Finite Group Databasebeta

← #29596971

Subgroups — #29596971

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455539C211yesmaximal, characteristic
2#21447546C211yesmaximal, characteristic, complemented
3C2×#16839568C211yesmaximal, characteristic, complemented
4C2×#16839546C211yesmaximal, characteristic, complemented
5#21443930C211yesmaximal, characteristic, complemented
6#21443912C211yesmaximal, characteristic, complemented
7C61×#2916C211yesmaximal, characteristic, complemented
8#16840560—21no—
9C2×#14519799C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16840037C412yes—
13#16840032C412yes—
14#16840025—22no—
15C2×#14519713C2211yescharacteristic
16#16839744—21no—
17#16839568—22no—
18#16839568—22no—
19#16839546—22no—
20C61×#568—21no—
21C2×#131×C61C2211yescharacteristic
22C61×#430—21no—
23C61×#430—22no—
24C2×#108×C61—22no—
25C2×#108×C61C2211yescharacteristic
26C2×#108×C61C2211yescharacteristic
27C2×#11758222—21no—
28#14519808—41no—
29#14519807—22no—
30#14519803—41no—
31#14519802—22no—
32#14519799—21no—
33#14519799—21no—
34#14519799—21no—
35#14519799—21no—
36#14519797—42no—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40C2×#11758194—21no—
41#14519717—21no—
42#14519717—21no—
43C2×#11758185—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47#14519713—21no—
48#14519713C2×C412yes—
49#14519695—22no—
50#14519693—22no—
51C2×#41×C61D411yescharacteristic
52#131×C61—21no—
53#131×C61—21no—
54#131×C61—42no—
55#131×C61—42no—
56#131×C61C2×C412yes—
57#131×C61D412yes—
58C2×M16×C61—21no—
59C2×M16×C61—24no—
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C2×M16×C61D411yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61C2311yescharacteristic
65#108×C61—24no—
66#108×C61—21no—
67#108×C61—21no—
68#108×C61D412yes—
69#108×C61D412yes—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61C22⋊C412yes—
73#41×C61D812yes—
74C2×Q8×C61SD1611yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61SD1611yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—41no—
80#11758222—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84C2×D244—21no—
85C2×C4×D61—41no—
86C2×Dic122—21no—
87M16×C61—21no—
88M16×C61—22no—
89M16×C61—22no—
90M16×C61—22no—
91M16×C61—22no—
92M16×C61—44no—
93M16×C61—41no—
94M16×C61—41no—
95M16×C61C22⋊C412yes—
96C2×C8×C61—21no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—44no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61C22×C411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61#4111yescharacteristic
107C2×C8×C61#4111yescharacteristic
108#11758202—42no—
109#11758201—42no—
110#11758200—42no—
111#11758199—42no—
112#11758194—22no—
113#11758194—41no—
114C2×#92418—41no—
115Dic244—21no—
116Dic244—21no—
117D488—21no—
118D488—21no—
119#11758190—41no—
120#11758190—41no—
121#11758185—41no—
122#11758185—41no—
123C23×C61—21no—
124C23×C61#13711yescharacteristic
125C22×D61—41no—
126Q8×C61—21no—
127Q8×C61#10212yes—
128D4×C61—22no—
129D4×C61—22no—
130D4×C61—21no—
131D4×C61#10212yes—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12311yescharacteristic
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—41no—
144D244—41no—
145D244—41no—
146C4×D61—81no—
147C4×D61—81no—
148Dic122—41no—
149Dic122—41no—
150C8×C61—22no—
151C8×C61—42no—
152C8×C61—42no—
153C8×C61C4×D411yescharacteristic
154C8×C61C4×D411yescharacteristic
155C8×C61#12111yescharacteristic
156C8×C61#12111yescharacteristic
157#92418—42no—
158#12995—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—81no—
162C22×C61#41711yescharacteristic
163C22×C61#44811yescharacteristic
164C22×C61#48011yescharacteristic
165C2×D61—81no—
166C2×D61—161no—
167C4×C61—22no—
168C4×C61#38611yescharacteristic
169C4×C61C2×#10211yescharacteristic
170C4×C61#44711yescharacteristic
171C4×C61#48111yescharacteristic
172Dic61—81no—
173#3067—611no—
174#2916D6111yescharacteristic, complemented
175#2143—611no—
176C2×#359—611no—
177C2×#350—611no—
178#1388—611no—
179#1381—611no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—42no—
184C2×C61#187411yescharacteristic
185D61—161no—
