Finite Group Databasebeta

← #15782071

Subgroups — #15782071

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718081C211yesmaximal, characteristic, complemented
2C2×#11718154C211yesmaximal, characteristic, complemented
3C2×#11718154C211yesmaximal, characteristic, complemented
4C2×C22⋊#6090C211yesmaximal, characteristic, complemented
5#13114865C211yesmaximal, characteristic, complemented
6#13112927C211yesmaximal, characteristic, complemented
7C2×C13×#466C211yesmaximal, characteristic
8C22×C13×D8C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C2×C13×#121—21no—
11C13×#466—22no—
12C13×#466—22no—
13C2×C13×#107C2211yescharacteristic
14C2×C13×#102—21no—
15#11718873—21no—
16C2×#88058C2211yescharacteristic
17C2×#88058C2211yescharacteristic
18C22×#6090C2211yescharacteristic
19C22×#6090C2211yescharacteristic
20#11718154—22no—
21#11718154—22no—
22#11718143—21no—
23C22⋊#6090—22no—
24#11718081—22no—
25C22×D4×C13—21no—
26C22×D4×C13—41no—
27C23×C4×C13D411yescharacteristic
28C2×C13×D8—21no—
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8—21no—
33C2×C13×D8D412yes—
34C22×C8×C13—21no—
35C22×C8×C13—21no—
36C22×C8×C13—21no—
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13D411yescharacteristic
41C22×C8×C13C2311yescharacteristic
42C13×#121—24no—
43C13×#121—42no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C22⋊C4—41no—
46C2×C22⋊Dic13—41no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C13×#107—21no—
50C13×#107D412yes—
51C13×#102—24no—
52#88071—41no—
53#88058—21no—
54#88058—21no—
55#88058—21no—
56#88058—21no—
57C2×#6090—21no—
58C2×#6090—21no—
59C2×#6090—21no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090D412yescomplemented
63#13380—131nomaximal, Sylow
64C24×C13—41no—
65C24×C13D811yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—44no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—82no—
74C2×D4×C13—82no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13D811yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—41no—
85C22×Dic13—41no—
86C13×D8—22no—
87C13×D8—22no—
88C13×D8—41no—
89C13×D8—41no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C13×C4⋊C4—22no—
104C13×C4⋊C4—41no—
105C13×C22⋊C4—44no—
106C22⋊Dic13—82no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111#6090—22no—
112#6090—41no—
113C2×#466D1311yescharacteristic
114C2×#366—131no—
115C2×#357—131no—
116C2×#357—131no—
117C2×C22⋊C16—131no—
118#1808—131no—
119#1380—131no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13—81no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13D1612yes—
134C23×C13C2×D811yescharacteristic
135D4×C13—42no—
136D4×C13—42no—
137D4×C13—88no—
138D4×C13—81no—
139D4×C13—81no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13#13711yescharacteristic
156C2×Dic13—81no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159C2×Dic13—81no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162C8×C13—41no—
163C8×C13#12111yescharacteristic
164C8×C13#12111yescharacteristic
165C8×C13#12311yescharacteristic
166C8×C13#12411yescharacteristic
167C22×D8C2×D1311yescharacteristic
168C23×C8C2×D1311yescharacteristic
169C2×#121—21no—
170C22×C16—131no—
171C22×C16—131no—
172#466—22no—
173#466—22no—
174C2×#107—131no—
175C2×#107—131no—
176C2×#107C2×D1311yescharacteristic
177C2×#102—21no—
178#380—261no—
179#366—262no—
180#357—262no—
181#357—262no—
182C22⋊C16—262no—
183#340—261no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13—161no—
195C22×C13—161no—
196C22×C13—161no—
197C22×C13—161no—
198C22×C13#44711yescharacteristic
199C22×C13#46611yescharacteristic
200C22×C13#48011yescharacteristic
201C22×C13C2×D1611yescharacteristic
