Finite Group Databasebeta

← #15763437

Subgroups — #15763437

Order 3328.

650 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125593C211yesmaximal, characteristic
2C2×#11718632C211yesmaximal, characteristic, complemented
3#13115821C211yesmaximal, characteristic, complemented
4#13114922C211yesmaximal, characteristic, complemented
5#13113404C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic, complemented
7C13×#2501C211yesmaximal, characteristic
8C2×C13×#123—22no—
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×#88178C2211yescharacteristic
12C13×#399—22no—
13C13×#390—21no—
14C13×#384—21no—
15C4×C13×C22⋊C4C2211yescharacteristic
16#11718879—21no—
17#11718873C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718702—22no—
21#11718701—21no—
22#11718695—21no—
23#11718632—22no—
24#11718632—21no—
25#11718632—22no—
26C2×#88050—21no—
27C2×#88048—21no—
28#11718129—22no—
29#11718121—22no—
30#11718119—22no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C22×Dic26D411yescharacteristic
36C13×#123—44no—
37C13×#123—44no—
38C13×#121—21no—
39C13×#121—21no—
40C13×#121—21no—
41C13×#121—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D412yes—
50C2×C13×C22⋊C4—24no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4D412yes—
53C2×C42×C13—21no—
54C2×C22⋊Dic13—21no—
55C2×C22⋊Dic13—21no—
56C2×#6105—22no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13D411yescharacteristic
59#88178—21no—
60#88178—21no—
61#88178—21no—
62#88178—21no—
63C2×#6101—21no—
64C22×#1055—21no—
65C22×#1055D412yes—
66C13×#95—21no—
67#88072—22no—
68#88071—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055D412yes—
73#88050—22no—
74#88050—24no—
75#88048—22no—
76#88048—24no—
77#9960—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—42no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—42no—
86C2×D4×C13—42no—
87C22×C4×C13—22no—
88C22×C4×C13—22no—
89C22×C4×C13—21no—
90C22×C4×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—41no—
104C2×Dic26—21no—
105C2×Dic26—21no—
106C2×Dic26—42no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—48no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—22no—
115C13×C22⋊C4—48no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4SD1614yescomplemented
119C42×C13—42no—
120C22⋊Dic13—41no—
121C22⋊Dic13—41no—
122C22⋊Dic13—42no—
123#6105—82no—
124C4⋊Dic13—21no—
125C4⋊Dic13—21no—
126C4⋊Dic13—42no—
127#6101—41no—
128#6101—41no—
129C2×#1055—22no—
130C2×#1055—22no—
131C2×#1055—42no—
132C2×#1055—42no—
133#3187—131no—
134C2×#483—131no—
135#2501D1311yescharacteristic
136#1996—131no—
137#1823—131no—
138#1519—131no—
139#1282—131no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13#12011yescharacteristic
147C23×C13#12111yescharacteristic
148C23×C13#12711yescharacteristic
149C23×C13C2×SD1612yes—
150C23×C13AGL(1,ℤ/8)12yes—
151D4×C13—42no—
152D4×C13—81no—
153D4×C13—82no—
154D4×C13—81no—
155D4×C13—81no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—24no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13—44no—
168C2×C4×C13—42no—
169C2×C4×C13—82no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—81no—
179C2×Dic13—81no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183Dic26—42no—
184Dic26—42no—
185#1055—42no—
186#1055—42no—
187C2×#123—22no—
188C2×C22⋊Q8—131no—
189C2×#121C2×D1311yescharacteristic
190C22×C4⋊C4C2×D1311yescharacteristic
191#483—262no—
192#483—262no—
193#483—261no—
194#481—261no—
195#465—262no—
196#450—261no—
197#448—261no—
198C2×#106—261no—
199C2×#103—261no—
200C2×C22⋊C8—131no—
201C2×C22⋊C8—131no—
202#399—22no—
203#390—21no—
204#384—21no—
205#380—131no—
206C4×C22⋊C4C2×D1311yescharacteristic
207#342—262no—
208#340—262no—
209#327—262no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—42no—
217C22×C13—42no—
