Finite Group Databasebeta

← #29599188

Subgroups — #29599188

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840000C211yesmaximal, characteristic
2C2×#16839588C211yesmaximal, characteristic, complemented
3C2×#16839566C211yesmaximal, characteristic, complemented
4C2×#16839541C211yesmaximal, characteristic
5#21445845C211yesmaximal, characteristic
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C2×#14519753—21no—
10C22×#11758185C2211yescharacteristic
11#16840000—22no—
12#16840000—22no—
13C2×#14519711C2211yescharacteristic
14C2×#14519711C2211yescharacteristic
15C2×#14519701—21no—
16#16839619—21no—
17#16839588—22no—
18#16839566—22no—
19#16839541—22no—
20#16839524—21no—
21C22×Q16×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#358—22no—
25C22×C4×D61D411yescharacteristic
26C22×#92418D411yescharacteristic
27C2×C8×D61—21no—
28C2×C8×D61—21no—
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33#14519753—24no—
34#14519753—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—41no—
38C2×#11758198—41no—
39C2×#11758198—41no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42C2×#11758185—21no—
43#14519711—21no—
44#14519711—21no—
45#14519711—21no—
46#14519711D412yes—
47#14519701—24no—
48#14519684—41no—
49C22×Q8×C61—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61D412yes—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61D412yes—
61#107×C61—21no—
62#107×C61—21no—
63C23×D61D811yescharacteristic
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61D811yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82Q16×C61—22no—
83Q16×C61—22no—
84Q16×C61—41no—
85Q16×C61—41no—
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—44no—
95#11758198—82no—
96C4⋊Dic61—22no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—44no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C8×D61—41no—
105C8×D61—41no—
106C8×D61—41no—
107C8×D61—41no—
108C16×C61—22no—
109#11758185—41no—
110C23×C61C2×D811yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61Q3212yes—
118Q8×C61—42no—
119Q8×C61—42no—
120Q8×C61—81no—
121Q8×C61—81no—
122C2×C4×C61—42no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61#12011yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12311yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C4×D61—41no—
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—41no—
147C8×C61#12111yescharacteristic
148C8×C61#12111yescharacteristic
149C8×C61#12311yescharacteristic
150C8×C61#12411yescharacteristic
151#92418—41no—
152#13383—611nomaximal, Sylow
153C22×C61#44711yescharacteristic
154C22×C61#46611yescharacteristic
155C22×C61#48011yescharacteristic
156C22×C61C2×Q3211yescharacteristic
157C22×C61#50811yescharacteristic
158C22×C61#50911yescharacteristic
159C22×C61#51011yescharacteristic
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C4×C61—82no—
168C4×C61—161no—
169C4×C61#39411yescharacteristic
170C4×C61#45211yescharacteristic
171C4×C61#46811yescharacteristic
172C4×C61#48211yescharacteristic
173Dic61—41no—
174Dic61—82no—
175Dic61—161no—
176C2×#467—611no—
177C2×#366—611no—
178C2×#358—611no—
179C2×#358D6111yescharacteristic, complemented
180C2×C22⋊C16—611no—
181#1808—611no—
182#1380—611no—
183C2×C61#203311yescharacteristic
184C2×C61#218611yescharacteristic
185C2×C61#218811yescharacteristic
186C2×C61#221611yescharacteristic
187C2×C61#222011yescharacteristic
188C2×C61#223611yescharacteristic
189C2×C61#223711yescharacteristic
190D61—42no—
191C22×Q16C2×D6111yescharacteristic
192C23×C8—611no—
193C2×C22⋊Q8—1221no—
194C22×C16—611no—
195C22×C16C2×D6111yescharacteristic
196#467—1222no—
197#467—1222no—
198C2×#107—611no—
199C2×#107—611no—
200C2×#107C2×D6111yescharacteristic
201C2×#103—1221no—
202#380—1221no—
203#366—1222no—
204#358—22no—
205#358—1222no—
206C22⋊C16—1222no—
207#340—1221no—
208C61#1338311yescharacteristic, complemented, Sylow
209C22×Q8—21no—
210C23×C4—611no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16D24412yes—
217C22×C8—611no—
218C22×C8—1221no—
219C22×C8—1221no—
220C22×C8—1221no—
221C22×C8—1221no—
222C22×C8—1221no—
223C22×C8—1221no—
224C22×C8C22×D6111yescharacteristic
225C22⋊Q8—1224no—
226C22⋊Q8—2442no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—2441no—
231C2×C22⋊C4—2441no—
232C2×C22⋊C4—2441no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—1221no—
236C2×C16—1221no—
237C2×C16—1221no—
238C2×C16C22⋊D6112yes—
239#107—21no—
240#107—21no—
241#107—612no—
242#107—1221no—
243#107—1221no—
244#107—1221no—
245#103—1224no—
246#95—2441no—
247C24—611no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4D4×D6111yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—1221no—
273C2×C8—2441no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8C2×D24411yescharacteristic
278C2×C8#1175822211yescharacteristic
279C2×C8D4×D6111yescharacteristic
280C2×C8#1175822411yescharacteristic
281C2×C8#1175822411yescharacteristic
282C2×C8C2×C22⋊D6111yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—1222no—
286C4⋊C4—2444no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C22⋊C4—4882no—
291C22⋊C4—2444no—
292C16—22no—
293C16—2441no—
294C23—612no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23D8×D6111yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—2442no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451974711yescharacteristic
326C2×C4#1451974811yescharacteristic
327C2×C4#1451975911yescharacteristic
328C2×C4#1451979611yescharacteristic
329C2×C4#1451980411yescharacteristic
330C2×C4#1451980611yescharacteristic
331C8—2441no—
332C8#1451974911yescharacteristic
333C8#1451975111yescharacteristic
334C8#1451976111yescharacteristic
335C8#1451976311yescharacteristic
336C22—1222no—
337C22—1222no—
338C22—1222no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22#1683989711yescharacteristic
344C22#1683999511yescharacteristic
345C22#1684007411yescharacteristic
346C22Q32×D6111yescharacteristic
347C22#1684019511yescharacteristic
348C22#1684019911yescharacteristic
349C22#1684020111yescharacteristic
350C4—82no—
351C4—161no—
352C4—9761no—
353C4—4882no—
354C4—2441no—
355C4#1683967811yescharacteristic
356C4#1683992511yescharacteristic
357C4#1684000511yescharacteristic
358C4#1684008411yescharacteristic
359C2—2442no—
360C2#2144700011yescharacteristic
361C2#2144774511yescharacteristic
362C2#2144775411yescharacteristic
363C2#2144790711yescharacteristic
364C2#2144792911yescharacteristic
365C2#2144802011yescharacteristic
366C2#2144802611yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC23×D61D8
hypercenterC2×#358D61
hypocenterC61#13383
LCSG ▷ C22×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
2. C2×#16839588C2semidirect
3. C2×#16839566C2semidirect
6. #21443910C2semidirect
7. C2×C61×#358C2semidirect
179. C2×#358D61semidirect
208. C61#13383semidirect

Maximal subgroups

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

subgroupindex
C2×#168400002
C2×#168395882
C2×#168395662
C2×#168395412
#214458452
#214439102
C2×C61×#3582
#1338361