Finite Group Databasebeta

← #15759457

Subgroups — #15759457

Order 3328.

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#13125977C211yesmaximal, characteristic
2#13115680C211yesmaximal, characteristic
3#13113526C211yesmaximal, characteristic
4C2×#11718074C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic
6#13112687C211yesmaximal, characteristic
7C13×#2962C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#446—22no—
11C13×#446—21no—
12C8×Q8×C13—21no—
13C13×#424—21no—
14C2×C13×C4⋊C8C2211yescharacteristic
15C13×#405—21no—
16C4×C13×M16C2211yescharacteristic
17C2×#88064—21no—
18C2×#88064—21no—
19#11718742—21no—
20#11718740—21no—
21#11718704C414yes—
22#11718681—22no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718139—21no—
27#11718138—21no—
28#11718074—21no—
29#11718074—21no—
30C22×Dic26—21no—
31C2×C13×M16D411yescharacteristic
32C2×C13×M16D411yescharacteristic
33C22×C8×C13—21no—
34C13×C4⋊Q8D411yescharacteristic
35C13×C4⋊Q8D411yescharacteristic
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8C2×C412yes—
39C4×Q8×C13—21no—
40C4×Q8×C13D412yes—
41C13×#117—21no—
42C2×C42×C13C2311yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13C2×C412yes—
45C2×#6099—21no—
46C22×#1055—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51C13×C4⋊C8—22no—
52C13×C4⋊C8—22no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8D411yescharacteristic
55C13×C4⋊C8D411yescharacteristic
56C13×#97—22no—
57C13×#97—21no—
58C4×C8×C13—22no—
59C4×C8×C13—21no—
60#88075—24no—
61C22⋊#1055C2×C412yes—
62#88064—42no—
63#88064—42no—
64#88048—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4×#1055—21no—
71#9272—131nomaximal, Sylow
72C2×Q8×C13—21no—
73C2×Q8×C13C22⋊C412yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—22no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C13×M16—21no—
85C13×M16—21no—
86C13×M16—21no—
87C13×M16SD1612yes—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4C22⋊C412yes—
100C13×C22⋊C4—22no—
101C42×C13—22no—
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13#4111yescharacteristic
106C4⋊Dic13—22no—
107C4⋊Dic13—22no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110#6099—41no—
111#6099—41no—
112C2×#1055—22no—
113C2×#1055—41no—
114C2×#1055—41no—
115C2×#1055—81no—
116#3229—131no—
117#2962D1311yescharacteristic
118#1966—131no—
119#1550—131no—
120C2×#332—131no—
121#1301—131no—
122#1283—131no—
123C23×C13C4×D411yescharacteristic
124Q8×C13—42no—
125Q8×C13—41no—
126Q8×C13—41no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—41no—
132C2×C4×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145Dic26—81no—
146Dic26—81no—
147Dic26—81no—
148Dic26—81no—
149C8×C13—22no—
150C8×C13—41no—
151C8×C13—41no—
152C8×C13—41no—
153#1055—42no—
154#1055—81no—
155#1055—81no—
156#533C2×D1311yescharacteristic
157C2×C4⋊Q8—131no—
158#498—261no—
159#487—261no—
160#483—134no—
161#475—262no—
162#446—22no—
163#446—21no—
164C8×Q8—21no—
165#431—131no—
166#424—21no—
167#423—131no—
168C2×C4⋊C8—131no—
169C2×C4⋊C8C2×D1311yescharacteristic
170C2×#101—261no—
171C2×#101—261no—
172#405—21no—
173C4×M16C2×D1311yescharacteristic
174#333—261no—
175#332—261no—
176#332—261no—
177#332—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#38611yescharacteristic
181C22×C13C4×SD1611yescharacteristic
182C22×C13#44011yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—42no—
187C4×C13—42no—
188C4×C13#44811yescharacteristic
189C4×C13#44911yescharacteristic
190C4×C13#46011yescharacteristic
191C4×C13#46411yescharacteristic
192C4×C13#47111yescharacteristic
193C4×C13#47311yescharacteristic
194Dic13—82no—
195C22×Q8—261no—
196C2×M16—261no—
197C2×M16C22⋊D1311yescharacteristic
198C2×M16C22⋊D1311yescharacteristic
199C22×C8—21no—
200C22×C8—261no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203C4⋊Q8—261no—
204C4⋊Q8—261no—
205C4⋊Q8D5211yescharacteristic
206C4⋊Q8D5211yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8C4×D1312yes—
210C4×Q8—21no—
211C4×Q8C22⋊D1312yes—
212#117—21no—
213C2×C4⋊C4—132no—
214C2×C4⋊C4—261no—
215C2×C42C22×D1311yescharacteristic
216#106—264no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—21no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225C4⋊C8C22⋊D1311yescharacteristic
226C4⋊C8C22⋊D1311yescharacteristic
227#103—264no—
228#101—522no—
229#101—522no—
230C22⋊C8—132no—
231#97—22no—
232#97—21no—
233C4×C8—22no—
234C4×C8—21no—
235C4×C8—261no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#188011yescharacteristic
239C2×C13#190811yescharacteristic
240C2×C13#191511yescharacteristic
241C2×Q8—21no—
242C2×Q8—521no—
243C2×Q8—521no—
244C2×Q8—521no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×Q8—521no—
248C2×Q8#610312yes—
249C22×C4—262no—
250C22×C4C2×C4×D1311yescharacteristic
251C22×C4#612711yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253M16—21no—
254M16—21no—
255M16—21no—
256M16—521no—
257M16—521no—
258M16#610612yes—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—262no—
266C2×C8—521no—
267C2×C8—521no—
268C2×C8—1041no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—262no—
275C4⋊C4—262no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4#610312yes—
279C22⋊C4—22no—
280C42—22no—
281C42C2×D5211yescharacteristic
282C42#612711yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C42C2×C22⋊D1311yescharacteristic
285C13#927211yescharacteristic, complemented, Sylow
286C23C4×C22⋊D1311yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—1041no—
291Q8—1041no—
292Q8—1041no—
293Q8—1041no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4C2×#610311yescharacteristic
303C2×C4C4×C22⋊D1311yescharacteristic
304C2×C4#8818311yescharacteristic
305C2×C4#8818411yescharacteristic
306C2×C4#8818411yescharacteristic
307C2×C4C2×#610611yescharacteristic
308C2×C4#8819611yescharacteristic
309C2×C4#8820311yescharacteristic
310C2×C4#8820411yescharacteristic
311C2×C4#8820711yescharacteristic
312C8—22no—
313C8—41no—
314C8—41no—
315C8—41no—
316C8—522no—
317C8—1041no—
318C8—1041no—
319C22—21no—
320C22—21no—
321C22C4×#610611yescharacteristic
322C22#1171868711yescharacteristic
323C22#1171887411yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—1042no—
330C4#1171868811yescharacteristic
331C4#1171868911yescharacteristic
332C4#1171880211yescharacteristic
333C4#1171880411yescharacteristic
334C4#1171888811yescharacteristic
335C4#1171889911yescharacteristic
336C2—21no—
337C2—21no—
338C2#1311519111yescharacteristic
339C2#1311535111yescharacteristic
340C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2962C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#2962D13
hypocenterC13#9272
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
285. C13#9272semidirect

Maximal subgroups

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

subgroupindex
#131259772
#131156802
#131135262
C2×#117180742
#131127332
#131126872
C13×#29622
#927213