Finite Group Databasebeta

← #15760954

Subgroups — #15760954

Order 3328.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123884C211yesmaximal, characteristic
2#13114926C211yesmaximal, characteristic, complemented
3#13114916C211yesmaximal, characteristic, complemented
4#13113379C211yesmaximal, characteristic
5#13112743C211yesmaximal, characteristic, complemented
6#13112712C211yesmaximal, characteristic, complemented
7C13×#3092C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#484—21no—
11C13×#483C412yescomplemented
12C13×#481—21no—
13C13×#480C412yescomplemented
14C13×#428—21no—
15C13×#417—21no—
16C13×#407C2211yescharacteristic
17#11718895—21no—
18#11718873C2211yescharacteristic
19#11718868C2211yescharacteristic
20#11718868C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22#11718673—21no—
23#11718672—21no—
24#11718672—21no—
25D4×#1055—21no—
26#11718661—21no—
27#11718130—21no—
28#11718129—21no—
29#11718122—21no—
30#11718122—21no—
31#11718121—21no—
32#11718121—21no—
33C2×C13×#41D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C2×C13×M16—21no—
37C13×#123—21no—
38C13×C22⋊Q8C2×C411yescharacteristic
39C13×C22⋊Q8D411yescharacteristic
40C13×#121C2×C411yescharacteristic
41C13×#121D411yescharacteristic
42C13×#120—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C13×#117D411yescharacteristic
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4C2×C412yes—
52C2×C22⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×#6099—21no—
55C2×#6099—21no—
56C2×#6099D411yescharacteristic
57C2×#6099D411yescharacteristic
58C22×#1055—21no—
59C22×#1055D411yescharacteristic
60C22×#1055D411yescharacteristic
61C13×#107—22no—
62C13×#106—22no—
63C13×#103—22no—
64C13×#102—22no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8C2×C412yes—
67#88071—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055—21no—
76C4⋊#1055—21no—
77C4⋊#1055—21no—
78#88043—21no—
79C4×#1055—21no—
80#9521—131nomaximal, Sylow
81C24×C13#4111yescharacteristic
82C13×#41—41no—
83C13×#41—41no—
84C2×Q8×C13C22⋊C411yescharacteristic
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13C22⋊C411yescharacteristic
89C22×C4×C13—21no—
90C22×C4×C13—22no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—82no—
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13#4111yescharacteristic
102C22×Dic13—41no—
103C13×M16—41no—
104C13×M16—41no—
105C2×C8×C13—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4C22⋊C411yescharacteristic
113C13×C4⋊C4C22⋊C411yescharacteristic
114C13×C22⋊C4—21no—
115C13×C22⋊C4—21no—
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C42×C13—21no—
120C22⋊Dic13—81no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123#6099—41no—
124#6099—41no—
125#6099—41no—
126#6099—41no—
127#6099—81no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—81no—
136#3092D1311yescharacteristic
137#2976—131no—
138#1824—131no—
139#1821—131no—
140#1513—131no—
141#1305—131no—
142#1293—131no—
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13C4×D411yescharacteristic
149C23×C13#12111yescharacteristic
150C23×C13#12311yescharacteristic
151Q8×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—81no—
156D4×C13—81no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—82no—
173C2×C4×C13—82no—
174C2×C4×C13—82no—
175C2×C4×C13C2×C22⋊C411yescharacteristic
176C2×C4×C13C4×D411yescharacteristic
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×Dic13—81no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C8×C13—42no—
183#1055—41no—
184#1055—41no—
185#1055—41no—
186#1055—41no—
187#1055—81no—
188#525C2×D1311yescharacteristic
189C22×C4⋊C4C2×D1311yescharacteristic
190#484—21no—
191#483Dic1312yescomplemented
192#481—21no—
193#480Dic1312yescomplemented
194#436—261no—
195#435—261no—
196#435—261no—
197C8×D4—261no—
198#433—261no—
199#428—21no—
200#417—21no—
201#408—261no—
202#407—131no—
203#407—131no—
204#407C2×D1311yescharacteristic
205C2×C22⋊C8—131no—
206#380—131no—
