Finite Group Databasebeta

← #15779969

Subgroups — #15779969

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718855C211yesmaximal, characteristic
2C2×#11718159C211yesmaximal, characteristic, complemented
3C2×#11718089C211yesmaximal, characteristic, complemented
4#13115724C211yesmaximal, characteristic, complemented
5#13112929C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C2×C13×#443C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×C13×#131—21no—
10C2×#88158C2211yescharacteristic
11C13×#443—22no—
12C13×#443—22no—
13C2×C13×#108C2211yescharacteristic
14C2×C13×#104—21no—
15C2×C4×C8×C13C2211yescharacteristic
16#11718855—22no—
17#11718855—22no—
18C2×#88069C411yescharacteristic, complemented
19C2×#88068C411yescharacteristic, complemented
20C2×#88067C411yescharacteristic, complemented
21C2×#88066C411yescharacteristic, complemented
22#11718771—21no—
23C2×#88059C2211yescharacteristic
24C22×#6090C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26C2×#88045—21no—
27#11718159—22no—
28#11718089—22no—
29C2×C13×#41—21no—
30C2×#6127—21no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135D412yes—
34C13×#135D412yes—
35C2×C13×Q16C2×C411yescharacteristic
36C2×C13×SD16—21no—
37C2×C13×D8C2×C411yescharacteristic
38C13×#131—24no—
39C13×#131—42no—
40C2×C13×M16—21no—
41C2×C13×M16—41no—
42C22×C8×C13—41no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×#6099—21no—
47C2×Dic52C2×C411yescharacteristic
48#88158—21no—
49#88158—21no—
50#88158—21no—
51#88158—21no—
52C2×D104C2×C411yescharacteristic
53C2×#6095—21no—
54C13×#108—21no—
55C13×#108D412yes—
56C13×#104—24no—
57C4×C8×C13—21no—
58C4×C8×C13—21no—
59#88069—22no—
60#88068—22no—
61#88067—22no—
62#88066—22no—
63#88060—41no—
64#88060—41no—
65#88059—21no—
66#88059—21no—
67C2×#6090—21no—
68C2×#6090—21no—
69C2×#6090—21no—
70C2×#6090—21no—
71C2×#6090—21no—
72C2×#6090C2×C411yescharacteristic
73C2×#6090C2×C411yescharacteristic
74#88045—42no—
75#13011—131nomaximal, Sylow
76C13×#41—22no—
77C13×#41—22no—
78C13×#41—41no—
79C13×#41—41no—
80C2×Q8×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—41no—
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C2×C22⋊D13—41no—
87#6127—41no—
88#6127—41no—
89#6127—41no—
90#6127—41no—
91C2×D52—21no—
92C2×C4×D13—41no—
93C2×Dic26—21no—
94C13×Q16—21no—
95C13×Q16C22⋊C412yes—
96C13×SD16—22no—
97C13×SD16—22no—
98C13×D8—21no—
99C13×D8C22⋊C412yes—
100C13×M16—22no—
101C13×M16—44no—
102C13×M16—41no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—44no—
106C2×C8×C13—41no—
107C2×C8×C13D811yescharacteristic
108C2×C8×C13D811yescharacteristic
109C2×C8×C13C22×C411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C2×C8×C13#4111yescharacteristic
115C42×C13—21no—
116C42×C13—21no—
117#6099—41no—
118#6099—41no—
119C2×#1055—41no—
120Dic52—21no—
121Dic52—21no—
122D104—21no—
123D104—21no—
124#6095—41no—
125#6095—41no—
126#6090—21no—
127#6090—21no—
128#6090—41no—
129C2×#508—131no—
130C2×#443D1311yescharacteristic, complemented
131C2×#359—131no—
132C2×#359—131no—
133#1974—131no—
134#1381—131no—
135#1374—131no—
136C23×C13—41no—
137C23×C13#13511yescharacteristic
138C22×D13—41no—
139Q8×C13—22no—
140Q8×C13—41no—
141D4×C13—22no—
142D4×C13—42no—
143D4×C13—42no—
144D4×C13—41no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C22⋊D13—81no—
158C22⋊D13—81no—
159C2×Dic13—41no—
160D52—41no—
161D52—41no—
162C4×D13—81no—
163C4×D13—81no—
164Dic26—41no—
165Dic26—41no—
166C8×C13—21no—
167C8×C13—21no—
168C8×C13—42no—
169C8×C13C2×C22⋊C411yescharacteristic
170C8×C13C4×D411yescharacteristic
171C8×C13#12111yescharacteristic
172C8×C13#12311yescharacteristic
173#1055—81no—
174C2×#135—131no—
175C2×#135C2×D1311yescharacteristic
176C2×#131—21no—
177#508—262no—
178#508—262no—
179C2×Q32—131no—
180C2×SD32—131no—
181C2×SD32—131no—
182C2×D16—131no—
183C22×C16—131no—
184C22×C16—131no—
185#443—22no—
186#443—22no—
187C2×#108—131no—
188C2×#108C2×D1311yescharacteristic
189C2×#104—21no—
190C2×#104—261no—
191#408—261no—
192C2×C4×C8C2×D1311yescharacteristic
193#359—262no—
194#359—262no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—42no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13C4×D811yescharacteristic
