Finite Group Databasebeta

← #15759230

Subgroups — #15759230

Order 3328.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#11718706C211yesmaximal, characteristic
2#13123496C211yesmaximal, characteristic
3#13114936C211yesmaximal, characteristic
4#13113200C211yesmaximal, characteristic
5#13112712C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic
7C13×#1508C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88180C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C4×C13×C22⋊C4C2211yescharacteristic
12C2×#88075C411yescharacteristic, complemented
13C2×#88075C411yescharacteristic, complemented
14#11718868C2211yescharacteristic
15C2×C22⋊#1055C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718783—21no—
18#11718780—21no—
19#11718706—21no—
20#11718706—21no—
21#11718706—21no—
22#11718706—21no—
23C2×#88048C411yescharacteristic, complemented
24C2×#88047C411yescharacteristic, complemented
25#11718381—22no—
26#11718380—21no—
27#11718379—21no—
28C13×#328—22no—
29#11718120—21no—
30#11718120—21no—
31#11718115—21no—
32#11718115—21no—
33C22×Q8×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C2×C13×M16—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—21no—
45C2×C22⋊Dic13—21no—
46#88180—21no—
47#88180—21no—
48#88180D411yescharacteristic
49#88180D411yescharacteristic
50#88180D411yescharacteristic
51#88180D411yescharacteristic
52C2×C4⋊Dic13C2×C411yescharacteristic
53C2×C4⋊Dic13C2×C411yescharacteristic
54C2×C4×Dic13—21no—
55C2×#6099—21no—
56C22×#1055—21no—
57C22×#1055C2×C411yescharacteristic
58C22×#1055C2×C411yescharacteristic
59C13×C22⋊C8—21no—
60C13×C22⋊C8D412yes—
61C13×#95—21no—
62#88075—21no—
63#88075—21no—
64#88075—21no—
65#88075—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055D411yescharacteristic
72C22⋊#1055D411yescharacteristic
73#88055—22no—
74#88054—22no—
75#88054—22no—
76C8×Dic13—22no—
77#88048—21no—
78#88048—21no—
79#88047—21no—
80#88047—21no—
81#9240—131nomaximal, Sylow
82C24×C13#4111yescharacteristic
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13—41no—
86C2×Q8×C13—41no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13C22×C411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×Dic13—21no—
99C22×Dic13—21no—
100C13×M16—41no—
101C13×M16—41no—
102C2×C8×C13—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C42×C13—41no—
112C42×C13—41no—
113C22⋊Dic13—21no—
114C22⋊Dic13—21no—
115C22⋊Dic13—21no—
116C22⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13C22⋊C411yescharacteristic
120C4⋊Dic13C22⋊C411yescharacteristic
121C4⋊Dic13C22⋊C411yescharacteristic
122C4⋊Dic13C22⋊C411yescharacteristic
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127#6099—41no—
128#6099—41no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055—21no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#485—131no—
139#2924—131no—
140#1826—131no—
141#1508D1311yescharacteristic
142#1472—131no—
143#1293—131no—
144#1282—131no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13C4×D411yescharacteristic
150C23×C13#12111yescharacteristic
151C23×C13#12311yescharacteristic
152Q8×C13—41no—
153Q8×C13—41no—
154Q8×C13—81no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13C2×C22⋊C411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—81no—
183C8×C13—42no—
184#1055—41no—
185#1055—41no—
186#1055—41no—
187#1055—41no—
188#1055—81no—
189C2×C22⋊Q8C2×D1311yescharacteristic
190C2×#117—131no—
191#485—261no—
192#485—261no—
193#485—261no—
194#485—261no—
195#433—262no—
196#432—261no—
197#431—261no—
198C2×#107—131no—
199C2×#106—131no—
200#424—261no—
201C2×#103—131no—
202C2×#103—131no—
203#407—131no—
204#407C2×D1311yescharacteristic
205C2×C22⋊C8—131no—
206C2×C22⋊C8—131no—
207#405—261no—
