Finite Group Databasebeta

← #29575096

Subgroups — #29575096

Order 15616.

516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454903C211yesmaximal, characteristic, complemented
2#21449105C211yesmaximal, characteristic
3C4×#14519695C211yesmaximal, characteristic, complemented
4#21444263C211yesmaximal, characteristic
5#21444261C211yesmaximal, characteristic
6#21443712C211yesmaximal, characteristic, complemented
7C61×#1300C211yesmaximal, characteristic, complemented
8C2×C4×Dic122C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839816—21no—
14#16839812—21no—
15C2×#14519695—21no—
16C4×#11758194C2211yescharacteristic
17#16839702C411yescharacteristic
18#16839702C411yescharacteristic
19#16839689—21no—
20#16839680C411yescharacteristic
21#16839680C411yescharacteristic
22#16839675—21no—
23C4×#11758198—21no—
24C4×#11758198—21no—
25#16839530—21no—
26#16839491—22no—
27#16839489—22no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C2×#11758194—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196C2×C411yescharacteristic
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C4⋊#92418D412yes—
55#14519706—22no—
56#14519706—22no—
57#14519695—24no—
58C22⋊#92418—21no—
59#14519688—21no—
60#14519688—21no—
61#14519687—22no—
62C4×#92418—21no—
63C8×Dic61—22no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C2×M16×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61D412yes—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61—21no—
75C4×C8×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C23×D61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101M16×C61—22no—
102M16×C61—41no—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C42×C61—42no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—42no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115#11758198—42no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—22no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61#10412yes—
169D244—22no—
170D244—22no—
171D244—41no—
172D244—41no—
173C4×D61—82no—
174C4×D61—82no—
175Dic122—42no—
176Dic122—42no—
177C8×C61—42no—
178C8×C61—42no—
179#92418—42no—
180#92418—42no—
181#9032—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—42no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61#45412yes—
202Dic61—22no—
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206Dic61—81no—
207#2983—611no—
208#2398—611no—
209C4×#101—611no—
210#1490—611no—
211#1490—611no—
212#1300—611no—
213#1300D6111yescharacteristic, complemented
214C2×C61—21no—
215C2×C61—21no—
216C2×C61#187111yescharacteristic
217C2×C61#188811yescharacteristic
218C2×C61#189111yescharacteristic
219D61—82no—
220C2×C4×Q8—611no—
221C2×C4×D4—611no—
222#446—1222no—
223#446—1222no—
224#432—611no—
225#432—1221no—
226#432C2×D6111yescharacteristic
227#431—1221no—
228C2×#101—1221no—
229C4×M16—611no—
230C4×M16C2×D6111yescharacteristic
231#400—611no—
232#400—611no—
233#397—1221no—
234#394—611no—
235#394—611no—
236#393—1221no—
237C4×C22⋊C4—1221no—
238C4×C22⋊C4—1221no—
239#376C2×D6111yescharacteristic
240#343—1221no—
241D4⋊C8—1222no—
242D4⋊C8—1222no—
243C61#903211yescharacteristic, complemented, Sylow
244C22×Q8—611no—
245C22×D4—611no—
246C23×C4—1221no—
247C2×M16—21no—
248C2×M16—1221no—
249C4×Q8—1221no—
250C4×Q8—1221no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C4×D4—1221no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42—21no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42C22×D6111yescharacteristic
270C4⋊C8—612no—
271C4⋊C8—1222no—
272C4⋊C8—1222no—
273C4⋊C8D24412yes—
274#101—1224no—
275C22⋊C8—21no—
276C22⋊C8—1221no—
277#97—21no—
278#97—21no—
279#97—1222no—
280#97—1221no—
281#97—1221no—
282C4×C8—21no—
283C4×C8—1222no—
284C4×C8—1221no—
285#95—21no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290#95C4×D6111yescharacteristic
291#95C4×D6111yescharacteristic
292C24—1221no—
293C2×Q8—1222no—
294C2×Q8—1221no—
295C2×Q8—1221no—
296C2×Q8—2441no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—2442no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1221no—
307C22×C4—2442no—
308C22×C4—2442no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4C2×C4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314M16—22no—
315M16—41no—
316M16—1222no—
317M16—2441no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—1222no—
321C2×C8—2441no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C22⋊C4—2442no—
331C22⋊C4—2442no—
332C22⋊C4—2442no—
333C22⋊C4—2442no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—42no—
337C42—1221no—
338C42—1221no—
339C42—1221no—
340C42—1221no—
341C42C2×D24411yescharacteristic
342C42#1175822211yescharacteristic
343C42D4×D6111yescharacteristic
344C42#1175822611yescharacteristic
345C23—1222no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23C22⋊C4×D6111yescharacteristic
353Q8—2442no—
354Q8—2442no—
355D4—1222no—
356D4—1222no—
357D4—2441no—
358D4—2441no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—612no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4882no—
378C2×C4—4882no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4#1451973911yescharacteristic
385C2×C4C4×D24411yescharacteristic
386C2×C4#1451974711yescharacteristic
387C2×C4#1451975011yescharacteristic
388C2×C4#1451975211yescharacteristic
389C2×C4#1451976211yescharacteristic
390C8—42no—
391C8—42no—
392C8—2442no—
393C8—2442no—
394C22—21no—
395C22—21no—
396C22—4881no—
397C22—4881no—
398C22—4881no—
399C22—4881no—
400C22—2442no—
401C22—2442no—
402C22—2442no—
403C22#1683964011yescharacteristic
404C22#104×D6111yescharacteristic
405C22#1683977711yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—1222no—
414C4—4881no—
415C4—2441no—
416C4—2441no—
417C4—2441no—
418C4#1683993612yes—
419C2—21no—
420C2—21no—
421C2—4882no—
422C2#2144612011yescharacteristic
423C2#2144622111yescharacteristic
424C2#2144623611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9032
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
1. #21454903C2semidirect
3. C4×#14519695C2semidirect
6. #21443712C2semidirect
7. C61×#1300C2semidirect
213. #1300D61semidirect
243. C61#9032semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214491052
C4×#145196952
#214442632
#214442612
#214437122
C61×#13002
#903261