Finite Group Databasebeta

← #29575051

Subgroups — #29575051

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839702C211yesmaximal, characteristic
2#21448436C211yesmaximal, characteristic
3#21445910C211yesmaximal, characteristic
4#21445907C211yesmaximal, characteristic
5C2×#16839487C211yesmaximal, characteristic
6#21443698C211yesmaximal, characteristic
7C61×#1294C211yesmaximal, characteristic
8C2×#14519733—21no—
9C22×C4⋊Dic61C2211yescharacteristic
10C22×#11758196C2211yescharacteristic
11C2×C22⋊#92418C2211yescharacteristic
12#16839702—22no—
13#16839702C414yescomplemented
14#16839659—22no—
15#16839657—22no—
16#16839622C2211yescharacteristic
17#16839620—21no—
18C2×#14519684—21no—
19C2×#14519684—21no—
20#16839525—22no—
21#16839524—22no—
22#16839487—22no—
23C2×C22⋊C8×C61C2211yescharacteristic
24C61×#380C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×#92418—21no—
30#14519733—42no—
31#14519733—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C412yes—
38C2×C4⋊Dic61D412yes—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—22no—
44C2×#11758196—22no—
45C2×#11758196C2×C412yes—
46C2×#11758196D412yes—
47C2×C22⋊Dic61—21no—
48C2×C4×Dic61—22no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—22no—
52#14519684—21no—
53#14519684—24no—
54#14519684—24no—
55C23×C4×C61—21no—
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—21no—
58C2×C4⋊C4×C61D412yes—
59C2×C22⋊C4×C61—21no—
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64#95×C61C2×C412yes—
65C24×C61C2×D411yescharacteristic
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61—42no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—42no—
88C22×Dic61—44no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61C22⋊C412yes—
92C22×Dic61C22⋊C412yes—
93C22×Dic61SD1612yes—
94C22×Dic61Q1612yes—
95C2×C8×C61—42no—
96C2×C8×C61—41no—
97C4⋊C4×C61—42no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—42no—
107#11758196—22no—
108#11758196—22no—
109#11758196—22no—
110#11758196—22no—
111#11758196—44no—
112#11758196—82no—
113C4×Dic61—44no—
114C2×#92418—42no—
115C2×#92418—41no—
116C23×C61—22no—
117C23×C61—22no—
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61#12011yescharacteristic
120C23×C61#12311yescharacteristic
121C23×C61C2×SD1611yescharacteristic
122C23×C61C2×Q1611yescharacteristic
123C23×C61AGL(1,ℤ/8)11yescharacteristic
124C23×C61#13711yescharacteristic
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—82no—
138C2×C4×C61—82no—
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—44no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—81no—
158C2×Dic61—82no—
159C2×Dic61—82no—
160C2×Dic61#10314yes—
161C8×C61—81no—
162#92418—81no—
163#9023—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61C2×#10311yescharacteristic
174C22×C61#41711yescharacteristic
175C22×C61#45011yescharacteristic
176C22×C61#45111yescharacteristic
177C22×C61#45412yes—
178C22×C61#45812yes—
179C22×C61#48311yescharacteristic
180C22×C61#48411yescharacteristic
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—82no—
186C4×C61—82no—
187Dic61—24no—
188Dic61—42no—
189Dic61—82no—
190Dic61—82no—
191C2×#400—611no—
192#2316—611no—
193#1824—611no—
194#1824—611no—
195C2×#324—611no—
196#1294—611no—
197#1294D6111yescharacteristic
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#161612yes—
203C2×C61#161712yes—
204C2×C61#187211yescharacteristic
205C2×C61#188811yescharacteristic
206C2×C61#189011yescharacteristic
207C2×#117—1221no—
208C22×C4⋊C4—611no—
209C22×C4⋊C4—611no—
210C2×C22⋊C8—611no—
211C2×C22⋊C8C2×D6111yescharacteristic
212#400—614no—
213#400—1222no—
214#389—1222no—
215#389—1222no—
216#380—611no—
217#380—1221no—
218#380C2×D6111yescharacteristic
219C2×#95—1221no—
220C2×#95—1221no—
221C2×#95C2×D6111yescharacteristic
222#340—1222no—
223#340—1222no—
224#324—1222no—
225C61#902311yescharacteristic, complemented, Sylow
226C23×C4—21no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—1221no—
230C23×C4C22×D6111yescharacteristic
231C22×C8—21no—
232C22×C8—1221no—
233#117—2442no—
234#117—2442no—
235C2×C4⋊C4—612no—
236C2×C4⋊C4—612no—
237C2×C4⋊C4—612no—
238C2×C4⋊C4—612no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4D24412yes—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—1221no—
253C2×C42—1222no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258#95—21no—
259#95—21no—
260#95—1224no—
261#95—1224no—
262#95—1222no—
263#95—1221no—
264#95C4×D6112yes—
265C24D4×D6111yescharacteristic
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—2444no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2442no—
289C22×C4C2×C4×D6111yescharacteristic
290C22×C4C2×D24411yescharacteristic
291C22×C4#1175822211yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4#1175822611yescharacteristic
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—2442no—
298C2×C8—2441no—
299C4⋊C4—42no—
300C4⋊C4—1222no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—1222no—
306C4⋊C4—4882no—
307C4⋊C4—2442no—
308C4⋊C4—2444no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C42—2444no—
316C23—22no—
317C23—22no—
318C23C22⋊C4×D6111yescharacteristic
319C23#1451974711yescharacteristic
320C23#1451976211yescharacteristic
321C23SD16×D6111yescharacteristic
322C23Q16×D6111yescharacteristic
323C23#1451980111yescharacteristic
324C23#1451980611yescharacteristic
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—614no—
340C2×C4—1222no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—4882no—
348C2×C4—4882no—
349C2×C4—4881no—
350C2×C4—2444no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4#1451973911yescharacteristic
358C2×C4C4×D24411yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4#1451975211yescharacteristic
361C8—81no—
362C8—4881no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22#1683964011yescharacteristic
372C22#103×D6111yescharacteristic
373C22#1683976011yescharacteristic
374C22#1683991411yescharacteristic
375C22#1683991911yescharacteristic
376C22#1683993612yes—
377C22#1683995312yes—
378C22#1684009411yescharacteristic
379C22#1684009911yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—1224no—
387C4—4882no—
388C4—4882no—
389C4—2442no—
390C2—21no—
391C2—21no—
392C2—21no—
393C2—21no—
394C2#2144485712yes—
395C2#2144486212yes—
396C2#2144612511yescharacteristic
397C2#2144622111yescharacteristic
398C2#2144623111yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9023
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
13. #16839702C4semidirect
225. C61#9023semidirect

Maximal subgroups

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

subgroupindex
C2×#168397022
#214484362
#214459102
#214459072
C2×#168394872
#214436982
C61×#12942
#902361