202C22×C13#50811yescharacteristic
203C22×C13#50911yescharacteristic
204C22×C13#51011yescharacteristic
205C4×C13—41no—
206C4×C13—82no—
207C4×C13#39411yescharacteristic
208C4×C13#45211yescharacteristic
209C4×C13#46811yescharacteristic
210C4×C13#48211yescharacteristic
211Dic13—161no—
212Dic13—161no—
213C22×D4—21no—
214C22×D4—41no—
215C23×C4C22⋊D1311yescharacteristic
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8C22⋊D1312yes—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C22⋊D1311yescharacteristic
229C22×C8C22×D1311yescharacteristic
230#121—24no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—521no—
237C2×C16—132no—
238C2×C16—261no—
239C2×C16—261no—
240C2×C16—261no—
241C2×C16—261no—
242C2×C16—261no—
243#107—21no—
244#107—261no—
245#107—261no—
246#107—261no—
247#107—261no—
248#107C22⋊D1312yes—
249#102—24no—
250#95—521no—
251C2×C13—42no—
252C2×C13—162no—
253C2×C13#203311yescharacteristic
254C2×C13#218411yescharacteristic
255C2×C13#218911yescharacteristic
256C2×C13#221511yescharacteristic
257C2×C13#222011yescharacteristic
258C2×C13#223211yescharacteristic
259C2×C13#223411yescharacteristic
260C24—41no—
261C24#610411yescharacteristic
262C2×D4—22no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—82no—
270C2×D4—82no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4#610411yescharacteristic
281C22×C4C2×C22⋊D1311yescharacteristic
282D8—22no—
283D8—22no—
284D8—41no—
285D8—41no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8D4×D1311yescharacteristic
294C2×C8#612911yescharacteristic
295C2×C8#612911yescharacteristic
296C2×C8#612911yescharacteristic
297C2×C8C2×C22⋊D1311yescharacteristic
298C2×C8C2×C22⋊D1311yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C22⋊C4—44no—
306C22⋊C4—1042no—
307C16—262no—
308C16—521no—
309C13#1338011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23#8806612yes—
324C23C2×#610411yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—1041no—
341C2×C4—1041no—
342C2×C4—1041no—
343C2×C4—1041no—
344C2×C4—1041no—
345C2×C4—1041no—
346C2×C4#8818611yescharacteristic
347C2×C4#8818911yescharacteristic
348C2×C4#8819311yescharacteristic
349C2×C4#8820411yescharacteristic
350C2×C4#8820511yescharacteristic
351C2×C4#8820711yescharacteristic
352C8—41no—
353C8#8818911yescharacteristic
354C8#8819011yescharacteristic
355C8#8819211yescharacteristic
356C8#8819311yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22#1171869411yescharacteristic
372C22#1171869911yescharacteristic
373C22C2×#8806611yescharacteristic
374C22#1171880811yescharacteristic
375C22#1171885511yescharacteristic
376C22#1171885611yescharacteristic
377C22#1171887811yescharacteristic
378C4—41no—
379C4—82no—
380C4—2081no—
381C4—2081no—
382C4#1171869611yescharacteristic
383C4#1171870311yescharacteristic
384C4#1171888311yescharacteristic
385C4#1171890011yescharacteristic
386C2—42no—
387C2—162no—
388C2#1311601511yescharacteristic
389C2#1311674811yescharacteristic
390C2#1311677611yescharacteristic
391C2#1311692011yescharacteristic
392C2#1311694711yescharacteristic
393C2#1311701411yescharacteristic
394C2#1311702411yescharacteristic
subgroupG/H
centerC23C2×#6104
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#466C2
socleC23×C13C2×D8
hypercenterC2×#466D13
hypocenterC13#13380
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#11718081C2semidirect
2. C2×#11718154C2semidirect
3. C2×#11718154C2semidirect
4. C2×C22⋊#6090C2semidirect
5. #13114865C2semidirect
6. #13112927C2semidirect
62. C2×#6090D4semidirect
309. C13#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#117180812
C2×#117181542
C2×C22⋊#60902
#131148652
#131129272
C2×C13×#4662
#1338013