Finite Group Databasebeta

← #29571848

Subgroups — #29571848

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459152C211yesmaximal, characteristic
2#21445803C211yesmaximal, characteristic, complemented
3#21444466C212yesmaximal, complemented
4#21444219C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic, complemented
6C22×#11758222—21no—
7#16840343—21no—
8#16840343C412yes—
9#16840338—22no—
10#16840331—22no—
11#16840324—21no—
12#16840324C412yes—
13#16840312—21no—
14#16840312C2212yes—
15#16840274—24no—
16C2×C4⋊#92418C2211yescharacteristic, complemented
17C2×C4⋊#92418C2211yescharacteristic, complemented
18C2×C22⋊#92418—21no—
19#16839517—21no—
20#16839507—22no—
21#16839505—22no—
22#16839491—24no—
23C2×#117×C61C2211yescharacteristic
24C61×#431C2212yescomplemented
25C61×#324—21no—
26C61×#323—21no—
27C2×#11758222—22no—
28C2×#11758222—22no—
29C2×#11758222—22no—
30C2×#11758222—22no—
31C2×#11758222—42no—
32C2×#11758222—42no—
33C2×#11758222—42no—
34C2×#11758222—42no—
35C22×Dic122—21no—
36C22×D244—21no—
37C22×C22⋊D61—22no—
38C22×C4×D61—22no—
39C22×#92418—21no—
40C22×#92418—21no—
41#14519777—21no—
42#14519777D412yes—
43#14519774—21no—
44#14519774D412yes—
45#14519765—22no—
46#14519765—22no—
47#14519761—24no—
48#14519761—24no—
49#14519757—24no—
50#14519757—24no—
51#14519752—24no—
52#14519752—24no—
53#14519751—22no—
54#14519751—22no—
55#14519751—22no—
56#14519751C2×C414yes—
57#14519747—24no—
58#14519747—24no—
59C4×D244—22no—
60C4×D244—22no—
61C4×D244—22no—
62C4×D244D414yes—
63C4⋊#92418—22no—
64C4⋊#92418—22no—
65C22⋊#92418—42no—
66C23×C4×C61D411yescharacteristic
67#117×C61—22no—
68#117×C61—22no—
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C22⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61D411yescharacteristic
73C2×C42×C61D411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—22no—
76C22⋊C8×C61—22no—
77C4×C8×C61—22no—
78C24×C61C22⋊C411yescharacteristic
79C23×D61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61D812yes—
88C22×C4×C61SD1612yes—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—24no—
93C2×C22⋊D61—24no—
94C2×C22⋊D61—44no—
95C2×C22⋊D61—44no—
96C22×Dic61—22no—
97#11758222—44no—
98#11758222—44no—
99#11758222—44no—
100#11758222—44no—
101#11758222—44no—
102#11758222—44no—
103#11758222—42no—
104#11758222—42no—
105#11758222—42no—
106#11758222—42no—
107C2×D244—22no—
108C2×D244—22no—
109C2×D244—22no—
110C2×D244—22no—
111C2×D244—22no—
112C2×D244—42no—
113C2×D244—42no—
114C2×D244C22⋊C414yes—
115C2×C4×D61—24no—
116C2×C4×D61—24no—
117C2×C4×D61—44no—
118C2×C4×D61—44no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—42no—
122C2×Dic122—42no—
123C2×C8×C61—42no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—22no—
128C42×C61—21no—
129C42×C61—21no—
130C42×C61C2×D412yes—
131C42×C61C2×D412yes—
132#11758198—24no—
133#11758198—24no—
134#11758198—24no—
135#11758198—24no—
136C4⋊Dic61—22no—
137C4⋊Dic61—22no—
138C4⋊Dic61—22no—
139C4⋊Dic61C22⋊C414yes—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61#10212yes—
151C23×C61C2×C22⋊C411yescharacteristic
152C22×D61—24no—
153C22×D61—44no—
154C22×D61—82no—
