Finite Group Databasebeta

← #15759868

Subgroups — #15759868

Order 3328.

438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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#13125662C211yesmaximal, characteristic
2#13123898C211yesmaximal, characteristic
3#13113368C211yesmaximal, characteristic, complemented
4#13113199C211yesmaximal, characteristic, complemented
5#13112744C211yesmaximal, characteristic, complemented
6#13112713C211yesmaximal, characteristic, complemented
7C13×#1516C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C13×#381C2211yescharacteristic
12#11718900—21no—
13#11718895—21no—
14#11718868C2211yescharacteristic
15#11718868C2211yescharacteristic
16#11718868C2211yescharacteristic
17#11718713—21no—
18#11718711C411yescharacteristic, complemented
19#11718705C411yescharacteristic, complemented
20#11718703—21no—
21#11718701C411yescharacteristic, complemented
22#11718695C411yescharacteristic, complemented
23#11718673—21no—
24#11718673—21no—
25#11718672—21no—
26#11718672—21no—
27#11718661—21no—
28#11718657—21no—
29C13×#328—21no—
30C13×#327—21no—
31#11718061—21no—
32#11718061—21no—
33#11718044—21no—
34#11718044—21no—
35C2×C13×#41D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×Dic26C2×C411yescharacteristic
38C22×C8×C13—21no—
39C13×#123—21no—
40C13×C22⋊Q8C2×C411yescharacteristic
41C13×C22⋊Q8D411yescharacteristic
42C13×#121C2×C411yescharacteristic
43C13×#121D411yescharacteristic
44C13×#120—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C13×#117D411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C22⋊Dic13—21no—
50C2×#6107—21no—
51C2×#6105—21no—
52C2×C4⋊Dic13C2×C411yescharacteristic
53#88178—21no—
54#88178—21no—
55#88178—21no—
56#88178—21no—
57C2×#6101—21no—
58C2×#6099—21no—
59C2×#6099—21no—
60C2×#6099—21no—
61C2×#6099—21no—
62C22×#1055—21no—
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65C13×#95—21no—
66C13×#95—21no—
67#88075—21no—
68#88072—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055C2×C411yescharacteristic
75C22⋊#1055C2×C411yescharacteristic
76C22⋊#1055D411yescharacteristic
77C22⋊#1055D411yescharacteristic
78C22⋊#1055D411yescharacteristic
79C22⋊#1055D411yescharacteristic
80#88050—21no—
81#88050—21no—
82#88048—21no—
83#88047—21no—
84C4⋊#1055—21no—
85C4⋊#1055—21no—
86#88043—21no—
87C4×#1055—21no—
88#9331—131nomaximal, Sylow
89C24×C13#4111yescharacteristic
90C13×#41—81no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13C22⋊C411yescharacteristic
96C22×C4×C13—21no—
97C22×C4×C13—41no—
98C22×C4×C13—81no—
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×Dic13—21no—
106C22×Dic13—21no—
107C2×Dic26—21no—
108C2×Dic26—21no—
109C2×Dic26—81no—
110C2×C8×C13—41no—
111C2×C8×C13—81no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4C22⋊C411yescharacteristic
115C13×C4⋊C4C22⋊C411yescharacteristic
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—81no—
122C42×C13—21no—
123C22⋊Dic13—41no—
124C22⋊Dic13—41no—
125#6107—81no—
126#6105—81no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129#6101—41no—
130#6101—41no—
131#6099—81no—
132#6099—81no—
133#6099—81no—
134#6099—81no—
135C2×#1055—21no—
136C2×#1055—21no—
137C2×#1055—21no—
138C2×#1055—21no—
139C2×#1055—21no—
140C2×#1055—21no—
141C2×#1055—81no—
142#3196—131no—
143#2978—131no—
144#1516D1311yescharacteristic
145#1511—131no—
146#1472—131no—
147#1306—131no—
148#1293—131no—
149C23×C13—21no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13C4×D411yescharacteristic
154C23×C13#12111yescharacteristic
155C23×C13#12311yescharacteristic
156Q8×C13—41no—
157D4×C13—41no—
158D4×C13—81no—
159D4×C13—81no—
160D4×C13—81no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13C2×C22⋊C411yescharacteristic
176C2×C4×C13C4×D411yescharacteristic
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×Dic13—42no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—81no—
183Dic26—41no—
184Dic26—41no—
185Dic26—81no—
186C8×C13—81no—
187#1055—41no—
188#1055—41no—
189#1055—41no—
190#1055—41no—
191#1055—41no—
192#1055—41no—
193#525C2×D1311yescharacteristic
194C2×C22⋊Q8—131no—
195#485—261no—
196#484—131no—
197#481—131no—
198#470—261no—
199#468—261no—
200#452—261no—
201#451—131no—
202#448—131no—
203#436—261no—
204#436—261no—
205#435—261no—
206#435—261no—
