Finite Group Databasebeta

← #29574348

Subgroups — #29574348

Order 15616.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446594C211yesmaximal, characteristic
2#21444577C211yesmaximal, characteristic
3#21444248C211yesmaximal, characteristic
4C2×Q8⋊#92418C211yesmaximal, characteristic
5#21443714C211yesmaximal, characteristic
6#21443657C211yesmaximal, characteristic
7Q8×M16×C61C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9C2×#14519712—21no—
10#16839786C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839526—21no—
14#16839514—22no—
15Q8⋊#92418—21no—
16Q8⋊#92418—21no—
17Q8⋊#92418C411yescharacteristic
18Q8⋊#92418C411yescharacteristic
19Q8⋊#92418C411yescharacteristic
20Q8⋊#92418C411yescharacteristic
21C2×C4×Q8×C61C2211yescharacteristic
22C61×#446—21no—
23C61×#446—22no—
24C8×Q8×C61—21no—
25C61×#423—21no—
26C61×#423C2211yescharacteristic
27C4×M16×C61—21no—
28C4×M16×C61C2211yescharacteristic
29C2×#11758194—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32#14519712—42no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418C2×C411yescharacteristic
38C4⋊#92418C2×C411yescharacteristic
39C22⋊#92418—21no—
40C4×#92418—21no—
41C4×#92418—21no—
42C4×#92418C2×C411yescharacteristic
43C4×#92418C2×C411yescharacteristic
44C22×Q8×C61Q811yescharacteristic
45C2×M16×C61—21no—
46C2×M16×C61D411yescharacteristic
47C2×M16×C61D411yescharacteristic
48C4×Q8×C61—21no—
49C4×Q8×C61—21no—
50C4×Q8×C61C2×C411yescharacteristic
51C4×Q8×C61C2×C411yescharacteristic
52C4×Q8×C61D411yescharacteristic
53C4×Q8×C61D411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61Q811yescharacteristic
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—22no—
59C4⋊C8×C61—22no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61D412yes—
62#97×C61—22no—
63#97×C61—21no—
64C4×C8×C61—22no—
65C4×C8×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61C4⋊C411yescharacteristic
70C2×Q8×C61C4⋊C411yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×Q811yescharacteristic
75C22×C4×C61#4111yescharacteristic
76M16×C61—21no—
77M16×C61—21no—
78M16×C61—21no—
79M16×C61—41no—
80M16×C61—41no—
81M16×C61Q1612yes—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—22no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61C4⋊C411yescharacteristic
91C4⋊C4×C61C4⋊C411yescharacteristic
92C42×C61—21no—
93C42×C61—21no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61C22×C411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61#4111yescharacteristic
100#11758194—41no—
101#11758194—41no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418—42no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C22⋊Q811yescharacteristic
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61—21no—
115Q8×C61—42no—
116Q8×C61#10812yescomplemented
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61C2×C4⋊C411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×Q1611yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C8×C61—22no—
137C8×C61—41no—
138C8×C61—42no—
139#92418—22no—
140#92418—41no—
141#92418—41no—
142#92418—41no—
143#92418—81no—
144#92418—81no—
145#8907—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#38511yescharacteristic
149C22×C61#47711yescharacteristic
150C22×C61#47911yescharacteristic
151C4×C61—21no—
152C4×C61—22no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C2×#10811yescharacteristic
159C4×C61#43011yescharacteristic
160C4×C61C4×Q1611yescharacteristic
161C4×C61#44011yescharacteristic
162C4×C61#44911yescharacteristic
163C4×C61#45111yescharacteristic
164Q8×M16D6111yescharacteristic
165#1950—611no—
166#1567—611no—
167#1487—611no—
168C2×Q8⋊C8—611no—
169#1301—611no—
170#1278—611no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61#185511yescharacteristic
