Finite Group Databasebeta

← #29575439

Subgroups — #29575439

Order 15616.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454842C211yesmaximal, characteristic, complemented
2C2×#16839875C211yesmaximal, characteristic
3#21444211C211yesmaximal, characteristic, complemented
4#21444209C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic, complemented
6#21443664C211yesmaximal, characteristic, complemented
7C61×#1275C211yesmaximal, characteristic, complemented
8C22×D488C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839875—22no—
12#16839875—22no—
13C8×D244—22no—
14#16839827—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17C2×#14519709C411yescharacteristic
18C2×#14519699C411yescharacteristic
19C2×#14519699C411yescharacteristic
20C22⋊C8×D61—22no—
21#16839491—22no—
22#16839489—22no—
23#16839485—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61—21no—
31C2×D488—22no—
32C2×D488—22no—
33C2×D488C814yescomplemented
34C2×C8×D61—24no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244D412yes—
42C4×D244D412yes—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519709—22no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519699—22no—
51#14519699—22no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519689—24no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×C8×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61D412yes—
68C23×D61—21no—
69C23×D61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4111yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244C22⋊C412yes—
84C2×D244C2×C812yes—
85C2×D244C2×C812yescomplemented
86C2×D244M1612yes—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—82no—
92C2×C4×D61—82no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—22no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—41no—
100C2×C8×C61C2×C812yescomplemented
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—22no—
106#11758198—22no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61C22⋊C412yes—
113C2×#92418—22no—
114C2×#92418—41no—
115D488—28no—
116C8×D61—84no—
117C23×C61C4×D411yescharacteristic
118C22×D61—22no—
119C22×D61—22no—
120C22×D61—22no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C2×Dic61—22no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144D244—22no—
145D244—22no—
146D244—22no—
147D244—22no—
148D244—22no—
149D244—41no—
150D244—41no—
151D244C22⋊C814yes—
152C4×D61—44no—
153C4×D61—82no—
154C4×D61—82no—
155C4×D61—82no—
156C8×C61—22no—
157C8×C61—42no—
158C8×C61—41no—
159C8×C61—81no—
160#92418—42no—
161#92418—81no—
162#9089—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61C8×D411yescharacteristic
167C22×C61#43511yescharacteristic
168C2×D61—24no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—82no—
173C2×D61—82no—
174C2×D61—82no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—82no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61C2×C22⋊C811yescharacteristic
183C4×C61#40811yescharacteristic
184C4×C61C8×D411yescharacteristic
185C4×C61#43511yescharacteristic
186Dic61—42no—
187Dic61—81no—
188#2972—611no—
189C2×#442—611no—
190#1478—611no—
191#1478—611no—
192#1460—611no—
193#1281—611no—
194#1275D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#186911yescharacteristic
198C2×C61#190311yescharacteristic
199C2×C61#190411yescharacteristic
200D61—44no—
201D61—82no—
202C22×D8—611no—
203C2×C4×D4—611no—
204C2×C4×D4—611no—
205#442—1222no—
206#442—1222no—
207C8×D4—1222no—
208C8×D4—1222no—
209#431—611no—
210#431—611no—
211#431C2×D6111yescharacteristic
212#431C2×D6111yescharacteristic
213C2×#106—611no—
214C2×#102—611no—
215C2×#102—611no—
216C2×C22⋊C8—1222no—
217C2×#97C2×D6111yescharacteristic
218D4⋊C8—1222no—
219D4⋊C8—1222no—
220#323—1222no—
221C61#908911yescharacteristic, complemented, Sylow
222C22×D4—611no—
223C22×D4—611no—
224C23×C4—1221no—
225C23×C4—1221no—
226C2×D8—614no—
227C2×D8—1222no—
228C2×D8—1222no—
229C22×C8—1224no—
230C22×C8C4×D6111yescharacteristic
231C22×C8C4×D6111yescharacteristic
232C4×D4—612no—
233C4×D4—612no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C4×D4—1221no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42C22×D6111yescharacteristic
245#106—1222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250#102—1222no—
251#102—1222no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—612no—
255C22⋊C8—1224no—
256C22⋊C8—1221no—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8—1221no—
261C4×C8—1221no—
262C4×C8D24412yes—
263C24—1221no—
264C24—1221no—
265C2×D4—612no—
266C2×D4—612no—
267C2×D4—612no—
268C2×D4—612no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C22×C4—1221no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—4882no—
282C22×C4—4882no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4C2×C4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C22×C4#1175822611yescharacteristic
288D8—1228no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—41no—
296C2×C8—1222no—
297C2×C8—4884no—
298C2×C8—2441no—
299C2×C8C8×D6112yescomplemented
300C4⋊C4—612no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C22⋊C4—1222no—
305C22⋊C4—1222no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42C2×D24411yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C23—1222no—
313C23—1222no—
314C23—1222no—
315C23—1222no—
316C23—4881no—
317C23—4881no—
318C23—4881no—
319C23—4881no—
320C23—2441no—
321C23—2441no—
322C23#1451973911yescharacteristic
323D4—614no—
324D4—1222no—
325D4—1222no—
326D4—1222no—
327D4—1222no—
328D4—1222no—
329D4—2441no—
330D4—2441no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—1222no—
334C2×C4—4882no—
335C2×C4—4882no—
336C2×C4—4882no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—2444no—
340C2×C4—2441no—
341C2×C4C22⋊C4×D6111yescharacteristic
342C2×C4C4×D24411yescharacteristic
343C2×C4#1451974711yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451975211yescharacteristic
346C2×C4#1451976211yescharacteristic
347C2×C4C2×C8×D6111yescharacteristic
348C2×C4M16×D6111yescharacteristic
349C2×C4#1451978311yescharacteristic
350C2×C4#1451978511yescharacteristic
351C8—22no—
352C8—42no—
353C8—41no—
354C8—81no—
355C8—4881no—
356C8—2442no—
357C22—21no—
358C22—21no—
359C22—1224no—
360C22—4882no—
361C22—4882no—
362C22—4882no—
363C22—4882no—
364C22—4881no—
365C22—4881no—
366C22—2442no—
367C22—2442no—
368C22—2442no—
369C22#1683964011yescharacteristic
370C22#1683982711yescharacteristic
371C22#1683983211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—4881no—
377C4—2442no—
378C4C22⋊C8×D6111yescharacteristic
379C4#1683972711yescharacteristic
380C4C8×D24411yescharacteristic
381C4#1683983511yescharacteristic
382C2—21no—
383C2—21no—
384C2—4882no—
385C2—2444no—
386C2#2144611011yescharacteristic
387C2#2144630011yescharacteristic
388C2#2144630711yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1275C2
socleC22×C61#386
prime radicalC22×D488C4
cosocleC2×C42×C61C23
hypercenter#1275D61
hypocenterC61#9089
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
1. #21454842C2semidirect
3. #21444211C2semidirect
4. #21444209C2semidirect
5. #21444139C2semidirect
6. #21443664C2semidirect
7. C61×#1275C2semidirect
33. C2×D488C8semidirect
85. C2×D244C2×C8semidirect
100. C2×C8×C61C2×C8semidirect
194. #1275D61semidirect
221. C61#9089semidirect
299. C2×C8C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548422
C2×#168398752
#214442112
#214442092
#214441392
#214436642
C61×#12752
#908961