Finite Group Databasebeta

← #29590515

Subgroups — #29590515

Order 15616.

622 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449154C211yesmaximal, characteristic
2C2×#16839531C211yesmaximal, characteristic, complemented
3#21443850C212yesmaximal, complemented
4#21443823C212yesmaximal, complemented
5C61×#1463C211yesmaximal, characteristic, complemented
6C22×#11758222C411yescharacteristic
7C22×#11758194—21no—
8C2×#14519760—21no—
9#16839682C411yescharacteristic
10#16839682C2211yescharacteristic
11#16839679C411yescharacteristic
12#16839679C2211yescharacteristic
13#16839641—21no—
14#16839633—21no—
15#16839633—21no—
16#16839625C411yescharacteristic
17#16839531—21no—
18#16839531C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C2×#11758222—41no—
24C2×#11758222—41no—
25C2×#11758222—44no—
26C22×Dic122C2×C411yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C4×D61—21no—
30C2×#11758194—24no—
31C2×#11758194—22no—
32C2×#11758194—41no—
33C2×#11758194—42no—
34C22×#92418—41no—
35#14519760—44no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684C2×C411yescharacteristic
47#14519684C2×C411yescharacteristic
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C2×M16×C61—41no—
52C2×C4⋊C4×C61—41no—
53C2×C4⋊C4×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—22no—
59C22⋊C8×C61—41no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—42no—
72C22×C4×C61—42no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—24no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86#11758222—44no—
87#11758222—44no—
88#11758222—44no—
89#11758222—44no—
90C2×D244—41no—
91C2×D244—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×Dic122—41no—
96C2×Dic122—42no—
97M16×C61—82no—
98C2×C8×C61—42no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C22⋊Dic61—42no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—41no—
108#11758198—41no—
109#11758196—42no—
110#11758196—42no—
111#11758194—24no—
112#11758194—44no—
113#11758194—42no—
114C2×#92418—44no—
115C2×#92418—42no—
116C23×C61—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—41no—
120C23×C61#9911yescharacteristic
121C23×C61#9911yescharacteristic
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—81no—
150C2×C4×C61#10412yes—
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C22⋊D61—44no—
154C22⋊D61—44no—
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164D244—42no—
165D244—42no—
166C4×D61—48no—
167Dic122—42no—
168Dic122—42no—
169C8×C61—82no—
170#92418—44no—
171#11762—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61AΣL(1,𝔽16)12yes—
182C22×C61C2×#9911yescharacteristic
183C22×C61#41711yescharacteristic
184C22×C61C2×#10411yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—22no—
194C4×C61—21no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199Dic61—42no—
200Dic61—81no—
201Dic61—81no—
202#2406—611no—
203C2×#343—611no—
204#1463D6111yescharacteristic, complemented
205#1354—612no—
206#1345—612no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—22no—
210C2×C61—41no—
211C2×C61#150411yescharacteristic
212C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C61#213311yescharacteristic
214D61—82no—
215C22×#41—611no—
216C22×M16—1221no—
217C2×#123—1221no—
218C22×C4⋊C4C2×D6111yescharacteristic
219#407—21no—
220#395—611no—
221#395—611no—
222#394—611no—
223#394—611no—
224#386—1221no—
225#385—1221no—
226#385—1221no—
227#381—611no—
228#343—612no—
229#343—1221no—
230#324—21no—
231#324C2×D6112yes—
232C61#1176211yescharacteristic, complemented, Sylow
233C2×#41—2441no—
234C2×#41—2441no—
235C2×#41—2444no—
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—1221no—
239C23×C4—1221no—
240C23×C4C4×D6111yescharacteristic
241C23×C4D24411yescharacteristic
242C23×C4C22⋊D6111yescharacteristic
243C2×M16—41no—
244C2×M16—1224no—
245C2×M16—1222no—
246C2×M16—2441no—
247C2×M16—2442no—
248C22×C8—2441no—
249#123—2444no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4—41no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4C4×D6111yescharacteristic
255C2×C4⋊C4D24411yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C4⋊C4C22×D6111yescharacteristic
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C22⋊C8—22no—
264C22⋊C8—41no—
265#95—611no—
266#95—611no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—1221no—
271C24#1175819811yescharacteristic
272#41—2444no—
273#41—2444no—
274#41—2444no—
275#41—2444no—
276C2×Q8—2441no—
277C2×Q8—2442no—
278C2×D4—1224no—
279C2×D4—2441no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4—2441no—
283C2×D4—2441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4#1175819811yescharacteristic
302C22×C4#1175819811yescharacteristic
303C22×C4#1175819811yescharacteristic
304C22×C4C2×C4×D6111yescharacteristic
305C22×C4C2×D24411yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307M16—82no—
308M16—1224no—
309M16—2444no—
310M16—2442no—
311C2×C8—42no—
312C2×C8—2444no—
313C2×C8—2442no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—2442no—
319C4⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2441no—
324C22⋊C4—2442no—
325C22⋊C4—2441no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—41no—
330C23—1222no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23#1451969111yescharacteristic
338C23#1451969111yescharacteristic
339C23C2×#1175819811yescharacteristic
340Q8—2442no—
341Q8—2442no—
342D4—2442no—
343D4—2442no—
344D4—2444no—
345D4—2444no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—1222no—
367C2×C4—2448no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451970312yes—
377C2×C4#1451980511yescharacteristic
378C2×C4#1451981011yescharacteristic
379C8—82no—
380C8—2444no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22#1683954812yes—
398C22C2×#1451969111yescharacteristic
399C22#1683976411yescharacteristic
400C22C2×#1451970311yescharacteristic
401C4—21no—
402C4—21no—
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—4881no—
409C4—4881no—
410C4—2442no—
411C2—21no—
412C2—21no—
413C2—22no—
414C2—41no—
415C2—4882no—
416C2#2144432411yescharacteristic
417C2C2×#1683954811yescharacteristic
418C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1463C2
socleC22×C61C2×#99
prime radicalC22×#11758222C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1463D61
hypocenterC61#11762
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. C2×#16839531C2semidirect
3. #21443850C2semidirect
4. #21443823C2semidirect
5. C61×#1463C2semidirect
204. #1463D61semidirect
232. C61#11762semidirect

Maximal subgroups

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

subgroupindex
#214491542
C2×#168395312
#214438502
#214438232
C61×#14632
#1176261