Finite Group Databasebeta

← #29597198

Subgroups — #29597198

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454703C211yesmaximal, characteristic, complemented
2#21447555C211yesmaximal, characteristic, complemented
3C2×#16839572C211yesmaximal, characteristic, complemented
4#21446718C211yesmaximal, characteristic, complemented
5#21443925C211yesmaximal, characteristic, complemented
6#21443906C211yesmaximal, characteristic, complemented
7C61×#3414C211yesmaximal, characteristic
8#16840245—21no—
9C2×#14519717C2211yescharacteristic
10#16839874—21no—
11#16839869—21no—
12SD16×Dic61—22no—
13#16839800C2211yescharacteristic
14C2×#14519709C2211yescharacteristic
15#16839779—21no—
16#16839763—21no—
17#16839736—21no—
18#16839717C2211yescharacteristic
19#16839572—22no—
20#16839572—22no—
21C2×#135×C61C2211yescharacteristic
22C2×#135×C61C2211yescharacteristic
23C61×#510—21no—
24C61×#510C412yescomplemented
25C61×#509—21no—
26C61×#509C412yescomplemented
27C61×#508—22no—
28C2×M32×C61C2211yescharacteristic
29C2×#11758194D411yescharacteristic
30Q8×Dic61—22no—
31D4×Dic61—22no—
32D4×Dic61—42no—
33#14519736—21no—
34#14519736—41no—
35#14519736D411yescharacteristic
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—41no—
38#14519717—21no—
39#14519717—21no—
40C2×#11758185—21no—
41#14519711—21no—
42#14519709—21no—
43#14519709—21no—
44#14519709D412yes—
45#14519704—42no—
46#14519701—22no—
47#14519698—22no—
48#14519692—42no—
49#14519687—21no—
50C8×Dic61—21no—
51C2×#41×C61—21no—
52C2×#41×C61—21no—
53#135×C61—21no—
54#135×C61—21no—
55#135×C61—21no—
56#135×C61—21no—
57#135×C61—21no—
58#135×C61—21no—
59#135×C61C2×C412yes—
60#135×C61D412yes—
61C2×Q16×C61C2×C411yescharacteristic, complemented
62C2×Q16×C61D411yescharacteristic
63C2×SD16×C61—21no—
64C2×SD16×C61—21no—
65C2×D8×C61C2×C411yescharacteristic, complemented
66C2×D8×C61D411yescharacteristic
67C22×C8×C61C2311yescharacteristic
68Q32×C61—22no—
69SD32×C61—22no—
70SD32×C61—22no—
71D16×C61—22no—
72M32×C61—21no—
73M32×C61C2×C412yescomplemented
74C2×C16×C61—21no—
75#41×C61—22no—
76#41×C61—22no—
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80#41×C61—41no—
81#41×C61—41no—
82#41×C61—41no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—42no—
93C22×Dic61—41no—
94Q16×C61—21no—
95Q16×C61—21no—
96Q16×C61—21no—
97Q16×C61C22⋊C412yes—
98SD16×C61—22no—
99SD16×C61—22no—
100SD16×C61—41no—
101SD16×C61—41no—
102D8×C61—21no—
103D8×C61—21no—
104D8×C61—21no—
105D8×C61C22⋊C412yes—
106C2×C8×C61C22×C411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61#4111yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C22⋊Dic61—42no—
113C22⋊Dic61—41no—
114C22⋊Dic61D812yes—
115C4⋊Dic61—21no—
116C4⋊Dic61—22no—
117C4⋊Dic61—42no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4×Dic61—21no—
121C4×Dic61—42no—
122C4×Dic61—41no—
123#11758194—21no—
124#11758194—21no—
125C2×#92418—21no—
126C16×C61—22no—
127#11758185—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61C2×D811yescharacteristic
131Q8×C61—22no—
132Q8×C61—41no—
133Q8×C61—41no—
134Q8×C61—41no—
135D4×C61—22no—
136D4×C61—42no—
137D4×C61—42no—
138D4×C61—41no—
139D4×C61—41no—
140D4×C61—41no—
141D4×C61—81no—
142D4×C61—81no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—42no—
157C2×Dic61—81no—
158C2×Dic61—162no—
159C2×Dic61—161no—
160C8×C61C2×C22⋊C411yescharacteristic
161C8×C61C4×D411yescharacteristic
162C8×C61#12111yescharacteristic
163C8×C61#12311yescharacteristic
164#92418—41no—
165#13030—611nomaximal, Sylow
166C22×C61—41no—
167C22×C61—42no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—161no—
172C22×C61C4×D811yescharacteristic
173C22×C61#44711yescharacteristic
174C22×C61#45911yescharacteristic
175C4×C61—42no—
176C4×C61—81no—
177C4×C61#38611yescharacteristic
178C4×C61#44211yescharacteristic
179C4×C61#44911yescharacteristic
180C4×C61#46311yescharacteristic
181Dic61—42no—
182Dic61—82no—
183Dic61—161no—
184#3414D6111yescharacteristic
185#2952—611no—
186#2145—611no—
187C2×#360—611no—
188#1976—611no—
