Finite Group Databasebeta

← #16789374

Subgroups — #16789374

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#350C211yesmaximal, characteristic
2#13131044C211yesmaximal, characteristic, complemented
3C2×#11718216C211yesmaximal, characteristic, complemented
4#13130610C211yesmaximal, characteristic
5#13129892C211yesmaximal, characteristic, complemented
6#13129879C211yesmaximal, characteristic, complemented
7D13×#504C211yesmaximal, characteristic
8D13×#131C2211yescharacteristic
9#11719165C411yescharacteristic
10D13⋊#104C411yescharacteristic
11#11719089C2211yescharacteristic
12C2×C8×#261C2211yescharacteristic
13D13⋊M32C2211yescharacteristic
14C2×D13⋊C16C2211yescharacteristic
15C13×#504C411yescharacteristic, complemented
16#11718801C411yescharacteristic, complemented
17#11718568—21no—
18#11718568C411yescharacteristic, complemented
19D13×M32—21no—
20D13×M32C2211yescharacteristic
21#11718562—21no—
22#11718562C411yescharacteristic, complemented
23C2×C16×D13—21no—
24C2×C16×D13C2211yescharacteristic
25#11718304C412yescomplemented
26#11718273C411yescharacteristic
27#11718272C411yescharacteristic
28#11718270C412yescomplemented
29#11718216—21no—
30#11718216—21no—
31#11718216—21no—
32C16×#261—21no—
33#41×D13C2×C411yescharacteristic
34#88237C2×C411yescharacteristic
35C2×C4×#261C2×C411yescharacteristic
36D13⋊M16C2×C411yescharacteristic
37C2×D13⋊C8C2×C411yescharacteristic
38C13×#131C2×C411yescharacteristic
39#88202C2×C411yescharacteristic
40#88161—21no—
41#88161C2×C411yescharacteristic
42M16×D13—21no—
43M16×D13C2×C411yescharacteristic
44#88155—21no—
45#88155C2×C411yescharacteristic
46C2×C8×D13—21no—
47C2×C8×D13C2311yescharacteristic
48#88118C812yes—
49#88117C812yes—
50#88116C812yes—
51#88115C812yes—
52#88106C2×C412yes—
53C2×#6092C2×C412yes—
54#88100—21no—
55C8×#261—21no—
56C8×#261—21no—
57C8×#261—21no—
58#88098—21no—
59D13⋊C16—21no—
60D13⋊C16—21no—
61D13⋊C16—21no—
62C13×M32—21no—
63C13×M32C2×C411yescharacteristic
64C2×C13×C16—21no—
65C2×C13×C16C2×C411yescharacteristic
66#88052—21no—
67#88052C2×C411yescharacteristic
68C2×#6090—21no—
69C2×#6090C2×C411yescharacteristic
70#88038—21no—
71#88038—21no—
72#88038—21no—
73C16×D13—21no—
74C16×D13—21no—
75C16×D13—21no—
76C16×D13D411yescharacteristic
77C16×D13D411yescharacteristic
78C16×D13D411yescharacteristic
79C16×D13D411yescharacteristic
80#12615—131nomaximal, Sylow
81C22×#261—21no—
82C13×#41C4211yescharacteristic
83#6131C2×C811yescharacteristic
84Q8×D13C2×C811yescharacteristic
85#6129—21no—
86#6129C2×C811yescharacteristic
87D4×D13—21no—
88D4×D13C2×C811yescharacteristic
89#6127—21no—
90#6127C4211yescharacteristic
91C2×C4×D13—21no—
92C2×C4×D13C22×C411yescharacteristic
93C22⋊#261—21no—
94#6122—21no—
95C2×#1057—21no—
96C4⋊#261C2×C812yes—
97C4×#261—21no—
98C4×#261—21no—
99C4×#261C2×C812yes—
100#6118C2×C812yes—
101D13⋊C8—21no—
102D13⋊C8—21no—
103D13⋊C8C2×C812yes—
104C13×M16—21no—
105C13×M16C4211yescharacteristic
106C2×C8×C13—21no—
