C22—9762no—
382C22—9762no—
383C22—4882no—
384C22—4882no—
385C22—4882no—
386C22#1683967111yescharacteristic
387C22#1683996212yes—
388C22#1683999111yescharacteristic
389C22#1684000811yescharacteristic
390C22#1684002512yes—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—81no—
395C4—4882no—
396C4#1683990311yescharacteristic
397C4#1683990911yescharacteristic
398C4#1683991212yes—
399C4#1683991511yescharacteristic
400C4#1683992611yescharacteristic
401C4#1684013611yescharacteristic
402C4#1684015211yescharacteristic
403C2—9762no—
404C2#2144516712yes—
405C2#2144529112yes—
406C2#2144682411yescharacteristic
407C2#2144690611yescharacteristic
408C2#2144693411yescharacteristic
subgroupG/H
centerC23#14519751
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1984C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1984D61
hypocenterC61#10268
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×#16840047C2semidirect
4. C2×#16839509C2semidirect
6. #21443654C2semidirect
7. C61×#1984C2semidirect
79. C2×Q8×C61SD16semidirect
107. C2×C8×C61SD16semidirect
202. #1984D61semidirect
233. C61#10268semidirect
288. C2×Q8#11758190semidirect
320. C2×C8#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168401352
C2×#168400472
C2×#168399622
C2×#168395092
C2×#168395052
#214436542
C61×#19842
#1026861