Finite Group Databasebeta

← #29569166

Subgroups — #29569166

Order 15616.

396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453796C211yesmaximal, characteristic
2#21447361C211yesmaximal, characteristic, complemented
3#21447290C211yesmaximal, characteristic, complemented
4#21447224C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519710—21no—
9C2×#14519709—21no—
10C2×#14519702—21no—
11C2×#14519699—21no—
12#16839688—21no—
13#16839679—21no—
14#16839675—21no—
15#16839668C2211yescharacteristic
16#16839664C2211yescharacteristic
17#16839654—21no—
18#16839652—21no—
19#16839648—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42#14519710—42no—
43#14519709—42no—
44#14519702—42no—
45#14519699—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C42×C61—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—81no—
93#11758198—81no—
94#11758198—81no—
95#11758198—81no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4×Dic61—81no—
105C2×#92418—22no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61#12011yescharacteristic
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146D244—42no—
147D244—81no—
148Dic122—42no—
149Dic122—81no—
150C8×C61—42no—
151C8×C61—81no—
152#92418—42no—
153#7805—611nomaximal, Sylow
154C22×C61#44911yescharacteristic
155C22×C61#44911yescharacteristic
156C22×C61#45211yescharacteristic
157C22×C61#45311yescharacteristic
158C22×C61#45511yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61#45811yescharacteristic
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—81no—
177Dic61—81no—
178Dic61—81no—
179Dic61—161no—
180#2808—611no—
181#2096—611no—
182#2083—611no—
183#2071—611no—
184#1272—611no—
185#1271D6111yescharacteristic, complemented
186#1270—611no—
187C2×C61#160911yescharacteristic
188C2×C61#161211yescharacteristic
189C2×C61#161811yescharacteristic
190C2×C61#162411yescharacteristic
191C2×C61#164011yescharacteristic
192C2×C61#165011yescharacteristic
193C2×C61#166111yescharacteristic
194D61—161no—
195C2×#107—1221no—
196C2×#106—1221no—
197C2×#103—1221no—
198C2×#102—1221no—
199#397—1221no—
200#394—1221no—
201#393—1221no—
202#391—611no—
203#390—611no—
204#389C2×D6111yescharacteristic
205#388—1221no—
206#388—1221no—
207#387—1221no—
208#384—611no—
209#340—1221no—
210#340—1221no—
211#336—611no—
212#336C2×D6111yescharacteristic
213#336C2×D6111yescharacteristic
214C61#780511yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×D4—611no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—1221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4D24411yescharacteristic
227C2×C4⋊C4D24411yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C42—1221no—
235C2×C42C22×D6111yescharacteristic
236#107—2442no—
237#106—2442no—
238#103—2442no—
239#102—2442no—
240#95—21no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—1221no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—2441no—
254C2×D4—2441no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—2441no—
261C22×C4C2×D24411yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—1222no—
271C2×C8—2441no—
272C2×C8—2441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—4881no—
287C22⋊C4—4881no—
288C22⋊C4—4881no—
289C22⋊C4—4881no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—41no—
295C42—4881no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23#1451974711yescharacteristic
304Q8—4881no—
305Q8—2442no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451979811yescharacteristic
333C2×C4#1451979811yescharacteristic
334C2×C4#1451979911yescharacteristic
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980511yescharacteristic
337C2×C4#1451980911yescharacteristic
338C8—42no—
339C8—81no—
340C8—2442no—
341C22—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—4881no—
346C22—4881no—
347C22—4881no—
348C22#1683990811yescharacteristic
349C22#1683990911yescharacteristic
350C22#1683992711yescharacteristic
351C22#1683993111yescharacteristic
352C22#1683994111yescharacteristic
353C22#1683994711yescharacteristic
354C22#1683995311yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—9761no—
364C4—4881no—
365C4—4881no—
366C4—4881no—
367C2—9761no—
368C2#2144481811yescharacteristic
369C2#2144483411yescharacteristic
370C2#2144487011yescharacteristic
371C2#2144490411yescharacteristic
372C2#2144500711yescharacteristic
373C2#2144507611yescharacteristic
374C2#2144513811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1271D61
hypocenterC61#7805
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21447361C2semidirect
3. #21447290C2semidirect
5. #21443644C2semidirect
7. C61×#1271C2semidirect
185. #1271D61semidirect
214. C61#7805semidirect

Maximal subgroups

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

subgroupindex
#214537962
#214473612
#214472902
#214472242
#214436442
#214436392
C61×#12712
#780561