Finite Group Databasebeta

← #29568013

Subgroups — #29568013

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D61C211yesmaximal, characteristic
2#21445798C211yesmaximal, characteristic
3#21445576C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D61—21no—
9C2×C4⋊C4×D61C411yescharacteristic
10C2×C4⋊C4×D61C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×#14519706—21no—
13C2×#14519689—21no—
14C2×#14519689—21no—
15C2×C8×Dic61—21no—
16#16839661C411yescharacteristic
17#16839660C2211yescharacteristic
18#16839659—21no—
19#16839658C411yescharacteristic
20#16839657—21no—
21#95×D61—21no—
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C4×D61—21no—
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—22no—
42C4⋊C4×D61—42no—
43C4⋊C4×D61—42no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61C814yescomplemented
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C42×D61—42no—
50#14519706—42no—
51#14519689—24no—
52#14519689—42no—
53C8×Dic61—42no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C42×C61C2311yescharacteristic
63#95×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—24no—
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61C2×C812yes—
90C2×C4×D61M1612yes—
91C2×C4×D61SD1612yes—
92C2×C4×D61Q1612yes—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61C2×C812yes—
104C42×C61—41no—
105C4⋊Dic61—21no—
106C4⋊Dic61—42no—
107C4⋊Dic61—41no—
108C4⋊Dic61C2×C812yes—
109#11758196—24no—
110#11758196—42no—
111#11758196—41no—
112#11758196—41no—
113#11758196—42no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61—41no—
117C2×#92418—22no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61C22⋊C812yes—
129C22×D61#10312yes—
130C22×D61#10412yes—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61C22×C811yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61C2×Q1611yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—22no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61C22⋊C812yes—
161C2×Dic61#9912yes—
162C2×Dic61#10112yes—
163C2×Dic61#10312yes—
164C4×D61—24no—
165C4×D61—24no—
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—48no—
171C4×D61—84no—
172C8×C61—42no—
173C8×C61—81no—
174#92418—42no—
175#92418—81no—
176#7576—611nomaximal, Sylow
177C22×C61C2×C22⋊C811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61C2×#10111yescharacteristic
180C22×C61C2×#10311yescharacteristic
181C22×C61#41811yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C22×C61#42111yescharacteristic
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61Q8⋊C814yes—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—42no—
198C4×C61—81no—
199Dic61—22no—
200Dic61—42no—
201Dic61—41no—
202Dic61—81no—
203Dic61#32414yes—
204C2×#389—611no—
205#1797—611no—
206C4×C22⋊C8—611no—
207#1271—611no—
208#1271—611no—
209#1271—611no—
210#1271D6111yescharacteristic, complemented
211C2×C61C2×#32411yescharacteristic
212C2×C61C2×Q8⋊C811yescharacteristic
213C2×C61#147811yescharacteristic
214C2×C61#150711yescharacteristic
215C2×C61#152011yescharacteristic
216C2×C61#152811yescharacteristic
217C2×C61#154911yescharacteristic
218D61—24no—
219C22×C4⋊C4—611no—
220C22×C4⋊C4—611no—
221C22×C4⋊C4—1221no—
222C22×C42—611no—
223C2×C4⋊C8—1221no—
224C2×C22⋊C8—1221no—
225C2×C22⋊C8—1221no—
226C2×C4×C8—1221no—
227#389—611no—
228#389—611no—
229#389—611no—
230#389—1221no—
231#389—1221no—
232#389C2×D6111yescharacteristic
233C2×#95—1221no—
234#336—611no—
235#336—611no—
236#336C2×D6111yescharacteristic
237#336C2×D6111yescharacteristic
238C61#757611yescharacteristic, complemented, Sylow
239C23×C4—611no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—1221no—
243C23×C4—1221no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—1221no—
247C22×C8—1221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—614no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1222no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—2442no—
259C2×C4⋊C4—2442no—
260C2×C4⋊C4—2442no—
261C2×C4⋊C4C4×D6111yescharacteristic
262C2×C4⋊C4C4×D6111yescharacteristic
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—611no—
266C2×C42—2442no—
267C2×C42C22×D6111yescharacteristic
268C4⋊C8—2442no—
269C22⋊C8—1224no—
270C22⋊C8—2442no—
271C4×C8—2442no—
272#95—21no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276C24—611no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—612no—
284C22×C4—612no—
285C22×C4—611no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1224no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4—2442no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—1222no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8—2441no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—612no—
322C4⋊C4—1224no—
323C4⋊C4—1221no—
324C4⋊C4—2441no—
325C4⋊C4—2442no—
326C4⋊C4—2442no—
327C4⋊C4—2442no—
328C4⋊C4—2441no—
329C4⋊C4—2441no—
330C4⋊C4C8×D6112yes—
331C42—41no—
332C42—1222no—
333C42—1222no—
334C42—2441no—
335C23—612no—
336C23—612no—
337C23—612no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23C22⋊C4×D6111yescharacteristic
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—612no—
356C2×C4—612no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—1224no—
360C2×C4—1224no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1222no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—4884no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2448no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4C2×C8×D6111yescharacteristic
379C2×C4M16×D6111yescharacteristic
380C2×C4SD16×D6111yescharacteristic
381C2×C4Q16×D6111yescharacteristic
382C2×C4#1451980111yescharacteristic
383C2×C4#1451980411yescharacteristic
384C8—42no—
385C8—81no—
386C8—4881no—
387C8—2442no—
388C22—614no—
389C22—1222no—
390C22—1222no—
391C22—1222no—
392C22—1222no—
393C22—1222no—
394C22—1222no—
395C22C22⋊C8×D6111yescharacteristic
396C22#99×D6111yescharacteristic
397C22#101×D6111yescharacteristic
398C22#103×D6111yescharacteristic
399C22#1683976511yescharacteristic
400C22#104×D6111yescharacteristic
401C22#1683977711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—614no—
411C4—1222no—
412C4—4881no—
413C4—2442no—
414C4—2441no—
415C2—1224no—
416C2#324×D6111yescharacteristic
417C2Q8⋊C8×D6111yescharacteristic
418C2#2144420811yescharacteristic
419C2#2144433311yescharacteristic
420C2#2144438911yescharacteristic
421C2#2144441911yescharacteristic
422C2#2144450211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7576
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #21443643C2semidirect
5. #21443642C2semidirect
6. #21443641C2semidirect
7. C61×#1271C2semidirect
45. C4⋊C4×D61C8semidirect
210. #1271D61semidirect
238. C61#7576semidirect

Maximal subgroups

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

subgroupindex
#389×D612
#214457982
#214455762
#214436432
#214436422
#214436412
C61×#12712
#757661