Finite Group Databasebeta

← #29578862

Subgroups — #29578862

Order 15616.

554 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×C4×#11758190C211yesmaximal, characteristic
2#21446754C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic
4C2×#16839492C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic
6C2×C8×#92418C211yesmaximal, characteristic, complemented
7C2×C61×#334C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C4×#11758190—22no—
12C4×#11758190—22no—
13C2×#14519709C411yescharacteristic
14C2×#14519702C411yescharacteristic
15C2×#14519699C411yescharacteristic
16C2×#14519689—22no—
17C2×C4×#92418C2211yescharacteristic
18C2×C4×#92418C2211yescharacteristic
19#16839516—22no—
20#16839492—22no—
21#16839489—22no—
22C8×#92418—22no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×#334—22no—
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758190—22no—
31C2×#11758190—22no—
32C2×#11758190C814yescomplemented
33C22×#92418—21no—
34C22×#92418D412yes—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48#14519709—22no—
49#14519702—22no—
50#14519699—22no—
51#14519689—44no—
52C4×#92418—21no—
53C4×#92418—21no—
54C4×#92418—21no—
55C4×#92418D412yes—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C22×C8×C61C2×C411yescharacteristic
59C22×C8×C61C2×C411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4×C8×C61D412yes—
66C4×C8×C61D412yes—
67C23×D61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244C2×C812yes—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122C2×C812yes—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—42no—
95C2×C8×C61—42no—
96C2×C8×C61C22⋊C412yes—
97C2×C8×C61C22⋊C412yes—
98C2×C8×C61C2×C812yes—
99C2×C8×C61M1612yes—
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C2×#92418—24no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418SD1614yescomplemented
119#11758190—28no—
120C23×C61C4×D411yescharacteristic
121C22×D61—22no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—42no—
125C22×D61—42no—
126C2×C4×C61—22no—
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12711yescharacteristic
133C2×C4×C61C22×C811yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×C4×C61#13111yescharacteristic
136C2×C4×C61#13111yescharacteristic
137C2×C4×C61C2×SD1612yes—
138C2×C4×C61#13512yes—
139C2×Dic61—22no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146D244—22no—
147D244—22no—
148D244—41no—
149D244—41no—
150C4×D61—82no—
151C4×D61—81no—
152C4×D61—81no—
153Dic122—22no—
154Dic122—22no—
155Dic122—41no—
156Dic122—41no—
157C8×C61—22no—
158C8×C61—81no—
159C8×C61—81no—
160C8×C61C22⋊C814yescomplemented
161#92418—24no—
162#92418—24no—
163#9655—611nomaximal, Sylow
164C22×C61#39011yescharacteristic
165C22×C61C8×D411yescharacteristic
166C22×C61#43611yescharacteristic
167C22×C61C4×SD1612yes—
168C22×C61#44312yes—
169C2×D61—44no—
170C2×D61—42no—
171C2×D61—82no—
172C2×D61—81no—
173C2×D61—81no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61C2×C22⋊C811yescharacteristic
177C4×C61#40811yescharacteristic
178C4×C61C8×D411yescharacteristic
179C4×C61#43611yescharacteristic
180C4×C61#46512yes—
181C4×C61#49211yescharacteristic
182C4×C61#49511yescharacteristic
183Dic61—42no—
184Dic61—81no—
185Dic61—81no—
186C2×C4×SD16—611no—
187#1984—611no—
188#1954—611no—
189C2×#334D6111yescharacteristic, complemented
190C2×Q8⋊C8—611no—
191C2×D4⋊C8—611no—
192C2×C82—611no—
193C2×C61C8×SD1612yes—
194C2×C61#159012yes—
195C2×C61#195411yescharacteristic
196C2×C61#196811yescharacteristic
197C2×C61#197411yescharacteristic
198D61—82no—
199C22×SD16—611no—
200C2×C4×Q8—611no—
201C2×C4×D4—611no—
202C4×SD16—1222no—
203C4×SD16—1222no—
204C2×#106—611no—
205C2×C4⋊C8C2×D6111yescharacteristic
206C2×C4⋊C8C2×D6111yescharacteristic
