Finite Group Databasebeta

← #30598835

Subgroups — #30598835

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461675C211yesmaximal, characteristic
2#21461673C211yesmaximal, characteristic
3C2×#16840607C212yesmaximal
4#21460657C212yesmaximal
5C2×#16839647C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×C22⋊#92420C2212yes—
9C2×C22⋊#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840607—24no—
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C411yescharacteristic
15C22×C4×Dic61C2211yescharacteristic
16#16839647—21no—
17#16839647—21no—
18#16839647—21no—
19#16839647—21no—
20C2×#14519684C411yescharacteristic
21C2×#14519684C411yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#95×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—42no—
27C4⋊#92420—42no—
28C22⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420—22no—
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2311yescharacteristic
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D412yes—
41C2×C4⋊Dic61Q812yes—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—42no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C23×C4×C61C2×C411yescharacteristic
57C23×C4×C61C2×C411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C24×C61C22×C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C4⋊C412yes—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C4⋊C412yes—
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×Q811yescharacteristic
96C22×Dic61#4111yescharacteristic
97C22×Dic61#4111yescharacteristic
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C4⋊Dic61—22no—
105C4⋊Dic61—22no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108#11758196—42no—
109#11758196—42no—
110C4×Dic61—22no—
111C4×Dic61—22no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61C2×C4⋊C411yescharacteristic
120C23×C61#11711yescharacteristic
121C23×C61#13112yes—
122C23×C61#13112yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—24no—
130C2×C4×C61—44no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—82no—
138C2×C4×C61#9912yes—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—44no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—82no—
162C2×Dic61#10112yes—
163C2×Dic61#12111yescharacteristic
164C2×Dic61#12111yescharacteristic
165C2×Dic61C22⋊Q811yescharacteristic
166C2×Dic61C22⋊Q811yescharacteristic
167#92420—82no—
168#92420—82no—
169#8562—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61#38011yescharacteristic
179C22×C61#40811yescharacteristic
180C22×C61#40811yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61#41011yescharacteristic
183C22×C61C2×#10111yescharacteristic
184C22×C61#41311yescharacteristic
185C22×C61#42412yes—
186C22×C61#43312yes—
187C4×C61—22no—
188C4×C61—42no—
189C4×C61—41no—
190C4×C61—81no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—22no—
196Dic61—42no—
197Dic61—41no—
198Dic61—81no—
199C2×#387—611no—
200#1797—611no—
201#1797—611no—
202C2×#324—612no—
203#1280—612no—
204C2×C61—22no—
205C2×C61—22no—
206C2×C61#146811yescharacteristic
207C2×C61#147011yescharacteristic
208C2×C61#147211yescharacteristic
209C2×C61#147311yescharacteristic
210C2×C61#179811yescharacteristic
211C2×C61#179911yescharacteristic
212C2×C61#180111yescharacteristic
213C22×C4⋊C4—611no—
214C22×C4⋊C4—611no—
215C22×C42—611no—
216C2×C4⋊C8—1221no—
217C2×C4⋊C8—1221no—
218C2×C22⋊C8—612no—
219C2×C22⋊C8—612no—
220#387—1221no—
221#387—1221no—
222#387—1221no—
223#387—1221no—
224C2×#95—611no—
225C2×#95—611no—
226C2×#95—611no—
227C2×#95#692311yescharacteristic
228#336—1221no—
229#336—1221no—
230#324—1224no—
231C61#856211yescharacteristic, complemented, Sylow
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4C2×#692311yescharacteristic
237C23×C4C2×#692311yescharacteristic
238C23×C4C2×#692311yescharacteristic
239C22×C8—1222no—
240C22×C8—1222no—
241C2×C4⋊C4—612no—
242C2×C4⋊C4—612no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—2442no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—2442no—
255C4⋊C8—2442no—
256C4⋊C8—2442no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260C22⋊C8—1222no—
261#95—21no—
262#95—21no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269C24C22×#692311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—612no—
290C22×C4—1222no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4C4⋊#692312yes—
304C22×C4C22⋊#692311yescharacteristic
305C22×C4C22⋊#692311yescharacteristic
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2442no—
309C2×C8—2442no—
310C2×C8—2442no—
311C2×C8—2442no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C4⋊C4—1222no—
315C4⋊C4—1222no—
316C4⋊C4—2442no—
317C4⋊C4—2442no—
318C42—1222no—
319C42—1222no—
320C42—2441no—
321C42—2441no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C22⋊#692311yescharacteristic
327C23C2×C4⋊#692311yescharacteristic
328C23#1451985611yescharacteristic
329C23#1451986412yes—
330C23#1451986412yes—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—82no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—4882no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2444no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2442no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2442no—
374C2×C4#1451983612yes—
375C8—4882no—
376C8—4882no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1684070411yescharacteristic
386C22#1684073511yescharacteristic
387C22#1684073611yescharacteristic
388C22C2×#1451983611yescharacteristic
389C22#1684074111yescharacteristic
390C22D61⋊#10111yescharacteristic
391C22#1684074911yescharacteristic
392C22#1684076812yes—
393C22#1684078612yes—
394C4—22no—
395C4—41no—
396C4—42no—
397C4—81no—
398C4—1222no—
399C4—1221no—
400C4—1221no—
401C4—1221no—
402C4—1221no—
403C4—4881no—
404C4—2441no—
405C4—2442no—
406C2—22no—
407C2—22no—
408C2#2146108611yescharacteristic
409C2#2146109111yescharacteristic
410C2#2146109711yescharacteristic
411C2#2146110011yescharacteristic
412C2#2146167711yescharacteristic
413C2#2146168011yescharacteristic
414C2#2146168611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#8562
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
231. C61#8562semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214616732
C2×#168406072
#214606572
C2×#168396472
#856261