Finite Group Databasebeta

← #29588277

Subgroups — #29588277

Order 15616.

798 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839628C211yesmaximal, characteristic
2C2×#16839525C212yesmaximal
3C2×#16839525C212yesmaximal
4#21444049C211yesmaximal, characteristic
5C2×C61×#336C211yesmaximal, characteristic
6C22×C4⋊Dic61C2212yes—
7C22×C4⋊Dic61C2211yescharacteristic
8C22×C4⋊Dic61C2211yescharacteristic
9#16839628—24no—
10C2×#14519684—22no—
11C2×#14519684—22no—
12#16839525—24no—
13#16839525—24no—
14C23×C8×C61C2212yes—
15C22×C42×C61C2211yescharacteristic
16C61×#336C414yescomplemented
17C23×Dic61—22no—
18C23×Dic61—21no—
19C23×Dic61—21no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61D412yes—
32C2×C4⋊Dic61D414yes—
33C2×C4⋊Dic61Q812yes—
34#14519684—28no—
35#14519684—44no—
36C23×C4×C61D412yes—
37C23×C4×C61C2311yescharacteristic
38C22×C8×C61—22no—
39C22×C8×C61—22no—
40C22×C8×C61—22no—
41C22×C8×C61—22no—
42C22×C8×C61—22no—
43C22×C8×C61—22no—
44C22×C8×C61C2×C414yes—
45C2×C42×C61—22no—
46C2×C42×C61—22no—
47C2×C42×C61C2×C412yes—
48C2×C42×C61Q812yes—
49C24×C61C2×D411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61C4⋊C414yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D412yes—
60C22×C4×C61C2×Q811yescharacteristic
61C22×C4×C61C2×Q811yescharacteristic
62C22×C4×C61#4112yes—
63C22×C4×C61#4112yes—
64C22×C4×C61#4112yes—
65C22×C4×C61#4111yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—24no—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—41no—
71C22×Dic61—42no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—42no—
75C22×Dic61—41no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C2×C8×C61—24no—
85C2×C8×C61—24no—
86C2×C8×C61—24no—
87C2×C8×C61—42no—
88C2×C8×C61—42no—
89C2×C8×C61—42no—
90C2×C8×C61—42no—
91C42×C61—24no—
92C42×C61—24no—
93C4⋊Dic61—24no—
94C4⋊Dic61—24no—
95C4⋊Dic61—24no—
96C4⋊Dic61—24no—
97C4⋊Dic61—42no—
98C4⋊Dic61—42no—
99C4⋊Dic61—42no—
100C4⋊Dic61—42no—
101C23×C61C2×C4⋊C411yescharacteristic
102C23×C61#12011yescharacteristic
103C23×C61#12111yescharacteristic
104C23×C61C22⋊Q811yescharacteristic
105C23×C61#12311yescharacteristic
106C23×C61#12411yescharacteristic
107C23×C61#12411yescharacteristic
108C23×C61#13512yes—
109C23×C61#13512yes—
110C23×C61AGL(1,ℤ/8)12yes—
111C23×C61#13712yes—
112C2×C4×C61—24no—
113C2×C4×C61—24no—
114C2×C4×C61—24no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61#11712yes—
120C2×C4×C61C4×D412yes—
121C2×C4×C61C4×D411yescharacteristic
122C2×C4×C61C4×Q811yescharacteristic
123C2×C4×C61#12112yes—
124C2×C4×C61C22⋊Q812yes—
125C2×C4×C61C22⋊Q812yes—
126C2×C4×C61#12312yes—
127C2×C4×C61#12312yes—
128C2×C4×C61#12412yes—
129C2×C4×C61#12512yes—
130C2×C4×C61#12512yes—
131C2×C4×C61#12511yescharacteristic
132C2×C4×C61#12612yes—
133C2×C4×C61#12612yes—
134C2×C4×C61C4⋊Q811yescharacteristic
135C2×Dic61—42no—
136C2×Dic61—44no—
137C2×Dic61—42no—
138C2×Dic61—44no—
139C2×Dic61—44no—
140C2×Dic61—44no—
141C2×Dic61—44no—
142C2×Dic61—82no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C2×Dic61—82no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—82no—
149C2×Dic61—82no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C8×C61—44no—
153#11268—611nomaximal, Sylow
154C22×C61#38211yescharacteristic
155C22×C61#38511yescharacteristic
156C22×C61#38911yescharacteristic
157C22×C61#39311yescharacteristic
158C22×C61#39411yescharacteristic
159C22×C61#39711yescharacteristic
160C22×C61#40011yescharacteristic
161C22×C61#42712yes—
162C22×C61#42812yes—
163C22×C61#44912yes—
164C22×C61#45212yes—
165C22×C61#46312yes—
166C22×C61#46412yes—
167C22×C61#47812yes—
168C22×C61#47912yes—
169C22×C61#48212yes—
170C22×C61#48512yes—
171C22×C61#48811yescharacteristic
172C22×C61#48811yescharacteristic
173C22×C61#48812yes—
174C22×C61#48912yes—
175C22×C61#49011yescharacteristic
176C22×C61#49111yescharacteristic
177C4×C61—44no—
178C4×C61#38712yes—
179C4×C61#38812yes—
180C4×C61#39812yes—
181C4×C61#40012yes—
182Dic61—82no—
183Dic61—82no—
184Dic61—84no—
185C2×#382—611no—
186C2×#340—612no—
187C2×#340—612no—
188C2×#336D6111yescharacteristic
189C4⋊#95—611no—
190C2×C61#144211yescharacteristic
191C2×C61#183511yescharacteristic
192C2×C61#183611yescharacteristic
193C2×C61#185412yes—
194C2×C61#194912yes—
195C2×C61#202511yescharacteristic
196C2×C61#202611yescharacteristic
197C2×C61#204212yes—
198C2×C61#207311yescharacteristic
199C2×C61#207411yescharacteristic
