Finite Group Databasebeta

← #29578957

Subgroups — #29578957

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758190C211yesmaximal, characteristic
2#21444215C211yesmaximal, characteristic, complemented
3#21444211C211yesmaximal, characteristic
4#21444142C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic
6#21444111C211yesmaximal, characteristic, complemented
7C61×#1564C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C4×#11758190—21no—
12C4×#11758190—21no—
13C4×#11758190—21no—
14C4×#11758190—21no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17C2×#14519709C411yescharacteristic
18C2×#14519702C411yescharacteristic
19C2×#14519699C411yescharacteristic
20#16839494—22no—
21#16839491—22no—
22#16839487—22no—
23#16839485—22no—
24#16839484—21no—
25#16839484—21no—
26C61×#431C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C61×#335—21no—
30C61×#334—21no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C2×#11758190—22no—
35C2×#11758190—22no—
36C2×#11758190—21no—
37C2×#11758190—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51#14519709—21no—
52#14519709—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yes—
55#14519702—21no—
56#14519702—21no—
57#14519699—21no—
58#14519699—21no—
59C22⋊#92418—21no—
60C22⋊#92418D412yes—
61C4×#92418—21no—
62C4×#92418—21no—
63C22×C8×C61C2×C411yescharacteristic
64C22×C8×C61C2×C411yescharacteristic
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61D411yescharacteristic
73C4×C8×C61D411yescharacteristic
74C4×C8×C61D411yescharacteristic
75C4×C8×C61D411yescharacteristic
76C23×D61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244M1612yes—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—82no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122M1612yes—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61C22⋊C411yescharacteristic
105C2×C8×C61C22⋊C411yescharacteristic
106C2×C8×C61C22⋊C411yescharacteristic
107C2×C8×C61C22⋊C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112#11758198—41no—
113#11758198—41no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118#11758196—41no—
119#11758196—41no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C2×#92418—22no—
123C2×#92418—22no—
124#11758190—24no—
125#11758190—24no—
126C23×C61C4×D411yescharacteristic
127C22×D61—22no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—81no—
131C22×D61—81no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12411yescharacteristic
139C2×C4×C61#12711yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C2×C4×C61#13111yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151D244—22no—
152D244—22no—
153D244—41no—
154D244—41no—
155C4×D61—82no—
156C4×D61—82no—
157Dic122—22no—
158Dic122—22no—
159Dic122—41no—
160Dic122—41no—
161C8×C61—21no—
162C8×C61—21no—
163C8×C61—21no—
164C8×C61—21no—
165C8×C61—81no—
166C8×C61—81no—
167#92418—42no—
168#92418—42no—
169#9672—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#39011yescharacteristic
173C22×C61#43511yescharacteristic
174C22×C61#43511yescharacteristic
175C2×D61—42no—
176C2×D61—82no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—82no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61#40711yescharacteristic
184C4×C61#40811yescharacteristic
185C4×C61#43511yescharacteristic
186C4×C61#43511yescharacteristic
187C4×C61#47112yes—
188Dic61—42no—
189Dic61—81no—
190Dic61—81no—
191C2×C4×SD16—611no—
192#1564D6111yescharacteristic, complemented
193#1479—611no—
194#1478—611no—
195#1461—611no—
196#1460—611no—
197#1452—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#195511yescharacteristic
201C2×C61#197611yescharacteristic
202C2×C61#197711yescharacteristic
203D61—82no—
204C22×SD16—611no—
205C2×C4×Q8—611no—
206C2×C4×D4—611no—
207C4×SD16—1221no—
208C4×SD16—1221no—
209C4×SD16—1221no—
210C4×SD16—1221no—
