Finite Group Databasebeta

← #15755897

Subgroups — #15755897

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123530C211yesmaximal, characteristic
2#13114865C211yesmaximal, characteristic, complemented
3#13113380C212yesmaximal
4#13112743C212yesmaximal, complemented
5C13×#1810C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7#11719496C2211yescharacteristic
8C2×#88155C411yescharacteristic, complemented
9C2×C13×#108—21no—
10C13×#407C2212yes—
11#11718873C2212yes—
12#11718868C2211yescharacteristic
13#11718772—21no—
14#11718772—21no—
15#11718771C411yescharacteristic, complemented
16C8×C22⋊D13—21no—
17C8×C22⋊D13—21no—
18C2×#88058—21no—
19#11718763C411yescharacteristic, complemented
20#11718762C411yescharacteristic, complemented
21C13×#341—21no—
22#11718143—21no—
23#11718062—22no—
24#11718059—22no—
25C23×C4×C13C2311yescharacteristic
26C2×#6127C2×C411yescharacteristic
27C2×C13×M16—22no—
28C22×C8×C13—42no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35#88207—21no—
36C2×C22⋊Dic13—22no—
37#88184D411yescharacteristic
38#88184Q811yescharacteristic
39#88183—21no—
40C4×C22⋊D13—21no—
41C4×C22⋊D13—21no—
42#88180C2×C411yescharacteristic
43C2×C4⋊Dic13—22no—
44#88178D411yescharacteristic
45#88178Q811yescharacteristic
46C2×#6099C2×C411yescharacteristic
47C2×#6099C2×C411yescharacteristic
48#88155—42no—
49C2×#6094—21no—
50C2×C8×D13—21no—
51C13×#108—42no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—22no—
54#88071—22no—
55C22⋊#1055—21no—
56C22⋊#1055—21no—
57#88060—21no—
58#88060—21no—
59#88058—42no—
60#88055—21no—
61#88054—21no—
62#88054—21no—
63C8×Dic13—21no—
64#8627—131nomaximal, Sylow
65C24×C13#4111yescharacteristic
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×Q811yescharacteristic
73C22×C4×C13#4111yescharacteristic
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C22×Dic13—42no—
78#6127—41no—
79#6127—41no—
80C2×D52C4⋊C411yescharacteristic
81C2×C4×D13—21no—
82C2×Dic26C4⋊C411yescharacteristic
83C13×M16—42no—
84C13×M16—42no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—42no—
92C2×C8×C13C22⋊C411yescharacteristic
93C2×C8×C13C22⋊C411yescharacteristic
94C2×C8×C13C22⋊C411yescharacteristic
95C2×C8×C13C22⋊C411yescharacteristic
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—82no—
100#6103—21no—
101#6103—21no—
102C4⋊Dic13—42no—
103C4⋊Dic13—42no—
104C4⋊Dic13C4⋊C411yescharacteristic
105C4⋊Dic13C4⋊C411yescharacteristic
106#6101—21no—
107#6101—21no—
108C4×Dic13—21no—
109#6099—41no—
110#6099—41no—
111C2×#1055—21no—
112C2×#1055—21no—
113#6094—42no—
114C8×D13—42no—
115#2929—131no—
116#1810D1311yescharacteristic, complemented
117#1808—131no—
118#1513—132no—
119#1305—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#11711yescharacteristic
125C23×C13#12111yescharacteristic
126C23×C13C22⋊Q811yescharacteristic
127C22×D13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13C2×C4⋊C411yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13C22⋊Q811yescharacteristic
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—41no—
144C22⋊D13—41no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—82no—
149C2×Dic13—82no—
150C2×Dic13—82no—
151D52—41no—
152C4×D13—41no—
153C4×D13—41no—
154Dic26—41no—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—82no—
159C8×C13#9912yes—
160#1055—41no—
161#1055—41no—
162C2×#131—131no—
163C23×C8C2×D1311yescharacteristic
164#525—131no—
165#435—261no—
166#435—261no—
167C8×D4—261no—
168C8×D4—261no—
169C2×#108—21no—
170C2×#107—261no—
171#424—131no—
172#408—131no—
173#407—131no—
174#407C2×D1312yes—
175#405—131no—
176#380—132no—
177#341—21no—
178#340—261no—
179#328—262no—
180#327—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13#38011yescharacteristic
192C22×C13#47211yescharacteristic