208C4×C22⋊C4C2×D1311yescharacteristic
209#339—261no—
210#339—261no—
211#328—22no—
212#324—261no—
213#324—261no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13#38611yescharacteristic
225C22×C13#44311yescharacteristic
226C22×C13#44411yescharacteristic
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—82no—
231C4×C13—81no—
232C4×C13—81no—
233C4×C13#41011yescharacteristic
234C4×C13#41011yescharacteristic
235Dic13—41no—
236Dic13—41no—
237Dic13—41no—
238Dic13—41no—
239C22×Q8C4×D1311yescharacteristic
240C23×C4C22×D1311yescharacteristic
241C2×M16—21no—
242C2×M16—261no—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8—261no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250#117—131no—
251#117—131no—
252#117—131no—
253#117—131no—
254#117—261no—
255#117—261no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—131no—
259C2×C4⋊C4C4×D1311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—261no—
263C2×C42—21no—
264C2×C42—261no—
265#107—261no—
266#107—261no—
267#106—261no—
268#106—261no—
269C4⋊C8—262no—
270C4⋊C8—262no—
271#103—261no—
272#103—261no—
273#103—261no—
274#103—261no—
275C22⋊C8—21no—
276C22⋊C8—131no—
277C22⋊C8—131no—
278C22⋊C8—261no—
279C22⋊C8—261no—
280C22⋊C8—261no—
281C22⋊C8—261no—
282C22⋊C8—261no—
283C22⋊C8C22⋊D1312yes—
284#97—262no—
285C4×C8—262no—
286#95—21no—
287C2×C13—21no—
288C2×C13—21no—
289C2×C13—41no—
290C2×C13—41no—
291C2×C13#187611yescharacteristic
292C2×C13#189911yescharacteristic
293C2×C13#190211yescharacteristic
294C24#612911yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—261no—
305C22×C4—261no—
306C22×C4C2×C4×D1311yescharacteristic
307C22×C4#612711yescharacteristic
308C22×C4D4×D1311yescharacteristic
309C22×C4D4×D1311yescharacteristic
310C22×C4D4×D1311yescharacteristic
311C22×C4C2×C22⋊D1311yescharacteristic
312M16—41no—
313M16—41no—
314M16—521no—
315M16—521no—
316C2×C8—22no—
317C2×C8—261no—
318C2×C8—261no—
319C2×C8—261no—
320C2×C8—261no—
321C2×C8—521no—
322C2×C8—521no—
323C2×C8—521no—
324C2×C8—521no—
325C2×C8—521no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—131no—
331C4⋊C4—131no—
332C4⋊C4—131no—
333C4⋊C4—131no—
334C4⋊C4—261no—
335C4⋊C4—261no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—261no—
341C22⋊C4—261no—
342C22⋊C4—261no—
343C22⋊C4—261no—
344C42—41no—
345C42—41no—
346C42—261no—
347C42—261no—
348C42—261no—
349C42—261no—
350C13#924011yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23#8813511yescharacteristic
356C23#8813711yescharacteristic
357C23#8819211yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—521no—
383C2×C4—521no—
384C2×C4—1041no—
385C2×C4C22⋊C4×D1311yescharacteristic
386C2×C4#8813811yescharacteristic
387C2×C4C4×C22⋊D1311yescharacteristic
388C2×C4#8819111yescharacteristic
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—81no—
404C22—81no—
405C22#1171848411yescharacteristic
406C22#1171848511yescharacteristic
407C22#1171861711yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—521no—
415C4—521no—
416C4—521no—
417C4—521no—
418C4#1171840111yescharacteristic
419C4#1171840111yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#1311516011yescharacteristic
425C2#1311529111yescharacteristic
426C2#1311530611yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1508C2
socleC22×C13#386
prime radicalC24×C13#41
cosocleC23×C4×C13C23
hypercenter#1508D13
hypocenterC13#9240
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
12. C2×#88075C4semidirect
13. C2×#88075C4semidirect
23. C2×#88048C4semidirect
24. C2×#88047C4semidirect
350. C13#9240semidirect

Maximal subgroups

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

subgroupindex
C2×#117187062
#131234962
#131149362
#131132002
#131127122
#131126842
C13×#15082
#924013