107C2×C8×C13C22×C411yescharacteristic
108#6099—21no—
109#6099C4211yescharacteristic
110C2×#1055—21no—
111C2×#1055C22×C411yescharacteristic
112#6094—21no—
113#6094—21no—
114#6094—21no—
115C8×D13—21no—
116C8×D13—21no—
117C8×D13—21no—
118C8×D13C2×D411yescharacteristic
119C8×D13C2×D411yescharacteristic
120C8×D13#4111yescharacteristic
121C8×D13#4111yescharacteristic
122#6092—22no—
123#6092—22no—
124C13×C16—21no—
125C13×C16C22⋊C411yescharacteristic
126C13×C16C22⋊C411yescharacteristic
127#6090—21no—
128#6090C22⋊C411yescharacteristic
129#6090C22⋊C411yescharacteristic
130C2×#504—131no—
131C2×#350—131no—
132#2108—131no—
133C2×#346—131no—
134#1764—131no—
135#1379—131no—
136#1376—131no—
137C22×D13—21no—
138C22×D13#13111yescharacteristic
139C2×#261—22no—
140C2×#261—22no—
141C2×#261—42no—
142Q8×C13C4×C811yescharacteristic
143D4×C13—21no—
144D4×C13C4×C811yescharacteristic
145C2×C4×C13—21no—
146C2×C4×C13C2×C4211yescharacteristic
147C22⋊D13—21no—
148C22⋊D13—21no—
149C22⋊D13—21no—
150C2×Dic13—21no—
151C2×Dic13#13111yescharacteristic
152D52—21no—
153D52C4×C811yescharacteristic
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13C4×D411yescharacteristic
158C4×D13C4×D411yescharacteristic
159C4×D13C22×C811yescharacteristic
160C4×D13C22×C811yescharacteristic
161Dic26—21no—
162Dic26C4×C811yescharacteristic
163#1057—22no—
164#1057—22no—
165C8×C13—21no—
166C8×C13C2×C22⋊C411yescharacteristic
167C8×C13#11711yescharacteristic
168#1055—21no—
169#1055C4×D411yescharacteristic
170#1055C4×D411yescharacteristic
171C2×#131—131no—
172#504—131no—
173#504—131no—
174#504—131no—
175#504—261no—
176#504—261no—
177#504#26111yescharacteristic, complemented
178C2×M32—131no—
179C2×M32—131no—
180C2×M32—261no—
181C22×C16—131no—
182C22×C16—131no—
183C22×C16—261no—
184C2×#104—131no—
185#416—131no—
186#405—131no—
187C2×C4×C8—131no—
188#350—132no—
189#350—132no—
190#346—261no—
191#346—261no—
192#346—261no—
193C4×C16—261no—
194#341—131no—
195#339—131no—
196C22×C13—21no—
197C22×C13#40511yescharacteristic
198C2×D13—22no—
199C2×D13—21no—
200C2×D13—42no—
201C2×D13C8×D411yescharacteristic
202C2×D13C8×D411yescharacteristic
203#261—42no—
204#261—42no—
205C4×C13—21no—
206C4×C13C4×C22⋊C411yescharacteristic
207C4×C13C2×C4×C811yescharacteristic
208Dic13—21no—
209Dic13C8×D411yescharacteristic
210Dic13C8×D411yescharacteristic
211C2×#41—131no—
212#131—131no—
213#131—131no—
214#131—131no—
215#131—261no—
216#131—261no—
217#131C2×#26111yescharacteristic
218C2×M16—131no—
219C2×M16—131no—
220C2×M16—261no—
221C22×C8—131no—
222C22×C8—131no—
223C22×C8—261no—
224#117—131no—
225C2×C42—131no—
226M32—21no—
227M32—132no—
228M32—131no—
229M32—261no—
230M32—261no—
231M32—261no—
232M32—261no—
233M32—261no—
234M32C2×#26111yescharacteristic
235C2×C16—21no—
236C2×C16—131no—
237C2×C16—131no—
238C2×C16—131no—
239C2×C16—131no—
240C2×C16—131no—
241C2×C16—132no—
242C2×C16—261no—
243C2×C16—261no—
244C2×C16—261no—
245C2×C16—261no—
246C2×C16—261no—
