Finite Group Databasebeta

← #15779967

Subgroups — #15779967

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×#11718857C211yesmaximal, characteristic, complemented
3C2×#11718102C211yesmaximal, characteristic, complemented
4#13115722C211yesmaximal, characteristic, complemented
5#13112929C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C2×C13×#359C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×#88202—21no—
10C2×#88158C2211yescharacteristic
11C22×C13×C16C2211yescharacteristic
12C2×C13×#108C2211yescharacteristic
13C2×#88077—21no—
14#11718857—22no—
15#11718857—22no—
16#11718855—22no—
17#11718855—22no—
18C2×#88069C411yescharacteristic, complemented
19C2×#88068C411yescharacteristic, complemented
20C2×#88067C411yescharacteristic, complemented
21C2×#88066C411yescharacteristic, complemented
22C2×#88065—21no—
23#11718790—21no—
24C2×#88059C2211yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C22×#6090C2211yescharacteristic
27C13×#359—22no—
28#11718102—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
38C2×C13×M16—21no—
39C22×C8×C13C2311yescharacteristic
40#88202—24no—
41#88202—42no—
42C2×C4×Dic13D411yescharacteristic
43C2×#6099—21no—
44C2×#6099—41no—
45C22×#1055—41no—
46C22×#1055D411yescharacteristic
47C2×Dic52C2×C411yescharacteristic
48#88158—21no—
49#88158—21no—
50#88158—21no—
51#88158—21no—
52C2×D104C2×C411yescharacteristic
53C2×#6095—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C13×#108—21no—
58C13×#108—21no—
59#88077—24no—
60#88069—22no—
61#88068—22no—
62#88067—22no—
63#88066—22no—
64#88065—42no—
65#88060—41no—
66#88060—41no—
67#88059—21no—
68#88059D412yes—
69C8×Dic13—21no—
70C8×Dic13—21no—
71C2×#6090—21no—
72C2×#6090—21no—
73C2×#6090C2×C411yescharacteristic
74C2×#6090C2×C411yescharacteristic
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—41no—
84C22×C4×C13C2×D411yescharacteristic
85C2×C22⋊D13—41no—
86C22×Dic13—21no—
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—41no—
101C13×M16—41no—
102C2×C8×C13—41no—
103C2×C8×C13C22×C411yescharacteristic
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13#4111yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C4×Dic13—21no—
110C4×Dic13—21no—
111#6099—22no—
112#6099—44no—
113#6099—41no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—44no—
117C2×#1055—41no—
118C2×#1055D811yescharacteristic
119C2×#1055D811yescharacteristic
120Dic52—21no—
121Dic52—21no—
122D104—21no—
123D104—21no—
124#6095—41no—
125#6095—41no—
126C13×C16—41no—
127#6090—21no—
128#6090—21no—
129C2×#508—131no—
130C2×#443—131no—
131C2×#359—131no—
132C2×#359D1311yescharacteristic, complemented
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—41no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13C2×D811yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C22⋊D13—81no—
155C22⋊D13—81no—
156C2×Dic13—22no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160D52—41no—
161D52—41no—
162C4×D13—81no—
163C4×D13—81no—
164Dic26—41no—
165Dic26—41no—
166C8×C13—81no—
167C8×C13C2×C22⋊C411yescharacteristic
168C8×C13C4×D411yescharacteristic
169C8×C13#12111yescharacteristic
170C8×C13#12311yescharacteristic
171#1055—21no—
172#1055—21no—
173#1055—42no—
174C2×#135—131no—
175C2×#135C2×D1311yescharacteristic
176C2×#131—261no—
177#508—262no—
178#508—262no—
179C2×Q32—131no—
180C2×SD32—131no—
181C2×SD32—131no—
182C2×D16—131no—
183C22×C16—131no—
184C22×C16C2×D1311yescharacteristic
185#443—262no—
186#443—262no—
187C2×#108—131no—
188C2×#108C2×D1311yescharacteristic
189C2×#104—261no—
190C2×#104—261no—
191#408—261no—
192C2×C4×C8—131no—
193#359—22no—
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#38611yescharacteristic
208C4×C13#44211yescharacteristic
209C4×C13#44711yescharacteristic
210C4×C13#45911yescharacteristic
211Dic13—42no—
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—264no—
230#131—522no—
231C2×M16—21no—
232C2×M16—261no—
233C2×M16—521no—
234C22×C8—131no—
235C22×C8—521no—
236C22×C8C22×D1311yescharacteristic
237C2×C42—131no—
238Q32—262no—
239SD32—262no—
240SD32—262no—
241D16—262no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—131no—
246C2×C16—131no—
247C2×C16—261no—
248C2×C16—261no—
249#108—21no—
250#108—21no—
251#108—132no—
252#108—261no—
253#104—264no—
254#104—522no—
255C22⋊C8—521no—
256C22⋊C8—521no—
257C4×C8—261no—
258C4×C8—261no—
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—41no—
281C22×C4—261no—
282C22×C4—521no—
283C22×C4D4×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—41no—
297M16—41no—
298M16—262no—
299M16—524no—
300M16—521no—
301C2×C8—41no—
302C2×C8—131no—
303C2×C8—131no—
304C2×C8—261no—
305C2×C8—261no—
306C2×C8—524no—
307C2×C8—521no—
308C2×C8C2×C4×D1311yescharacteristic
309C2×C8C2×D5211yescharacteristic
310C2×C8D4×D1311yescharacteristic
311C2×C8#612911yescharacteristic
312C2×C8#612911yescharacteristic
313C2×C8C2×C22⋊D1311yescharacteristic
314C42—261no—
315C42—261no—
316C16—41no—
317C16—261no—
318C16—261no—
319C13#1301111yescharacteristic, complemented, Sylow
320C23—41no—
321C23—521no—
322C23#8817011yescharacteristic
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—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—262no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—1041no—
343C2×C4—1041no—
344C2×C4#8813511yescharacteristic
345C2×C4#8813611yescharacteristic
346C2×C4D8×D1311yescharacteristic
347C2×C4#8816511yescharacteristic
348C2×C4#8816811yescharacteristic
349C2×C4#8819311yescharacteristic
350C8—81no—
351C8—261no—
352C8—261no—
353C8—522no—
354C8#8813511yescharacteristic
355C8#8814011yescharacteristic
356C8C2×#610311yescharacteristic
357C8#8819311yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22#1171841711yescharacteristic
367C22#1171844211yescharacteristic
368C22#1171882611yescharacteristic
369C4—42no—
370C4—522no—
371C4—1041no—
372C4#1171843411yescharacteristic
373C4#1171844611yescharacteristic
374C4#1171861911yescharacteristic
375C4#1171881111yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—2081no—
380C2#1311518211yescharacteristic
381C2#1311671411yescharacteristic
382C2#1311671911yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#359C2
socleC22×C13C4×D8
prime radicalC2×#11718855C2
cosocleC22×C8×C13C23
hypercenterC2×#359D13
hypocenterC13#13011
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#11718857C2semidirect
3. C2×#11718102C2semidirect
4. #13115722C2semidirect
5. #13112929C2semidirect
6. #13112913C2semidirect
7. C2×C13×#359C2semidirect
18. C2×#88069C4semidirect
19. C2×#88068C4semidirect
20. C2×#88067C4semidirect
21. C2×#88066C4semidirect
132. C2×#359D13semidirect
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×#117188572
C2×#117181022
#131157222
#131129292
#131129132
C2×C13×#3592
#1301113