207#433—261no—
208#408—261no—
209#407—131no—
210#407—131no—
211#407—131no—
212C2×C22⋊C8C2×D1311yescharacteristic
213#381C2×D1311yescharacteristic
214#328—21no—
215#328—261no—
216#328—261no—
217#327—21no—
218#324—261no—
219#324—261no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—82no—
233C22×C13#38611yescharacteristic
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—41no—
241C4×C13—161no—
242Dic13—81no—
243Dic13—81no—
244C2×#41D5211yescharacteristic
245C22×Q8—131no—
246C23×C4C22×D1311yescharacteristic
247C2×Q16—261no—
248C2×SD16—261no—
249C2×M16—261no—
250C2×M16—261no—
251C2×M16—261no—
252C2×M16—261no—
253C22×C8—21no—
254C22×C8—261no—
255#123—21no—
256C22⋊Q8—261no—
257C22⋊Q8—261no—
258C22⋊Q8—261no—
259C22⋊Q8—261no—
260C22⋊Q8C4×D1311yescharacteristic
261C22⋊Q8C22⋊D1311yescharacteristic
262#121C4×D1311yescharacteristic
263#121C22⋊D1311yescharacteristic
264#120—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117D5211yescharacteristic
268C2×C4⋊C4—131no—
269C2×C4⋊C4—261no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—261no—
272#107—261no—
273#106—261no—
274C4⋊C8—261no—
275C4⋊C8—261no—
276#103—261no—
277#103—261no—
278#103—261no—
279#102—261no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—131no—
283C22⋊C8—131no—
284C22⋊C8—131no—
285C22⋊C8—131no—
286C22⋊C8—131no—
287C22⋊C8—131no—
288C22⋊C8—261no—
289C22⋊C8—261no—
290C22⋊C8—261no—
291C22⋊C8—261no—
292C22⋊C8—261no—
293#97—261no—
294C4×C8—261no—
295#95—21no—
296#95—21no—
297C2×C13—41no—
298C2×C13—41no—
299C2×C13—41no—
300C2×C13—81no—
301C2×C13#188111yescharacteristic
302C2×C13#190211yescharacteristic
303C2×C13#191311yescharacteristic
304C24#612911yescharacteristic
305#41—81no—
306C2×Q8—261no—
307C2×Q8—261no—
308C2×Q8—1041no—
309C2×Q8#610311yescharacteristic
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4#610311yescharacteristic
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—81no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4C2×C4×D1311yescharacteristic
320C22×C4C2×D5211yescharacteristic
321C22×C4D4×D1311yescharacteristic
322C22×C4D4×D1311yescharacteristic
323C22×C4#612911yescharacteristic
324C22×C4C2×C22⋊D1311yescharacteristic
325Q16—1041no—
326SD16—1041no—
327M16—1041no—
328M16—1041no—
329M16—1041no—
330M16—1041no—
331C2×C8—41no—
332C2×C8—81no—
333C2×C8—261no—
334C2×C8—261no—
335C2×C8—261no—
336C2×C8—261no—
337C2×C8—261no—
338C2×C8—261no—
339C2×C8—1041no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—261no—
343C4⋊C4—261no—
344C4⋊C4—521no—
345C4⋊C4—521no—
346C4⋊C4#610311yescharacteristic
347C4⋊C4#610311yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—81no—
354C22⋊C4—521no—
355C22⋊C4—521no—
356C42—21no—
357C13#933111yescharacteristic, complemented, Sylow
358C23—21no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23#8813511yescharacteristic
363C23#8814011yescharacteristic
364C23#8819311yescharacteristic
365Q8—41no—
366Q8—521no—
367Q8—521no—
368Q8—1041no—
369D4—41no—
370D4—81no—
371D4—81no—
372D4—81no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—522no—
388C2×C4—521no—
389C2×C4—521no—
390C2×C4—1041no—
391C2×C4#8813511yescharacteristic
392C2×C4#8813611yescharacteristic
393C2×C4C2×#610311yescharacteristic
394C2×C4#8819311yescharacteristic
395C8—81no—
396C8—521no—
397C8—521no—
398C8—521no—
399C8—521no—
400C8—521no—
401C8—521no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22#1171861911yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—161no—
424C4—1041no—
425C4—1041no—
426C2—41no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2#1311519611yescharacteristic
431C2#1311530711yescharacteristic
432C2#1311537611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1516C2
socleC22×C13#386
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#1516D13
hypocenterC13#9331
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
3. #13113368C2semidirect
4. #13113199C2semidirect
5. #13112744C2semidirect
6. #13112713C2semidirect
18. #11718711C4semidirect
19. #11718705C4semidirect
21. #11718701C4semidirect
22. #11718695C4semidirect
357. C13#9331semidirect

Maximal subgroups

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

subgroupindex
#131256622
#131238982
#131133682
#131131992
#131127442
#131127132
C13×#15162
#933113