Finite Group Databasebeta

← #15760980

Subgroups — #15760980

Order 3328.

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

normal subgroups only

This group has 538 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#13124772C211yesmaximal, characteristic
2#13114936C211yesmaximal, characteristic, complemented
3#13114911C211yesmaximal, characteristic, complemented
4#13113365C211yesmaximal, characteristic
5#13112744C211yesmaximal, characteristic, complemented
6#13112689C211yesmaximal, characteristic, complemented
7C13×#2333C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C2×#88180C2211yescharacteristic
10C13×#390—21no—
11C13×#388—21no—
12C13×#387—21no—
13C13×#386—21no—
14C13×#386—21no—
15C13×#381C2211yescharacteristic
16C4×C13×C22⋊C4—21no—
17C4×C13×C22⋊C4C2211yescharacteristic
18#11718876—21no—
19#11718872C2211yescharacteristic
20#11718868C2211yescharacteristic
21#11718868C2211yescharacteristic
22#11718696—22no—
23#11718695C412yescomplemented
24#11718694C412yescomplemented
25#11718625—21no—
26#11718129—22no—
27#11718119—21no—
28#11718119—21no—
29#11718115—21no—
30#11718115—21no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C13×#121—21no—
36C13×#121—21no—
37C13×#121C2×C412yes—
38C13×#121D412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13D411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—21no—
53#88180—21no—
54#88180—21no—
55#88180—21no—
56#88180—21no—
57C2×C4⋊Dic13C2×C411yescharacteristic, complemented
58C2×C4⋊Dic13C2×C411yescharacteristic, complemented
59C2×C4×Dic13—21no—
60C2×#6099—21no—
61C2×#6099—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—21no—
67#88072—22no—
68#88072—22no—
69#88071—21no—
70#88071—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055C2×C412yescomplemented
75#88048—22no—
76#88047—22no—
77#9525—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—81no—
86C2×D4×C13—81no—
87C2×D4×C13C22⋊C412yes—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—42no—
96C22×C4×C13—81no—
97C22×C4×C13—81no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×Dic13—21no—
105C22×Dic13—21no—
106C22×Dic13—41no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—81no—
109C13×C4⋊C4C22⋊C412yes—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—22no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—81no—
117C13×C22⋊C4—81no—
118C42×C13—41no—
119C42×C13—41no—
120C42×C13—81no—
121C22⋊Dic13—41no—
122C22⋊Dic13—41no—
123C22⋊Dic13—41no—
124C22⋊Dic13—41no—
125C4⋊Dic13—21no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129C4×Dic13—41no—
130C4×Dic13—41no—
131#6099—41no—
132#6099—41no—
133#6099—41no—
134#6099—41no—
135C2×#1055—22no—
136C2×#1055—41no—
137#3094—131no—
138#2333D1311yescharacteristic
139#1826—131no—
140#1820—131no—
141#1510—131no—
142#1306—131no—
143#1284—131no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—22no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13C4×D411yescharacteristic
156C23×C13#12011yescharacteristic
157C23×C13#12111yescharacteristic
158D4×C13—42no—
159D4×C13—81no—
160D4×C13—82no—
161D4×C13—82no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—84no—
186C2×C4×C13C2×C22⋊C411yescharacteristic
187C2×C4×C13C4×D411yescharacteristic
188C2×C4×C13#12111yescharacteristic
189C2×C4×C13#12311yescharacteristic
190C2×Dic13—41no—
191C2×Dic13—41no—
192C2×Dic13—81no—
193C2×Dic13—81no—
194C2×Dic13—81no—
195C2×Dic13—81no—
196C2×Dic13—81no—
197#1055—42no—
198#1055—81no—
199C2×#121C2×D1311yescharacteristic
200C2×#117—131no—
201#482—262no—
202#481—132no—
203#480—132no—
204#428—261no—
205#418—261no—
206#407—131no—
207#407—131no—
208#390—21no—
209#388—21no—
210#387—21no—
211#386—21no—
212#386—21no—
213#381—131no—
214#381C2×D1311yescharacteristic
215C4×C22⋊C4—21no—
216C4×C22⋊C4C2×D1311yescharacteristic
217#342—261no—
218#342—261no—
219#339—261no—
220#339—261no—
221#327—262no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—42no—
231C22×C13—42no—
232C22×C13—42no—