193C22×C13#47311yescharacteristic
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13C2×#9911yescharacteristic
201C4×C13#41011yescharacteristic
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205Dic13—162no—
206C2×#41—131no—
207C23×C4C22×D1311yescharacteristic
208#131—522no—
209C2×M16—22no—
210C2×M16—131no—
211C2×M16—131no—
212C2×M16—261no—
213C22×C8—42no—
214C22×C8—261no—
215C22×C8C4×D1311yescharacteristic
216C22×C8C4×D1311yescharacteristic
217C22×C8D5211yescharacteristic
218C22×C8D5211yescharacteristic
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22⋊D1311yescharacteristic
221#123—261no—
222C22⋊Q8—131no—
223C22⋊Q8—131no—
224#121—131no—
225#121—131no—
226#120—261no—
227C4×D4—261no—
228C4×D4—261no—
229#117—131no—
230C2×C4⋊C4—262no—
231C2×C22⋊C4—262no—
232#108—42no—
233#107—522no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—261no—
239C22⋊C8—261no—
240C22⋊C8—261no—
241C22⋊C8—261no—
242#97—261no—
243C4×C8—261no—
244#95—262no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—41no—
248C2×C13—41no—
249C2×C13#179911yescharacteristic
250C2×C13#181411yescharacteristic
251C2×C13#181611yescharacteristic
252D13—81no—
253C24#613111yescharacteristic
254#41—521no—
255#41—521no—
256C2×Q8—131no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—261no—
264C22×C4—522no—
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C22×C4D4×D1311yescharacteristic
268C22×C4#612911yescharacteristic
269C22×C4Q8×D1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271M16—42no—
272M16—42no—
273M16—522no—
274M16—521no—
275M16—521no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—42no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—522no—
286C2×C8#610311yescharacteristic
287C2×C8#610311yescharacteristic
288C2×C8#610311yescharacteristic
289C2×C8#610311yescharacteristic
290C4⋊C4—131no—
291C4⋊C4—131no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4—522no—
295C4⋊C4—522no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—1042no—
302C42—261no—
303C13#862711yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—261no—
309C23#8814611yescharacteristic
310C23#8814911yescharacteristic
311C23#8820011yescharacteristic
312Q8—521no—
313D4—521no—
314D4—522no—
315D4—522no—
316D4—521no—
317D4—521no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—1042no—
333C2×C4—1042no—
334C2×C4—1042no—
335C2×C4C4⋊C4×D1311yescharacteristic
336C2×C4#8815111yescharacteristic
337C2×C4C2×#610311yescharacteristic
338C2×C4#8819211yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—82no—
343C8—521no—
344C8—521no—
345C8#8804612yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22#1171855711yescharacteristic
360C22#1171855811yescharacteristic
361C22#1171864811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—521no—
366C4—521no—
367C4—521no—
368C4—2082no—
369C4C2×#8804611yescharacteristic
370C4#1171866711yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—1041no—
376C2#1311482111yescharacteristic
377C2#1311489111yescharacteristic
378C2#1311489711yescharacteristic
subgroupG/H
centerC22#11718648
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1810C2
socleC22×C13#380
prime radical#11719496C22
cosocleC23×C4×C13C23
hypercenter#1810D13
hypocenterC13#8627
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1810

Complements

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

NH ≅ G/Ntype
2. #13114865C2semidirect
4. #13112743C2semidirect
5. C13×#1810C2semidirect
8. C2×#88155C4semidirect
15. #11718771C4semidirect
19. #11718763C4semidirect
20. #11718762C4semidirect
116. #1810D13semidirect
303. C13#8627semidirect

Maximal subgroups

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

subgroupindex
#131235302
#131148652
#131133802
#131127432
C13×#18102
#862713