Finite Group Databasebeta

← #15773126

Subgroups — #15773126

Order 3328.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11718122C211yesmaximal, characteristic, complemented
2C2×#11718120C211yesmaximal, characteristic, complemented
3#13112842C212yesmaximal, complemented
4#13112839C212yesmaximal, complemented
5C13×#2618C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C22×#6099—21no—
10C13×#398C411yescharacteristic
11C13×#398C2211yescharacteristic
12C13×#396—21no—
13C13×#396—21no—
14C13×#394C411yescharacteristic
15C13×#394C2211yescharacteristic
16C13×#386—21no—
17C13×#380C411yescharacteristic
18C2×C22⋊#1055—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#123—42no—
29C13×#123—42no—
30C13×#121—41no—
31C13×#121—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4C2311yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×#6099—24no—
49C2×#6099—22no—
50C2×#6099—41no—
51C2×#6099—42no—
52C22×#1055—41no—
53C22×#1055—41no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic
57C13×#95C2×C411yescharacteristic
58C22⋊#1055—22no—
59C22⋊#1055—41no—
60#11698—131nomaximal, Sylow
61C24×C13—21no—
62C24×C13C22⋊C411yescharacteristic
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—42no—
67C2×D4×C13—42no—
68C2×D4×C13—81no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—81no—
80C22×C4×C13—81no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13D812yes—
85C22×C4×C13SD1612yes—
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—81no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4—81no—
105#6099—24no—
106#6099—44no—
107#6099—42no—
108C2×#1055—44no—
109C2×#1055—42no—
110C2×#1055—42no—
111C2×#1055—82no—
112#2618D1311yescharacteristic
113C2×#343—131no—
114C2×#324—131no—
115#1346—132no—
116#1345—132no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13#9911yescharacteristic
127C23×C13#9911yescharacteristic
128C23×C13#10212yes—
129C23×C13#10412yes—
130C23×C13C2×C22⋊C411yescharacteristic
131D4×C13—82no—
132D4×C13—82no—
133D4×C13—82no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—42no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—81no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13#10212yes—
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×SD1611yescharacteristic
166#1055—44no—
167#1055—82no—
168C22×M16—261no—
169C2×#123—21no—
170C2×#121Dic1311yescharacteristic
171C22×C4⋊C4C2×D1311yescharacteristic
172C2×C22⋊C8—261no—
173#398Dic1311yescharacteristic
174#398C2×D1311yescharacteristic
175#396—21no—
176#396—21no—
177#394Dic1311yescharacteristic
178#394C2×D1311yescharacteristic
179#386—21no—
180#380Dic1311yescharacteristic
181#343—132no—
182#343—261no—
183#324—132no—
184#324—261no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13#32712yes—
201C22×C13#32712yes—
202C22×C13C2×#9911yescharacteristic
203C22×C13C2×#10211yescharacteristic
204C22×C13C2×#10411yescharacteristic
205C4×C13—21no—
206C4×C13—22no—
207C4×C13—21no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—81no—
215C22×D4—21no—
216C22×D4C2×Dic1311yescharacteristic
217C23×C4C2×Dic1311yescharacteristic
218C23×C4C22⋊D1311yescharacteristic
219C23×C4C22⋊D1311yescharacteristic
220C2×M16—264no—
221C2×M16—262no—
222C2×M16—521no—
223C2×M16—522no—
224C22×C8—521no—
225C22×C8—521no—
226#123—42no—
227#123—42no—
228#121—41no—
229#121—41no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4C2×Dic1311yescharacteristic
236C2×C4⋊C4C2×Dic1311yescharacteristic
237C2×C4⋊C4C22⋊D1311yescharacteristic
238C2×C4⋊C4C22⋊D1311yescharacteristic
239C2×C4⋊C4C22×D1311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C22⋊C8—262no—
247C22⋊C8—521no—
248#95—21no—
249#95—21no—
250#95C2×Dic1311yescharacteristic
251#95C2×Dic1311yescharacteristic
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—22no—
255C2×C13—22no—
256C2×C13—161no—
257C2×C13C2×#32711yescharacteristic
258C2×C13#212111yescharacteristic
259C2×C13#213311yescharacteristic
260C24—21no—
261C24C22⋊Dic1311yescharacteristic
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—81no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4#610412yes—
281C22×C4#610512yes—
282C22×C4C22⋊Dic1311yescharacteristic
283C22×C4C22⋊Dic1311yescharacteristic
284C22×C4C22⋊Dic1311yescharacteristic
285C22×C4C22×Dic1311yescharacteristic
286C22×C4C2×C22⋊D1311yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288M16—264no—
289M16—524no—
290M16—522no—
291C2×C8—522no—
292C2×C8—524no—
293C2×C8—522no—
294C2×C8—1042no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—81no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C13#1169811yescharacteristic, complemented, Sylow
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#8807212yes—
322C23#8807411yescharacteristic
323C23#8807411yescharacteristic
324C23#8807712yes—
325C23C2×C22⋊Dic1311yescharacteristic
326D4—82no—
327D4—82no—
328D4—82no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4#8807212yes—
359C2×C4C2×#610411yescharacteristic
360C2×C4C2×#610511yescharacteristic
361C8—524no—
362C8—1042no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1171812912yes—
379C22#1171812912yes—
380C22C2×#8807211yescharacteristic
381C22C2×#8807411yescharacteristic
382C22C2×#8807711yescharacteristic
383C4—21no—
384C4—22no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—161no—
398C2C2×#1171812911yescharacteristic
399C2#1311648211yescharacteristic
400C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2618C2
socleC22×C13C2×#99
prime radicalC2×C13×#121C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2618D13
hypocenterC13#11698
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#11718122C2semidirect
2. C2×#11718120C2semidirect
3. #13112842C2semidirect
4. #13112839C2semidirect
311. C13#11698semidirect

Maximal subgroups

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

subgroupindex
C2×#117181222
C2×#117181202
#131128422
#131128392
C13×#26182
#1169813