Finite Group Databasebeta

← #15782091

Subgroups — #15782091

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718548C211yesmaximal, characteristic
2C2×#11718082C211yesmaximal, characteristic, complemented
3C2×#11718095C211yesmaximal, characteristic, complemented
4C2×#11718084C211yesmaximal, characteristic, complemented
5C2×#11718099C211yesmaximal, characteristic
6#13114862C211yesmaximal, characteristic
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×#88151—21no—
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×C13×#107C2211yescharacteristic
14C2×#88058C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718648—21no—
17C2×#88050—21no—
18#11718548—22no—
19#11718548—22no—
20#11718121—21no—
21#11718099—22no—
22#11718095—22no—
23#11718084—22no—
24#11718082—22no—
25C22×C4×D13D411yescharacteristic
26C22×Dic26—21no—
27C22×C8×C13C2311yescharacteristic
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×#6103—41no—
31C2×#6103—41no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—41no—
34C22×#1055D411yescharacteristic
35C2×Dic52—21no—
36C2×Dic52—21no—
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52D412yes—
41C2×C8×D13—21no—
42C2×C8×D13—21no—
43C2×C8×D13—21no—
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13—21no—
47#88151—24no—
48#88151—42no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C13×#107—21no—
53C13×#107—21no—
54C13×#107—21no—
55C13×#107D412yes—
56#88071—41no—
57#88058—21no—
58#88058—21no—
59C2×#6090—21no—
60C2×#6090—21no—
61C2×#6090D412yes—
62#88050—24no—
63#13382—131nomaximal, Sylow
64C23×D13D811yescharacteristic
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13D811yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×Dic26—22no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×C8×C13C2×D411yescharacteristic
84C2×C8×C13C2×D411yescharacteristic
85C2×C8×C13C2×D411yescharacteristic
86C2×C8×C13#4111yescharacteristic
87C2×C8×C13#4111yescharacteristic
88C2×C8×C13#4111yescharacteristic
89C13×C4⋊C4—22no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93#6103—44no—
94#6103—82no—
95C4⋊Dic13—44no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—21no—
101Dic52—22no—
102Dic52—22no—
103Dic52—41no—
104Dic52—41no—
105C8×D13—41no—
106C8×D13—41no—
107C8×D13—41no—
108C8×D13—41no—
109C13×C16—41no—
110#6090—22no—
111C2×#467—131no—
112C2×#367—131no—
113C2×#358—131no—
114C2×#358—131no—
115C2×C22⋊C16—131no—
116#1808—131no—
117#1380D1311yescharacteristic, complemented
118C23×C13C2×D811yescharacteristic
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13SD3212yes—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12311yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—42no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C4×D13—41no—
148C4×D13—41no—
149C4×D13—41no—
150C4×D13—41no—
151Dic26—42no—
152Dic26—42no—
153Dic26—81no—
154Dic26—81no—
155C8×C13#12111yescharacteristic
156C8×C13#12111yescharacteristic
157C8×C13#12311yescharacteristic
158C8×C13#12411yescharacteristic
159#1055—41no—
160C22×Q16—131no—
161C23×C8—131no—
162C2×C22⋊Q8—261no—
163C22×C16—131no—
164C22×C16C2×D1311yescharacteristic
165#467—262no—
166#467—262no—
167C2×#107—131no—
168C2×#107C2×D1311yescharacteristic
169C2×#107C2×D1311yescharacteristic
170C2×#103—261no—
171#380—261no—
172#367—262no—
173#358—262no—
174#358—262no—
175C22⋊C16—262no—
176#340—261no—
177C22×C13#44711yescharacteristic
178C22×C13#46611yescharacteristic
179C22×C13#48011yescharacteristic
180C22×C13C2×SD3211yescharacteristic
181C22×C13#50811yescharacteristic
182C22×C13#51011yescharacteristic
183C22×C13#51011yescharacteristic
184C2×D13—22no—
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C4×C13—82no—
