Finite Group Databasebeta

← #29597061

Subgroups — #29597061

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840192C211yesmaximal, characteristic
2C2×#16839879C211yesmaximal, characteristic, complemented
3C2×#16839570C211yesmaximal, characteristic, complemented
4#21446705C211yesmaximal, characteristic, complemented
5#21443912C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C2×C61×#359C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9C2×#14519784—21no—
10#16840192—22no—
11#16840192—22no—
12C2×#14519723C411yescharacteristic, complemented
13C2×#14519721C411yescharacteristic, complemented
14C2×#14519720C411yescharacteristic, complemented
15C2×#14519718C411yescharacteristic, complemented
16C22×#11758185C2211yescharacteristic
17#16839879—22no—
18#16839879—22no—
19C2×#14519713C2211yescharacteristic
20C2×#14519704—21no—
21C2×#14519703—21no—
22#16839730—21no—
23C2×C8×Dic61C2211yescharacteristic
24#16839570—22no—
25C2×#135×C61C2211yescharacteristic
26C22×C16×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#359—22no—
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799—21no—
33#14519799—21no—
34C2×Dic244C2×C411yescharacteristic
35C2×#11758190—21no—
36C2×D488C2×C411yescharacteristic
37#14519784—24no—
38#14519784—42no—
39C2×#11758194—21no—
40C2×#11758194—41no—
41C22×#92418—41no—
42C22×#92418D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519723—22no—
45#14519721—22no—
46#14519720—22no—
47#14519718—22no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50C2×#11758185C2×C411yescharacteristic
51C2×#11758185C2×C411yescharacteristic
52#14519713—21no—
53#14519713D412yes—
54#14519704—24no—
55#14519703—42no—
56#14519689—41no—
57#14519689—41no—
58C8×Dic61—21no—
59C8×Dic61—21no—
60C2×#41×C61—21no—
61#135×C61—21no—
62#135×C61—21no—
63#135×C61D412yes—
64#135×C61D412yes—
65C2×Q16×C61C2×C411yescharacteristic
66C2×SD16×C61—21no—
67C2×D8×C61C2×C411yescharacteristic
68C2×M16×C61—21no—
69C22×C8×C61C2311yescharacteristic
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61—21no—
73#108×C61—21no—
74#108×C61—21no—
75#41×C61—22no—
76#41×C61—22no—
77#41×C61—41no—
78#41×C61—41no—
79C2×Q8×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C2×C22⋊D61—41no—
85C22×Dic61—21no—
86#11758222—41no—
87#11758222—41no—
88#11758222—41no—
89#11758222—41no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93Q16×C61—21no—
94Q16×C61C22⋊C412yes—
95SD16×C61—22no—
96SD16×C61—22no—
97D8×C61—21no—
98D8×C61C22⋊C412yes—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61C22×C411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61#4111yescharacteristic
107C2×C8×C61#4111yescharacteristic
108C4×Dic61—21no—
109C4×Dic61—21no—
110#11758194—22no—
111#11758194—44no—
112#11758194—41no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—44no—
116C2×#92418—41no—
117C2×#92418D811yescharacteristic
118C2×#92418D811yescharacteristic
119Dic244—21no—
120Dic244—21no—
121D488—21no—
122D488—21no—
123#11758190—41no—
124#11758190—41no—
125C16×C61—41no—
126#11758185—21no—
127#11758185—21no—
128C23×C61—41no—
129C23×C61#13511yescharacteristic
130C22×D61—41no—
131Q8×C61—22no—
132Q8×C61—41no—
133D4×C61—22no—
134D4×C61—42no—
135D4×C61—42no—
136D4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152D244—41no—
153D244—41no—
154C4×D61—81no—
155C4×D61—81no—
156Dic122—41no—
157Dic122—41no—
158C8×C61—81no—
159C8×C61C2×C22⋊C411yescharacteristic
160C8×C61C4×D411yescharacteristic
161C8×C61#12111yescharacteristic
162C8×C61#12311yescharacteristic
163#92418—21no—
164#92418—21no—
165#92418—42no—
166#13011—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—42no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C4×D811yescharacteristic
173C22×C61#44911yescharacteristic
174C22×C61#46311yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—42no—
179C4×C61#38611yescharacteristic
180C4×C61#44211yescharacteristic
181C4×C61#44711yescharacteristic
182C4×C61#45911yescharacteristic
183Dic61—42no—
184Dic61—81no—
185C2×#508—611no—
186C2×#443—611no—
187C2×#359—611no—
188C2×#359D6111yescharacteristic, complemented
189#1974—611no—
190#1381—611no—
191#1374—611no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—82no—
195C2×C61#187911yescharacteristic