211#431—611no—
212#431—611no—
213#431C2×D6111yescharacteristic
214#431C2×D6111yescharacteristic
215C2×#106—611no—
216C2×#103—611no—
217C2×#102—611no—
218C2×C4×C8C2×D6111yescharacteristic
219#335—21no—
220#334—21no—
221Q8⋊C8—1222no—
222D4⋊C8—1222no—
223#324—1222no—
224#323—1222no—
225#322—1221no—
226#322—1221no—
227C61#967211yescharacteristic, complemented, Sylow
228C22×Q8—611no—
229C22×D4—611no—
230C23×C4—1221no—
231C2×SD16—1222no—
232C2×SD16—1222no—
233C2×SD16—1221no—
234C2×SD16—1221no—
235C22×C8C4×D6111yescharacteristic
236C22×C8C4×D6111yescharacteristic
237C4×Q8—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×Q8—1221no—
241C4×D4—1221no—
242C4×D4—1221no—
243C4×D4—1221no—
244C4×D4—1221no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#106—1221no—
252#106—1221no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—612no—
256C4⋊C8—1221no—
257#103—1221no—
258#103—1221no—
259#102—1221no—
260#102—1221no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—612no—
264C22⋊C8—1221no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8—1221no—
268C4×C8—1221no—
269C4×C8D24411yescharacteristic
270C4×C8D24411yescharacteristic
271C4×C8C22⋊D6111yescharacteristic
272C4×C8C22⋊D6111yescharacteristic
273C24—1221no—
274C2×Q8—612no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×Q8—1221no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4882no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4#1175822611yescharacteristic
295SD16—1224no—
296SD16—1224no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—1222no—
304C2×C8—1222no—
305C2×C8#1175819811yescharacteristic
306C2×C8#1175819811yescharacteristic
307C2×C8#1175819811yescharacteristic
308C2×C8#1175819811yescharacteristic
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—2441no—
318C42—2441no—
319C42C2×D24411yescharacteristic
320C42D4×D6111yescharacteristic
321C42#1175822611yescharacteristic
322C42C2×C22⋊D6111yescharacteristic
323C23—1222no—
324C23—4881no—
325C23—4881no—
326C23—2441no—
327C23—2441no—
328C23#1451973911yescharacteristic
329Q8—1222no—
330Q8—1222no—
331Q8—2441no—
332Q8—2441no—
333D4—1222no—
334D4—1222no—
335D4—2441no—
336D4—2441no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—1222no—
340C2×C4—4882no—
341C2×C4—4882no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4C2×#1175819811yescharacteristic
349C2×C4#1451973911yescharacteristic
350C2×C4#1451975211yescharacteristic
351C2×C4#1451975211yescharacteristic
352C2×C4#1451976611yescharacteristic
353C2×C4#1451977311yescharacteristic
354C2×C4M16×D6111yescharacteristic
355C2×C4M16×D6111yescharacteristic
356C2×C4#1451978311yescharacteristic
357C2×C4#1451978311yescharacteristic
358C8—21no—
359C8—21no—
360C8—21no—
361C8—21no—
362C8—81no—
363C8—81no—
364C8—2442no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—4882no—
369C22—4882no—
370C22—4881no—
371C22—4881no—
372C22—2442no—
373C22#1683966311yescharacteristic
374C22#1683983211yescharacteristic
375C22#1683983211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—4881no—
380C4—4881no—
381C4—2442no—
382C4#1683972511yescharacteristic
383C4#1683972811yescharacteristic
384C4#1683983211yescharacteristic
385C4#1683983211yescharacteristic
386C4#1684002612yes—
387C2—21no—
388C2—21no—
389C2—4882no—
390C2#2144661611yescharacteristic
391C2#2144671511yescharacteristic
392C2#2144672011yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1564C2
socleC22×C61#390
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1564D61
hypocenterC61#9672
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
4. #21444142C2semidirect
6. #21444111C2semidirect
7. C61×#1564C2semidirect
192. #1564D61semidirect
227. C61#9672semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581902
#214442152
#214442112
#214441422
#214441392
#214441112
C61×#15642
#967261