189#1386—611no—
190#1378—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—82no—
195C2×C61—161no—
196C2×C61#187911yescharacteristic
197C2×#135C2×D6111yescharacteristic
198C2×#135C2×D6111yescharacteristic
199#520—1221no—
200#510—21no—
201#510Dic6112yescomplemented
202#509—21no—
203#509Dic6112yescomplemented
204#508—22no—
205C2×M32—611no—
206C2×M32C2×D6111yescharacteristic
207#442—1221no—
208#441—1221no—
209C4×SD16—1222no—
210#427—611no—
211C2×#106—611no—
212#421—1221no—
213#417—1221no—
214#410—1221no—
215#405—611no—
216#360—1222no—
217#360—1222no—
218C61#1303011yescharacteristic, complemented, Sylow
219C2×#41—21no—
220C2×#41—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135C2×Dic6112yes—
228#135C22⋊D6112yes—
229C2×Q16C2×Dic6111yescharacteristic, complemented
230C2×Q16C22⋊D6111yescharacteristic
231C2×SD16—21no—
232C2×SD16—21no—
233C2×D8C2×Dic6111yescharacteristic, complemented
234C2×D8C22⋊D6111yescharacteristic
235C2×M16—611no—
236C22×C8C22×D6111yescharacteristic
237C4×Q8—1222no—
238C4×D4—1222no—
239C4×D4—2442no—
240#117—611no—
241#117—1221no—
242#117—2441no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—2441no—
245Q32—22no—
246SD32—22no—
247SD32—22no—
248D16—22no—
249M32—21no—
250M32—1221no—
251M32—1221no—
252M32C2×Dic6112yescomplemented
253C2×C16—21no—
254C2×C16—1221no—
255#107—1221no—
256#106—612no—
257#106—1221no—
258#106—1221no—
259#104—2442no—
260#103—1222no—
261#102—1222no—
262#99—2442no—
263#97—1221no—
264C4×C8—1221no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—2442no—
282C22×C4—2441no—
283C22×C4D4×D6111yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊Dic6112yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊Dic6112yes—
296M16—1221no—
297M16—1221no—
298C2×C8—1221no—
299C2×C8D4×D6111yescharacteristic
300C2×C8#1175822411yescharacteristic
301C2×C8#1175822411yescharacteristic
302C2×C8C22×Dic6111yescharacteristic
303C2×C8C2×C22⋊D6111yescharacteristic
304C2×C8C2×C22⋊D6111yescharacteristic
305C4⋊C4—1221no—
306C4⋊C4—1222no—
307C4⋊C4—2442no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—612no—
311C22⋊C4—2442no—
312C22⋊C4—2441no—
313C42—1221no—
314C42—2442no—
315C42—2441no—
316C16—22no—
317C16—2441no—
318C23—41no—
319C23—41no—
320C23D8×D6111yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—1222no—
340C2×C4—9761no—
341C2×C4—9762no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4D4×Dic6111yescharacteristic
345C2×C4#1451974511yescharacteristic
346C2×C4#1451974911yescharacteristic
347C2×C4#1451979611yescharacteristic
348C2×C4#1451980111yescharacteristic
349C2×C4#1451980111yescharacteristic
350C8—2441no—
351C8C2×C22⋊Dic6111yescharacteristic
352C8D4×Dic6111yescharacteristic
353C8#1451974911yescharacteristic
354C8#1451975811yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22D8×Dic6111yescharacteristic
362C22#1683989411yescharacteristic
363C22#1683995511yescharacteristic
364C4—42no—
365C4—81no—
366C4—9761no—
367C4—4882no—
368C4—2442no—
369C4#1683964211yescharacteristic
370C4#1683987411yescharacteristic
371C4#1683990411yescharacteristic
372C4#1683997511yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2#2144616911yescharacteristic
subgroupG/H
centerC2#21446169
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
Fitting, prime radicalC61×#3414C2
socleC2×C61#1879
cosocleC22×C8×C61C23
hypercenter#3414D61
hypocenterC61#13030
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #21454703C2semidirect
2. #21447555C2semidirect
3. C2×#16839572C2semidirect
4. #21446718C2semidirect
5. #21443925C2semidirect
6. #21443906C2semidirect
24. C61×#510C4semidirect
26. C61×#509C4semidirect
61. C2×Q16×C61C2×C4semidirect
65. C2×D8×C61C2×C4semidirect
73. M32×C61C2×C4semidirect
201. #510Dic61semidirect
203. #509Dic61semidirect
218. C61#13030semidirect
229. C2×Q16C2×Dic61semidirect
233. C2×D8C2×Dic61semidirect
252. M32C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#214547032
#214475552
C2×#168395722
#214467182
#214439252
#214439062
C61×#34142
#1303061