233C22×C13—81no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13#38611yescharacteristic
240C22×C13#45811yescharacteristic
241C22×C13#45811yescharacteristic
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—21no—
246C4×C13—42no—
247C4×C13—42no—
248C4×C13—81no—
249C4×C13—81no—
250C4×C13—81no—
251Dic13—81no—
252Dic13—81no—
253Dic13—161no—
254C22×D4—21no—
255C22×D4C22⋊D1311yescharacteristic
256C23×C4—21no—
257C23×C4C22×D1311yescharacteristic
258C2×M16—261no—
259C2×M16—261no—
260#121—21no—
261#121—21no—
262#121C4×D1312yes—
263#121D5212yes—
264#117—261no—
265#117—261no—
266#117—261no—
267#117—261no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—131no—
270C2×C4⋊C4—131no—
271C2×C4⋊C4C22⋊D1311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—261no—
278C2×C22⋊C4—261no—
279C2×C22⋊C4C22⋊D1311yescharacteristic
280C2×C22⋊C4C22⋊D1311yescharacteristic
281C2×C42—21no—
282C2×C42—261no—
283C2×C42C22⋊D1311yescharacteristic
284C2×C42C22⋊D1311yescharacteristic
285#107—262no—
286#106—262no—
287#102—262no—
288#102—262no—
289C22⋊C8—132no—
290C22⋊C8—261no—
291C22⋊C8—261no—
292C22⋊C8—261no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—261no—
299#95—261no—
300C2×C13—21no—
301C2×C13—21no—
302C2×C13—41no—
303C2×C13—41no—
304C2×C13—82no—
305C2×C13#189011yescharacteristic
306C2×C13#190411yescharacteristic
307C2×C13#190611yescharacteristic
308C24—21no—
309C24C2×C22⋊D1311yescharacteristic
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—81no—
316C2×D4—81no—
317C2×D4#610312yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—42no—
326C22×C4—81no—
327C22×C4—81no—
328C22×C4—261no—
329C22×C4—261no—
330C22×C4—521no—
331C22×C4C2×C4×D1311yescharacteristic
332C22×C4C2×D5211yescharacteristic
333C22×C4#612711yescharacteristic
334C22×C4#612711yescharacteristic
335C22×C4C2×C22⋊D1311yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337M16—521no—
338M16—521no—
339M16—521no—
340M16—521no—
341C2×C8—262no—
342C2×C8—521no—
343C4⋊C4—21no—
344C4⋊C4—81no—
345C4⋊C4—261no—
346C4⋊C4—261no—
347C4⋊C4—261no—
348C4⋊C4—261no—
349C4⋊C4#610312yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C22⋊C4—81no—
358C22⋊C4—521no—
359C22⋊C4—521no—
360C22⋊C4—521no—
361C22⋊C4—521no—
362C42—41no—
363C42—41no—
364C42—81no—
365C42—521no—
366C42—521no—
367C13#952511yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—22no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C4×C22⋊D1311yescharacteristic
380C23#8818411yescharacteristic
381C23#8820711yescharacteristic
382D4—42no—
383D4—81no—
384D4—82no—
385D4—82no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—84no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—1041no—
413C2×C4—1041no—
414C2×C4—1041no—
415C2×C4—1041no—
416C2×C4—1041no—
417C2×C4C2×#610311yescharacteristic
418C2×C4C4×C22⋊D1311yescharacteristic
419C2×C4#8818311yescharacteristic
420C2×C4#8818411yescharacteristic
421C8—522no—
422C8—1041no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—42no—
432C22—42no—
433C22—42no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22#1171887411yescharacteristic
441C22#1171890411yescharacteristic
442C22#1171890411yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—1041no—
453C4—1041no—
454C4—2081no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—82no—
460C2#1311524911yescharacteristic
461C2#1311532311yescharacteristic
462C2#1311533711yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2333C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2333D13
hypocenterC13#9525
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #13114936C2semidirect
3. #13114911C2semidirect
5. #13112744C2semidirect
6. #13112689C2semidirect
23. #11718695C4semidirect
24. #11718694C4semidirect
57. C2×C4⋊Dic13C2×C4semidirect
58. C2×C4⋊Dic13C2×C4semidirect
74. C22⋊#1055C2×C4semidirect
367. C13#9525semidirect

Maximal subgroups

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

subgroupindex
#131247722
#131149362
#131149112
#131133652
#131127442
#131126892
C13×#23332
#952513