Finite Group Databasebeta

← #15781570

Subgroups — #15781570

Order 3328.

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

normal subgroups only

This group has 484 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#13120179C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13112953C212yesmaximal
4#13112953C212yesmaximal
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×#6101C411yescharacteristic, complemented
8C2×C13×#99C2212yes—
9C13×#380—21no—
10#11718881C2211yescharacteristic
11#11718881C2211yescharacteristic
12C2×#88073C2212yes—
13#11718873C411yescharacteristic, complemented
14#11718871—21no—
15#11718645—21no—
16#11718609—21no—
17#11718607C411yescharacteristic, complemented
18#11718607C411yescharacteristic, complemented
19#11718594—21no—
20C4×#6099—21no—
21C13×#342—21no—
22#11718122—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13C2×C411yescharacteristic
39C2×C22⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—41no—
46C2×#6101—41no—
47C2×#6099—22no—
48C13×#99—24no—
49C13×#95—41no—
50#88073—22no—
51#88073Q814yes—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88043—41no—
58C4×#1055—41no—
59#13294—131nomaximal, Sylow
60C24×C13C22×C411yescharacteristic
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13C2×Q812yes—
65C2×D4×C13#4112yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—42no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—42no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—81no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—82no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C42×C13—21no—
93C42×C13—21no—
94C22⋊Dic13—42no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97C22⋊Dic13—81no—
98C4⋊Dic13—81no—
99#6101—42no—
100#6101—42no—
101#6101—41no—
102#6101—41no—
103#6101—81no—
104#6099—24no—
105#6099—42no—
106C2×#1055—42no—
107#2579—131no—
108#1799D1311yescharacteristic
109C4×#100—131no—
110#1390—132no—
111#1390—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C4×Q812yes—
122C23×C13#12411yescharacteristic
123C23×C13C4⋊Q811yescharacteristic
124D4×C13—42no—
125D4×C13—42no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—82no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×C4×C13#9911yescharacteristic
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13C22⋊Q812yes—
145C2×Dic13—22no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—82no—
160#1055—44no—
161C2×C4×D4C2×D1311yescharacteristic
162C22×C4⋊C4—131no—
163C2×#100—132no—
164C2×#99C2×D1312yes—
165C4×M16—261no—
166#398—261no—
167#396—261no—
168#387—261no—
169#386—131no—
170#386—131no—
171#385—131no—
172#385—131no—
173#385—261no—
174#380—21no—
175#380—131no—
176#343—261no—
177#342—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—22no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—42no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—81no—
192C22×C13#39111yescharacteristic
193C22×C13C2×#9911yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—162no—
202Dic13—42no—
203Dic13—81no—
204Dic13—81no—
205Dic13—81no—
206C22×D4C22×D1311yescharacteristic
207C23×C4—131no—
208C23×C4—131no—
209C23×C4C4×D1311yescharacteristic
210C23×C4C22⋊D1311yescharacteristic
211C2×M16—262no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—521no—
221C2×C4⋊C4—521no—
222C2×C4⋊C4D5211yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—131no—
225C2×C22⋊C4—131no—
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4C4×D1311yescharacteristic
229C2×C22⋊C4C22⋊D1311yescharacteristic
230C2×C42D5211yescharacteristic
231#100—134no—
232#100—262no—
233#99—24no—
234#97—521no—
235C4×C8—521no—
236#95—41no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241#95—261no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—41no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13#199611yescharacteristic
248C2×C13#212011yescharacteristic
249C2×C13#212111yescharacteristic
250C24C2×C4×D1311yescharacteristic
251C24C2×C22⋊D1311yescharacteristic
252C2×D4—41no—
253C2×D4—41no—
254C2×D4#612912yes—
255C2×D4Q8×D1312yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—522no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—1041no—
271C22×C4#610311yescharacteristic
272C22×C4#610311yescharacteristic
273C22×C4#610311yescharacteristic
274C22×C4#610311yescharacteristic
275C22×C4C2×D5211yescharacteristic
276M16—264no—
277M16—522no—
278C2×C8—522no—
279C4⋊C4—41no—
280C4⋊C4—82no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—1041no—
286C4⋊C4—1041no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—522no—
292C22⋊C4—521no—
293C22⋊C4—521no—
294C22⋊C4—1041no—
295C42—21no—
296C42—21no—
297C13#1329411yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23#8814112yes—
307C23C2×#610311yescharacteristic
308C23#8819011yescharacteristic
309C23#8819811yescharacteristic
310D4—42no—
311D4—42no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—262no—
329C2×C4—521no—
330C2×C4—522no—
331C2×C4—521no—
332C2×C4—522no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—1042no—
343C2×C4#8804611yescharacteristic
344C2×C4#8804611yescharacteristic
345C2×C4#8815112yes—
346C8—524no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22C2×#8804611yescharacteristic
362C22#1171863511yescharacteristic
363C22#1171866711yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—162no—
371C4—522no—
372C4—1041no—
373C4—1041no—
374C4—1041no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—42no—
379C2—41no—
380C2#1311582011yescharacteristic
381C2#1311647511yescharacteristic
382C2#1311648011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1799D13
hypocenterC13#13294
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C22×#6101C4semidirect
13. #11718873C4semidirect
17. #11718607C4semidirect
18. #11718607C4semidirect
297. C13#13294semidirect

Maximal subgroups

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

subgroupindex
#131201792
C4×#880732
#131129532
C13×#17992
#1329413