186#575—1221no—
187C2×#135—611no—
188#568—21no—
189C2×#131C2×D6111yescharacteristic
190C2×M32—611no—
191C22×C16—611no—
192#473—612no—
193#472—612no—
194#471—1222no—
195#430—21no—
196#430—22no—
197C2×#108—22no—
198C2×#108—611no—
199C2×#108C2×D6111yescharacteristic
200C2×#108C2×D6111yescharacteristic
201#413—1221no—
202#359—1222no—
203#359—1222no—
204#350—1222no—
205C61#1299511yescharacteristic, complemented, Sylow
206C2×#41—1221no—
207C2×#41C22⋊D6111yescharacteristic
208#137—1222no—
209#137—2441no—
210AGL(1,ℤ/8)—1222no—
211AGL(1,ℤ/8)—2441no—
212#135—1221no—
213#135—1221no—
214#135—1221no—
215#135—1221no—
216#135—2442no—
217C2×Q16—611no—
218C2×SD16—1221no—
219C2×D8—611no—
220#131—21no—
221#131—21no—
222#131—42no—
223#131—42no—
224#131C4×D6112yes—
225#131D24412yes—
226C2×M16—21no—
227C2×M16—24no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—1221no—
231C2×M16C22⋊D6111yescharacteristic
232C22×C8—21no—
233C22×C8C22×D6111yescharacteristic
234M32—1221no—
235M32—1221no—
236C2×C16—1221no—
237C2×C16—1221no—
238C2×C16—1221no—
239C2×C16—1221no—
240#108—24no—
241#108—21no—
242#108—21no—
243#108—612no—
244#108—1221no—
245#108C22⋊D6112yes—
246#108C22⋊D6112yes—
247#101—1222no—
248#100—1222no—
249#41—21no—
250#41—21no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254#41—2441no—
255#41#1175819812yes—
256#41#1175819912yes—
257C2×Q8—1221no—
258C2×Q8#1175820111yescharacteristic
259C2×D4—21no—
260C2×D4—1221no—
261C2×D4—2441no—
262C2×D4#1175820111yescharacteristic
263C22×C4—21no—
264C22×C4—2441no—
265C22×C4C2×C22⋊D6111yescharacteristic
266Q16—1221no—
267Q16—1221no—
268Q16—2442no—
269SD16—2442no—
270SD16—2442no—
271SD16—2441no—
272SD16—2441no—
273D8—1221no—
274D8—1221no—
275D8—2442no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—44no—
282M16—41no—
283M16—41no—
284M16—1222no—
285M16—2441no—
286M16#1175819812yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—2441no—
294C2×C8C2×C4×D6111yescharacteristic
295C2×C8C2×D24411yescharacteristic
296C2×C8#1175822211yescharacteristic
297C2×C8#1175822211yescharacteristic
298C2×C8C2×C22⋊D6111yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C16—2441no—
301C16—2441no—
302C23—21no—
303C23—2441no—
304C23#1451980811yescharacteristic
305Q8—21no—
306Q8—2441no—
307Q8—2441no—
308Q8#1451969712yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—4881no—
313D4—4881no—
314D4—2441no—
315D4—2441no—
316D4#1451969712yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—2441no—
323C2×C4C2×#1175819811yescharacteristic
324C2×C4#1451974611yescharacteristic
325C2×C4#1451976011yescharacteristic
326C2×C4C2×#1175819911yescharacteristic
327C2×C4C2×#1175820111yescharacteristic
328C2×C4#1451980311yescharacteristic
329C8—22no—
330C8—42no—
331C8—42no—
332C8—2442no—
333C8C4×C22⋊D6111yescharacteristic
334C8C4×C22⋊D6111yescharacteristic
335C8#1451975111yescharacteristic
336C8#1451975111yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—9761no—
341C22—4881no—
342C22#1683976111yescharacteristic
343C22#1683990111yescharacteristic
344C22#1684007511yescharacteristic
345C4—22no—
346C4—4881no—
347C4#1683964111yescharacteristic
348C4C2×#1451969711yescharacteristic
349C4#1683989611yescharacteristic
350C4#1684008011yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—9761no—
356C2#2144613611yescharacteristic
subgroupG/H
centerC4#16839896
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2916C2
socleC2×C61#1874
prime radical#21455539C2
cosocleC22×C8×C61C23
hypercenter#2916D61
hypocenterC61#12995
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #2916

Complements

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

NH ≅ G/Ntype
2. #21447546C2semidirect
3. C2×#16839568C2semidirect
4. C2×#16839546C2semidirect
5. #21443930C2semidirect
6. #21443912C2semidirect
7. C61×#2916C2semidirect
174. #2916D61semidirect
205. C61#12995semidirect

Maximal subgroups

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

subgroupindex
#214555392
#214475462
C2×#168395682
C2×#168395462
#214439302
#214439122
C61×#29162
#1299561