Finite Group Databasebeta

← #15781248

Subgroups — #15781248

Order 3328.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119812C211yesmaximal, characteristic
2C2×#11718070C212yesmaximal, complemented
3C2×#11718069C212yesmaximal
4C4×#88076C211yesmaximal, characteristic, complemented
5C13×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201C2211yescharacteristic
8C2×#88198C2211yescharacteristic
9C2×#88129C411yescharacteristic
10C13×#423—21no—
11C2×C13×#101C2212yes—
12C2×#88076C2212yes—
13#11718655—21no—
14#11718655—21no—
15#11718649C411yescharacteristic
16#11718635C411yescharacteristic
17#11718601—21no—
18#11718601—21no—
19C4×C4⋊Dic13C411yescharacteristic
20C4×#6099—21no—
21C13×#343—21no—
22#11718122—21no—
23#11718070—24no—
24#11718069—24no—
25C22×Q8×C13C2311yescharacteristic
26C22×D52C2×C411yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C2×C13×M16—22no—
29C4×Q8×C13—41no—
30C4×Q8×C13—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37#88201—22no—
38#88201—22no—
39#88198—22no—
40#88198—22no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×C4⋊Dic13—21no—
48C2×#6101—21no—
49C2×#6101—21no—
50C2×C4×Dic13C2×C411yescharacteristic
51C2×C4×Dic13C2×C411yescharacteristic
52C2×#6099—22no—
53#88129—41no—
54#88129—41no—
55C13×C4⋊C8—41no—
56C13×C4⋊C8—41no—
57C13×#101—22no—
58C13×#101—22no—
59#88076—22no—
60#88076D414yes—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88043—41no—
65C4×#1055—41no—
66#13228—131nomaximal, Sylow
67C23×D13—21no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13C2×D412yes—
71C2×Q8×C13#4112yes—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×D52—22no—
83C2×D52—41no—
84C2×D52—41no—
85C2×Dic26—22no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C13×M16—42no—
89C13×M16—42no—
90C2×C8×C13—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—21no—
100#6103—42no—
101#6103—42no—
102#6103—42no—
103#6103—41no—
104#6103—41no—
105#6103—42no—
106#6103—41no—
107#6103—41no—
108C4⋊Dic13—42no—
109#6101—42no—
110#6101—41no—
111#6101—41no—
112C4×Dic13—22no—
113C4×Dic13—22no—
114#6099—24no—
115#6099—42no—
116C2×#1055—42no—
117#2545—131no—
118C2×#356—132no—
119C2×#355—132no—
120#1801D1311yescharacteristic, complemented
121C4×#101—131no—
122C23×C13C2×C22⋊C411yescharacteristic
123C22×D13—41no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130Q8×C13—42no—
131Q8×C13—42no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13C4×D412yes—
148C2×C4×C13#12112yes—
149C2×C4×C13#12411yescharacteristic
150C2×C4×C13#12711yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160D52—82no—
161Dic26—82no—
162C8×C13—82no—
163#1055—44no—
164C2×C4⋊Q8—131no—
165C2×#124—131no—
166C2×#124—131no—
167C2×C4×Q8C2×D1311yescharacteristic
168#423—21no—
169C2×#101—132no—
170C2×#101C2×D1312yes—
171C4×M16—261no—
172#396—261no—
173#396—261no—
174#391—131no—
175#390—131no—
176#388—261no—
177#388—261no—
178C4×C4⋊C4—131no—
179#356—264no—
180#355—264no—
181#343—21no—
182#343—261no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13#39011yescharacteristic
186C22×C13C2×#9911yescharacteristic
187C22×C13#41011yescharacteristic
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C2×D13—81no—
192C2×D13—81no—
193C2×D13—81no—
194C2×D13—81no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—21no—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204Dic13—42no—
205Dic13—81no—
206Dic13—81no—
207C22×Q8—131no—
208C22×Q8C22×D1311yescharacteristic
209C22×D4—131no—
210C2×M16—22no—
211C2×M16—262no—
212C4⋊Q8—262no—
213C4⋊Q8—262no—
214#124—262no—
215#124—262no—
216#124—521no—
217#124—521no—
218C4×Q8—41no—
219C4×Q8—41no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4C4×D1311yescharacteristic
224C2×C4⋊C4D5211yescharacteristic
225C2×C4⋊C4C22⋊D1311yescharacteristic
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4—261no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42C4×D1311yescharacteristic
235C2×C42D5211yescharacteristic
236C2×C42C22⋊D1311yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#101—22no—
240#101—22no—
241#101—134no—
242#101—262no—
243#97—521no—
244C4×C8—521no—
245#95—261no—
246#95—261no—
247#95—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13#196411yescharacteristic
251C2×C13#213211yescharacteristic
252C2×C13#213311yescharacteristic
253D13—161no—
254C24—261no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—262no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8D4×D1312yes—
261C2×Q8#613112yes—
262C2×D4—262no—
263C2×D4—521no—
264C2×D4—521no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4#610311yescharacteristic
269C22×C4#610311yescharacteristic
270C22×C4#610311yescharacteristic
271C22×C4#610311yescharacteristic
272C22×C4C2×C4×D1311yescharacteristic
273C22×C4C2×D5211yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275M16—42no—
276M16—42no—
277M16—264no—
278M16—522no—
279C2×C8—42no—
280C2×C8—522no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—522no—
285C4⋊C4—522no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C22⋊C4—522no—
291C22⋊C4—522no—
292C22⋊C4—521no—
293C22⋊C4—521no—
294C22⋊C4—521no—
295C22⋊C4—521no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—262no—
303C42—262no—
304C13#1322811yescharacteristic, complemented, Sylow
305C23—521no—
306C23—521no—
307C23—521no—
308C23—521no—
309C23—521no—
310C23—521no—
311C23—521no—
312C23C2×#610311yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—1042no—
316D4—1042no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—262no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4#8804611yescharacteristic
340C2×C4#8804611yescharacteristic
341C2×C4#8814712yes—
342C2×C4#8814912yes—
343C2×C4#8819411yescharacteristic
344C2×C4#8820111yescharacteristic
345C8—82no—
346C8—524no—
347C22—21no—
348C22—21no—
349C22—1041no—
350C22—1041no—
351C22—1041no—
352C22—1041no—
353C22—1041no—
354C22—1041no—
355C22—1041no—
356C22C2×#8804611yescharacteristic
357C22#1171864911yescharacteristic
358C22#1171866711yescharacteristic
359C4—21no—
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—522no—
369C4—1041no—
370C4—1041no—
371C2—21no—
372C2—21no—
373C2—2081no—
374C2#1311567111yescharacteristic
375C2#1311651911yescharacteristic
376C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1801C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC22×Q8×C13C23
hypercenter#1801D13
hypocenterC13#13228
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C2×#11718070C2semidirect
4. C4×#88076C2semidirect
5. C13×#1801C2semidirect
120. #1801D13semidirect
304. C13#13228semidirect

Maximal subgroups

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

subgroupindex
#131198122
C2×#117180702
C2×#117180692
C4×#880762
C13×#18012
#1322813