218C22×C13—84no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13#39211yescharacteristic
223C22×C13#45012yes—
224C22×C13#46012yes—
225C22×C13#49211yescharacteristic
226C22×C13#49611yescharacteristic
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—44no—
231C4×C13—82no—
232C4×C13—81no—
233C4×C13#45812yes—
234Dic13—81no—
235Dic13—81no—
236Dic13—161no—
237C22×Q8—131no—
238C22×D4—21no—
239C22×D4C22⋊D1311yescharacteristic
240C23×C4—21no—
241C23×C4C22×D1311yescharacteristic
242C2×SD16—262no—
243C22×C8—132no—
244C22×C8—261no—
245#123—44no—
246#123—44no—
247C22⋊Q8—261no—
248C22⋊Q8—261no—
249C22⋊Q8—261no—
250C22⋊Q8—261no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—131no—
262C2×C4⋊C4—261no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4C22⋊D1312yes—
265C2×C4⋊C4C22⋊D1311yescharacteristic
266C2×C22⋊C4—24no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—261no—
269C2×C22⋊C4—261no—
270C2×C22⋊C4C22⋊D1312yes—
271C2×C42—21no—
272#106—264no—
273#106—262no—
274#103—264no—
275#103—262no—
276#102—262no—
277C22⋊C8—132no—
278C22⋊C8—261no—
279C22⋊C8—261no—
280C22⋊C8—261no—
281#95—21no—
282#95—261no—
283C2×C13—21no—
284C2×C13—22no—
285C2×C13—22no—
286C2×C13—21no—
287C2×C13—161no—
288C2×C13#200911yescharacteristic
289C2×C13#201411yescharacteristic
290C2×C13#202211yescharacteristic
291C24—21no—
292C24C2×C22⋊D1311yescharacteristic
293C2×Q8—261no—
294C2×Q8—261no—
295C2×Q8—522no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—261no—
312C22×C4—261no—
313C22×C4—521no—
314C22×C4D4×D1311yescharacteristic
315C22×C4D4×D1311yescharacteristic
316C22×C4D4×D1311yescharacteristic
317C22×C4#612911yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320SD16—1042no—
321C2×C8—262no—
322C2×C8—262no—
323C2×C8—522no—
324C2×C8—522no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—48no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—261no—
333C4⋊C4—261no—
334C4⋊C4—522no—
335C4⋊C4—521no—
336C4⋊C4—521no—
337C22⋊C4—22no—
338C22⋊C4—48no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—521no—
342C22⋊C4—521no—
343C22⋊C4—522no—
344C22⋊C4#610514yescomplemented
345C42—42no—
346C13#996011yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23#8818612yes—
354C23C2×#610512yes—
355C23#8819211yescharacteristic
356C23#8819411yescharacteristic
357C23#8820711yescharacteristic
358Q8—522no—
359Q8—522no—
360D4—42no—
361D4—81no—
362D4—81no—
363D4—82no—
364D4—81no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—82no—
380C2×C4—81no—
381C2×C4—521no—
382C2×C4—521no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4—1041no—
386C2×C4—1041no—
387C2×C4—1041no—
388C2×C4#8819111yescharacteristic
389C2×C4#8819111yescharacteristic
390C2×C4#8819311yescharacteristic
391C2×C4#8819311yescharacteristic
392C8—522no—
393C8—522no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1171873511yescharacteristic
407C22#1171873612yes—
408C22#1171873711yescharacteristic
409C22#1171887912yes—
410C22#1171888411yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—44no—
415C4—82no—
416C4—81no—
417C4—1041no—
418C4—1041no—
419C4—2081no—
420C4#1171871412yes—
421C2—22no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—161no—
426C2#1311589611yescharacteristic
427C2#1311592411yescharacteristic
428C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2501C2
socleC22×C13#392
prime radicalC2×C13×#121C22
hypercenter#2501D13
hypocenterC13#9960
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
2. C2×#11718632C2semidirect
3. #13115821C2semidirect
4. #13114922C2semidirect
6. #13112684C2semidirect
118. C13×C22⋊C4SD16semidirect
344. C22⋊C4#6105semidirect
346. C13#9960semidirect

Maximal subgroups

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

subgroupindex
#131255932
C2×#117186322
#131158212
#131149222
#131134042
#131126842
C13×#25012
#996013