155C22×D61—82no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61#10212yes—
169C2×C4×C61C2×C22⋊C412yes—
170C2×C4×C61#12012yes—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61C2×D811yescharacteristic
174C2×C4×C61C2×SD1611yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C22⋊D61—48no—
178C22⋊D61—44no—
179C22⋊D61—44no—
180C2×Dic61—24no—
181C2×Dic61—44no—
182D244—44no—
183D244—44no—
184D244—42no—
185D244—42no—
186D244—82no—
187D244—82no—
188D244—82no—
189C4×D61—48no—
190C4×D61—44no—
191C4×D61—44no—
192Dic122—44no—
193Dic122—42no—
194Dic122—42no—
195C8×C61—82no—
196#92418—81no—
197#92418—81no—
198#8409—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—22no—
202C22×C61—42no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—81no—
206C22×C61#37911yescharacteristic
207C22×C61C2×#10211yescharacteristic
208C22×C61#41811yescharacteristic
209C2×D61—44no—
210C2×D61—44no—
211C2×D61—44no—
212C2×D61—88no—
213C4×C61—22no—
214C4×C61—22no—
215C4×C61—22no—
216C4×C61—41no—
217C4×C61—41no—
218C4×C61#44711yescharacteristic
219C4×C61#44711yescharacteristic
220C4×C61#45011yescharacteristic
221C4×C61#45011yescharacteristic
222Dic61—44no—
223#3449—611no—
224#1798—611no—
225#1540—612no—
226#1480—612no—
227#1458D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—42no—
231C2×C61#178611yescharacteristic
232C2×C61#179111yescharacteristic
233C2×C61#179411yescharacteristic
234D61—84no—
235C22×#41—1221no—
236#537—612no—
237#537—1221no—
238#536—1222no—
239#535—1222no—
240#534—612no—
241#534—1221no—
242#532—612no—
243#532—1221no—
244#525—1224no—
245C2×#117C2×D6111yescharacteristic
246#431C2×D6112yescomplemented
247C2×C4⋊C8—611no—
248C2×C4⋊C8—611no—
249C2×C22⋊C8—1221no—
250#336—1221no—
251#332—1222no—
252#331—1222no—
253D4⋊C8—1224no—
254#324—21no—
255#323—21no—
256C61#840911yescharacteristic, complemented, Sylow
257C2×#41—1222no—
258C2×#41—1222no—
259C2×#41—1222no—
260C2×#41—1222no—
261C2×#41—2442no—
262C2×#41—2442no—
263C2×#41—2442no—
264C2×#41—2442no—
265C22×Q8—1221no—
266C22×D4—1221no—
267C22×D4—1222no—
268C23×C4—1222no—
269C23×C4D24411yescharacteristic
270C22×C8—1221no—
271C22×C8—1221no—
272C4⋊Q8—612no—
273C4⋊Q8—1221no—
274#127—612no—
275#127—1221no—
276#124—1222no—
277#124—1222no—
278#123—1224no—
279#123—1224no—
280C22⋊Q8—1224no—
281C22⋊Q8—1224no—
282#121—614no—
283#121—1224no—
284#121—1224no—
285#121—1222no—
286#121—1222no—
287#121—1222no—
288#120—1224no—
289#120—1224no—
290C4×D4—614no—
291C4×D4—1222no—
292C4×D4—1222no—
293C4×D4—1222no—
294#117—22no—
295#117—22no—
296C2×C4⋊C4C4×D6111yescharacteristic
297C2×C4⋊C4C22⋊D6111yescharacteristic
298C2×C22⋊C4C4×D6111yescharacteristic
299C2×C22⋊C4C22⋊D6111yescharacteristic
300C2×C42D24411yescharacteristic
301C2×C42C22×D6111yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—1222no—
304C4⋊C8—1222no—
305C22⋊C8—22no—
306C22⋊C8—2442no—
307C4×C8—22no—
308C24—1222no—
309C24#1175819811yescharacteristic
310#41—2444no—
311#41—2444no—
312#41—2444no—
313#41—2444no—
314#41—2444no—
315#41—2444no—
316#41—2442no—
317#41—2442no—
318#41—2442no—
319#41—2442no—
320C2×Q8—1222no—
321C2×Q8—1222no—