196C2×C61#217811yescharacteristic
197C2×C61#217911yescharacteristic
198D61—161no—
199C2×#135—611no—
200C2×#135C2×D6111yescharacteristic
201C2×#131—1221no—
202#508—1222no—
203#508—1222no—
204C2×Q32—611no—
205C2×SD32—611no—
206C2×SD32—611no—
207C2×D16—611no—
208C22×C16—611no—
209C22×C16C2×D6111yescharacteristic
210#443—1222no—
211#443—1222no—
212C2×#108—611no—
213C2×#108C2×D6111yescharacteristic
214C2×#104—1221no—
215C2×#104—1221no—
216#408—1221no—
217C2×C4×C8—611no—
218#359—22no—
219#359—1222no—
220C61#1301111yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—1221no—
223#135—21no—
224#135—21no—
225#135—1221no—
226#135—1221no—
227#135—1221no—
228#135—1221no—
229#135D24412yes—
230#135C22⋊D6112yes—
231C2×Q16—611no—
232C2×Q16C4×D6111yescharacteristic
233C2×SD16—21no—
234C2×SD16—1221no—
235C2×D8—611no—
236C2×D8C4×D6111yescharacteristic
237#131—1224no—
238#131—2442no—
239C2×M16—21no—
240C2×M16—1221no—
241C2×M16—2441no—
242C22×C8—611no—
243C22×C8—2441no—
244C22×C8C22×D6111yescharacteristic
245C2×C42—611no—
246Q32—1222no—
247SD32—1222no—
248SD32—1222no—
249D16—1222no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—611no—
254C2×C16—611no—
255C2×C16—1221no—
256C2×C16—1221no—
257#108—21no—
258#108—21no—
259#108—612no—
260#108—1221no—
261#104—1224no—
262#104—2442no—
263C22⋊C8—2441no—
264C22⋊C8—2441no—
265C4×C8—1221no—
266C4×C8—1221no—
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—2441no—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275C2×Q8—21no—
276C2×Q8—1221no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—1221no—
280C2×D4—2441no—
281C22×C4—41no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4D4×D6111yescharacteristic
285Q16—21no—
286Q16—1221no—
287Q16—1221no—
288Q16#1175819812yes—
289SD16—22no—
290SD16—22no—
291SD16—2441no—
292SD16—2441no—
293D8—21no—
294D8—1221no—
295D8—1221no—
296D8#1175819812yes—
297M16—41no—
298M16—41no—
299M16—1222no—
300M16—2444no—
301M16—2441no—
302C2×C8—41no—
303C2×C8—611no—
304C2×C8—611no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8—2444no—
308C2×C8—2441no—
309C2×C8C2×C4×D6111yescharacteristic
310C2×C8C2×D24411yescharacteristic
311C2×C8D4×D6111yescharacteristic
312C2×C8#1175822411yescharacteristic
313C2×C8#1175822411yescharacteristic
314C2×C8C2×C22⋊D6111yescharacteristic
315C42—1221no—
316C42—1221no—
317C16—41no—
318C16—1221no—
319C16—1221no—
320C23—41no—
321C23—2441no—
322C23#1451979811yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—2441no—
326Q8—2441no—
327D4—22no—
328D4—42no—
329D4—42no—
330D4—41no—
331D4—4881no—
332D4—4881no—
333D4—2441no—
334D4—2441no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—1222no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4#1451973711yescharacteristic
345C2×C4#1451974711yescharacteristic
346C2×C4#1451974911yescharacteristic
347C2×C4D8×D6111yescharacteristic
348C2×C4#1451980111yescharacteristic
349C2×C4#1451980411yescharacteristic
350C8—81no—
351C8—1221no—
352C8—1221no—
353C8—2442no—
354C8C2×#1175819811yescharacteristic
355C8#1451973711yescharacteristic
356C8#1451974911yescharacteristic
357C8#1451976111yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22#1683984211yescharacteristic
367C22#1683990811yescharacteristic
368C22#1683997911yescharacteristic
369C4—42no—
370C4—4881no—
371C4—2442no—
372C4#1683963911yescharacteristic
373C4#1683987111yescharacteristic
374C4#1683989711yescharacteristic
375C4#1683995511yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—9761no—
380C2#2144616511yescharacteristic
381C2#2144769711yescharacteristic
382C2#2144770211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#359C2
socleC22×C61C4×D8
prime radicalC2×#16840192C2
cosocleC22×C8×C61C23
hypercenterC2×#359D61
hypocenterC61#13011
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#16839879C2semidirect
3. C2×#16839570C2semidirect
4. #21446705C2semidirect
5. #21443912C2semidirect
6. #21443896C2semidirect
7. C2×C61×#359C2semidirect
12. C2×#14519723C4semidirect
13. C2×#14519721C4semidirect
14. C2×#14519720C4semidirect
15. C2×#14519718C4semidirect
188. C2×#359D61semidirect
220. C61#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#168401922
C2×#168398792
C2×#168395702
#214467052
#214439122
#214438962
C2×C61×#3592
#1301161