Finite Group Databasebeta

← #15779984

Subgroups — #15779984

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88040C211yesmaximal, characteristic
2C2×#11718534C211yesmaximal, characteristic, complemented
3C2×#11718084C211yesmaximal, characteristic, complemented
4C2×#11718083C211yesmaximal, characteristic
5#13115700C211yesmaximal, characteristic
6#13112913C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×D104C2211yescharacteristic
10C2×#88141—21no—
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×C13×#107C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718649—21no—
17C2×#88050—21no—
18C2×#88049—21no—
19C2×#88040—22no—
20C2×#88040—22no—
21C2×#88040C414yescomplemented
22#11718534—22no—
23#11718534—22no—
24#11718084—22no—
25#11718083—22no—
26C22×D52—21no—
27C22×Dic26—21no—
28C22×C8×C13C2311yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×#6103—41no—
32C2×#6103—41no—
33C2×#6101—41no—
34C2×C4×Dic13—41no—
35C2×C4×Dic13D411yescharacteristic
36C22×#1055D411yescharacteristic
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52C2×C412yes—
41C2×Dic52D412yes—
42C2×Dic52D412yes—
43C2×D104—21no—
44C2×D104—21no—
45C2×D104—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104C2×C412yes—
49#88141—24no—
50#88141—42no—
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16C2×C412yes—
54C13×#107—21no—
55C13×#107—21no—
56C13×#107—21no—
57C13×#107D412yes—
58C8×Dic13—21no—
59C8×Dic13—21no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090—21no—
63#88050—24no—
64#88049—42no—
65#88040—28no—
66#13013—131nomaximal, Sylow
67C23×D13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—41no—
72C22×Dic13D811yescharacteristic
73C22×Dic13D811yescharacteristic
74C2×D52—22no—
75C2×D52—41no—
76C2×D52—41no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×Dic26—22no—
81C2×Dic26—22no—
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×C8×C13C22×C411yescharacteristic
87C2×C8×C13C2×D411yescharacteristic
88C2×C8×C13C2×D411yescharacteristic
89C2×C8×C13C2×D411yescharacteristic
90C2×C8×C13#4111yescharacteristic
91C2×C8×C13#4111yescharacteristic
92C13×C4⋊C4—22no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96#6103—82no—
97#6103—82no—
98#6101—44no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—44no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105Dic52—22no—
106Dic52—22no—
107Dic52—22no—
108Dic52C22⋊C414yescomplemented
109D104—22no—
110D104—22no—
111D104—41no—
112D104—41no—
113C13×C16—22no—
114#6090—41no—
115C22×SD32—131no—
116C2×C4×Q16—131no—
117C2×#358—131no—
118C2×#357—131no—
119#1970—131no—
120#1380D1311yescharacteristic, complemented
121#1374—131no—
122C23×C13C2×D811yescharacteristic
123C22×D13—42no—
124C22×D13—81no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—81no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13SD3212yescomplemented
151D52—42no—
152D52—42no—
153D52—81no—
154D52—81no—
155Dic26—24no—
156Dic26—42no—
157Dic26—42no—
158Dic26—42no—
159C8×C13C2×C22⋊C411yescharacteristic
160C8×C13C4×D411yescharacteristic
161C8×C13#12111yescharacteristic
162C8×C13#12311yescharacteristic
163#1055—41no—
164C22×Q16—131no—
165C22×D8—131no—
166C2×C4×Q8—261no—
167C2×SD32—134no—
168C2×SD32—262no—
169C2×SD32—262no—
170C22×C16—131no—
171C22×C16C2×D1311yescharacteristic
172C4×Q16—262no—
173C4×Q16—262no—
174C2×#107C2×D1311yescharacteristic
175C2×#107C2×D1311yescharacteristic
176C2×#103—261no—
177C2×#102—261no—
178C2×C4×C8—131no—
179#390—261no—
180#358—262no—
181#357—262no—
182C22×C13C4×D811yescharacteristic
183C22×C13#44711yescharacteristic
184C22×C13#45911yescharacteristic
185C22×C13C2×SD3211yescharacteristic
186C22×C13#50811yescharacteristic
187C22×C13#50911yescharacteristic
188C22×C13#51011yescharacteristic
189C2×D13—82no—
190C2×D13—82no—
191C2×D13—82no—
192C2×D13—161no—
193C2×D13—161no—
194C2×D13—161no—
195C2×D13—161no—
196C4×C13—82no—
197C4×C13—161no—
198C4×C13#38611yescharacteristic
199C4×C13#44211yescharacteristic
200C4×C13#44911yescharacteristic
