Finite Group Databasebeta

← #29576817

Subgroups — #29576817

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455291C211yesmaximal, characteristic
2#21445834C211yesmaximal, characteristic, complemented
3#21444380C211yesmaximal, characteristic
4#21444219C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#2983C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840312C2211yescharacteristic
10#16839984—22no—
11#16839972C412yescomplemented
12#16839962C412yescomplemented
13#16839786C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15#16839761—21no—
16C2×#14519701—21no—
17#16839628C2211yescharacteristic
18#16839524—21no—
19#16839497—22no—
20#16839491—22no—
21C2×C4×Q8×C61C2211yescharacteristic
22C61×#446—22no—
23C61×#446—22no—
24C61×#432—22no—
25C61×#431C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C2×#11758222—21no—
28#14519808—42no—
29#14519808—42no—
30C2×#11758202—22no—
31C2×#11758201—22no—
32C2×#11758194—21no—
33C22×#92418—21no—
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418C2×C412yes—
46#14519701—42no—
47#14519700—22no—
48#14519697—22no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61D411yescharacteristic
52C4×Q8×C61—21no—
53C4×Q8×C61—21no—
54C4×Q8×C61C2×C412yes—
55C4×Q8×C61D412yes—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C42×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—24no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61D412yes—
65#97×C61—24no—
66C4×C8×C61—21no—
67C4×C8×C61D412yes—
68C2×Q8×C61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61C22⋊C412yes—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—41no—
80C22×Dic61—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C2×C8×C61—22no—
91C2×C8×C61—22no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61C22⋊C412yes—
96C42×C61—22no—
97C42×C61—22no—
98C42×C61C22×C411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102#11758202—44no—
103#11758201—44no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110#11758194—41no—
111#11758194—41no—
112C2×#92418—22no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61#12111yescharacteristic
117C22×D61—41no—
118Q8×C61—22no—
119Q8×C61—22no—
120Q8×C61—41no—
121Q8×C61—41no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12311yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145D244—42no—
146D244—41no—
147D244—41no—
148D244—81no—
149C4×D61—81no—
150C4×D61—81no—
151Dic122—41no—
152Dic122—41no—
153C8×C61—42no—
154C8×C61—42no—
155#92418—42no—
156#92418—81no—
157#9310—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38611yescharacteristic
161C22×C61#46811yescharacteristic
162C22×C61#46911yescharacteristic
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—42no—
171C4×C61—42no—
172C4×C61#41711yescharacteristic
173C4×C61#41811yescharacteristic
174C4×C61#46811yescharacteristic
175C4×C61#46911yescharacteristic
176Dic61—81no—
177Dic61—161no—
178#3037—611no—
179#2983D6111yescharacteristic, complemented
180#1805—611no—
181#1517—611no—
182#1480—611no—
183#1301—611no—
184#1286—611no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#188111yescharacteristic
188C2×C61#189511yescharacteristic
189C2×C61#190511yescharacteristic
190D61—161no—
191C2×#137—1221no—
192#532—611no—
193C2×C4×Q8C2×D6111yescharacteristic
194#464—1222no—
195#462—612no—
196#460—612no—
197#446—22no—
198#446—22no—
199#432—22no—
200#431C2×D6111yescharacteristic
201#431C2×D6111yescharacteristic
202#423—611no—
203C2×C4⋊C8—611no—
204#417—1221no—
205C2×#103—1221no—
206#382—611no—
207#340—1221no—
208#327—1222no—
209D4⋊C8—1222no—
210C61#931011yescharacteristic, complemented, Sylow
211C2×#41—1221no—
212C22×Q8D24411yescharacteristic
213#137—2442no—
214#137—2442no—
215C2×Q16—1222no—
216C2×SD16—1222no—
217C2×M16—1221no—
218C22×C8—1221no—
219C4⋊Q8—611no—
220#127—611no—
221#124—1221no—
222#121—1221no—
223#121—1221no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C4×D6112yes—
227C4×Q8C22⋊D6112yes—
228C4×D4—1221no—
229C4×D4—1221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4D24411yescharacteristic
233C2×C42—21no—
234C2×C42C22×D6111yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—612no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242#103—1222no—
243#103—2442no—
244#102—1222no—
245C22⋊C8—21no—
246C22⋊C8C22⋊D6112yes—
247#97—24no—
248C4×C8—21no—
249C4×C8C22⋊D6112yes—
250#95—1221no—
251#95—1221no—
252#41—2441no—
253#41—2441no—
254#41—2441no—
255#41—2441no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—1221no—
262C2×Q8#1175819812yes—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—2441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4C2×D24411yescharacteristic
272C22×C4#1175822211yescharacteristic
273C22×C4C2×C22⋊D6111yescharacteristic
274Q16—2444no—
275SD16—2444no—
276M16—2441no—
277M16—2441no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—1222no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4#1175819812yes—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—22no—
295C42—22no—
296C42C2×C4×D6111yescharacteristic
297C42#1175822211yescharacteristic
298C42C2×C22⋊D6111yescharacteristic
299C42C2×C22⋊D6111yescharacteristic
300C23—2441no—
301C23#1451975111yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—41no—
305Q8—41no—
306Q8—2441no—
307Q8—2441no—
308D4—4881no—
309D4—4881no—
310D4—4881no—
311D4—2442no—
312D4—2441no—
313D4—2441no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—2441no—
327C2×C4C2×#1175819811yescharacteristic
328C2×C4C4×C22⋊D6111yescharacteristic
329C2×C4C4×C22⋊D6111yescharacteristic
330C2×C4#1451974611yescharacteristic
331C2×C4#1451975111yescharacteristic
332C2×C4#1451976011yescharacteristic
333C2×C4#1451980511yescharacteristic
334C2×C4#1451980511yescharacteristic
335C2×C4#1451980511yescharacteristic
336C2×C4#1451981011yescharacteristic
337C8—42no—
338C8—42no—
339C8—4881no—
340C8—2442no—
341C22—21no—
342C22—21no—
343C22—4881no—
344C22—4881no—
345C22—4881no—
346C22#1683964111yescharacteristic
347C22#1684000811yescharacteristic
348C22#1684001511yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—42no—
355C4—9761no—
356C4—4881no—
357C4#1683976411yescharacteristic
358C4#1683976811yescharacteristic
359C4#1684000811yescharacteristic
360C4#1684001511yescharacteristic
361C2—21no—
362C2—21no—
363C2—9761no—
364C2#2144618111yescharacteristic
365C2#2144625711yescharacteristic
366C2#2144631311yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9310
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #21445834C2semidirect
5. #21443715C2semidirect
6. #21443678C2semidirect
7. C61×#2983C2semidirect
11. #16839972C4semidirect
12. #16839962C4semidirect
179. #2983D61semidirect
210. C61#9310semidirect

Maximal subgroups

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

subgroupindex
#214552912
#214458342
#214443802
#214442192
#214437152
#214436782
C61×#29832
#931061