207C2×#103—611no—
208C2×#102—611no—
209C2×C22⋊C8—1222no—
210C2×C4×C8—611no—
211C2×C4×C8—611no—
212C2×C4×C8C2×D6111yescharacteristic
213#336—1222no—
214#334—22no—
215Q8⋊C8—1222no—
216D4⋊C8—1222no—
217C82—1222no—
218C61#965511yescharacteristic, complemented, Sylow
219C22×Q8—611no—
220C22×D4—611no—
221C23×C4—1221no—
222C2×SD16—614no—
223C2×SD16—1222no—
224C2×SD16—1222no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—612no—
228C22×C8—1221no—
229C22×C8C4×D6111yescharacteristic
230C22×C8C4×D6111yescharacteristic
231C4×Q8—1221no—
232C4×Q8—1221no—
233C4×Q8—1221no—
234C4×Q8—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C42—1221no—
244C2×C42C22×D6111yescharacteristic
245#106—1222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#103—1222no—
251#102—1222no—
252C22⋊C8—2444no—
253C4×C8—612no—
254C4×C8—1221no—
255C4×C8—1221no—
256C4×C8—1221no—
257C4×C8D24412yes—
258C4×C8C22⋊D6112yes—
259C24—1221no—
260C2×Q8—612no—
261C2×Q8—1221no—
262C2×Q8—1221no—
263C2×Q8—1221no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×D4—612no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2442no—
278C22×C4—2442no—
279C22×C4C2×C4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4#1175822611yescharacteristic
282SD16—1228no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—614no—
290C2×C8—1224no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8—1222no—
294C2×C8C8×D6112yes—
295C2×C8#1175818912yes—
296C2×C8#1175819812yes—
297C2×C8#1175819812yes—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—2441no—
307C42—2441no—
308C42C2×D24411yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—1222no—
313C23—2441no—
314C23—2442no—
315C23—2442no—
316C23—2441no—
317C23#1451973911yescharacteristic
318Q8—1222no—
319Q8—1222no—
320Q8—2441no—
321Q8—2441no—
322D4—1222no—
323D4—1222no—
324D4—2441no—
325D4—2441no—
326C2×C4—22no—
327C2×C4—1222no—
328C2×C4—4882no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4C2×#1175819811yescharacteristic
338C2×C4#1451973911yescharacteristic
339C2×C4#1451975211yescharacteristic
340C2×C4#1451975211yescharacteristic
341C2×C4#1451976611yescharacteristic
342C2×C4#1451977311yescharacteristic
343C2×C4C2×C8×D6111yescharacteristic
344C2×C4C2×#1175818911yescharacteristic
345C2×C4#1451978511yescharacteristic
346C2×C4#1451978511yescharacteristic
347C2×C4SD16×D6112yes—
348C2×C4#1451979812yes—
349C8—22no—
350C8—81no—
351C8—81no—
352C8—1224no—
353C8—1224no—
354C8#1451968914yescomplemented
355C22—4881no—
356C22—4881no—
357C22—4882no—
358C22—2444no—
359C22—2442no—
360C22#1683966311yescharacteristic
361C22#1683982711yescharacteristic
362C22#1683983911yescharacteristic
363C22#1683984912yes—
364C22#1683987812yes—
365C4—21no—
366C4—21no—
367C4—4881no—
368C4—4881no—
369C4—2442no—
370C4C2×#1451968911yescharacteristic
371C4#1683973011yescharacteristic
372C4#1683982711yescharacteristic
373C4#1683983911yescharacteristic
374C4#1683999212yes—
375C4#1684013311yescharacteristic
376C4#1684014311yescharacteristic
377C2—4882no—
378C2#2144461812yes—
379C2#2144470812yes—
380C2#2144661211yescharacteristic
381C2#2144667111yescharacteristic
382C2#2144670511yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×#334C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×#334D61
hypocenterC61#9655
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #21446754C2semidirect
4. C2×#16839492C2semidirect
6. C2×C8×#92418C2semidirect
7. C2×C61×#334C2semidirect
32. C2×#11758190C8semidirect
118. C2×#92418SD16semidirect
160. C8×C61C22⋊C8semidirect
189. C2×#334D61semidirect
218. C61#9655semidirect
354. C8#14519689semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581902
#214467542
#214466122
C2×#168394922
C2×#168394892
C2×C8×#924182
C2×C61×#3342
#965561