Finite Group Databasebeta

← #29576547

Subgroups — #29576547

Order 15616.

496 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#21456940C211yesmaximal, characteristic
2#21454565C211yesmaximal, characteristic
3#21444497C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1966C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10#16840165—21no—
11#16840110—21no—
12#16840075C414yes—
13#16840039—22no—
14#16839841—21no—
15#16839835—22no—
16C8×D244—21no—
17#16839815C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839730—21no—
21#16839509—21no—
22#16839508—21no—
23#16839508—21no—
24#16839505—21no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×#101×C61—21no—
28C2×#101×C61—21no—
29C4×M16×C61C2211yescharacteristic
30C2×#11758222—21no—
31#14519785—42no—
32#14519785—42no—
33C2×#11758189—22no—
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—22no—
37#14519777D411yescharacteristic
38#14519774D411yescharacteristic
39#14519765—21no—
40#14519751—21no—
41#14519751C2×C412yes—
42C4×D244—21no—
43C4×D244D412yes—
44#14519710—24no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418D411yescharacteristic
50C4⋊#92418D411yescharacteristic
51#14519697—24no—
52C22⋊#92418C2×C412yes—
53#14519689—22no—
54#14519689—22no—
55C4×#92418—21no—
56C22×Q8×C61—21no—
57C2×M16×C61—21no—
58C2×M16×C61D411yescharacteristic
59C2×M16×C61D411yescharacteristic
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61C2×C412yes—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#101×C61—42no—
70#101×C61—42no—
71#97×C61—21no—
72C4×C8×C61—21no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C22×C4×C61—22no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—22no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244C22⋊C412yes—
91C2×C4×D61—22no—
92C2×Dic122—21no—
93M16×C61—21no—
94M16×C61—21no—
95M16×C61—21no—
96M16×C61—41no—
97M16×C61—41no—
98M16×C61D812yes—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—41no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—22no—
111#11758198—22no—
112C4⋊Dic61—21no—
113C4⋊Dic61C22⋊C412yes—
114C2×#92418—22no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—81no—
121#11758189—44no—
122C8×D61—44no—
123C23×C61C4×D411yescharacteristic
124C22×D61—22no—
125Q8×C61—81no—
126Q8×C61—81no—
127Q8×C61—81no—
128Q8×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61C2×D811yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C22⋊D61—42no—
146C22⋊D61—42no—
147C2×Dic61—22no—
148D244—42no—
149D244—41no—
150D244—41no—
151D244—41no—
152D244—41no—
153C4×D61—42no—
154C4×D61—42no—
155Dic122—41no—
156Dic122—41no—
157C8×C61—22no—
158C8×C61—41no—
159C8×C61—81no—
160#92418—42no—
161#92418—41no—
162#92418—41no—
163#92418—81no—
164#9271—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61C4×D811yescharacteristic
169C22×C61#44211yescharacteristic
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—42no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61#44711yescharacteristic
178C4×C61#44911yescharacteristic
179C4×C61#45911yescharacteristic
180C4×C61#46311yescharacteristic
181C4×C61#47111yescharacteristic
182C4×C61#47311yescharacteristic
183Dic61—42no—
184#3226—611no—
185#2935—611no—
186#1966D6111yescharacteristic, complemented
187#1547—611no—
188C2×#332—611no—
189#1301—611no—
190#1283—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#187911yescharacteristic
194C2×C61#190811yescharacteristic
195C2×C61#191511yescharacteristic
196D61—82no—
197C2×#131—1221no—
198#532—611no—
199C2×C4⋊Q8C2×D6111yescharacteristic
200#500—1221no—
201#486—1221no—
202#480—614no—
203#474—1222no—
204#436—1221no—
205#435—1222no—
206C8×D4—1221no—
207#431—611no—
208#423C2×D6111yescharacteristic
209C2×C4⋊C8—611no—
210C2×C4⋊C8—611no—
211C2×#101—21no—
212C2×#101—21no—
213#408—1221no—
214C4×M16C2×D6111yescharacteristic
215#332—1221no—
216#332—1221no—
217#332—1221no—
218#331—1221no—
219C61#927111yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×Q8—21no—
222#131—2442no—
223#131—2442no—
224C2×M16—21no—
225C2×M16—1222no—
226C2×M16C22⋊D6111yescharacteristic
227C2×M16C22⋊D6111yescharacteristic
228C22×C8—1222no—
229C22×C8—1221no—
230C22×C8—1221no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—611no—
236#127—611no—
237#124—1221no—
238#121—612no—
239#121—1221no—
240C4×D4—612no—
241C4×D4—1221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C4×D6112yes—
244C2×C42C22×D6111yescharacteristic
245#107—1224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254#102—1224no—
255#101—42no—
256#101—42no—
257C22⋊C8—612no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260#97—21no—
261C4×C8—21no—
262C4×C8—1221no—
263#41—2441no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—1221no—
274C2×D4—612no—
275C2×D4—1222no—
276C2×D4—1221no—
277C2×D4—1221no—
278C22×C4—22no—
279C22×C4—1222no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4#1175822211yescharacteristic
282C22×C4C2×C22⋊D6111yescharacteristic
283M16—21no—
284M16—21no—
285M16—21no—
286M16—41no—
287M16—41no—
288M16—2444no—
289M16#1175819912yes—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—1222no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—4881no—
297C2×C8—2444no—
298C2×C8—2441no—
299C2×C8—2441no—
300C2×C8—2441no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—612no—
306C4⋊C4—1221no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C42D4×D6111yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C42#1175822411yescharacteristic
313C23—1222no—
314C23C4×C22⋊D6111yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—2441no—
320Q8—2441no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4—2441no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—1222no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4C22⋊C4×D6111yescharacteristic
338C2×C4#1451973711yescharacteristic
339C2×C4#1451974511yescharacteristic
340C2×C4#1451974811yescharacteristic
341C2×C4#1451975011yescharacteristic
342C2×C4#1451975911yescharacteristic
343C2×C4C2×#1175819911yescharacteristic
344C2×C4#1451979711yescharacteristic
345C2×C4#1451980211yescharacteristic
346C2×C4#1451980311yescharacteristic
347C8—22no—
348C8—41no—
349C8—81no—
350C8—4881no—
351C8—2442no—
352C8—2441no—
353C8—2441no—
354C22—21no—
355C22—21no—
356C22—2442no—
357C22—2442no—
358C22—2442no—
359C22#1683963811yescharacteristic
360C22C4×#1175819911yescharacteristic
361C22#1683987211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—2442no—
367C4#1683989511yescharacteristic
368C4#1683990511yescharacteristic
369C4#1683995411yescharacteristic
370C4#1683997411yescharacteristic
371C4#1684002811yescharacteristic
372C4#1684003611yescharacteristic
373C2—21no—
374C2—21no—
375C2—4882no—
376C2#2144617011yescharacteristic
377C2#2144633111yescharacteristic
378C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1966C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1966D61
hypocenterC61#9271
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
4. C2×#16839508C2semidirect
5. #21443714C2semidirect
6. #21443670C2semidirect
7. C61×#1966C2semidirect
186. #1966D61semidirect
219. C61#9271semidirect

Maximal subgroups

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

subgroupindex
#214569402
#214545652
#214444972
C2×#168395082
#214437142
#214436702
C61×#19662
#927161