201C4×C13#46311yescharacteristic
202Dic13—22no—
203Dic13—44no—
204Dic13—41no—
205C22×Q8—261no—
206C22×D4—261no—
207C2×Q16—132no—
208C2×Q16—132no—
209C2×Q16—132no—
210C2×Q16—261no—
211C2×Q16—261no—
212C2×Q16—261no—
213C2×D8—132no—
214C2×D8—261no—
215C2×D8—261no—
216C2×D8—261no—
217C2×D8—261no—
218C2×D8—261no—
219C22×C8—131no—
220C22×C8C22×D1311yescharacteristic
221C4×Q8—264no—
222C4×Q8—522no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—521no—
226C2×C22⋊C4—521no—
227C2×C22⋊C4—521no—
228C2×C42—131no—
229C2×C42—521no—
230SD32—268no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—261no—
234C2×C16—261no—
235C2×C16—261no—
236C2×C16C4×D1312yes—
237#107—21no—
238#107—21no—
239#107—21no—
240#107D5212yes—
241#103—264no—
242#102—522no—
243C4×C8—261no—
244C4×C8—261no—
245C2×C13#187911yescharacteristic
246C2×C13C4×SD3211yescharacteristic
247C2×C13#217511yescharacteristic
248C2×C13#218511yescharacteristic
249C2×C13#218611yescharacteristic
250C2×C13#220711yescharacteristic
251C2×C13#221111yescharacteristic
252D13—162no—
253C24—521no—
254C2×Q8—262no—
255C2×Q8—262no—
256C2×Q8—262no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×D4—262no—
261C2×D4—521no—
262C2×D4—521no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4—521no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—521no—
271C22×C4D4×D1311yescharacteristic
272Q16—134no—
273Q16—262no—
274Q16—262no—
275Q16—262no—
276D8—262no—
277D8—262no—
278D8—521no—
279D8—521no—
280C2×C8—261no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8C2×C4×D1311yescharacteristic
284C2×C8C2×D5211yescharacteristic
285C2×C8#612711yescharacteristic
286C2×C8D4×D1311yescharacteristic
287C2×C8D4×D1311yescharacteristic
288C2×C8#613111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—524no—
294C22⋊C4—1042no—
295C22⋊C4—1042no—
296C42—261no—
297C42—261no—
298C42—524no—
299C16—22no—
300C16—521no—
301C13#1301311yescharacteristic, complemented, Sylow
302C23—522no—
303C23—1041no—
304C23—1041no—
305C23—1041no—
306C23—1041no—
307C23—1041no—
308C23—1041no—
309C23D8×D1311yescharacteristic
310Q8—264no—
311Q8—522no—
312Q8—522no—
313Q8—522no—
314D4—522no—
315D4—522no—
316D4—1041no—
317D4—1041no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—132no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4#8813611yescharacteristic
334C2×C4#8813811yescharacteristic
335C2×C4#8814711yescharacteristic
336C2×C4#8816811yescharacteristic
337C2×C4#8816811yescharacteristic
338C2×C4#8817311yescharacteristic
339C8—521no—
340C8C4×D5211yescharacteristic
341C8C22⋊C4×D1311yescharacteristic
342C8#8814811yescharacteristic
343C8#8814911yescharacteristic
344C22—1042no—
345C22—1042no—
346C22—1042no—
347C22—2081no—
348C22—2081no—
349C22—2081no—
350C22—2081no—
351C22#1171843411yescharacteristic
352C22#1171844711yescharacteristic
353C22#1171853311yescharacteristic
354C22#1171857211yescharacteristic
355C22D13×SD3211yescharacteristic
356C22#1171857711yescharacteristic
357C22#1171857911yescharacteristic
358C4—82no—
359C4—161no—
360C4—262no—
361C4—524no—
362C4—521no—
363C4#1171832611yescharacteristic
364C4#1171847211yescharacteristic
365C4#1171848011yescharacteristic
366C4#1171853011yescharacteristic
367C2—2082no—
368C2#1311518511yescharacteristic
369C2#1311668711yescharacteristic
370C2#1311669911yescharacteristic
371C2#1311675411yescharacteristic
372C2#1311676011yescharacteristic
373C2#1311687511yescharacteristic
374C2#1311690111yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenter#1380D13
hypocenterC13#13013
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#11718534C2semidirect
3. C2×#11718084C2semidirect
6. #13112913C2semidirect
7. C13×#1380C2semidirect
21. C2×#88040C4semidirect
108. Dic52C22⋊C4semidirect
120. #1380D13semidirect
150. C2×Dic13SD32semidirect
301. C13#13013semidirect

Maximal subgroups

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

subgroupindex
C22×#880402
C2×#117185342
C2×#117180842
C2×#117180832
#131157002
#131129132
C13×#13802
#1301313