Finite Group Databasebeta

← #29579072

Subgroups — #29579072

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454177C211yesmaximal, characteristic
2#21445970C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic61C211yesmaximal, characteristic, complemented
4C2×#16839508C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6C2×#16839505C211yesmaximal, characteristic
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519766—22no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519706—22no—
13C2×C8×Dic61—21no—
14#16839663—21no—
15#16839663—21no—
16#16839663C414yes—
17C42×Dic61C2211yescharacteristic
18#16839516—21no—
19#16839508—22no—
20#16839505—22no—
21#16839505—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#332—22no—
26C22×D244—21no—
27C22×D244—21no—
28C22×D244C2×C412yes—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519774—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774—21no—
35#14519766—44no—
36#14519766—44no—
37C2×#11758198—24no—
38C2×#11758198—24no—
39C2×C4×Dic61C2×C412yes—
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D412yes—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418D412yes—
47#14519706—44no—
48C8×Dic61—42no—
49C22×Q8×C61—21no—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C412yes—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61D412yes—
63C23×D61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—42no—
67C2×Q8×C61—42no—
68C22×C4×C61—22no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61C22⋊C412yes—
73C22×Dic61C22⋊C412yes—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—44no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—42no—
82C2×D244—42no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—42no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C42×C61#4111yescharacteristic
100#11758198—48no—
101#11758198—48no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—42no—
107C4×Dic61D814yes—
108C4×Dic61SD1614yes—
109C2×#92418—22no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—42no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—42no—
116C22×D61—44no—
117C22×D61—44no—
118C22×D61—42no—
119C22×D61—42no—
120Q8×C61—82no—
121Q8×C61—81no—
122Q8×C61—81no—
123C2×C4×C61—22no—
124C2×C4×C61—42no—
125C2×C4×C61—44no—
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12411yescharacteristic
131C2×C4×C61#12711yescharacteristic
132C2×C4×C61C2×D812yes—
133C2×C4×C61C2×SD1612yes—
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61#10214yes—
143C2×Dic61#10214yes—
144D244—82no—
145D244—82no—
146D244—81no—
147D244—81no—
148D244—81no—
149D244—81no—
150D244—82no—
151D244—81no—
152D244—81no—
153C8×C61—42no—
154C8×C61—81no—
155#92418—42no—
156#92418—81no—
157#9698—611nomaximal, Sylow
158C22×C61#39011yescharacteristic
159C22×C61#41312yes—
160C22×C61C2×#10212yes—
161C22×C61#41611yescharacteristic
162C22×C61#41711yescharacteristic
163C2×D61—84no—
164C2×D61—84no—
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—82no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—82no—
171C4×C61#46311yescharacteristic
172C4×C61#46311yescharacteristic
173C4×C61#46411yescharacteristic
174C4×C61#46411yescharacteristic
175C4×C61#48612yes—
176C4×C61#49211yescharacteristic
177C4×C61#49311yescharacteristic
178Dic61—24no—
179Dic61—24no—
180#2858—611no—
181#1842—611no—
182C4×C4⋊C8—611no—
183C2×#332—611no—
184C2×#332D6111yescharacteristic, complemented
185C2×#331—611no—
186C2×#331—611no—
187C2×C61#154012yes—
188C2×C61#154712yes—
189C2×C61#195711yescharacteristic
190C2×C61#196711yescharacteristic
191C2×C61#198311yescharacteristic
192D61—162no—
193C2×C4⋊Q8C2×D6111yescharacteristic
194C2×#127—611no—
195C2×#124—1222no—
196C2×C4⋊C8—611no—
197C2×C4⋊C8—611no—
198C2×C4⋊C8—1222no—
199C2×C4⋊C8C2×D6111yescharacteristic
200C2×C4⋊C8C2×D6111yescharacteristic
201C2×C4×C8—1221no—
202#390—614no—
203#390—1221no—
204#390—1221no—
205C43—611no—
206#336—1221no—
207#332—22no—
208#332—1222no—
209#331—1222no—
210#331—1222no—
211C61#969811yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C22×D4—612no—
214C22×D4—1221no—
215C22×D4—1221no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—1221no—
219C22×C8—1221no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224#127—1221no—
225#127—1221no—
226#127—1221no—
227#127—1221no—
228#124—2444no—
229#124—2444no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C4×D6112yes—
232C2×C22⋊C4—1224no—
233C2×C22⋊C4—1224no—
234C2×C42—612no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—612no—
238C2×C42C22×D6111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—612no—
243C4⋊C8—1221no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
246C4⋊C8—2444no—
247C4⋊C8C22⋊D6112yes—
248C4×C8—2442no—
249C24—1222no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—2444no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2441no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2442no—
263C2×D4—2442no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—22no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—42no—
278C2×C8—1222no—
279C2×C8—2441no—
280C2×C8—2442no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—2448no—
288C22⋊C4—2448no—
289C42—614no—
290C42—614no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42—2442no—
296C42#1175822211yescharacteristic
297C42D4×D6111yescharacteristic
298C42#1175822411yescharacteristic
299C42C2×C22⋊D6111yescharacteristic
300C23—2444no—
301C23—2444no—
302C23—2442no—
303C23—2442no—
304C23—2442no—
305C23C22⋊C4×D6111yescharacteristic
306Q8—82no—
307Q8—81no—
308Q8—81no—
309D4—4882no—
310D4—4882no—
311D4—4881no—
312D4—4881no—
313D4—4881no—
314D4—4881no—
315D4—4882no—
316D4—4881no—
317D4—4881no—
318C2×C4—22no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—614no—
322C2×C4—614no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4#1451973711yescharacteristic
328C2×C4C4×C22⋊D6111yescharacteristic
329C2×C4#1451974911yescharacteristic
330C2×C4#1451975011yescharacteristic
331C2×C4#1451976311yescharacteristic
332C2×C4#1451977311yescharacteristic
333C2×C4D8×D6112yes—
334C2×C4SD16×D6112yes—
335C2×C4#1451979811yescharacteristic
336C2×C4#1451980011yescharacteristic
337C2×C4#1451980411yescharacteristic
338C2×C4#1451980911yescharacteristic
339C8—42no—
340C8—81no—
341C8—4881no—
342C8—2442no—
343C22—4882no—
344C22—4882no—
345C22—4884no—
346C22—4884no—
347C22—4882no—
348C22#1683966211yescharacteristic
349C22#1683974512yes—
350C22#102×D6112yes—
351C22#1683975711yescharacteristic
352C22#1683976211yescharacteristic
353C4—21no—
354C4—21no—
355C4—82no—
356C4—1224no—
357C4—1224no—
358C4#1683997911yescharacteristic
359C4#1683998011yescharacteristic
360C4#1683998611yescharacteristic
361C4#1683998711yescharacteristic
362C4#1684010712yes—
363C4#1684013311yescharacteristic
364C4#1684013711yescharacteristic
365C2—9762no—
366C2#2144446712yes—
367C2#2144449512yes—
368C2#2144662311yescharacteristic
369C2#2144666711yescharacteristic
370C2#2144674811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9698
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #21445970C2semidirect
3. C4⋊C8×Dic61C2semidirect
4. C2×#16839508C2semidirect
7. C2×C61×#332C2semidirect
184. C2×#332D61semidirect
211. C61#9698semidirect

Maximal subgroups

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

subgroupindex
#214541772
#214459702
C4⋊C8×Dic612
C2×#168395082
C2×#168395052
C2×C61×#3322
#969861