Finite Group Databasebeta

← #29576698

Subgroups — #29576698

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456734C211yesmaximal, characteristic
2#21446643C211yesmaximal, characteristic, complemented
3#21444488C211yesmaximal, characteristic, complemented
4#21444379C211yesmaximal, characteristic, complemented
5#21443679C211yesmaximal, characteristic, complemented
6#21443650C211yesmaximal, characteristic, complemented
7C61×#2932C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840138C412yescomplemented
10#16840110C412yescomplemented
11#16839957—22no—
12#16839895—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15C2×#14519699—21no—
16C2×#14519699—21no—
17#16839628C2211yescharacteristic
18#16839505—22no—
19#16839496—22no—
20C2×#131×C61—21no—
21C61×#532C2211yescharacteristic
22C61×#435—22no—
23C61×#435—22no—
24C61×#423C2211yescharacteristic
25C61×#408—21no—
26C2×#97×C61C2211yescharacteristic
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758199—24no—
31#14519774—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774C2×C412yes—
35C2×C4⋊Dic61—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38#14519699—42no—
39#14519699—42no—
40#14519697—24no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C4×#92418—21no—
44C4×#92418C2×C412yes—
45#14519684—21no—
46#14519684—21no—
47C2×#41×C61—21no—
48#131×C61—42no—
49#131×C61—42no—
50C2×M16×C61—22no—
51C2×M16×C61—21no—
52C22×C8×C61—22no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61D411yescharacteristic
55C4⋊Q8×C61C2×C411yescharacteristic
56#127×C61C2×C411yescharacteristic
57#124×C61—21no—
58#121×C61—21no—
59#121×C61D412yes—
60C4×D4×C61—21no—
61C4×D4×C61D412yes—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C22⋊C8×C61—24no—
66#97×C61—21no—
67#97×C61—21no—
68C23×D61—41no—
69#41×C61—41no—
70#41×C61—41no—
71#41×C61—41no—
72#41×C61—41no—
73C2×Q8×C61—21no—
74C2×D4×C61—22no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61C22⋊C412yes—
78C22×C4×C61—22no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×Dic61—41no—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—22no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—82no—
94C2×D244—82no—
95M16×C61—44no—
96M16×C61—41no—
97M16×C61—41no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—22no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—44no—
105C2×C8×C61D812yescomplemented
106C4⋊C4×C61—21no—
107C4⋊C4×C61C22⋊C412yes—
108C22⋊C4×C61—22no—
109C22⋊C4×C61—22no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114#11758199—84no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C2×#92418—22no—
118C2×#92418—41no—
119C23×C61—22no—
120C23×C61#12111yescharacteristic
121C22×D61—42no—
122C22×D61—82no—
123C22×D61—82no—
124C22×D61—81no—
125C22×D61—81no—
126Q8×C61—41no—
127Q8×C61—41no—
128D4×C61—42no—
129D4×C61—42no—
130D4×C61—42no—
131D4×C61—41no—
132D4×C61—41no—
133D4×C61—81no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152D244—44no—
153D244—42no—
154D244—42no—
155D244—82no—
156D244—82no—
157D244—82no—
158D244—81no—
159D244—81no—
160C8×C61—22no—
161C8×C61—42no—
162C8×C61—41no—
163#92418—42no—
164#92418—81no—
165#9293—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61#38611yescharacteristic
172C22×C61#45911yescharacteristic
173C22×C61#46311yescharacteristic
174C2×D61—82no—
175C2×D61—82no—
176C2×D61—82no—
177C2×D61—162no—
178C2×D61—162no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—42no—
184C4×C61C4×D811yescharacteristic
185C4×C61#44211yescharacteristic
186C4×C61#44711yescharacteristic
187C4×C61#44911yescharacteristic
188Dic61—161no—
189#3205—611no—
190#2932D6111yescharacteristic, complemented
191#1961—611no—
192#1545—611no—
193#1517—611no—
194#1286—611no—
195#1275—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—82no—
199C2×C61#187911yescharacteristic
200C2×C61#190311yescharacteristic
201C2×C61#191011yescharacteristic
202D61—162no—
203C2×#131—21no—
204#532C2×D6111yescharacteristic
205C2×#127—611no—
