Finite Group Databasebeta

← #29568469

Subgroups — #29568469

Order 15616.

568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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#21454157C211yesmaximal, characteristic
2#21445511C211yesmaximal, characteristic
3#336×D61C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443642C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C22×C8×D61—21no—
10C2×#14519757C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12#16839668C2211yescharacteristic
13#16839667C411yescharacteristic
14#16839658C411yescharacteristic
15#16839649—21no—
16#16839648—21no—
17#16839633—21no—
18#16839624—21no—
19#16839619C411yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—24no—
32C2×#11758189—42no—
33C2×#11758189—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—24no—
37C2×C8×D61—42no—
38C2×C8×D61—42no—
39#14519757—42no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C42×D61—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61SD1612yes—
84C2×C4×D61Q1612yes—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61—41no—
101#11758198—42no—
102#11758198—42no—
103C4⋊Dic61—42no—
104C4⋊Dic61—41no—
105#11758196—42no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C2×#92418—22no—
110C2×#92418—22no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115#11758189—48no—
116C8×D61—48no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61#9912yes—
123C22×D61#10312yes—
124C22×D61#10412yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#13111yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61C2×Q1611yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61#10312yes—
157C2×Dic61#10412yes—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—24no—
161C4×D61—24no—
162C4×D61—42no—
163C4×D61—42no—
164Dic122—81no—
165Dic122—81no—
166C8×C61—42no—
167C8×C61—42no—
168#92418—42no—
169#92418—42no—
170#7681—611nomaximal, Sylow
171C22×C61#40811yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61#41311yescharacteristic
174C22×C61C2×#10311yescharacteristic
175C22×C61#41711yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61#32814yes—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61—81no—
193Dic61—22no—
194Dic61—22no—
195Dic61—41no—
196Dic61—81no—
197Dic61—81no—
198#2855—611no—
199#1728—611no—
200C2×#336—611no—
201#1272—611no—
202#1272—611no—
203#1271—611no—
204#1271D6111yescharacteristic, complemented
205C2×C61#146811yescharacteristic
206C2×C61#148311yescharacteristic
207C2×C61#149311yescharacteristic
208C2×C61C2×#32811yescharacteristic
209C2×C61#150411yescharacteristic
210C2×C61#152411yescharacteristic
211C2×C61#155011yescharacteristic
212D61—24no—
213C22×M16—1221no—
214C23×C8—1221no—
215C2×C22⋊Q8—611no—
216C22×C42—611no—
217#391—611no—
218#391—611no—
219#389—611no—
220#389C2×D6111yescharacteristic
221#387—1221no—
222#387—1221no—
223#385—1221no—
224#381—1221no—
225#380—611no—
226#336—611no—
227#336—611no—
228#336—1221no—
229#336—1221no—
230#336C2×D6111yescharacteristic
231#336C2×D6111yescharacteristic
232C61#768111yescharacteristic, complemented, Sylow
233C22×Q8—611no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C2×M16—1224no—
238C2×M16—2442no—
239C2×M16—2442no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—1224no—
243C22×C8—1221no—
244C22×C8—1221no—
245C22×C8—2442no—
246C22×C8—2442no—
247C22⋊Q8—2442no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C4×D6111yescharacteristic
253C2×C4⋊C4C4×D6111yescharacteristic
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42—2442no—
260C2×C42C22×D6111yescharacteristic
261#95—21no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268C24—611no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—2441no—
272C2×Q8—2441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—611no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—2441no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295M16—2448no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—1222no—
303C2×C8—1222no—
304C2×C8—2448no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C2×C8—2441no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—2441no—
315C4⋊C4—2442no—
316C4⋊C4—2442no—
317C22⋊C4—2442no—
318C22⋊C4—2442no—
319C42—41no—
320C42—2441no—
321C42—2441no—
322C42—2441no—
323C23—612no—
324C23—612no—
325C23—612no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23C22⋊C4×D6111yescharacteristic
331Q8—4881no—
332Q8—4881no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—1224no—
348C2×C4—1224no—
349C2×C4—1224no—
350C2×C4—1224no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4#1451978311yescharacteristic
367C2×C4#1451978511yescharacteristic
368C2×C4SD16×D6111yescharacteristic
369C2×C4Q16×D6111yescharacteristic
370C2×C4#1451980111yescharacteristic
371C2×C4#1451980611yescharacteristic
372C8—42no—
373C8—42no—
374C8—2442no—
375C8—2442no—
376C22—614no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—1222no—
381C22—1222no—
382C22—1222no—
383C22#1683972711yescharacteristic
384C22#99×D6111yescharacteristic
385C22#1683974511yescharacteristic
386C22#103×D6111yescharacteristic
387C22#1683976011yescharacteristic
388C22#104×D6111yescharacteristic
389C22#104×D6111yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—1222no—
399C4—1222no—
400C4—4881no—
401C4—4881no—
402C4—2441no—
403C2—1224no—
404C2#2144416611yescharacteristic
405C2#2144422911yescharacteristic
406C2#2144427211yescharacteristic
407C2#328×D6111yescharacteristic
408C2#2144432011yescharacteristic
409C2#2144440611yescharacteristic
410C2#2144450811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7681
LCSG ▷ C22×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. #21443644C2semidirect
5. #21443644C2semidirect
6. #21443642C2semidirect
7. C61×#1271C2semidirect
204. #1271D61semidirect
232. C61#7681semidirect

Maximal subgroups

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

subgroupindex
#214541572
#214455112
#336×D612
#214436442
#214436422
C61×#12712
#768161