Finite Group Databasebeta

← #15779183

Subgroups — #15779183

Order 3328.

638 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#11718891C211yesmaximal, characteristic
2#13114760C211yesmaximal, characteristic
3#13112962C214yesmaximal, complemented
4C13×#1784C211yesmaximal, characteristic
5C23×Q8×C13C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8C2×C13×#101—21no—
9C2×C13×#101C2212yes—
10C13×#407—21no—
11#11718891—21no—
12#11718891—21no—
13#11718891C412yes—
14#11718891C2212yes—
15C2×#88076—21no—
16C2×#88076C2212yes—
17C2×#88071—21no—
18C2×#88071—21no—
19#11718868—21no—
20C22×Q8×C13—24no—
21C22×Q8×C13—41no—
22C22×Q8×C13—41no—
23C22×Q8×C13—42no—
24C22×Q8×C13C2×C411yescharacteristic
25C22×Q8×C13D411yescharacteristic
26C22×Q8×C13D411yescharacteristic
27C22×Q8×C13C2311yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C23×Dic13—21no—
32C23×Dic13—21no—
33C2×C13×M16—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—41no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13C2×C412yes—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—42no—
40C2×C4×Dic13C2×C412yes—
41C2×#6099—22no—
42C13×#101—24no—
43C13×#101—42no—
44C13×C22⋊C8—41no—
45C13×C22⋊C8—41no—
46#88076—24no—
47#88076—42no—
48#88071—22no—
49#88071—22no—
50#88071—22no—
51#88071—22no—
52C22⋊#1055—41no—
53C22⋊#1055—41no—
54#12860—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—48no—
68C2×Q8×C13—48no—
69C2×Q8×C13#4114yes—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×Dic13—24no—
89C22×Dic13—22no—
90C22×Dic13—22no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C22×Dic13—44no—
94C22×Dic13—41no—
95C22×Dic13—41no—
96C13×M16—42no—
97C13×M16—42no—
98C2×C8×C13—42no—
99C4⋊Dic13—42no—
100C4⋊Dic13—42no—
101C4×Dic13—42no—
102C4×Dic13—42no—
103#6099—42no—
104#6099—42no—
105C2×#1055—42no—
106C2×#391—131no—
107#1784—131no—
108#1784D1311yescharacteristic
109#1394—134no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13#9911yescharacteristic
115C23×C13#9911yescharacteristic
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—44no—
118Q8×C13—44no—
119Q8×C13—44no—
120Q8×C13—44no—
121C2×C4×C13—24no—
122C2×C4×C13—24no—
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—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13#9912yes—
142C2×C4×C13#11712yes—
143C2×C4×C13#12312yes—
144C2×C4×C13#12312yes—
145C2×Dic13—24no—
146C2×Dic13—48no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—44no—
150C2×Dic13—42no—
151C2×Dic13—82no—
152C2×Dic13—82no—
153C8×C13—82no—
154#1055—82no—
155C23×Q8C2×D1311yescharacteristic
156C22×C4⋊C4—131no—
157C22×C42—131no—
158C2×#101—21no—
159C2×#101—132no—
160C2×#101—261no—
161C2×#101C2×D1312yes—
162#407—21no—
163#407—261no—
164#391—132no—
165#391—132no—
166#391—261no—
167#391—261no—
168C2×#95—261no—
169C2×#95—261no—
170C22×C13—24no—
171C22×C13—24no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13#35512yes—
179C22×C13#35612yes—
180C22×C13#38111yescharacteristic
181C22×C13C2×#9911yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—41no—
189Dic13—44no—
190Dic13—82no—
191C22×Q8—24no—
192C22×Q8—41no—
193C22×Q8—41no—
194C22×Q8—42no—
195C22×Q8C4×D1311yescharacteristic
196C22×Q8D5211yescharacteristic
197C22×Q8C22⋊D1311yescharacteristic
198C22×Q8C22×D1311yescharacteristic
199C23×C4—261no—
200C23×C4—261no—
201C23×C4C4×D1311yescharacteristic
202C23×C4D5211yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C2×M16—22no—
205C2×M16—262no—
206C2×C4⋊C4—132no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—521no—
209C2×C4⋊C4—521no—
210C2×C42—132no—
211C2×C42—261no—
212C2×C42—522no—
213#101—24no—
214#101—42no—
215#101—264no—
216#101—522no—
217C22⋊C8—41no—
218C22⋊C8—41no—
219C22⋊C8—521no—
220C22⋊C8—521no—
221#95—262no—
222#95—262no—
223#95—262no—
224#95—262no—
225C2×C13—21no—
226C2×C13—22no—
227C2×C13—22no—
228C2×C13—21no—
229C2×C13#181911yescharacteristic
230C2×C13C2×#35511yescharacteristic
231C2×C13C2×#35611yescharacteristic
232C24#610311yescharacteristic
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—48no—
245C2×Q8—48no—
246C2×Q8#612914yes—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—264no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—522no—
263C22×C4—522no—
264C22×C4—524no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4#610311yescharacteristic
268C22×C4#610311yescharacteristic
269C22×C4#610311yescharacteristic
270C22×C4C2×C4×D1311yescharacteristic
271C22×C4C2×D5211yescharacteristic
272C22×C4C2×C22⋊D1311yescharacteristic
273M16—42no—
274M16—42no—
275M16—522no—
276M16—522no—
277C2×C8—42no—
278C2×C8—522no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C42—522no—
282C42—522no—
283C13#1286011yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23—21no—
287C23—21no—
288C23#8804611yescharacteristic
289C23#8804611yescharacteristic
290C23C2×#610311yescharacteristic
291Q8—44no—
292Q8—44no—
293Q8—44no—
294Q8—44no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
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—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—264no—
316C2×C4—528no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—524no—
320C2×C4—522no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4#8804612yes—
324C2×C4#8813112yes—
325C2×C4#8814012yes—
326C2×C4#8818912yes—
327C8—82no—
328C8—1042no—
329C22—24no—
330C22—24no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22#1171806912yes—
338C22#1171807012yes—
339C22#1171860411yescharacteristic
340C22C2×#8804611yescharacteristic
341C22C2×#8804611yescharacteristic
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—524no—
349C4—1042no—
350C2—21no—
351C2—22no—
352C2—22no—
353C2—21no—
354C2#1311490811yescharacteristic
355C2C2×#1171806911yescharacteristic
356C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1784C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1784D13
hypocenterC13#12860
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
3. #13112962C2semidirect
283. C13#12860semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
#131147602
#131129622
C13×#17842
#1286013