Finite Group Databasebeta

← #15779982

Subgroups — #15779982

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×C4×Dic52C211yesmaximal, characteristic, complemented
3C2×#11718095C211yesmaximal, characteristic, complemented
4C2×#11718101C211yesmaximal, characteristic
5#13115702C211yesmaximal, characteristic
6#13112928C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×D104C2211yescharacteristic
10C2×C4×Dic26—21no—
11C22×C13×C16C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88061—21no—
15C2×#88058C2211yescharacteristic
16C2×#88058C2211yescharacteristic
17C2×#88056—21no—
18#11718600—21no—
19C2×#88040—22no—
20C2×#88040—22no—
21C2×#88040C414yescomplemented
22C4×Dic52—22no—
23C4×Dic52—22no—
24#11718101—22no—
25#11718095—22no—
26C22×D52—21no—
27C22×Dic26—21no—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13C2311yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×#6103—41no—
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×#6101—41no—
36C2×C4×Dic13—41no—
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—
49C4×Dic26—24no—
50C4×Dic26—42no—
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16C2×C412yes—
57C4×C8×C13—21no—
58C4×C8×C13—21no—
59#88061—42no—
60#88058—21no—
61#88058—21no—
62#88058—21no—
63#88058D412yes—
64#88056—24no—
65#88040—28no—
66#13013—131nomaximal, Sylow
67C23×D13—41no—
68C22×C4×C13D811yescharacteristic
69C22×C4×C13D811yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
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×C13—21no—
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13C22×C411yescharacteristic
90C2×C8×C13C2×D411yescharacteristic
91C2×C8×C13C2×D411yescharacteristic
92C2×C8×C13C2×D411yescharacteristic
93C2×C8×C13#4111yescharacteristic
94C2×C8×C13#4111yescharacteristic
95C42×C13—21no—
96C42×C13—21no—
97#6103—82no—
98#6103—82no—
99C4⋊Dic13—22no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103#6101—44no—
104C4×Dic13—44no—
105Dic52—22no—
106Dic52—22no—
107Dic52—22no—
108Dic52C22⋊C414yescomplemented
109D104—22no—
110D104—22no—
111D104—41no—
112D104—41no—
113C13×C16—22no—
114C13×C16—41no—
115C22×SD32—131no—
116C2×C4×Q16—131no—
117C2×#358—131no—
118C2×#357—131no—
119#1970—131no—
120#1380—131no—
121#1374D1311yescharacteristic, complemented
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—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13SD3212yescomplemented
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—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151D52—42no—
152D52—42no—
153D52—81no—
154D52—81no—
155Dic26—24no—
156Dic26—42no—
157Dic26—42no—
158Dic26—42no—
159C8×C13—41no—
160C8×C13C2×C22⋊C411yescharacteristic
161C8×C13C4×D411yescharacteristic
162C8×C13#12111yescharacteristic
163C8×C13#12311yescharacteristic
164C22×Q16—131no—
165C22×D8—131no—
166C2×C4×Q8—261no—
167C2×SD32—134no—
168C2×SD32—262no—
169C2×SD32—262no—
170C22×C16C2×D1311yescharacteristic
171C22×C16C2×D1311yescharacteristic
172C4×Q16—262no—
173C4×Q16—262no—
174C2×#107—131no—
175C2×#107—131no—
176C2×#103—261no—
177C2×#102—261no—
178C2×C4×C8C2×D1311yescharacteristic
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—22no—
197C4×C13—41no—
198C4×C13#38611yescharacteristic
199C4×C13#44211yescharacteristic
200C4×C13#44911yescharacteristic
201C4×C13#46311yescharacteristic
202Dic13—44no—
203Dic13—82no—
204Dic13—161no—
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×C8D5211yescharacteristic
220C22×C8C22×D1311yescharacteristic
221C4×Q8—264no—
222C4×Q8—522no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—521no—
226C2×C22⋊C4—521no—
227C2×C22⋊C4—521no—
228C2×C42—521no—
229C2×C42D5211yescharacteristic
230SD32—268no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16C4×D1312yes—
237#107—132no—
238#107—261no—
239#107—261no—
240#107—261no—
241#103—264no—
242#102—522no—
243C4×C8—21no—
244C4×C8—21no—
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—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4D10411yescharacteristic
270C22×C4D10411yescharacteristic
271C22×C4C2×D5211yescharacteristic
272Q16—134no—
273Q16—262no—
274Q16—262no—
275Q16—262no—
276D8—262no—
277D8—262no—
278D8—521no—
279D8—521no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8C2×C4×D1311yescharacteristic
284C2×C8#612711yescharacteristic
285C2×C8D4×D1311yescharacteristic
286C2×C8D4×D1311yescharacteristic
287C2×C8D4×D1311yescharacteristic
288C2×C8#613111yescharacteristic
289C4⋊C4—262no—
290C4⋊C4—524no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—1042no—
295C22⋊C4—1042no—
296C42—21no—
297C42—21no—
298C42—524no—
299C16—22no—
300C16—41no—
301C13#1301311yescharacteristic, complemented, Sylow
302C23—522no—
303C23—1041no—
304C23—1041no—
305C23—1041no—
306C23—1041no—
307C23—1041no—
308C23—1041no—
309C23C2×D10411yescharacteristic
310Q8—264no—
311Q8—522no—
312Q8—522no—
313Q8—522no—
314D4—522no—
315D4—522no—
316D4—1041no—
317D4—1041no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—1041no—
328C2×C4—1041no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4#8804012yescomplemented
333C2×C4C4×D5211yescharacteristic
334C2×C4#8813611yescharacteristic
335C2×C4#8814911yescharacteristic
336C2×C4#8815811yescharacteristic
337C2×C4#8816211yescharacteristic
338C2×C4#8816211yescharacteristic
339C8—41no—
340C8C22⋊C4×D1311yescharacteristic
341C8#8813811yescharacteristic
342C8#8814711yescharacteristic
343C8#8814811yescharacteristic
344C22—1042no—
345C22—1042no—
346C22—1042no—
347C22—2081no—
348C22—2081no—
349C22—2081no—
350C22—2081no—
351C22C4×D10411yescharacteristic
352C22#1171839311yescharacteristic
353C22#1171850411yescharacteristic
354C22C2×#8804011yescharacteristic
355C22#1171856511yescharacteristic
356C22#1171856911yescharacteristic
357C22#1171857011yescharacteristic
358C4—22no—
359C4—41no—
360C4—524no—
361C4—1042no—
362C4—2081no—
363C4#1171832611yescharacteristic
364C4#1171837211yescharacteristic
365C4#1171839511yescharacteristic
366C4#1171850511yescharacteristic
367C2—2082no—
368C2#1311518311yescharacteristic
369C2C4×#8804011yescharacteristic
370C2#1311670211yescharacteristic
371C2#1311675511yescharacteristic
372C2#1311676111yescharacteristic
373C2#1311687711yescharacteristic
374C2#1311689911yescharacteristic
subgroupG/H
centerC23C2×D104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1374C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenter#1374D13
hypocenterC13#13013
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic52C2semidirect
3. C2×#11718095C2semidirect
6. #13112928C2semidirect
7. C13×#1374C2semidirect
21. C2×#88040C4semidirect
108. Dic52C22⋊C4semidirect
121. #1374D13semidirect
135. C2×C4×C13SD32semidirect
301. C13#13013semidirect
332. C2×C4#88040semidirect

Maximal subgroups

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

subgroupindex
C22×#880402
C2×C4×Dic522
C2×#117180952
C2×#117181012
#131157022
#131129282
C13×#13742
#1301313