201C22×C13#44911yescharacteristic
202C22×C13#46311yescharacteristic
203C2×D13—81no—
204C2×D13—81no—
205C2×D13—81no—
206C4×C13—42no—
207C4×C13—42no—
208C4×C13#38611yescharacteristic
209C4×C13#44211yescharacteristic
210C4×C13#44711yescharacteristic
211C4×C13#45911yescharacteristic
212Dic13—81no—
213C2×#41—21no—
214C2×#41—261no—
215#135—21no—
216#135—21no—
217#135—261no—
218#135—261no—
219#135—261no—
220#135—261no—
221#135D5212yes—
222#135C22⋊D1312yes—
223C2×Q16—131no—
224C2×Q16C4×D1311yescharacteristic
225C2×SD16—21no—
226C2×SD16—261no—
227C2×D8—131no—
228C2×D8C4×D1311yescharacteristic
229#131—24no—
230#131—42no—
231C2×M16—21no—
232C2×M16—41no—
233C2×M16—261no—
234C22×C8—41no—
235C22×C8C22⋊D1311yescharacteristic
236C22×C8C22×D1311yescharacteristic
237C2×C42C22⋊D1311yescharacteristic
238Q32—262no—
239SD32—262no—
240SD32—262no—
241D16—262no—
242C2×C16—131no—
243C2×C16—131no—
244C2×C16—261no—
245C2×C16—261no—
246C2×C16—261no—
247C2×C16—261no—
248C2×C16—261no—
249#108—21no—
250#108—261no—
251#108—261no—
252#108C22⋊D1312yes—
253#104—24no—
254#104—522no—
255C22⋊C8—521no—
256C22⋊C8—521no—
257C4×C8—21no—
258C4×C8—21no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—82no—
262C2×C13#187911yescharacteristic
263C2×C13#217811yescharacteristic
264C2×C13#217911yescharacteristic
265D13—161no—
266#41—22no—
267#41—22no—
268#41—41no—
269#41—41no—
270#41—521no—
271#41—521no—
272#41—521no—
273#41—521no—
274C2×Q8—21no—
275C2×Q8—261no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—261no—
279C2×D4—521no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—521no—
283C22×C4C2×C22⋊D1311yescharacteristic
284Q16—21no—
285Q16—261no—
286Q16—261no—
287Q16#610312yes—
288SD16—22no—
289SD16—22no—
290SD16—521no—
291SD16—521no—
292D8—21no—
293D8—261no—
294D8—261no—
295D8#610312yes—
296M16—22no—
297M16—44no—
298M16—41no—
299M16—521no—
300M16—521no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—44no—
304C2×C8—41no—
305C2×C8—521no—
306C2×C8#610411yescharacteristic
307C2×C8#610411yescharacteristic
308C2×C8C2×C4×D1311yescharacteristic
309C2×C8C2×D5211yescharacteristic
310C2×C8#612711yescharacteristic
311C2×C8#612711yescharacteristic
312C2×C8C2×C22⋊D1311yescharacteristic
313C2×C8C2×C22⋊D1311yescharacteristic
314C42—21no—
315C42—21no—
316C16—261no—
317C16—261no—
318C16—521no—
319C13#1301111yescharacteristic, complemented, Sylow
320C23—41no—
321C23—521no—
322C23#8820411yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—521no—
326Q8—521no—
327D4—22no—
328D4—42no—
329D4—42no—
330D4—41no—
331D4—521no—
332D4—521no—
333D4—1041no—
334D4—1041no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—521no—
342C2×C4—1041no—
343C2×C4—1041no—
344C2×C4C4×C22⋊D1311yescharacteristic
345C2×C4#8818411yescharacteristic
346C2×C4C2×#610411yescharacteristic
347C2×C4#8818611yescharacteristic
348C2×C4#8820311yescharacteristic
349C2×C4#8820711yescharacteristic
350C8—21no—
351C8—21no—
352C8—42no—
353C8—1041no—
354C8C2×#610311yescharacteristic
355C8C4×C22⋊D1311yescharacteristic
356C8#8818311yescharacteristic
357C8#8818411yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22C4×#610411yescharacteristic
367C22#1171867711yescharacteristic
368C22#1171889911yescharacteristic
369C4—42no—
370C4—42no—
371C4—1041no—
372C4#1171867511yescharacteristic
373C4#1171867611yescharacteristic
374C4#1171887411yescharacteristic
375C4#1171887811yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—2081no—
380C2#1311518411yescharacteristic
381C2#1311671511yescharacteristic
382C2#1311672011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#443C2
socleC22×C13C4×D8
prime radicalC2×#11718855C2
cosocleC22×C8×C13C23
hypercenterC2×#443D13
hypocenterC13#13011
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#11718159C2semidirect
3. C2×#11718089C2semidirect
4. #13115724C2semidirect
5. #13112929C2semidirect
6. #13112914C2semidirect
7. C2×C13×#443C2semidirect
18. C2×#88069C4semidirect
19. C2×#88068C4semidirect
20. C2×#88067C4semidirect
21. C2×#88066C4semidirect
130. C2×#443D13semidirect
319. C13#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#117188552
C2×#117181592
C2×#117180892
#131157242
#131129292
#131129142
C2×C13×#4432
#1301113