Finite Group Databasebeta

← #29588206

Subgroups — #29588206

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519709C211yesmaximal, characteristic
2C2×#16839524C212yesmaximal
3C2×#16839516C211yesmaximal, characteristic
4#21444048C212yesmaximal
5C2×C61×#340C211yesmaximal, characteristic
6C23×#92418C2211yescharacteristic
7C22×C4⋊Dic61C2212yes—
8C22×C4×Dic61C2211yescharacteristic
9C2×#14519709—24no—
10C2×#14519709—22no—
11C2×#14519684—22no—
12C2×#14519684—22no—
13#16839524—24no—
14#16839516—22no—
15C23×C8×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2212yes—
17C61×#340C414yescomplemented
18C23×Dic61—22no—
19C23×Dic61D412yes—
20C22×#92418—21no—
21C22×#92418—22no—
22C22×#92418—22no—
23C22×#92418—21no—
24C22×#92418Q812yes—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61D414yes—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—22no—
33C2×C4×Dic61—22no—
34C2×C4×Dic61—21no—
35#14519709—28no—
36#14519684—44no—
37#14519684—44no—
38C23×C4×C61—22no—
39C23×C4×C61C2311yescharacteristic
40C22×C8×C61—22no—
41C22×C8×C61—22no—
42C22×C8×C61C2×C412yes—
43C22×C8×C61D412yes—
44C22×C8×C61Q812yes—
45C2×C4⋊C4×C61—22no—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61—22no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61C2×C414yes—
51C24×C61C2×D411yescharacteristic
52C22×C4×C61—24no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61—42no—
57C22×C4×C61—42no—
58C22×C4×C61—42no—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D412yes—
62C22×C4×C61C2×Q811yescharacteristic
63C22×C4×C61C2×Q811yescharacteristic
64C22×C4×C61#4112yes—
65C22×C4×C61#4112yes—
66C22×C4×C61#4112yes—
67C22×C4×C61#4111yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—24no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61SD1614yes—
83C2×C8×C61—24no—
84C2×C8×C61—22no—
85C2×C8×C61—24no—
86C2×C8×C61—22no—
87C2×C8×C61C4⋊C414yes—
88C4⋊C4×C61—24no—
89C4⋊C4×C61—24no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—42no—
92C4⋊Dic61—24no—
93C4⋊Dic61—24no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—42no—
99C2×#92418—24no—
100C2×#92418—22no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—42no—
104C23×C61C4×D411yescharacteristic
105C23×C61#12112yes—
106C23×C61#12111yescharacteristic
107C23×C61#12312yes—
108C23×C61C4⋊Q811yescharacteristic
109C23×C61C2×SD1612yes—
110C23×C61#13512yes—
111C23×C61AGL(1,ℤ/8)12yes—
112C23×C61#13712yes—
113C2×C4×C61—44no—
114C2×C4×C61—44no—
115C2×C4×C61—44no—
116C2×C4×C61—82no—
117C2×C4×C61—82no—
118C2×C4×C61—82no—
119C2×C4×C61—82no—
120C2×C4×C61C2×C4⋊C411yescharacteristic
121C2×C4×C61#11712yes—
122C2×C4×C61C4×D412yes—
123C2×C4×C61C4×Q811yescharacteristic
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61C22⋊Q812yes—
126C2×C4×C61C22⋊Q812yes—
127C2×C4×C61C22⋊Q811yescharacteristic
128C2×C4×C61#12311yescharacteristic
129C2×C4×C61#12312yes—
130C2×C4×C61#12411yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12412yes—
133C2×C4×C61#12512yes—
134C2×C4×C61#12512yes—
135C2×C4×C61#12511yescharacteristic
136C2×C4×C61#12612yes—
137C2×C4×C61#12612yes—
138C2×Dic61—24no—
139C2×Dic61—24no—
140C2×Dic61—24no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—44no—
146C2×Dic61—44no—
147C2×Dic61—44no—
148C2×Dic61—82no—
149C2×Dic61—82no—
150C2×Dic61—82no—
151C2×Dic61—82no—
152C8×C61—24no—
153#92418—42no—
154#11257—611nomaximal, Sylow
155C22×C61#38812yes—
156C22×C61#38911yescharacteristic
157C22×C61#39411yescharacteristic
158C22×C61#39711yescharacteristic
159C22×C61#39812yes—
160C22×C61C4×SD1612yes—
161C22×C61#44111yescharacteristic
162C22×C61#44211yescharacteristic
163C22×C61#46012yes—
164C22×C61#46112yes—
165C22×C61#46312yes—
166C22×C61#46412yes—
167C22×C61#46512yes—
168C22×C61#46812yes—
169C22×C61#48112yes—
170C22×C61#48212yes—
171C22×C61#48312yes—
172C22×C61#48512yes—
173C22×C61#49811yescharacteristic
174C22×C61#49911yescharacteristic
175C22×C61#50112yes—
176C4×C61—84no—
177C4×C61#38211yescharacteristic
178C4×C61#38511yescharacteristic
179C4×C61#38712yes—
180C4×C61#39311yescharacteristic
181C4×C61#40011yescharacteristic
182C4×C61#40012yes—
183Dic61—44no—
184Dic61—84no—
185C22×#106—611no—
186C2×#340—612no—
187C2×#340D6111yescharacteristic
188C2×#336—611no—
189C4⋊#95—612no—
190C2×C61#144211yescharacteristic
191C2×C61#192612yes—
192C2×C61#192712yes—
193C2×C61#194111yescharacteristic
