Finite Group Databasebeta

← #29590749

Subgroups — #29590749

Order 15616.

586 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 73 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#395×D61C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic
3#21444147C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443849C211yesmaximal, characteristic, complemented
6#21443848C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C22×Q8×D61C411yescharacteristic
9C2×C4⋊C4×D61—21no—
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839725—21no—
12#16839724—21no—
13#16839683—21no—
14#16839683C411yescharacteristic
15#16839682—21no—
16#16839682C2211yescharacteristic
17#16839681C411yescharacteristic
18#95×D61—21no—
19#95×D61C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122C2×C411yescharacteristic
29C2×Q8×D61—44no—
30C2×Q8×D61—41no—
31C2×Q8×D61—41no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C2×#11758194—21no—
38C2×#11758189—41no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C4⋊C4×D61—44no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519689—41no—
51#14519689—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—42no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77Q8×D61—44no—
78Q8×D61—44no—
79Q8×D61—44no—
80Q8×D61—44no—
81C2×C4×D61—24no—
82C2×C4×D61—24no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—41no—
103C2×Dic122—42no—
104M16×C61—41no—
105M16×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—42no—
110C4⋊Dic61—41no—
111C4⋊Dic61—42no—
112#11758196—41no—
113#11758196—41no—
114#11758196—42no—
115#11758196—42no—
116#11758194—41no—
117#11758194—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120#11758189—82no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61#9911yescharacteristic
127C22×D61#9911yescharacteristic
128Q8×C61—42no—
129Q8×C61—42no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61#13711yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—48no—
162C4×D61—42no—
163C4×D61—44no—
164C4×D61—42no—
165C4×D61—44no—
166C4×D61—42no—
167C4×D61—81no—
168Dic122—48no—
169Dic122—42no—
170Dic122—42no—
171C8×C61—81no—
172C8×C61—81no—
173#92418—81no—
174#92418—81no—
175#11815—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61C2×#9911yescharacteristic
179C22×C61#41911yescharacteristic
180C22×C61#42111yescharacteristic
181C2×D61—24no—
182C2×D61—24no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61AΣL(1,𝔽16)12yes—
188C2×D61#35612yes—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—41no—
193C4×C61—42no—
194C4×C61—41no—
195Dic61—42no—
196Dic61—41no—
197Dic61—42no—
198Dic61—41no—
199Dic61—41no—
200C2×#395—611no—
201#1821—611no—
202#1463—611no—
203#1354—611no—
204#1354—611no—
205#1354—611no—
206#1354D6111yescharacteristic, complemented
207C2×C61—21no—
208C2×C61—21no—
209C2×C61#151111yescharacteristic
210C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
211C2×C61C2×#35611yescharacteristic
212D61—22no—
213D61—22no—
214C23×Q8—611no—
215C22×C4⋊C4—611no—
216C22×C4⋊C4—1221no—
217#407—1221no—
218#407—1221no—
219#395—611no—
220#395—611no—
221#395—611no—
222#395—1221no—
223#395—1221no—
224#395C2×D6111yescharacteristic
225C2×#95—611no—
226C2×#95—1221no—
227#343—611no—
228#343—1221no—
229#343C2×D6111yescharacteristic
230#324—611no—
231#324—1221no—
232#324C2×D6111yescharacteristic
233C61#1181511yescharacteristic, complemented, Sylow
234C22×Q8—611no—
235C22×Q8—1221no—
236C22×Q8—2444no—
237C22×Q8—2441no—
238C22×Q8—2441no—
239C22×Q8C4×D6111yescharacteristic
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—1221no—
244C23×C4—1221no—
245C2×M16—21no—
246C2×M16—1221no—
247C2×M16—2441no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—2441no—
256C2×C4⋊C4—2441no—
257C2×C4⋊C4—2444no—
258C2×C4⋊C4C22×D6111yescharacteristic
259C22⋊C8—21no—
260C22⋊C8—1221no—
261C22⋊C8—2441no—
262C22⋊C8—2441no—
263C22⋊C8—2441no—
264#95—21no—
265#95—611no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270#95C4×D6111yescharacteristic
271C24—611no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—2442no—
275C2×Q8—2441no—
276C2×Q8—2442no—
277C2×Q8—2442no—
278C2×Q8—2442no—
279C2×Q8—2444no—
280C2×Q8—2444no—
281C2×Q8—2444no—
282C2×Q8—2444no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1224no—
295C22×C4—1224no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—2441no—
301C22×C4—2442no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2442no—
305C22×C4—2442no—
306C22×C4—2442no—
307C22×C4—2442no—
308C22×C4C2×C4×D6111yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311M16—41no—
312M16—41no—
313M16—4882no—
314M16—2441no—
315M16—2441no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—2441no—
319C2×C8—2441no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2442no—
326C4⋊C4—2442no—
327C4⋊C4—2442no—
328C23—611no—
329C23—611no—
330C23—1222no—
331C23—1222no—
332C23—1221no—
333C23—1221no—
334C23C22⋊C4×D6111yescharacteristic
335Q8—42no—
336Q8—42no—
337Q8—2442no—
338Q8—2448no—
339Q8—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—4881no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2442no—
365C2×C4—2444no—
366C2×C4—2442no—
367C2×C4—2448no—
368C2×C4—2444no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451980611yescharacteristic
377C2×C4#1451980911yescharacteristic
378C8—81no—
379C8—81no—
380C8—4881no—
381C8—4881no—
382C22—21no—
383C22—21no—
384C22—612no—
385C22—612no—
386C22—1224no—
387C22—1224no—
388C22—1221no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22#99×D6111yescharacteristic
393C22#1683976911yescharacteristic
394C22#1683977711yescharacteristic
395C4—21no—
396C4—21no—
397C4—42no—
398C4—41no—
399C4—42no—
400C4—41no—
401C4—2442no—
402C4—2441no—
403C4—2442no—
404C4—2441no—
405C4—2441no—
406C2—21no—
407C2—21no—
408C2—1222no—
409C2—1222no—
410C2#2144435011yescharacteristic
411C2AΣL(1,𝔽16)×D6111yescharacteristic
412C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11815
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443849C2semidirect
6. #21443848C2semidirect
7. C61×#1354C2semidirect
206. #1354D61semidirect
233. C61#11815semidirect

Maximal subgroups

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

subgroupindex
#395×D612
#214458982
#214441472
#214438502
#214438492
#214438482
C61×#13542
#1181561