Finite Group Databasebeta

← #29596973

Subgroups — #29596973

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#21454430C211yesmaximal, characteristic, complemented
2#21447547C211yesmaximal, characteristic, complemented
3C2×#16839569C211yesmaximal, characteristic, complemented
4C2×#16839546C211yesmaximal, characteristic, complemented
5#21443932C211yesmaximal, characteristic, complemented
6#21443912C211yesmaximal, characteristic, complemented
7C61×#3067C211yesmaximal, characteristic
8#16840529—21no—
9C2×#14519717C2211yescharacteristic
10C22×#11758185C2211yescharacteristic
11#16839811—22no—
12#16839811—21no—
13C2×#14519713—22no—
14C2×#14519713C2211yescharacteristic
15C2×#14519713C2211yescharacteristic
16#16839569—22no—
17#16839569—22no—
18#16839546—22no—
19C61×#575—21no—
20C2×#135×C61C2211yescharacteristic
21C2×#131×C61C2211yescharacteristic
22C61×#473C412yes—
23C61×#472C412yes—
24C61×#471—22no—
25C2×#108×C61C2211yescharacteristic
26C61×#413—21no—
27#14519784—42no—
28#14519784—42no—
29C2×#11758194—24no—
30C2×#11758194—21no—
31C2×#11758194—21no—
32#14519717—21no—
33#14519717—21no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36C2×#11758185—21no—
37C2×#11758185—21no—
38#14519713—24no—
39#14519713—21no—
40#14519713—21no—
41#14519713D412yes—
42#14519713D412yes—
43C2×#41×C61—21no—
44C2×#41×C61D411yescharacteristic
45#137×C61—22no—
46#137×C61—41no—
47AGL(1,ℤ/8)×C61—22no—
48AGL(1,ℤ/8)×C61—41no—
49#135×C61—21no—
50#135×C61—21no—
51#135×C61—21no—
52#135×C61—21no—
53#135×C61—42no—
54C2×Q16×C61C2×C411yescharacteristic
55C2×SD16×C61—21no—
56C2×D8×C61C2×C411yescharacteristic
57#131×C61—21no—
58#131×C61—21no—
59#131×C61C2×C412yes—
60#131×C61D412yes—
61C2×M16×C61—21no—
62C2×M16×C61—21no—
63C2×M16×C61D411yescharacteristic
64C22×C8×C61—21no—
65C22×C8×C61C2311yescharacteristic
66#108×C61—21no—
67#108×C61C2×C412yes—
68#101×C61—22no—
69#100×C61—22no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61—41no—
73#41×C61—41no—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61C22⋊C412yes—
77#41×C61D812yes—
78C2×Q8×C61—21no—
79C2×Q8×C61SD1611yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C2×D4×C61SD1611yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87Q16×C61—21no—
88Q16×C61—21no—
89Q16×C61—42no—
90SD16×C61—42no—
91SD16×C61—42no—
92SD16×C61—41no—
93SD16×C61—41no—
94D8×C61—21no—
95D8×C61—21no—
96D8×C61—42no—
97M16×C61—21no—
98M16×C61—22no—
99M16×C61—22no—
100M16×C61—22no—
101M16×C61—41no—
102M16×C61C22⋊C412yes—
103C2×C8×C61—21no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61C22×C411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C2×C8×C61#4111yescharacteristic
113#11758194—22no—
114#11758194—22no—
115#11758194—44no—
116#11758194—41no—
117#11758194—41no—
118C2×#92418—44no—
119C2×#92418—41no—
120C2×#92418—41no—
121#11758185—41no—
122#11758185—41no—
123C23×C61—21no—
124C23×C61—41no—
125C23×C61#13711yescharacteristic
126Q8×C61—21no—
127Q8×C61—41no—
128Q8×C61—41no—
129Q8×C61#10212yes—
130D4×C61—22no—
131D4×C61—22no—
132D4×C61—21no—
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—81no—
136D4×C61—81no—
137D4×C61#10212yes—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C8×C61—22no—
151C8×C61—42no—
152C8×C61C4×D411yescharacteristic
153C8×C61C4×D411yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12111yescharacteristic
156#92418—42no—
157#92418—42no—
158#12995—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—161no—
164C22×C61#41711yescharacteristic
165C22×C61#44811yescharacteristic
166C22×C61#48011yescharacteristic
167C4×C61—22no—
168C4×C61—81no—
169C4×C61#38611yescharacteristic
170C4×C61C2×#10211yescharacteristic
171C4×C61#44711yescharacteristic
172C4×C61#48111yescharacteristic
173#3067D6111yescharacteristic
174#2916—611no—
