Finite Group Databasebeta

← #29597387

Subgroups — #29597387

Order 15616.

506 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519716C211yesmaximal, characteristic
2C2×#16840000C211yesmaximal, characteristic
3C2×#16839566C211yesmaximal, characteristic, complemented
4#21445845C211yesmaximal, characteristic
5#21443911C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C2×#14519753—21no—
10C2×#14519716—22no—
11C2×#14519716—22no—
12C2×#14519716—22no—
13C22×#11758185C2211yescharacteristic
14#16840000—22no—
15#16840000C414yescomplemented
16C2×#14519711C2211yescharacteristic
17C2×#14519711C2211yescharacteristic
18C2×#14519701—21no—
19#16839619—21no—
20#16839566—22no—
21#16839524—21no—
22C22×Q16×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C61×#358—22no—
26C22×C4×D61D411yescharacteristic
27C22×#92418D411yescharacteristic
28C2×C8×D61—21no—
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61C2×C412yes—
33C2×C8×D61D412yes—
34#14519753—24no—
35#14519753—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—41no—
39C2×#11758198—41no—
40C2×#11758198—41no—
41#14519716—28no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44C2×#11758185D412yes—
45#14519711—21no—
46#14519711—21no—
47#14519711—21no—
48#14519711C2×C412yes—
49#14519701—24no—
50#14519684—41no—
51C22×Q8×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—21no—
56C2×Q16×C61—21no—
57C2×Q16×C61C2×C412yes—
58C22×C8×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61D412yes—
63#107×C61—21no—
64#107×C61—21no—
65C23×D61D811yescharacteristic
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61D811yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C22⋊C412yes—
83C2×C4×D61SD1612yes—
84Q16×C61—22no—
85Q16×C61—22no—
86Q16×C61—41no—
87Q16×C61—41no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96#11758198—44no—
97#11758198—82no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102#11758196—44no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418C22⋊C412yes—
106C8×D61—22no—
107C8×D61—22no—
108C8×D61—22no—
109C8×D61—22no—
110C16×C61—22no—
111#11758185—22no—
112C23×C61C2×D811yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61#10212yes—
120Q8×C61—42no—
121Q8×C61—42no—
122Q8×C61—81no—
123Q8×C61—81no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61C2×SD1611yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61#10212yes—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C8×C61C4×D411yescharacteristic
150C8×C61C4×D411yescharacteristic
151C8×C61#12011yescharacteristic
152C8×C61#12311yescharacteristic
153#92418—22no—
154#13062—611nomaximal, Sylow
155C22×C61C2×#10211yescharacteristic
156C22×C61#46611yescharacteristic
157C22×C61#46611yescharacteristic
158C22×C61#50911yescharacteristic
159C22×C61#51011yescharacteristic
160C22×C61#51011yescharacteristic
161C22×C61#51011yescharacteristic
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C4×C61—82no—
170C4×C61—161no—
171C4×C61#38611yescharacteristic
172C4×C61#41611yescharacteristic
173C4×C61#46511yescharacteristic
174C4×C61#46511yescharacteristic
175Dic61—22no—
176Dic61—82no—
177Dic61—161no—
178C22×M32—611no—
179C2×#467—611no—
180C2×#358—611no—
181C2×#358D6111yescharacteristic, complemented
182#1808—611no—
183#1380—611no—
184#1380—611no—
185C2×C61#189311yescharacteristic
186C2×C61#213911yescharacteristic
187C2×C61#214111yescharacteristic
188C2×C61#221911yescharacteristic
189C2×C61#221911yescharacteristic
190C2×C61#222011yescharacteristic
191C2×C61#222011yescharacteristic
192D61—42no—
193C22×Q16C2×D6111yescharacteristic
194C23×C8—611no—
195C2×C22⋊Q8—1221no—
196C2×M32—1222no—
197C2×M32—1222no—
198C2×M32—1222no—
199C22×C16—611no—
200C22×C16C2×D6111yescharacteristic
201#467—614no—
202#467—1222no—
203C2×#107—611no—
204C2×#107—611no—
205C2×#107C2×D6111yescharacteristic
206C2×#103—1221no—
207#380—1221no—
208#358—22no—
209#358—1222no—
210#340—1221no—
211C61#1306211yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C23×C4—611no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16C4×D6112yes—
220C22×C8—611no—
221C22×C8—612no—
222C22×C8—612no—
223C22×C8—1221no—
224C22×C8—1221no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8C22×D6111yescharacteristic
228C22⋊Q8—1224no—
229C22⋊Q8—2442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—2441no—
234C2×C22⋊C4—2441no—
235C2×C22⋊C4—2441no—
236M32—1228no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—612no—
240C2×C16—1221no—
241C2×C16—1221no—
242C2×C16C22⋊D6112yes—
243#107—21no—
244#107—21no—
245#107—612no—
246#107—1221no—
247#107—1221no—
248#107—1221no—
249#103—1224no—
250#95—2441no—
251C24—611no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4D4×D6111yescharacteristic
270Q16—22no—
271Q16—22no—
272Q16—41no—
273Q16—41no—
274C2×C8—612no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—1222no—
278C2×C8—1222no—
279C2×C8—1222no—
280C2×C8—1222no—
281C2×C8C2×C4×D6111yescharacteristic
282C2×C8#1175822211yescharacteristic
283C2×C8D4×D6111yescharacteristic
284C2×C8D4×D6111yescharacteristic
285C2×C8#1175822411yescharacteristic
286C2×C8C2×C22⋊D6111yescharacteristic
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—1222no—
290C4⋊C4—2444no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—4882no—
295C22⋊C4—2444no—
296C16—22no—
297C16—1222no—
298C23—612no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23D8×D6111yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—81no—
309Q8—81no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—612no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2442no—
329C2×C4C22⋊C4×D6111yescharacteristic
330C2×C4#1451974811yescharacteristic
331C2×C4#1451975011yescharacteristic
332C2×C4SD16×D6111yescharacteristic
333C2×C4#1451979611yescharacteristic
334C2×C4#1451979811yescharacteristic
335C8—1222no—
336C8#1451973711yescharacteristic
337C8C4×C22⋊D6111yescharacteristic
338C8#1451974511yescharacteristic
339C8#1451975911yescharacteristic
340C22—1222no—
341C22—1222no—
342C22—1222no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22#102×D6111yescharacteristic
348C22#1683999511yescharacteristic
349C22#1683999711yescharacteristic
350C22#1684019911yescharacteristic
351C22#1684020111yescharacteristic
352C22#1684020411yescharacteristic
353C22#1684020411yescharacteristic
354C4—82no—
355C4—161no—
356C4—1222no—
357C4—9761no—
358C4—4882no—
359C4#1683963811yescharacteristic
360C4#1683975511yescharacteristic
361C4#1683998811yescharacteristic
362C4#1683999011yescharacteristic
363C2—2442no—
364C2#2144624411yescharacteristic
365C2#2144753011yescharacteristic
366C2#2144753711yescharacteristic
367C2#2144792411yescharacteristic
368C2#2144792611yescharacteristic
369C2#2144792911yescharacteristic
370C2#2144793511yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenterC2×#358D61
hypocenterC61#13062
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. C2×#16839566C2semidirect
5. #21443911C2semidirect
6. #21443910C2semidirect
7. C2×C61×#358C2semidirect
15. #16840000C4semidirect
181. C2×#358D61semidirect
211. C61#13062semidirect

Maximal subgroups

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

subgroupindex
C22×#145197162
C2×#168400002
C2×#168395662
#214458452
#214439112
#214439102
C2×C61×#3582
#1306261