247C2×C16—261no—
248C2×C16—261no—
249C2×C16C2×#26111yescharacteristic
250#104—132no—
251#104—132no—
252#103—132no—
253#102—132no—
254#97—261no—
255C4×C8—261no—
256C4×C8—261no—
257C4×C8—261no—
258C2×C13—21no—
259C2×C13—41no—
260C2×C13C8×C22⋊C411yescharacteristic
261D13—21no—
262D13—41no—
263D13#217112yes—
264#41—131no—
265#41—131no—
266#41—131no—
267#41—261no—
268#41—261no—
269#41C4×#26111yescharacteristic
270C2×Q8—131no—
271C2×D4—131no—
272C2×D4—261no—
273C22×C4—131no—
274C22×C4—261no—
275C22×C4—261no—
276M16—21no—
277M16—132no—
278M16—131no—
279M16—261no—
280M16—261no—
281M16—261no—
282M16—261no—
283M16—261no—
284M16C4×#26111yescharacteristic
285C2×C8—21no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—131no—
289C2×C8—131no—
290C2×C8—131no—
291C2×C8—132no—
292C2×C8—261no—
293C2×C8—261no—
294C2×C8—261no—
295C2×C8—261no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—261no—
299C2×C8C22×#26111yescharacteristic
300C4⋊C4—132no—
301C22⋊C4—261no—
302C42—132no—
303C42—261no—
304C42—261no—
305C16—21no—
306C16—131no—
307C16—131no—
308C16—262no—
309C16—262no—
310C16—261no—
311C16C22⋊#26111yescharacteristic
312C16C22⋊#26111yescharacteristic
313C13#1261511yescharacteristic, complemented, Sylow
314C23—131no—
315C23—261no—
316Q8—131no—
317Q8—261no—
318Q8C8×#26111yescharacteristic
319D4—21no—
320D4—131no—
321D4—261no—
322D4—261no—
323D4—261no—
324D4—261no—
325D4C8×#26111yescharacteristic
326C2×C4—21no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—131no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—262no—
337C2×C4—262no—
338C2×C4—522no—
339C2×C4C2×C4×#26111yescharacteristic
340C8—21no—
341C8—131no—
342C8—131no—
343C8—262no—
344C8—262no—
345C8—261no—
346C8#8823711yescharacteristic
347C8C2×C22⋊#26111yescharacteristic
348C22—21no—
349C22—131no—
350C22—131no—
351C22—262no—
352C22—261no—
353C22—522no—
354C22#1171908911yescharacteristic
355C4—21no—
356C4—131no—
357C4—131no—
358C4—261no—
359C4—522no—
360C4—522no—
361C4C2×C8×#26111yescharacteristic
362C4C4×C22⋊#26111yescharacteristic
363C2—21no—
364C2—41no—
365C2—132no—
366C2—261no—
367C2—521no—
368C2C8×C22⋊#26111yescharacteristic
subgroupG/H
centerC8C2×C22⋊#261
commutatorC4×C13C2×C4×C8
FrattiniC2×C8C22×#261
FittingC13×#504C4
socleC2×C13C8×C22⋊C4
prime radical#41×D13C2×C4
cosocleC2×C8×D13C23
hypercenter#504#261
hypocenterC13#12615
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C16 ◁ #504

Complements

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

NH ≅ G/Ntype
2. #13131044C2semidirect
3. C2×#11718216C2semidirect
5. #13129892C2semidirect
6. #13129879C2semidirect
15. C13×#504C4semidirect
16. #11718801C4semidirect
18. #11718568C4semidirect
22. #11718562C4semidirect
25. #11718304C4semidirect
28. #11718270C4semidirect
177. #504#261semidirect
313. C13#12615semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3502
#131310442
C2×#117182162
#131306102
#131298922
#131298792
D13×#5042
#1261513