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—161no—
185C2×C61#187411yescharacteristic
186#575—21no—
187C2×#135C2×D6111yescharacteristic
188#568—1221no—
189C2×#131C2×D6111yescharacteristic
190C2×M32—611no—
191C22×C16—611no—
192#473Dic6112yes—
193#472Dic6112yes—
194#471—22no—
195#430—1222no—
196#430—1221no—
197C2×#108—611no—
198C2×#108—611no—
199C2×#108—1222no—
200C2×#108C2×D6111yescharacteristic
201#413—21no—
202#359—1222no—
203#359—1222no—
204#350—1222no—
205C61#1299511yescharacteristic, complemented, Sylow
206C2×#41—21no—
207C2×#41C22⋊D6111yescharacteristic
208#137—22no—
209#137—41no—
210AGL(1,ℤ/8)—22no—
211AGL(1,ℤ/8)—41no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—42no—
217C2×Q16C2×Dic6111yescharacteristic
218C2×SD16—21no—
219C2×D8C2×Dic6111yescharacteristic
220#131—21no—
221#131—21no—
222#131—2442no—
223#131—2442no—
224#131C2×Dic6112yes—
225#131C22⋊D6112yes—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—1224no—
229C2×M16—1221no—
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—21no—
241#108—612no—
242#108—612no—
243#108—1224no—
244#108—1221no—
245#108—1221no—
246#108C2×Dic6112yes—
247#101—22no—
248#100—22no—
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41#1175819912yes—
256#41C22⋊Dic6112yes—
257C2×Q8—21no—
258C2×Q8#1175820011yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4#1175820011yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4C2×C22⋊D6111yescharacteristic
266Q16—21no—
267Q16—21no—
268Q16—42no—
269SD16—42no—
270SD16—42no—
271SD16—41no—
272SD16—41no—
273D8—21no—
274D8—21no—
275D8—42no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—41no—
281M16—1222no—
282M16—1222no—
283M16—2444no—
284M16—2441no—
285M16—2441no—
286M16C22⋊Dic6112yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—2444no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8D4×D6111yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C2×C8#1175822411yescharacteristic
297C2×C8#1175822411yescharacteristic
298C2×C8C22×Dic6111yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C16—2441no—
301C16—2441no—
302C23—21no—
303C23—41no—
304C23#1451980711yescharacteristic
305Q8—21no—
306Q8—41no—
307Q8—41no—
308Q8#1451969812yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316D4#1451969812yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊Dic6111yescharacteristic
324C2×C4#1451974511yescharacteristic
325C2×C4#1451975811yescharacteristic
326C2×C4C2×#1175819911yescharacteristic
327C2×C4C2×#1175820011yescharacteristic
328C2×C4#1451980211yescharacteristic
329C8—22no—
330C8—42no—
331C8—2442no—
332C8—2442no—
333C8D4×Dic6111yescharacteristic
334C8D4×Dic6111yescharacteristic
335C8#1451974911yescharacteristic
336C8#1451974911yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—81no—
341C22—161no—
342C22#1683976311yescharacteristic
343C22#1683990011yescharacteristic
344C22#1684007311yescharacteristic
345C4—22no—
346C4—81no—
347C4#1683964211yescharacteristic
348C4C2×#1451969811yescharacteristic
349C4#1683989511yescharacteristic
350C4#1684007811yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2#2144613711yescharacteristic
subgroupG/H
centerC4#16839895
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
Fitting, prime radicalC61×#3067C2
socleC2×C61#1874
cosocleC22×C8×C61C23
hypercenter#3067D61
hypocenterC61#12995
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #21454430C2semidirect
2. #21447547C2semidirect
3. C2×#16839569C2semidirect
4. C2×#16839546C2semidirect
5. #21443932C2semidirect
6. #21443912C2semidirect
205. C61#12995semidirect

Maximal subgroups

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

subgroupindex
#214544302
#214475472
C2×#168395692
C2×#168395462
#214439322
#214439122
C61×#30672
#1299561