192C4×C13—161no—
193C4×C13#39411yescharacteristic
194C4×C13#45211yescharacteristic
195C4×C13#46811yescharacteristic
196C4×C13#48211yescharacteristic
197Dic13—41no—
198Dic13—82no—
199Dic13—161no—
200C22×Q8—261no—
201C23×C4—131no—
202C2×Q16—132no—
203C2×Q16—261no—
204C2×Q16—261no—
205C2×Q16—261no—
206C2×Q16—261no—
207C2×Q16—261no—
208C22×C8—131no—
209C22×C8—261no—
210C22×C8—261no—
211C22×C8—261no—
212C22×C8—261no—
213C22×C8—261no—
214C22×C8—261no—
215C22×C8C22×D1311yescharacteristic
216C22⋊Q8—264no—
217C22⋊Q8—522no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—521no—
222C2×C22⋊C4—521no—
223C2×C22⋊C4—521no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—132no—
228C2×C16—261no—
229C2×C16—261no—
230#107—21no—
231#107—21no—
232#107—21no—
233#107—261no—
234#107—261no—
235#107D5212yes—
236#103—264no—
237#95—521no—
238C2×C13#203311yescharacteristic
239C2×C13#218511yescharacteristic
240C2×C13#218911yescharacteristic
241C2×C13#221711yescharacteristic
242C2×C13#221911yescharacteristic
243C2×C13#223511yescharacteristic
244C2×C13#223711yescharacteristic
245D13—42no—
246C24—131no—
247C2×Q8—262no—
248C2×Q8—521no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×Q8—521no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—131no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4D4×D1311yescharacteristic
265Q16—262no—
266Q16—262no—
267Q16—521no—
268Q16—521no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8C2×D5211yescharacteristic
277C2×C8#612711yescharacteristic
278C2×C8#612711yescharacteristic
279C2×C8D4×D1311yescharacteristic
280C2×C8D4×D1311yescharacteristic
281C2×C8#613111yescharacteristic
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—524no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C22⋊C4—524no—
290C22⋊C4—1042no—
291C16—41no—
292C16—262no—
293C13#1338211yescharacteristic, complemented, Sylow
294C23—132no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23D8×D1311yescharacteristic
302Q8—522no—
303Q8—522no—
304Q8—1041no—
305Q8—1041no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4#8813611yescharacteristic
326C2×C4#8813811yescharacteristic
327C2×C4#8814811yescharacteristic
328C2×C4#8816811yescharacteristic
329C2×C4#8817011yescharacteristic
330C2×C4#8817211yescharacteristic
331C8—521no—
332C8#8812911yescharacteristic
333C8#8813811yescharacteristic
334C8#8814811yescharacteristic
335C8#8814911yescharacteristic
336C22—262no—
337C22—262no—
338C22—262no—
339C22—521no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22#1171843411yescharacteristic
344C22#1171843611yescharacteristic
345C22#1171854311yescharacteristic
346C22#1171857311yescharacteristic
347C22D13×SD3211yescharacteristic
348C22#1171857611yescharacteristic
349C22#1171857911yescharacteristic
350C4—82no—
351C4—161no—
352C4—521no—
353C4—1042no—
354C4—2081no—
355C4#1171833311yescharacteristic
356C4#1171847111yescharacteristic
357C4#1171847311yescharacteristic
358C4#1171852711yescharacteristic
359C2—522no—
360C2#1311602111yescharacteristic
361C2#1311675411yescharacteristic
362C2#1311677711yescharacteristic
363C2#1311693111yescharacteristic
364C2#1311694311yescharacteristic
365C2#1311703511yescharacteristic
366C2#1311704611yescharacteristic
subgroupG/H
centerC23D8×D13
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC23×D13D8
hypercenter#1380D13
hypocenterC13#13382
LCSG ▷ C22×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×#11718082C2semidirect
3. C2×#11718095C2semidirect
4. C2×#11718084C2semidirect
7. C13×#1380C2semidirect
117. #1380D13semidirect
293. C13#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#117185482
C2×#117180822
C2×#117180952
C2×#117180842
C2×#117180992
#131148622
C13×#13802
#1338213