Finite Group Databasebeta

← #29597062

Subgroups — #29597062

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×#16840194C211yesmaximal, characteristic
2C2×#16839880C211yesmaximal, characteristic, complemented
3C2×#16839570C211yesmaximal, characteristic, complemented
4C2×#16839570C211yesmaximal, characteristic, complemented
5#21446707C211yesmaximal, characteristic, complemented
6#21443913C211yesmaximal, characteristic, complemented
7C61×#1374C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9C2×#14519799C2211yescharacteristic
10C2×#14519783—21no—
11#16840194—22no—
12#16840194—22no—
13C2×Dic488C411yescharacteristic, complemented
14C2×#14519722C411yescharacteristic, complemented
15C2×#14519722C411yescharacteristic, complemented
16C2×D976C411yescharacteristic, complemented
17#16839880—22no—
18#16839880—22no—
19C2×#14519713C2211yescharacteristic
20C2×#14519713C2211yescharacteristic
21C2×#14519705—21no—
22C2×#14519705—21no—
23#16839728—21no—
24#16839570—22no—
25#16839570—22no—
26C22×C16×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C2×#11758222—21no—
30C2×#11758222—21no—
31#14519799—21no—
32#14519799—21no—
33#14519799—21no—
34#14519799—21no—
35#14519799—21no—
36#14519799—21no—
37#14519799D412yes—
38#14519799D412yes—
39C2×Dic244C2×C411yescharacteristic
40C2×Dic244C2×C411yescharacteristic
41C2×#11758190—21no—
42C2×#11758190—21no—
43C2×D488C2×C411yescharacteristic
44C2×D488C2×C411yescharacteristic
45#14519783—24no—
46#14519783—42no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758189—41no—
50C2×C8×D61—41no—
51Dic488—22no—
52#14519722—22no—
53#14519722—22no—
54D976—22no—
55#14519713—21no—
56#14519713—21no—
57#14519713—21no—
58#14519713D412yes—
59#14519705—24no—
60#14519705—42no—
61#14519689—41no—
62#14519689—41no—
63C22×C8×C61D411yescharacteristic
64C22×C8×C61C2311yescharacteristic
65C2×C42×C61D411yescharacteristic
66C2×C16×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61—21no—
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61C2×C411yescharacteristic
72C2×C16×C61C2×C411yescharacteristic
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79#11758222—22no—
80#11758222—22no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61D811yescharacteristic
96C2×C8×C61D811yescharacteristic
97C2×C8×C61C22×C411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C2×C8×C61#4111yescharacteristic
103C42×C61—21no—
104C42×C61—21no—
105#11758194—22no—
106#11758194—41no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111Dic244—21no—
112Dic244—21no—
113Dic244—21no—
114Dic244C22⋊C412yes—
115D488—21no—
116D488—21no—
117D488—21no—
118D488C22⋊C412yes—
119#11758190—22no—
120#11758190—22no—
121#11758190—41no—
122#11758190—41no—
123#11758189—44no—
124C8×D61—44no—
125C16×C61—21no—
126C16×C61—21no—
127C16×C61—41no—
128C23×C61#13511yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61C2×D811yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146D244—22no—
147D244—41no—
148D244—41no—
149D244—41no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—81no—
153C4×D61—81no—
154Dic122—22no—
155Dic122—41no—
156Dic122—41no—
157Dic122—41no—
158C8×C61—21no—
159C8×C61—21no—
160C8×C61C2×C22⋊C411yescharacteristic
161C8×C61C4×D411yescharacteristic
162C8×C61#12111yescharacteristic
163C8×C61#12311yescharacteristic
164#92418—42no—
165#92418—81no—
166#13011—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61C4×D811yescharacteristic
170C22×C61#44911yescharacteristic
171C22×C61#46311yescharacteristic
172C2×D61—42no—
173C2×D61—81no—
174C2×D61—81no—
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×#359—611no—
189#1974—611no—
190#1381—611no—
191#1374D6111yescharacteristic, complemented
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#187911yescharacteristic
195C2×C61#217811yescharacteristic
196C2×C61#217911yescharacteristic
197D61—82no—
198D61—161no—
199C2×#135—611no—
200C2×#135—611no—
201C2×#131—1221no—
202#508—1222no—
203#508—1222no—
204C2×Q32—611no—
205C2×SD32—611no—
