Finite Group Databasebeta

← #29576553

Subgroups — #29576553

Order 15616.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454768C211yesmaximal, characteristic
2#21446664C211yesmaximal, characteristic
3#21444509C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic
6#21443668C211yesmaximal, characteristic
7C61×#3229C211yesmaximal, characteristic
8#16839893—21no—
9#16839893—22no—
10Q8×#92418—21no—
11#16839789—21no—
12#16839786C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519696—21no—
16C2×#14519696—21no—
17#16839718—21no—
18C4×#11758194C2211yescharacteristic
19#16839511—21no—
20#16839508—21no—
21#16839508—21no—
22#16839508—21no—
23C61×#533C2211yescharacteristic
24C2×C4⋊Q8×C61C2211yescharacteristic
25C61×#498—21no—
26C61×#487—21no—
27C61×#483C414yes—
28C61×#475—22no—
29C61×#431C2211yescharacteristic
30C2×#11758194—21no—
31C2×#11758194D411yescharacteristic
32C2×#11758194D411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35C4⋊#92418—22no—
36C4⋊#92418—22no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43C4⋊#92418D411yescharacteristic
44#14519696—42no—
45#14519696—42no—
46#14519688—22no—
47#14519688—21no—
48C4×#92418—22no—
49C4×#92418—21no—
50C22×Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61D411yescharacteristic
56C4⋊Q8×C61D411yescharacteristic
57#125×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61C2×C412yes—
60C4×Q8×C61—21no—
61C4×Q8×C61D412yes—
62#117×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61C2×C412yes—
65C2×C42×C61C2311yescharacteristic
66#106×C61—24no—
67C4⋊C8×C61—21no—
68#103×C61—24no—
69C22⋊C8×C61C2×C412yes—
70C4×C8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61C22⋊C412yes—
79C22×C4×C61—22no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C8×C61—22no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61C22⋊C412yes—
94C22⋊C4×C61—22no—
95C42×C61—22no—
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61#4111yescharacteristic
100#11758194—21no—
101#11758194—21no—
102#11758194—21no—
103#11758194—41no—
104#11758194—41no—
105#11758194SD1612yes—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—81no—
115C23×C61C4×D411yescharacteristic
116Q8×C61—42no—
117Q8×C61—41no—
118Q8×C61—41no—
119Q8×C61—81no—
120Q8×C61—81no—
121Q8×C61—81no—
122Q8×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61C2×SD1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C8×C61—42no—
142#92418—22no—
143#92418—41no—
144#92418—41no—
145#92418—41no—
146#92418—81no—
147#92418—81no—
148#9272—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#38611yescharacteristic
152C22×C61C4×SD1611yescharacteristic
153C22×C61#44011yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—42no—
158C4×C61—42no—
159C4×C61—82no—
160C4×C61#44811yescharacteristic
161C4×C61#44911yescharacteristic
162C4×C61#46011yescharacteristic
163C4×C61#46411yescharacteristic
164C4×C61#47111yescharacteristic
165C4×C61#47311yescharacteristic
166#3229D6111yescharacteristic
167#2962—611no—
168#1966—611no—
169#1550—611no—
170C2×#332—611no—
171#1301—611no—
172#1283—611no—
173C2×C61—21no—
174C2×C61—21no—
175C2×C61#188011yescharacteristic
176C2×C61#190811yescharacteristic
177C2×C61#191511yescharacteristic
178#533C2×D6111yescharacteristic
179C2×C4⋊Q8C2×D6111yescharacteristic
180#498—21no—
181#487—21no—
182#483Dic6114yes—
183#475—22no—
184#446—1221no—
185#446—1222no—
186C8×Q8—1221no—
187#431C2×D6111yescharacteristic
188#424—1221no—
189#423—611no—
190C2×C4⋊C8—611no—
191C2×C4⋊C8—611no—
192C2×#101—1221no—
193C2×#101—1221no—
194#405—1221no—
195C4×M16—611no—
196#333—1221no—
197#332—1221no—
198#332—1221no—
199#332—1221no—
200C61#927211yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C2×M16—611no—
203C2×M16—611no—
204C2×M16—1221no—
205C22×C8—1221no—
206C22×C8—1221no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C22⋊D6111yescharacteristic
212C4⋊Q8C22⋊D6111yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8C2×Dic6112yes—
216C4×Q8—21no—
217C4×Q8C22⋊D6112yes—
218#117—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic6112yes—
221C2×C42C22×D6111yescharacteristic
222#106—24no—
223C4⋊C8—21no—
224C4⋊C8—611no—
225C4⋊C8—611no—
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C4⋊C8—1221no—
229C4⋊C8—1221no—
230C4⋊C8—1221no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233#103—24no—
234#101—2442no—
235#101—2442no—
236C22⋊C8C2×Dic6112yes—
237#97—1222no—
238#97—1221no—
239C4×C8—21no—
240C4×C8—1222no—
241C4×C8—1221no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C22⋊Dic6112yes—
250C22×C4—22no—
251C22×C4D4×D6111yescharacteristic
252C22×C4#1175822411yescharacteristic
253C22×C4C22×Dic6111yescharacteristic
254M16—612no—
255M16—1221no—
256M16—1221no—
257M16—1221no—
258M16—2441no—
259M16—2441no—
260C2×C8—22no—
261C2×C8—1221no—
262C2×C8—1221no—
263C2×C8—1221no—
264C2×C8—1221no—
265C2×C8—4881no—
266C2×C8—2441no—
267C2×C8—2441no—
268C2×C8—2441no—
269C2×C8—2441no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4C22⋊Dic6112yes—
280C22⋊C4—22no—
281C42—22no—
282C42D4×D6111yescharacteristic
283C42#1175822411yescharacteristic
284C42C2×C22⋊D6111yescharacteristic
285C42C2×C22⋊D6111yescharacteristic
286C23D4×Dic6111yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—81no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4C2×C22⋊Dic6111yescharacteristic
303C2×C4D4×Dic6111yescharacteristic
304C2×C4#1451974511yescharacteristic
305C2×C4#1451974911yescharacteristic
306C2×C4#1451974911yescharacteristic
307C2×C4#1451975811yescharacteristic
308C2×C4SD16×D6111yescharacteristic
309C2×C4#1451979811yescharacteristic
310C2×C4#1451980411yescharacteristic
311C2×C4#1451980611yescharacteristic
312C8—42no—
313C8—1222no—
314C8—4881no—
315C8—4881no—
316C8—2441no—
317C8—2441no—
318C8—2441no—
319C22—21no—
320C22—21no—
321C22#1683964211yescharacteristic
322C22SD16×Dic6111yescharacteristic
323C22#1683986311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—82no—
330C4#1683989911yescharacteristic
331C4#1683990611yescharacteristic
332C4#1683996011yescharacteristic
333C4#1683998211yescharacteristic
334C4#1684002711yescharacteristic
335C4#1684003511yescharacteristic
336C2—21no—
337C2—21no—
338C2#2144617611yescharacteristic
339C2#2144633611yescharacteristic
340C2#2144637211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3229C2
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#3229D61
hypocenterC61#9272
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
200. C61#9272semidirect

Maximal subgroups

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

subgroupindex
#214547682
#214466642
#214445092
C2×#168395082
#214437152
#214436682
C61×#32292
#927261