Finite Group Databasebeta

← #15766513

Subgroups — #15766513

Order 3328.

440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11718680C211yesmaximal, characteristic
2#13113612C211yesmaximal, characteristic, complemented
3#13113509C211yesmaximal, characteristic, complemented
4#13113509C211yesmaximal, characteristic, complemented
5#13113227C211yesmaximal, characteristic
6#13112731C211yesmaximal, characteristic, complemented
7C13×#1800C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×#6105—21no—
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C2×C13×#100—21no—
14#11718680—22no—
15#11718680—22no—
16C2×#88050—21no—
17#11718586C2211yescharacteristic
18#11718586C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#343—21no—
21D4⋊#1055—22no—
22#11718074—22no—
23#11718074—22no—
24#11718071—22no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13—21no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C2×C13×M16—21no—
30C4×D4×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13—21no—
33C4×D4×C13—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6105—24no—
38C2×#6105—42no—
39C2×#6105—42no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055—21no—
43#88123—21no—
44#88123—21no—
45#88123—21no—
46#88123D412yes—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×#100—42no—
52C22⋊#1055—21no—
53C22⋊#1055—21no—
54#88050—24no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055D412yes—
58C4⋊#1055D412yes—
59C4×#1055—21no—
60C4×#1055—21no—
61#10444—131nomaximal, Sylow
62C24×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13D812yes—
69C22×C4×C13—21no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—82no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4111yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×Dic13—41no—
77C2×Dic26—22no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C13×M16—41no—
84C13×M16—41no—
85C13×M16—41no—
86C13×M16—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97#6105—48no—
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#461—131no—
108#1800D1311yescharacteristic
109#1571—131no—
110#1546—131no—
111#1546—131no—
112#1478—131no—
113#1301—131no—
114C23×C13—22no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—81no—
118C23×C13—81no—
119C23×C13#12311yescharacteristic
120D4×C13—22no—
121D4×C13—22no—
122D4×C13—41no—
123D4×C13—41no—
124C2×C4×C13—22no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—82no—
128C2×C4×C13—82no—
129C2×C4×C13—81no—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12311yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13C2×D811yescharacteristic
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—42no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143Dic26—42no—
144Dic26—42no—
145Dic26—81no—
146Dic26—81no—
147C8×C13—81no—
148C8×C13—81no—
149#1055—42no—
150#1055—42no—
151#1055—81no—
152C22×SD16—261no—
153C2×C4⋊Q8—131no—
154C2×C4×D4C2×D1311yescharacteristic
155#461—262no—
156#461—262no—
157#431—131no—
158#431—131no—
159#423C2×D1311yescharacteristic
160#423C2×D1311yescharacteristic
161C2×C4⋊C8—131no—
162C2×#103—261no—
163C2×#100—21no—
164#343—21no—
165#335—262no—
166#332—262no—
167#332—262no—
168D4⋊C8—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—42no—
172C22×C13—82no—
173C22×C13—82no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13#39411yescharacteristic
177C22×C13#48011yescharacteristic
178C22×C13#48211yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—81no—
183C4×C13#44711yescharacteristic
184C4×C13#45211yescharacteristic
185C4×C13#46611yescharacteristic
186C4×C13#46811yescharacteristic
187C4×C13#47112yes—
188Dic13—82no—
189C22×Q8—261no—
190C22×D4C22⋊D1311yescharacteristic
191C23×C4—21no—
192C2×SD16—264no—
193C2×SD16—522no—
194C2×SD16—522no—
195C2×M16—21no—
196C2×M16—21no—
197C22×C8—261no—
198C4⋊Q8—132no—
199C4⋊Q8—261no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C22×D1311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—132no—
216C4⋊C8—132no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219#103—264no—
220#100—42no—
221C22⋊C8—261no—
222C22⋊C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—82no—
228C2×C13#203311yescharacteristic
229C2×C13#204611yescharacteristic
230C2×C13#204911yescharacteristic
231C24—21no—
232C2×Q8—262no—
233C2×Q8—521no—
234C2×Q8—521no—
235C2×Q8—521no—
236C2×Q8—521no—
237C2×Q8—521no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4#610412yes—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—82no—
248C22×C4—521no—
249C22×C4#612711yescharacteristic
250C22×C4#612711yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252SD16—528no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42D4×D1311yescharacteristic
273C42D4×D1311yescharacteristic
274C42D4×D1311yescharacteristic
275C42#612911yescharacteristic
276C13#1044411yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23#8818311yescharacteristic
283Q8—522no—
284Q8—522no—
285Q8—1041no—
286Q8—1041no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—522no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4#8813711yescharacteristic
301C2×C4#8813811yescharacteristic
302C2×C4#8813811yescharacteristic
303C2×C4#8813911yescharacteristic
304C2×C4C2×#610411yescharacteristic
305C2×C4#8819111yescharacteristic
306C2×C4#8819311yescharacteristic
307C2×C4#8819611yescharacteristic
308C2×C4#8820311yescharacteristic
309C2×C4#8820411yescharacteristic
310C8—81no—
311C8—81no—
312C8—522no—
313C8—522no—
314C8—1041no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22#1171862011yescharacteristic
323C22#1171862811yescharacteristic
324C22#1171866411yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—1042no—
330C4#1171840912yes—
331C4#1171869711yescharacteristic
332C4#1171869911yescharacteristic
333C4#1171870811yescharacteristic
334C4#1171871011yescharacteristic
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1311601811yescharacteristic
339C2#1311609711yescharacteristic
340C2#1311611611yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1800C2
socleC22×C13#394
prime radicalC22×D4×C13D4
hypercenter#1800D13
hypocenterC13#10444
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13113612C2semidirect
3. #13113509C2semidirect
4. #13113509C2semidirect
6. #13112731C2semidirect
276. C13#10444semidirect

Maximal subgroups

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

subgroupindex
C2×#117186802
#131136122
#131135092
#131132272
#131127312
C13×#18002
#1044413