Finite Group Databasebeta

← #29576541

Subgroups — #29576541

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#21454562C211yesmaximal, characteristic
3#21446664C211yesmaximal, characteristic, complemented
4#21444494C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443669C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9#16840312C2211yescharacteristic
10#16840165—21no—
11#16840110—21no—
12#16840075C414yes—
13#16840039—22no—
14#16839839—21no—
15#16839832—22no—
16#16839827—21no—
17#16839815C2211yescharacteristic
18#16839786C2211yescharacteristic
19C2×#14519696—21no—
20C2×#14519696—21no—
21#16839728—21no—
22C4×#11758194C2211yescharacteristic
23#16839507—21no—
24#16839505—21no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#332—21no—
29C61×#332—21no—
30C2×#11758222—21no—
31#14519783—42no—
32#14519783—42no—
33C2×#11758194—21no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C2×#11758189—22no—
37C2×C8×D61—22no—
38#14519777D411yescharacteristic
39#14519774D411yescharacteristic
40#14519765—21no—
41#14519751—21no—
42#14519751C2×C412yes—
43C4×D244—21no—
44C4×D244D412yes—
45#14519710—24no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519697—24no—
50#14519696—42no—
51#14519696—42no—
52C22⋊#92418C2×C412yes—
53#14519689—22no—
54#14519689—22no—
55#14519688—21no—
56C4×#92418—21no—
57C4×#92418—21no—
58C22×Q8×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61D411yescharacteristic
72C4⋊C8×C61D411yescharacteristic
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—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—81no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—22no—
108#11758198—22no—
109C4⋊Dic61—21no—
110C4⋊Dic61C22⋊C412yes—
111#11758194—21no—
112#11758194—21no—
113#11758194—21no—
114#11758194—41no—
115#11758194—41no—
116#11758194D812yes—
117C2×#92418—21no—
118C2×#92418—22no—
119C2×#92418—21no—
120C2×#92418—41no—
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—41no—
158C8×C61—41no—
159C8×C61—81no—
160#92418—22no—
161#92418—42no—
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#1966—611no—
187#1547—611no—
188C2×#332D6111yescharacteristic, complemented
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#423—611no—
209C2×C4⋊C8C2×D6111yescharacteristic
210C2×C4⋊C8C2×D6111yescharacteristic
211C2×#101—1221no—
212C2×#101—1221no—
213#408—1221no—
214C4×M16—611no—
215#332—21no—
216#332—21no—
217#332—1221no—
218#331—1221no—
219C61#927111yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×Q8—21no—
222#131—2442no—
223#131—2442no—
224C2×M16—611no—
225C2×M16—611no—
226C2×M16—1222no—
227C2×M16—1221no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—1222no—
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—21no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8C22⋊D6111yescharacteristic
253C4⋊C8C22⋊D6111yescharacteristic
254#102—1224no—
255#101—2442no—
256#101—2442no—
257C22⋊C8—612no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260#97—1221no—
261C4×C8—1221no—
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×C4D4×D6111yescharacteristic
282C22×C4#1175822411yescharacteristic
283M16—612no—
284M16—1221no—
285M16—1221no—
286M16—1221no—
287M16—2444no—
288M16—2441no—
289M16—2441no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—1221no—
297C2×C8—1222no—
298C2×C8—1221no—
299C2×C8—2444no—
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—
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C42C2×C22⋊D6111yescharacteristic
313C23—1222no—
314C23#1451973711yescharacteristic
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×C4C4×C22⋊D6111yescharacteristic
339C2×C4#1451974511yescharacteristic
340C2×C4#1451974811yescharacteristic
341C2×C4#1451975011yescharacteristic
342C2×C4#1451975911yescharacteristic
343C2×C4D8×D6111yescharacteristic
344C2×C4#1451979811yescharacteristic
345C2×C4#1451980111yescharacteristic
346C2×C4#1451980411yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—1222no—
351C8—4881no—
352C8—2442no—
353C8—2441no—
354C22—21no—
355C22—21no—
356C22—2442no—
357C22—2442no—
358C22—2442no—
359C22#1683963811yescharacteristic
360C22#1683984211yescharacteristic
361C22#1683987111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—2442no—
367C4#1683989411yescharacteristic
368C4#1683990611yescharacteristic
369C4#1683995611yescharacteristic
370C4#1683997611yescharacteristic
371C4#1684002211yescharacteristic
372C4#1684003411yescharacteristic
373C2—21no—
374C2—21no—
375C2—4882no—
376C2#2144616411yescharacteristic
377C2#2144633711yescharacteristic
378C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9271
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21446664C2semidirect
5. #21443716C2semidirect
6. #21443669C2semidirect
7. C2×C61×#332C2semidirect
188. C2×#332D61semidirect
219. C61#9271semidirect

Maximal subgroups

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

subgroupindex
#214569402
#214545622
#214466642
#214444942
#214437162
#214436692
C2×C61×#3322
#927161