Finite Group Databasebeta

← #15753850

Subgroups — #15753850

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88129C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic, complemented
3C2×#11718056C212yesmaximal
4#13112718C212yesmaximal, complemented
5C4×C13×#97C211yesmaximal, characteristic, complemented
6C2×#88129C2211yescharacteristic
7C2×C4×D52C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×C13×#97—21no—
10C2×C13×#97C2212yes—
11C2×C4×C8×C13—21no—
12C43×C13C2211yescharacteristic
13#11718601—21no—
14#11718601—21no—
15#11718600C411yescharacteristic
16C4×#6103—21no—
17C4×#6103—21no—
18#11718597C2211yescharacteristic
19#11718590C411yescharacteristic
20C2×#88043C2212yes—
21#11718116—21no—
22#11718116—21no—
23#11718056C418yescomplemented
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—22no—
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C22×#1055—22no—
45#88129—22no—
46#88129C2×C414yes—
47C4×D52—42no—
48C4×Dic26—42no—
49C13×#97—24no—
50C13×#97—22no—
51C13×#97C2×C414yescomplemented
52C4×C8×C13—24no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88043—22no—
58#88043C2×C414yescomplemented
59#8226—131nomaximal, Sylow
60C23×D13—21no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C2×D52—21no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52C4212yes—
75C2×C4×D13—42no—
76C2×C4×D13—42no—
77C2×C4×D13—42no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26C4212yes—
82C2×C8×C13—24no—
83C2×C8×C13—24no—
84C2×C8×C13—24no—
85C42×C13—22no—
86C42×C13—22no—
87C42×C13—22no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13C22×C412yes—
92C42×C13#4112yes—
93#6103—24no—
94#6103—24no—
95#6103—42no—
96#6103—42no—
97#6103—42no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6101—42no—
101C4×Dic13—42no—
102C2×#1055—24no—
103C2×#1055—42no—
104C2×#1055—42no—
105C4×#124—131no—
106#1745—131no—
107C4×#97D1311yescharacteristic, complemented
108C2×#329—132no—
109#1295—132no—
110C23×C13C2×C22⋊C411yescharacteristic
111C22×D13—22no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13#10012yes—
134C2×C4×C13#10412yes—
135C2×C4×C13#10412yes—
136C2×C4×C13C2×C4211yescharacteristic
137C2×C4×C13#11711yescharacteristic
138C2×C4×C13C4×D412yes—
139C2×C4×C13C4×D412yes—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149D52—42no—
150D52—42no—
151C4×D13—84no—
152Dic26—42no—
153Dic26—42no—
154C8×C13—28no—
155#1055—44no—
156C2×#124—131no—
157C2×C4×Q8—131no—
158C2×C4×D4—131no—
159C2×#97—21no—
160C2×#97—132no—
161C2×#97C2×D1312yes—
162C2×C4×C8—21no—
163#391—131no—
164#390—131no—
165#388—261no—
166#388—261no—
167#382—131no—
168C4×C22⋊C4—261no—
169C4×C22⋊C4—261no—
170C43C2×D1311yescharacteristic
171#336—261no—
172#336—261no—
173#329—138no—
174C22×C13C4×C22⋊C411yescharacteristic
175C22×C13C2×#10011yescharacteristic
176C22×C13#41311yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13#42111yescharacteristic
180C22×C13#42111yescharacteristic
181C2×D13—42no—
182C2×D13—42no—
183C2×D13—42no—
184C2×D13—81no—
185C2×D13—81no—
186C2×D13—81no—
187C2×D13—81no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196Dic13—42no—
197Dic13—81no—
198Dic13—81no—
199C22×Q8—131no—
200C22×D4—131no—
201C23×C4—261no—
202C22×C8—22no—
203C22×C8—262no—
204#124—134no—
205#124—262no—
206C4×Q8—522no—
207C4×D4—522no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C42—261no—
217C2×C42C4×D1311yescharacteristic
218C2×C42C4×D1311yescharacteristic
219C2×C42D5211yescharacteristic
220C2×C42D5211yescharacteristic
221C2×C42C22⋊D1311yescharacteristic
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22×D1311yescharacteristic
224#97—24no—
225#97—22no—
226#97—134no—
227#97—262no—
228#97C4×D1314yescomplemented
229C4×C8—24no—
230#95—261no—
231#95—261no—
232#95—261no—
233#95—261no—
234C2×C13#152711yescharacteristic
235C2×C13#152911yescharacteristic
236C2×C13#153011yescharacteristic
237C2×C13#153211yescharacteristic
238C2×C13C4×#10011yescharacteristic
239C2×C13C4×#10411yescharacteristic
240C2×C13#175911yescharacteristic
241D13—82no—
242C24—261no—
243C2×Q8—132no—
244C2×Q8—261no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×D4—132no—
248C2×D4—261no—
249C2×D4—521no—
250C2×D4—521no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—522no—
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4#610311yescharacteristic
261C22×C4C2×C4×D1311yescharacteristic
262C22×C4C2×D5211yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264C2×C8—24no—
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—264no—
268C2×C8—522no—
269C2×C8—522no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—522no—
273C22⋊C4—264no—
274C22⋊C4—264no—
275C22⋊C4—522no—
276C22⋊C4—522no—
277C22⋊C4—522no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42—522no—
285C42C2×C4×D1312yes—
286C42#612712yes—
287C13#822611yescharacteristic, complemented, Sylow
288C23—262no—
289C23—521no—
290C23—521no—
291C23—521no—
292C23—521no—
293C23—521no—
294C23—521no—
295C23C2×#610311yescharacteristic
296Q8—522no—
297Q8—522no—
298D4—522no—
299D4—522no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—262no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—1044no—
325C2×C4#8804512yes—
326C2×C4#8804512yes—
327C2×C4#8806312yes—
328C2×C4C42×D1311yescharacteristic
329C2×C4#8812611yescharacteristic
330C2×C4C4×D5212yes—
331C2×C4C4×C22⋊D1312yes—
332C8—28no—
333C8—524no—
334C22—522no—
335C22—522no—
336C22—522no—
337C22—1041no—
338C22—1041no—
339C22—1041no—
340C22—1041no—
341C22C2×#8804511yescharacteristic
342C22C2×#8804511yescharacteristic
343C22C4×#610311yescharacteristic
344C22C2×#8806311yescharacteristic
345C22#1171879311yescharacteristic
346C22#1171880011yescharacteristic
347C22#1171880011yescharacteristic
348C4—21no—
349C4—21no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—522no—
357C4—1041no—
358C4—1041no—
359C2—1042no—
360C2#1311343311yescharacteristic
361C2#1311344111yescharacteristic
362C2#1311344611yescharacteristic
363C2#1311345411yescharacteristic
364C2C4×#8806311yescharacteristic
365C2C4×#8804511yescharacteristic
366C2#1311464911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC4×C13×#97C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenterC4×#97D13
hypocenterC13#8226
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
2. #13114585C2semidirect
4. #13112718C2semidirect
5. C4×C13×#97C2semidirect
23. #11718056C4semidirect
51. C13×#97C2×C4semidirect
58. #88043C2×C4semidirect
107. C4×#97D13semidirect
228. #97C4×D13semidirect
287. C13#8226semidirect

Maximal subgroups

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

subgroupindex
C4×#881292
#131145852
C2×#117180562
#131127182
C4×C13×#972
#822613