206C2×SD32—611no—
207C2×D16—611no—
208C22×C16C2×D6111yescharacteristic
209C22×C16C2×D6111yescharacteristic
210#443—1222no—
211#443—1222no—
212C2×#108—611no—
213C2×#108—611no—
214C2×#104—1221no—
215C2×#104—1221no—
216#408—1221no—
217C2×C4×C8C2×D6111yescharacteristic
218#359—1222no—
219#359—1222no—
220C61#1301111yescharacteristic, complemented, Sylow
221C2×#41—1221no—
222C2×#41—1221no—
223#135—612no—
224#135—612no—
225#135—1221no—
226#135—1221no—
227#135—1221no—
228#135—1221no—
229#135—1221no—
230#135—1221no—
231C2×Q16—611no—
232C2×Q16—611no—
233C2×SD16—1221no—
234C2×SD16—1221no—
235C2×D8—611no—
236C2×D8—611no—
237#131—1224no—
238#131—2442no—
239C2×M16—1221no—
240C2×M16—1221no—
241C2×M16—2441no—
242C22×C8—2441no—
243C22×C8D24411yescharacteristic
244C22×C8C22×D6111yescharacteristic
245C2×C42D24411yescharacteristic
246Q32—1222no—
247SD32—1222no—
248SD32—1222no—
249D16—1222no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16C4×D6111yescharacteristic
256C2×C16C4×D6111yescharacteristic
257#108—612no—
258#108—1221no—
259#108—1221no—
260#108—1221no—
261#104—1224no—
262#104—2442no—
263C22⋊C8—2441no—
264C22⋊C8—2441no—
265C4×C8—21no—
266C4×C8—21no—
267#41—1222no—
268#41—1222no—
269#41—2441no—
270#41—2441no—
271#41—2441no—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C2×D4—2441no—
281C22×C4—21no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4C2×D24411yescharacteristic
285Q16—612no—
286Q16—1221no—
287Q16—1221no—
288Q16—1221no—
289SD16—1222no—
290SD16—1222no—
291SD16—2441no—
292SD16—2441no—
293D8—612no—
294D8—1221no—
295D8—1221no—
296D8—1221no—
297M16—1222no—
298M16—2444no—
299M16—2441no—
300M16—2441no—
301M16—2441no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—2444no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8D48811yescharacteristic
308C2×C8D48811yescharacteristic
309C2×C8C2×C4×D6111yescharacteristic
310C2×C8#1175822211yescharacteristic
311C2×C8D4×D6111yescharacteristic
312C2×C8D4×D6111yescharacteristic
313C2×C8D4×D6111yescharacteristic
314C2×C8#1175822611yescharacteristic
315C42—21no—
316C42—21no—
317C16—21no—
318C16—21no—
319C16—41no—
320C23—2441no—
321C23—2441no—
322C23#1451979911yescharacteristic
323Q8—1222no—
324Q8—2441no—
325Q8—2441no—
326Q8—2441no—
327D4—1222no—
328D4—4881no—
329D4—4881no—
330D4—2442no—
331D4—2442no—
332D4—2441no—
333D4—2441no—
334D4—2441no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4C4×D24411yescharacteristic
345C2×C4#1451974711yescharacteristic
346C2×C4#1451975211yescharacteristic
347C2×C4C2×D48811yescharacteristic
348C2×C4#1451980511yescharacteristic
349C2×C4#1451980511yescharacteristic
350C8—21no—
351C8—21no—
352C8—4881no—
353C8—2442no—
354C8C22⋊C4×D6111yescharacteristic
355C8#1451973911yescharacteristic
356C8#1451975011yescharacteristic
357C8#1451976211yescharacteristic
358C22—21no—
359C22—21no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—2442no—
366C22C4×D48811yescharacteristic
367C22#1683990911yescharacteristic
368C22#1683997811yescharacteristic
369C4—42no—
370C4—4881no—
371C4—2442no—
372C4#1683964011yescharacteristic
373C4#1683987511yescharacteristic
374C4#1683989811yescharacteristic
375C4#1683995811yescharacteristic
376C2—21no—
377C2—21no—
378C2—9761no—
379C2—4882no—
380C2#2144616611yescharacteristic
381C2#2144770111yescharacteristic
382C2#2144770611yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1374C2
socleC22×C61C4×D8
prime radicalC2×#16840194C2
cosocleC22×C8×C61C23
hypercenter#1374D61
hypocenterC61#13011
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#16839880C2semidirect
3. C2×#16839570C2semidirect
4. C2×#16839570C2semidirect
5. #21446707C2semidirect
6. #21443913C2semidirect
7. C61×#1374C2semidirect
13. C2×Dic488C4semidirect
14. C2×#14519722C4semidirect
15. C2×#14519722C4semidirect
16. C2×D976C4semidirect
191. #1374D61semidirect
220. C61#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#168401942
C2×#168398802
C2×#168395702
#214467072
#214439132
C61×#13742
#1301161