Finite Group Databasebeta

← #29575397

Subgroups — #29575397

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839815C211yesmaximal, characteristic
2C2×#16839646C211yesmaximal, characteristic
3C2×#16839487C212yesmaximal
4#21443661C212yesmaximal
5C61×#1817C211yesmaximal, characteristic
6C22×#11758196C411yescharacteristic
7C22×#11758196C2211yescharacteristic
8#16839815—24no—
9C2×C4⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11C2×C4×#92418—21no—
12#16839646—21no—
13#16839646—21no—
14#16839646—21no—
15#16839646—21no—
16C2×#14519684C411yescharacteristic
17C2×#14519684C411yescharacteristic
18C2×#14519684C411yescharacteristic
19C2×#14519684C2211yescharacteristic
20#16839487—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C22⋊C8×C61C2212yes—
23C61×#336—21no—
24C61×#336—21no—
25C23×Dic61C2×C411yescharacteristic
26C23×Dic61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C22×#92418—22no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—22no—
37C2×#11758196C814yescomplemented
38C4⋊#92418—24no—
39C22⋊#92418—22no—
40C22⋊#92418D414yes—
41C4×#92418—24no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—22no—
54C2×C42×C61—22no—
55C2×C42×C61—22no—
56C2×C42×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C22⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62C24×C61C22×C411yescharacteristic
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C2×C812yes—
75C22×C4×C61M1612yes—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D412yes—
79C22×C4×C61#4112yes—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61C2×C812yes—
97C22×Dic61C2×C812yes—
98C2×C8×C61—42no—
99C2×C8×C61—42no—
100C2×C8×C61—42no—
101C42×C61—21no—
102C42×C61—21no—
103C42×C61—22no—
104C42×C61—22no—
105C42×C61—21no—
106C42×C61—21no—
107#11758196—24no—
108#11758196—24no—
109#11758196—41no—
110#11758196—42no—
111#11758196—41no—
112C2×#92418—24no—
113C2×#92418—42no—
114C2×#92418—42no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C4×D412yes—
121C23×C61C22×C811yescharacteristic
122C23×C61C2×M1611yescharacteristic
123C23×C61#13112yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—24no—
135C2×C4×C61—24no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—44no—
142C2×C4×C61C22⋊C812yes—
143C2×C4×C61C22⋊C812yes—
144C2×C4×C61#10112yes—
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12112yes—
147C2×C4×C61#12311yescharacteristic
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—24no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—82no—
165C2×Dic61—82no—
166C8×C61—82no—
167#92418—44no—
168#9082—611nomaximal, Sylow
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61#38611yescharacteristic
178C22×C61C2×C22⋊C811yescharacteristic
179C22×C61#40811yescharacteristic
180C22×C61#41011yescharacteristic
181C22×C61#41011yescharacteristic
182C22×C61C2×#10111yescharacteristic
183C22×C61#41311yescharacteristic
184C22×C61C8×D412yes—
185C22×C61#43512yes—
186C4×C61—22no—
187C4×C61—22no—
188C4×C61—21no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61—22no—
192C4×C61—41no—
193Dic61—42no—
194Dic61—42no—
195Dic61—81no—
196Dic61—81no—
197C2×#431—611no—
198C2×#387—611no—
199#1817D6111yescharacteristic
200C2×#324—612no—
201#1280—612no—
202C2×C61—22no—
203C2×C61—22no—
204C2×C61#145811yescharacteristic
205C2×C61#146111yescharacteristic
206C2×C61#147011yescharacteristic
207C2×C61#147311yescharacteristic
208C2×C61#186911yescharacteristic
209C2×C61#189911yescharacteristic
210C2×C61#190111yescharacteristic
211C22×C4⋊C4—611no—
212C22×C4⋊C4—611no—
213C22×C42C2×D6111yescharacteristic
214#431—1224no—
215C2×C4⋊C8—1221no—
216C2×C22⋊C8—612no—
217C2×C22⋊C8C2×D6112yes—
218C2×C4×C8—1221no—
219#387—1221no—
220#387—1221no—
221#387—1221no—
222#387—1221no—
223C2×#95—611no—
224C2×#95—611no—
225C2×#95—611no—
226C2×#95—611no—
227#336—21no—
228#336—21no—
229#324—1224no—
230C61#908211yescharacteristic, complemented, Sylow
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4C4×D6111yescharacteristic
236C23×C4C4×D6111yescharacteristic
237C23×C4C22×D6111yescharacteristic
238C22×C8—22no—
239C22×C8—1222no—
240C2×C4⋊C4—614no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4—1222no—
247C2×C4⋊C4—1221no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42D24411yescharacteristic
251C2×C42D24411yescharacteristic
252C2×C42C22⋊D6111yescharacteristic
253C2×C42C22⋊D6111yescharacteristic
254C4⋊C8—1224no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—614no—
258C22⋊C8—1222no—
259C4×C8—1224no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268C24C2×C4×D6111yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4C8×D6112yes—
295C22×C4#1175818912yes—
296C22×C4#1175819811yescharacteristic
297C22×C4#1175819811yescharacteristic
298C22×C4#1175819811yescharacteristic
299C22×C4#1175819811yescharacteristic
300C22×C4C2×D24411yescharacteristic
301C22×C4D4×D6112yes—
302C22×C4#1175822412yes—
303C22×C4C2×C22⋊D6111yescharacteristic
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—1224no—
308C2×C8—2442no—
309C2×C8—2442no—
310C4⋊C4—1224no—
311C4⋊C4—1224no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2441no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×#1175819811yescharacteristic
326C23#1451973712yes—
327C23C2×C8×D6111yescharacteristic
328C23C2×#1175818911yescharacteristic
329C23#1451978512yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1224no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4#1451968912yes—
367C2×C4#1451968912yes—
368C2×C4#1451969512yes—
369C2×C4#1451974711yescharacteristic
370C2×C4#1451974912yes—
371C2×C4#1451976111yescharacteristic
372C8—82no—
373C8—2444no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1683963911yescharacteristic
383C22C2×#1451968911yescharacteristic
384C22#1683973011yescharacteristic
385C22#1683973511yescharacteristic
386C22#1683973511yescharacteristic
387C22C2×#1451969511yescharacteristic
388C22#1683974411yescharacteristic
389C22#1683982512yes—
390C22#1683983012yes—
391C4—22no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—22no—
396C4—22no—
397C4—41no—
398C4—4881no—
399C4—4881no—
400C4—2442no—
401C4—2442no—
402C2—22no—
403C2—22no—
404C2#2144413111yescharacteristic
405C2#2144414211yescharacteristic
406C2#2144417611yescharacteristic
407C2#2144418911yescharacteristic
408C2#2144610911yescharacteristic
409C2#2144627511yescharacteristic
410C2#2144628511yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1817C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×C4×C61C23
hypercenter#1817D61
hypocenterC61#9082
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
37. C2×#11758196C8semidirect
230. C61#9082semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
C2×#168396462
C2×#168394872
#214436612
C61×#18172
#908261