206#493—612no—
207#486—612no—
208#459—1222no—
209#447—1222no—
210#435—22no—
211#435—22no—
212#431—611no—
213#431—611no—
214#423C2×D6111yescharacteristic
215C2×#102—1221no—
216C2×#102—1221no—
217#408—21no—
218C2×#97C2×D6111yescharacteristic
219#382—611no—
220#331—1222no—
221#327—1222no—
222C61#929311yescharacteristic, complemented, Sylow
223C2×#41—21no—
224C22×D4—1221no—
225C22×D4—1221no—
226C22×D4—1221no—
227C2×D8—1224no—
228#131—42no—
229#131—42no—
230C2×M16—22no—
231C2×M16—21no—
232C22×C8—22no—
233C22×C8C22⋊D6111yescharacteristic
234C22×C8C22⋊D6111yescharacteristic
235C4⋊Q8C4×D6111yescharacteristic
236#127—612no—
237#127—1221no—
238#127—1221no—
239#127—1221no—
240#127C4×D6111yescharacteristic
241#124—21no—
242#121—21no—
243#121D24412yes—
244C4×D4—21no—
245C4×D4C22⋊D6112yes—
246C2×C4⋊C4—1221no—
247C2×C42C22×D6111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8C22⋊D6112yes—
252#102—1224no—
253#102—2442no—
254#102—2442no—
255C22⋊C8—24no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258#97—21no—
259#97—21no—
260C4×C8—612no—
261C4×C8—1221no—
262#95—1221no—
263#95—1221no—
264C24—2441no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—22no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—1222no—
274C2×D4—1222no—
275C2×D4—1222no—
276C2×D4—4882no—
277C2×D4—4882no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4#1175819812yes—
286C22×C4—22no—
287C22×C4—2441no—
288C22×C4C2×D24411yescharacteristic
289C22×C4#1175822211yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291D8—4884no—
292M16—44no—
293M16—41no—
294M16—41no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—22no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—44no—
302C2×C8—1222no—
303C2×C8—2441no—
304C2×C8#1175819912yescomplemented
305C4⋊C4—21no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4#1175819812yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42C2×C4×D6111yescharacteristic
312C42#1175822211yescharacteristic
313C42C2×C22⋊D6111yescharacteristic
314C42C2×C22⋊D6111yescharacteristic
315C23—22no—
316C23—4882no—
317C23—4882no—
318C23—4881no—
319C23—4881no—
320C23—2442no—
321C23#1451975111yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—4882no—
331D4—4882no—
332D4—4882no—
333D4—4881no—
334D4—4881no—
335D4—2444no—
336D4—2442no—
337D4—2442no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4C2×#1175819811yescharacteristic
347C2×C4C4×C22⋊D6111yescharacteristic
348C2×C4C4×C22⋊D6111yescharacteristic
349C2×C4#1451974611yescharacteristic
350C2×C4#1451975111yescharacteristic
351C2×C4#1451976011yescharacteristic
352C2×C4C2×#1175819911yescharacteristic
353C2×C4#1451979711yescharacteristic
354C2×C4#1451980211yescharacteristic
355C2×C4#1451980311yescharacteristic
356C8—22no—
357C8—42no—
358C8—41no—
359C8—4881no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—9762no—
367C22—9762no—
368C22—4882no—
369C22—4882no—
370C22—4882no—
371C22#1683964111yescharacteristic
372C22#1683995711yescharacteristic
373C22#1683997711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—9761no—
380C4C4×#1175819911yescharacteristic
381C4#1683987211yescharacteristic
382C4#1683989611yescharacteristic
383C4#1683990711yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—9762no—
388C2#2144616711yescharacteristic
389C2#2144629911yescharacteristic
390C2#2144634611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2932C2
socleC22×C61#386
prime radical#21456734C2
cosocleC2×C42×C61C23
hypercenter#2932D61
hypocenterC61#9293
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #21446643C2semidirect
3. #21444488C2semidirect
4. #21444379C2semidirect
5. #21443679C2semidirect
6. #21443650C2semidirect
7. C61×#2932C2semidirect
9. #16840138C4semidirect
10. #16840110C4semidirect
105. C2×C8×C61D8semidirect
190. #2932D61semidirect
222. C61#9293semidirect
304. C2×C8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214567342
#214466432
#214444882
#214443792
#214436792
#214436502
C61×#29322
#929361