174C2×C61#186111yescharacteristic
175C2×C61#186311yescharacteristic
176C2×C4×Q8C2×D6111yescharacteristic
177#446—21no—
178#446—22no—
179C8×Q8—21no—
180#431—611no—
181C2×#108—1221no—
182#423—21no—
183#423—611no—
184#423C2×D6111yescharacteristic
185C2×C4⋊C8—611no—
186C4×M16—21no—
187C4×M16C2×D6111yescharacteristic
188C2×C4×C8—611no—
189#341—1221no—
190#335—1222no—
191Q8⋊C8—611no—
192Q8⋊C8—611no—
193Q8⋊C8—611no—
194Q8⋊C8—611no—
195Q8⋊C8—1221no—
196Q8⋊C8—1221no—
197C61#890711yescharacteristic, complemented, Sylow
198C22×Q8Dic12211yescharacteristic
199C2×M16—21no—
200C2×M16—1221no—
201C2×M16C22⋊D6111yescharacteristic
202C2×M16C22⋊D6111yescharacteristic
203C22×C8—1221no—
204C22×C8—1221no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C4×D6111yescharacteristic
208C4×Q8C4×D6111yescharacteristic
209C4×Q8C22⋊D6111yescharacteristic
210C4×Q8C22⋊D6111yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Dic12211yescharacteristic
213C2×C42—21no—
214C2×C42C22×D6111yescharacteristic
215#108—2442no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—611no—
220C4⋊C8—611no—
221C4⋊C8—1221no—
222C4⋊C8—1221no—
223C4⋊C8—1221no—
224C4⋊C8—1221no—
225C4⋊C8C22⋊D6112yes—
226C22⋊C8—1221no—
227#97—22no—
228#97—21no—
229C4×C8—22no—
230C4×C8—21no—
231C4×C8—611no—
232C4×C8—611no—
233C4×C8—1221no—
234C4×C8—1221no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8#1175819611yescharacteristic
239C2×Q8#1175819611yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic12211yescharacteristic
243C22×C4#1175822211yescharacteristic
244C22×C4C2×C22⋊D6111yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—2441no—
251M16—2441no—
252M16#1175820212yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—1221no—
257C2×C8—1221no—
258C2×C8—1221no—
259C2×C8—1221no—
260C2×C8—2442no—
261C2×C8—2441no—
262C2×C8—2441no—
263C2×C8—2441no—
264C2×C8—2441no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4#1175819611yescharacteristic
271C4⋊C4#1175819611yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C2×C4×D6111yescharacteristic
277C42#1175822211yescharacteristic
278C42C2×C22⋊D6111yescharacteristic
279C42C2×C22⋊D6111yescharacteristic
280C23#1451975611yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#1451971212yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×#1175819611yescharacteristic
296C2×C4C4×C22⋊D6111yescharacteristic
297C2×C4C4×C22⋊D6111yescharacteristic
298C2×C4#1451974611yescharacteristic
299C2×C4#1451975611yescharacteristic
300C2×C4#1451976011yescharacteristic
301C2×C4C2×#1175820211yescharacteristic
302C2×C4#1451979711yescharacteristic
303C2×C4#1451980211yescharacteristic
304C2×C4#1451980811yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—1222no—
309C8—4881no—
310C8—4881no—
311C8—2441no—
312C8—2441no—
313C8—2441no—
314C22—21no—
315C22—21no—
316C22#1683963511yescharacteristic
317C22#1684005711yescharacteristic
318C22#1684006911yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#1451971211yescharacteristic
327C4#1683981011yescharacteristic
328C4C4×#1175820211yescharacteristic
329C4#1683986011yescharacteristic
330C4#1683990711yescharacteristic
331C4#1683991811yescharacteristic
332C2—21no—
333C2—21no—
334C2#2144602411yescharacteristic
335C2#2144605911yescharacteristic
336C2#2144607311yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingQ8×M16×C61C2
socleC22×C61#385
prime radicalC23×C61C22⋊Q8
cosocleC2×C42×C61C23
hypercenterQ8×M16D61
hypocenterC61#8907
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
116. Q8×C61#108semidirect
197. C61#8907semidirect
285. Q8#14519712semidirect

Maximal subgroups

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

subgroupindex
#214465942
#214445772
#214442482
C2×Q8⋊#924182
#214437142
#214436572
Q8×M16×C612
#890761