Finite Group Databasebeta

← #16782143

Subgroups — #16782143

Order 3328.

540 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 124 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#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5#13117238C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×#88131—21no—
8C2×C22⋊#1057—21no—
9C2×C22⋊#1057—21no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12C13×#380C411yescharacteristic
13#11718873C411yescharacteristic
14#11718637C411yescharacteristic
15#11718637C411yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C4⋊C4×Dic13C2211yescharacteristic
18#11718603—21no—
19#11718311—21no—
20#11718310—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C22⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—24no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88131—42no—
46#88131—42no—
47C22⋊#1057—24no—
48C22⋊#1057—42no—
49C4⋊#1057—24no—
50C4×#1057—24no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#8709—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—41no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13D812yes—
74C22×Dic13SD1612yes—
75C22×Dic13C2×D411yescharacteristic
76C22×Dic13C2×D411yescharacteristic
77C2×#1057—24no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C22⋊C4—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89#6101—42no—
90#6101—42no—
91#6101—42no—
92#6101—42no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13#4114yes—
101#2285—131no—
102#1797—131no—
103C4×C22⋊C8—131no—
104#1279—132no—
105#1279—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13#10212yes—
113C23×C13C2×C22⋊C411yescharacteristic
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—44no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13#11712yes—
125C2×C4×C13#13112yes—
126C2×C4×C13#13112yes—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—24no—
134C2×Dic13—24no—
135C2×Dic13—44no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13#10212yes—
143C2×Dic13#10412yes—
144C2×Dic13#12312yes—
145C2×Dic13#12312yes—
146C2×Dic13C2×D811yescharacteristic
147C2×Dic13C2×SD1611yescharacteristic
148C2×Dic13#13712yes—
149#1057—44no—
150#1057—82no—
151C2×#117—261no—
152C22×C42—131no—
153C2×C4⋊C8—132no—
154C2×C22⋊C8—261no—
155C2×C22⋊C8—261no—
156C2×C4×C8—132no—
157#384—131no—
158#384—131no—
159#382—261no—
160#380—131no—
161#380—261no—
162#380#26111yescharacteristic
163C4×C4⋊C4—131no—
164C4×C4⋊C4—131no—
165C4×C4⋊C4—261no—
166#336—261no—
167#336—261no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13#38111yescharacteristic
176C22×C13#40811yescharacteristic
177C22×C13#40811yescharacteristic
178C22×C13C2×#10211yescharacteristic
179C22×C13#41911yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13#42111yescharacteristic
182C4×C13—41no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13#43314yes—
186Dic13—22no—
187Dic13—22no—
188Dic13—22no—
189Dic13—81no—
190Dic13—81no—
191Dic13#48012yes—
192Dic13#48312yes—
193C23×C4—131no—
194C23×C4—131no—
195C23×C4C2×#26111yescharacteristic
196C22×C8—262no—
197C22×C8—262no—
198#117—522no—
199#117—522no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4C2×#26111yescharacteristic
207C2×C4⋊C4C2×#26111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—261no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—264no—
215C2×C42—261no—
216C2×C42—261no—
217C4⋊C8—264no—
218C22⋊C8—264no—
219C22⋊C8—522no—
220C4×C8—264no—
221#95—21no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13—42no—
226C2×C13#148011yescharacteristic
227C2×C13#148511yescharacteristic
228C2×C13#149211yescharacteristic
229C2×C13#149711yescharacteristic
230C2×C13#181811yescharacteristic
231C2×C13#182311yescharacteristic
232C2×C13#182611yescharacteristic
233C24C22⋊#26111yescharacteristic
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—131no—
240C22×C4—132no—
241C22×C4—132no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—262no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—521no—
252C22×C4C22⋊#26111yescharacteristic
253C22×C4C22×#26111yescharacteristic
254C2×C8—264no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—262no—
263C4⋊C4—262no—
264C4⋊C4—522no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C22⋊C4—42no—
269C22⋊C4—522no—
270C42—134no—
271C42—262no—
272C42—262no—
273C42—262no—
274C42—521no—
275C42—521no—
276C42—521no—
277C42—521no—
278C13#870911yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#8811512yes—
286C23C2×C22⋊#26111yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—132no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—132no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—264no—
305C2×C4—264no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—524no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4#8823712yes—
320C2×C4#8823812yes—
321C2×C4#8823812yes—
322C8—524no—
323C8—1042no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22#1171913511yescharacteristic
332C22C2×#8811511yescharacteristic
333C22#1171914611yescharacteristic
334C22#1171914611yescharacteristic
335C22#1171915311yescharacteristic
336C22D13⋊#10411yescharacteristic
337C22#1171916611yescharacteristic
338C4—41no—
339C4—81no—
340C4—81no—
341C4—132no—
342C4—132no—
343C4—262no—
344C4—262no—
345C4—262no—
346C4—1041no—
347C4—1041no—
348C4#1171906814yes—
349C2—42no—
350C2#1313014111yescharacteristic
351C2#1313015811yescharacteristic
352C2#1313018111yescharacteristic
353C2#1313019811yescharacteristic
354C2#1313072911yescharacteristic
355C2#1313073911yescharacteristic
356C2#1313074411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#8709
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129672C2semidirect
4. #13129672C2semidirect
278. C13#8709semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296722
#131172382
#870913