322C2×Q8—2442no—
323C2×Q8—2442no—
324C2×D4—614no—
325C2×D4—1222no—
326C2×D4—1222no—
327C2×D4—1222no—
328C2×D4—1224no—
329C2×D4—1224no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—2442no—
333C2×D4—2442no—
334C2×D4—2444no—
335C2×D4—2444no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—1224no—
341C22×C4—1222no—
342C22×C4—1224no—
343C22×C4—2444no—
344C22×C4—2444no—
345C22×C4#1175819012yes—
346C22×C4D48812yes—
347C22×C4#1175819811yescharacteristic
348C22×C4#1175819811yescharacteristic
349C22×C4#1175819811yescharacteristic
350C22×C4C2×C4×D6111yescharacteristic
351C22×C4C2×D24411yescharacteristic
352C22×C4C2×C22⋊D6111yescharacteristic
353C2×C8—42no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C2×C8—2441no—
358C2×C8—2441no—
359C2×C8—2441no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—614no—
363C4⋊C4—1222no—
364C4⋊C4—1222no—
365C4⋊C4—1222no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—1224no—
369C22⋊C4—1224no—
370C22⋊C4—1224no—
371C22⋊C4—1224no—
372C42—21no—
373C42—21no—
374C42D4×D6112yes—
375C42D4×D6112yes—
376C23—21no—
377C23—21no—
378C23—41no—
379C23—41no—
380C23—1224no—
381C23—4882no—
382C23—4882no—
383C23—2444no—
384C23#1451969912yes—
385C23C2×#1175819811yescharacteristic
386Q8—2444no—
387Q8—2442no—
388Q8—2442no—
389D4—4882no—
390D4—4882no—
391D4—4882no—
392D4—2444no—
393D4—2444no—
394D4—2448no—
395D4—2444no—
396D4—2444no—
397D4—2442no—
398D4—2442no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—1224no—
412C2×C4—2448no—
413C2×C4—2444no—
414C2×C4—2444no—
415C2×C4—2444no—
416C2×C4#1451969912yes—
417C2×C4C22⋊C4×D6112yes—
418C2×C4#1451974512yes—
419C2×C4#1451974711yescharacteristic
420C2×C4#1451974711yescharacteristic
421C2×C4C2×D48811yescharacteristic
422C2×C4C2×#1175819011yescharacteristic
423C2×C4#1451980511yescharacteristic
424C2×C4#1451980511yescharacteristic
425C8—82no—
426C8—4881no—
427C8—4881no—
428C22—21no—
429C22—21no—
430C22—22no—
431C22—42no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—4888no—
436C22—2444no—
437C22—2444no—
438C22—2444no—
439C22#1683961711yescharacteristic
440C22C2×#1451969911yescharacteristic
441C22#1683976811yescharacteristic
442C4—22no—
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—2444no—
448C4#1683989811yescharacteristic
449C4#1683989811yescharacteristic
450C4#1683991511yescharacteristic
451C4#1683991511yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—4884no—
456C2#2144575111yescharacteristic
457C2#2144576811yescharacteristic
458C2#2144578511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#379
prime radical#21459152C2
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8409
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21445803C2semidirect
3. #21444466C2semidirect
4. #21444219C2semidirect
5. C61×#1458C2semidirect
16. C2×C4⋊#92418C22semidirect
17. C2×C4⋊#92418C22semidirect
24. C61×#431C22semidirect
227. #1458D61semidirect
246. #431C2×D61semidirect
256. C61#8409semidirect

Maximal subgroups

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

subgroupindex
#214591522
#214458032
#214444662
#214442192
C61×#14582
#840961