200C2×C61#210112yes—
201C23×C8C2×D6112yes—
202C22×C4⋊C4—611no—
203C22×C4⋊C4—611no—
204C22×C4⋊C4—612no—
205C22×C42C2×D6111yescharacteristic
206#382—1224no—
207C2×#95—1222no—
208C2×#95—1222no—
209#340—1224no—
210#340—1224no—
211#336Dic6114yescomplemented
212C61#1126811yescharacteristic, complemented, Sylow
213C23×C4—1222no—
214C23×C4—1221no—
215C23×C4—1221no—
216C23×C4D24412yes—
217C23×C4C22×D6111yescharacteristic
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8C2×Dic6114yes—
225C2×C4⋊C4—612no—
226C2×C4⋊C4—614no—
227C2×C4⋊C4—612no—
228C2×C4⋊C4—1222no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—1222no—
231C2×C4⋊C4—1222no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42Dic12212yes—
242C2×C42C2×Dic6112yes—
243#95—1228no—
244#95—2444no—
245C24C2×D24411yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—1224no—
253C22×C4—1222no—
254C22×C4—1222no—
255C22×C4—2442no—
256C22×C4—2441no—
257C22×C4—2442no—
258C22×C4—2441no—
259C22×C4—2442no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4—2442no—
269C22×C4C4⋊Dic6114yes—
270C22×C4C2×Dic12211yescharacteristic
271C22×C4#1175822212yes—
272C22×C4#1175822212yes—
273C22×C4D4×D6111yescharacteristic
274C22×C4D4×D6112yes—
275C22×C4#1175822412yes—
276C22×C4#1175822411yescharacteristic
277C22×C4Q8×D6111yescharacteristic
278C22×C4#1175822611yescharacteristic
279C22×C4C22×Dic6111yescharacteristic
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—24no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C4⋊C4—1224no—
288C4⋊C4—1224no—
289C4⋊C4—1224no—
290C4⋊C4—1224no—
291C4⋊C4—2442no—
292C4⋊C4—2442no—
293C4⋊C4—2442no—
294C4⋊C4—2442no—
295C42—24no—
296C42—24no—
297C23C2×C4⋊Dic6111yescharacteristic
298C23#1451974711yescharacteristic
299C23#1451975211yescharacteristic
300C23#1451975711yescharacteristic
301C23#1451976111yescharacteristic
302C23#1451976511yescharacteristic
303C23#1451976511yescharacteristic
304C23#1451979912yes—
305C23#1451979912yes—
306C23#1451980512yes—
307C23#1451981012yes—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—4882no—
316C2×C4—4882no—
317C2×C4—4882no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4882no—
321C2×C4—4882no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4882no—
325C2×C4—2444no—
326C2×C4—2442no—
327C2×C4—2444no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4—2444no—
331C2×C4—2442no—
332C2×C4#1451973612yes—
333C2×C4D4×Dic6112yes—
334C2×C4D4×Dic6111yescharacteristic
335C2×C4Q8×Dic6111yescharacteristic
336C2×C4#1451975012yes—
337C2×C4#1451975412yes—
338C2×C4#1451975512yes—
339C2×C4#1451975912yes—
340C2×C4#1451976212yes—
341C2×C4#1451976312yes—
342C2×C4#1451976712yes—
343C2×C4#1451976811yescharacteristic
344C2×C4#1451976912yes—
345C2×C4#1451977012yes—
346C2×C4#1451977212yes—
347C2×C4#1451977611yescharacteristic
348C8—44no—
349C22#1683962811yescharacteristic
350C22#1683963711yescharacteristic
351C22#1683966111yescharacteristic
352C22#1683967511yescharacteristic
353C22#1683968011yescharacteristic
354C22#1683968911yescharacteristic
355C22#1683970211yescharacteristic
356C22#1683980012yes—
357C22#1683980412yes—
358C22#1683990912yes—
359C22#1683992612yes—
360C22#1683997812yes—
361C22#1683998512yes—
362C22#1684006312yes—
363C22#1684007012yes—
364C22#1684008712yes—
365C22#1684010412yes—
366C22#1684011711yescharacteristic
367C22#1684011711yescharacteristic
368C22#1684011712yes—
369C22#1684012212yes—
370C22#1684012711yescharacteristic
371C22#1684013111yescharacteristic
372C4—44no—
373C4—4882no—
374C4—4882no—
375C4—4884no—
376C4#1683964812yes—
377C4#1683965512yes—
378C4#1683969612yes—
379C4#1683970412yes—
380C2#2144407611yescharacteristic
381C2#2144595011yescharacteristic
382C2#2144595311yescharacteristic
383C2#2144602012yes—
384C2#2144658912yes—
385C2#2144696611yescharacteristic
386C2#2144697111yescharacteristic
387C2#2144706112yes—
388C2#2144723411yescharacteristic
389C2#2144723911yescharacteristic
390C2#2144738812yes—
subgroupG/H
centerC24C2×D244
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#336C2
socle, prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#336D61
hypocenterC61#11268
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
16. C61×#336C4semidirect
211. #336Dic61semidirect
212. C61#11268semidirect

Maximal subgroups

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

subgroupindex
C2×#168396282
C2×#168395252
#214440492
C2×C61×#3362
#1126861