Finite Group Databasebeta

← #30602174

Subgroups — #30602174

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461675C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460657C212yesmaximal
4#21460657C212yesmaximal
5C2×#16839643C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C22⋊#92420C2212yes—
8C2×C22⋊#92420C2212yes—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12C22×#11758196C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14#16839643—21no—
15#16839643—21no—
16#16839643—21no—
17#16839643—21no—
18C2×#14519684C411yescharacteristic
19C2×#14519684C411yescharacteristic
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22C22×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C22⋊#92420—22no—
27C22⋊#92420—24no—
28C22⋊#92420Q814yes—
29C4×#92420—42no—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2311yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—22no—
37C2×#11758196C814yescomplemented
38C2×C4×Dic61—42no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—42no—
57C24×C61C22×C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C2×C812yes—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—22no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C2×C812yes—
87C22×Dic61C2×C812yes—
88C22×Dic61M1612yes—
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×Q812yes—
92C22×Dic61#4112yes—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—42no—
101#11758196—24no—
102#11758196—24no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61C2×C22⋊C411yescharacteristic
112C23×C61C4×Q812yes—
113C23×C61C22×C811yescharacteristic
114C23×C61C2×M1611yescharacteristic
115C23×C61#13112yes—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—82no—
131C2×C4×C61#9912yes—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—22no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—82no—
153C2×Dic61C22⋊C812yes—
154C2×Dic61C22⋊C812yes—
155C2×Dic61C22⋊Q812yes—
156C2×Dic61#12411yescharacteristic
157C2×Dic61C4⋊Q811yescharacteristic
158#92420—44no—
159#92420—82no—
160#9880—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61#39111yescharacteristic
170C22×C61C2×C22⋊C811yescharacteristic
171C22×C61#40811yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61#41011yescharacteristic
174C22×C61#41311yescharacteristic
175C22×C61#41311yescharacteristic
176C22×C61C8×Q812yes—
177C22×C61#44612yes—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61—41no—
181C4×C61—81no—
182Dic61—22no—
183Dic61—22no—
184Dic61—22no—
185Dic61—21no—
186Dic61—21no—
187Dic61—42no—
188Dic61—81no—
189C2×#387—611no—
190#1797—611no—
191C4×C22⋊C8—611no—
192#1280—612no—
193#1280—612no—
194C2×C61—22no—
195C2×C61—22no—
196C2×C61#145811yescharacteristic
197C2×C61#145911yescharacteristic
198C2×C61#146811yescharacteristic
199C2×C61#147311yescharacteristic
200C2×C61#198411yescharacteristic
201C2×C61#199611yescharacteristic
202C2×C61#199811yescharacteristic
203C22×C4⋊C4—611no—
204C22×C4⋊C4#692311yescharacteristic
205C22×C42—611no—
206C2×C4⋊C8—1221no—
207C2×C22⋊C8—612no—
208C2×C22⋊C8—612no—
209C2×C4×C8—1221no—
210#387—1221no—
211#387—1221no—
212#387—1221no—
213#387—1221no—
214C2×#95—611no—
215C2×#95—611no—
216C2×#95—611no—
217C2×#95—611no—
218#336—1221no—
219#336—1221no—
220C61#988011yescharacteristic, complemented, Sylow
221C23×C4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C23×C4C2×#692311yescharacteristic
226C23×C4C2×#692311yescharacteristic
227C23×C4C2×#692311yescharacteristic
228C22×C8—1222no—
229C22×C8—1222no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—614no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1222no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—2442no—
242C4⋊C8—2442no—
243C22⋊C8—614no—
244C22⋊C8—1222no—
245C22⋊C8—1224no—
246C4×C8—2442no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24C22×#692311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1222no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4D61⋊C812yes—
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22⋊#692311yescharacteristic
291C2×C8—1224no—
292C2×C8—2442no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2442no—
296C2×C8—2442no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—1224no—
300C4⋊C4—1224no—
301C42—1222no—
302C42—1222no—
303C42—2441no—
304C42—2441no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C22⋊#692311yescharacteristic
310C23Q8×#692312yes—
311C23C2×D61⋊C811yescharacteristic
312C23D61⋊M1611yescharacteristic
313C23#1451986412yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—82no—
329C2×C4—612no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1222no—
343C2×C4—4882no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4#1451983512yes—
356C8—4882no—
357C8—2444no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22(C2×#6923)⋊Q811yescharacteristic
367C22D61⋊(C22⋊C8)11yescharacteristic
368C22#1684073511yescharacteristic
369C22C2×#1451983511yescharacteristic
370C22#1684074311yescharacteristic
371C22#1684074811yescharacteristic
372C22#1684074911yescharacteristic
373C22#1684081112yes—
374C22#1684081412yes—
375C4—22no—
376C4—42no—
377C4—41no—
378C4—81no—
379C4—1222no—
380C4—1222no—
381C4—1221no—
382C4—1222no—
383C4—1221no—
384C4—4881no—
385C4—2442no—
386C2—22no—
387C2—22no—
388C2#2146105311yescharacteristic
389C2#2146105411yescharacteristic
390C2#2146108411yescharacteristic
391C2#2146110311yescharacteristic
392C2#2146199011yescharacteristic
393C2#2146200811yescharacteristic
394C2#2146201311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9880
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C2×#11758196C8semidirect
220. C61#9880semidirect

Maximal subgroups

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

subgroupindex
#214616752
C4×C22⋊#924202
#214606572
C2×#168396432
#988061