207#343—261no—
208#343—261no—
209#340—261no—
210#340—261no—
211#328—261no—
212#327—261no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13#38611yescharacteristic
227C22×C13#47111yescharacteristic
228C22×C13#47311yescharacteristic
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—82no—
236C4×C13#45811yescharacteristic
237C4×C13#45811yescharacteristic
238Dic13—161no—
239C2×#41C22⋊D1311yescharacteristic
240C23×C4—21no—
241C23×C4C22×D1311yescharacteristic
242C2×M16—21no—
243C2×M16—131no—
244C2×M16—131no—
245C2×M16—261no—
246C2×M16—261no—
247C22×C8—131no—
248C22×C8—131no—
249C22×C8—261no—
250#123—21no—
251C22⋊Q8C2×Dic1311yescharacteristic
252C22⋊Q8C22⋊D1311yescharacteristic
253#121C2×Dic1311yescharacteristic
254#121C22⋊D1311yescharacteristic
255#120—21no—
256C4×D4—21no—
257C4×D4—21no—
258#117C22⋊D1311yescharacteristic
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4C2×Dic1312yes—
266C2×C22⋊C4—261no—
267#107—22no—
268#106—22no—
269C4⋊C8—261no—
270C4⋊C8—261no—
271#103—22no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—261no—
275C22⋊C8—261no—
276C22⋊C8—261no—
277C22⋊C8—261no—
278C22⋊C8—261no—
279C22⋊C8—261no—
280C22⋊C8—261no—
281C22⋊C8—261no—
282C22⋊C8C2×Dic1312yes—
283#97—261no—
284C4×C8—261no—
285#95—261no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—41no—
289C2×C13—41no—
290C2×C13—81no—
291C2×C13#189011yescharacteristic
292C2×C13#190311yescharacteristic
293C2×C13#190811yescharacteristic
294C24#612911yescharacteristic
295#41—41no—
296#41—41no—
297C2×Q8C22⋊Dic1311yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4C22⋊Dic1311yescharacteristic
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4—521no—
310C22×C4D4×D1311yescharacteristic
311C22×C4D4×D1311yescharacteristic
312C22×C4#612911yescharacteristic
313C22×C4C22×Dic1311yescharacteristic
314C22×C4C2×C22⋊D1311yescharacteristic
315C22×C4C2×C22⋊D1311yescharacteristic
316M16—41no—
317M16—41no—
318M16—521no—
319M16—521no—
320M16—521no—
321M16—521no—
322M16—1041no—
323C2×C8—22no—
324C2×C8—261no—
325C2×C8—261no—
326C2×C8—261no—
327C2×C8—261no—
328C2×C8—521no—
329C2×C8—521no—
330C2×C8—521no—
331C2×C8—1041no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C4⋊C4C22⋊Dic1311yescharacteristic
341C4⋊C4C22⋊Dic1311yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—1041no—
348C42—21no—
349C13#952111yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic1311yescharacteristic
356C23#8818911yescharacteristic
357C23#8819311yescharacteristic
358Q8—41no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—81no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—1041no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4D4×Dic1311yescharacteristic
386C2×C4#8819111yescharacteristic
387C2×C4#8819311yescharacteristic
388C2×C4C2×C22⋊Dic1311yescharacteristic
389C8—42no—
390C8—521no—
391C8—521no—
392C8—521no—
393C8—521no—
394C8—1041no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22#1171886411yescharacteristic
409C22#1171886511yescharacteristic
410C22#1171888111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—82no—
418C4—2081no—
419C4#1171871411yescharacteristic
420C4#1171871411yescharacteristic
421C2—21no—
422C2—21no—
423C2—41no—
424C2—41no—
425C2—81no—
426C2#1311525011yescharacteristic
427C2#1311531811yescharacteristic
428C2#1311535311yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3092C2
socleC22×C13#386
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#3092D13
hypocenterC13#9521
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
2. #13114926C2semidirect
3. #13114916C2semidirect
5. #13112743C2semidirect
6. #13112712C2semidirect
11. C13×#483C4semidirect
13. C13×#480C4semidirect
191. #483Dic13semidirect
193. #480Dic13semidirect
349. C13#9521semidirect

Maximal subgroups

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

subgroupindex
#131238842
#131149262
#131149162
#131133792
#131127432
#131127122
C13×#30922
#952113