194C2×C61#194311yescharacteristic
195C2×C61#205512yes—
196C2×C61#207712yes—
197C2×C61#208412yes—
198C2×C61#208512yes—
199C23×C8—611no—
200C23×C8C2×D6111yescharacteristic
201C22×C4⋊C4—612no—
202C22×C4⋊C4C2×D6112yes—
203C22×C42—611no—
204C2×#106—1224no—
205C2×#106—1222no—
206C2×#95—1222no—
207C2×#95—1222no—
208#340—1224no—
209#340Dic6114yescomplemented
210#336—1222no—
211C61#1125711yescharacteristic, complemented, Sylow
212C23×C4—22no—
213C23×C4—612no—
214C23×C4—1222no—
215C23×C4C22×D6111yescharacteristic
216C22×C8—22no—
217C22×C8—22no—
218C22×C8—612no—
219C22×C8—1221no—
220C22×C8—1222no—
221C22×C8—1222no—
222C22×C8—1221no—
223C22×C8Dic12212yes—
224C22×C8D24412yes—
225C22×C8C2×Dic6112yes—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—614no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4C2×Dic6114yes—
238C2×C42—1221no—
239C2×C42—1222no—
240C2×C42—1222no—
241C2×C42—1221no—
242#106—1228no—
243#95—2444no—
244#95—2444no—
245C24D4×D6111yescharacteristic
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—614no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1224no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4C2×Dic12211yescharacteristic
268C22×C4C2×D24411yescharacteristic
269C22×C4#1175822212yes—
270C22×C4#1175822212yes—
271C22×C4D4×D6112yes—
272C22×C4#1175822412yes—
273C22×C4#1175822411yescharacteristic
274C22×C4Q8×D6111yescharacteristic
275C22×C4#1175822611yescharacteristic
276C22×C4C22×Dic6111yescharacteristic
277C2×C8—24no—
278C2×C8—22no—
279C2×C8—24no—
280C2×C8—22no—
281C2×C8—1224no—
282C2×C8—1222no—
283C2×C8—2441no—
284C2×C8—2442no—
285C2×C8—2441no—
286C2×C8C4⋊Dic6114yes—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—1224no—
292C4⋊C4—1224no—
293C4⋊C4—2442no—
294C4⋊C4—2442no—
295C42—2441no—
296C42—2441no—
297C42—2442no—
298C23D4×Dic6111yescharacteristic
299C23#1451975012yes—
300C23#1451975211yescharacteristic
301C23#1451975912yes—
302C23#1451977611yescharacteristic
303C23SD16×D6112yes—
304C23#1451979812yes—
305C23#1451980112yes—
306C23#1451980912yes—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—1224no—
317C2×C4—4882no—
318C2×C4—4882no—
319C2×C4—4882no—
320C2×C4—4882no—
321C2×C4—2444no—
322C2×C4—2444no—
323C2×C4—2444no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C2×C4⋊Dic6111yescharacteristic
329C2×C4#1451973612yes—
330C2×C4D4×Dic6112yes—
331C2×C4Q8×Dic6111yescharacteristic
332C2×C4#1451974711yescharacteristic
333C2×C4#1451975412yes—
334C2×C4#1451975512yes—
335C2×C4#1451975711yescharacteristic
336C2×C4#1451976111yescharacteristic
337C2×C4#1451976212yes—
338C2×C4#1451976312yes—
339C2×C4#1451976511yescharacteristic
340C2×C4#1451976511yescharacteristic
341C2×C4#1451976712yes—
342C2×C4#1451976811yescharacteristic
343C2×C4#1451976912yes—
344C2×C4#1451977012yes—
345C2×C4#1451977212yes—
346C8—24no—
347C8—2442no—
348C22#1683965512yes—
349C22#1683966111yescharacteristic
350C22#1683968011yescharacteristic
351C22#1683968911yescharacteristic
352C22#1683969612yes—
353C22SD16×Dic6112yes—
354C22#1683986911yescharacteristic
355C22#1683987411yescharacteristic
356C22#1683996112yes—
357C22#1683996612yes—
358C22#1683997612yes—
359C22#1683998712yes—
360C22#1683999212yes—
361C22#1684000912yes—
362C22#1684007912yes—
363C22#1684008512yes—
364C22#1684009112yes—
365C22#1684010112yes—
366C22#1684015911yescharacteristic
367C22#1684016211yescharacteristic
368C22#1684017012yes—
369C4—84no—
370C4—4884no—
371C4—2444no—
372C4#1683962811yescharacteristic
373C4#1683963711yescharacteristic
374C4#1683964812yes—
375C4#1683967511yescharacteristic
376C4#1683970211yescharacteristic
377C4#1683970412yes—
378C2#2144407611yescharacteristic
379C2#2144644812yes—
380C2#2144645512yes—
381C2#2144654811yescharacteristic
382C2#2144655811yescharacteristic
383C2#2144713812yes—
384C2#2144725412yes—
385C2#2144729912yes—
386C2#2144730512yes—
subgroupG/H
centerC24D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#340C2
socle, prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#340D61
hypocenterC61#11257
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
17. C61×#340C4semidirect
209. #340Dic61semidirect
211. C61#11257semidirect

Maximal subgroups

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

subgroupindex
C22×#145197092
C2×#168395242
C2×#168395162
#214440482
C2×C61×#3402
#1125761