Finite Group Databasebeta

← #15778888

Subgroups — #15778888

Order 3328.

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

normal subgroups only

This group has 540 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
1C4×#88189C211yesmaximal, characteristic
2C2×#11718068C212yesmaximal
3#13114824C211yesmaximal, characteristic
4#13112955C212yesmaximal
5C13×#1800C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C2211yescharacteristic
8C22×C4×Dic13C411yescharacteristic, complemented
9C13×#423—21no—
10C2×C13×#100C2212yes—
11#11718881C2211yescharacteristic
12C2×#88074C2212yes—
13#11718873—21no—
14C4×C22⋊Dic13—21no—
15C4×C22⋊Dic13C411yescharacteristic, complemented
16#11718639—21no—
17#11718607C411yescharacteristic, complemented
18#11718605—21no—
19#11718604C411yescharacteristic, complemented
20C4×#6101—21no—
21C13×#343—21no—
22#11718118—21no—
23#11718068—24no—
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C2×C13×M16—22no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13C2×C411yescharacteristic
40C2×C22⋊Dic13C2×C411yescharacteristic
41#88189—21no—
42#88189—21no—
43#88189D412yes—
44#88189Q812yes—
45C2×C4⋊Dic13—41no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13—21no—
51C2×C4×Dic13—41no—
52C2×C4×Dic13—41no—
53C13×C4⋊C8—41no—
54C13×C4⋊C8—41no—
55C13×#100—22no—
56C13×#100—22no—
57#88074—22no—
58#88074—22no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88071—41no—
65#12794—131nomaximal, Sylow
66C24×C13C22×C411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13C2×D411yescharacteristic
71C2×D4×C13C2×Q811yescharacteristic
72C2×D4×C13#4111yescharacteristic
73C2×D4×C13#4111yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—42no—
91C22×Dic13—41no—
92C22×Dic13—41no—
93C22×Dic13—41no—
94C22×Dic13—42no—
95C22×Dic13C4⋊C412yescomplemented
96C13×M16—42no—
97C13×M16—42no—
98C2×C8×C13—42no—
99C13×C4⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C42×C13—21no—
103C42×C13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—42no—
108C22⋊Dic13—41no—
109C22⋊Dic13—42no—
110C22⋊Dic13—42no—
111C22⋊Dic13C4⋊C412yescomplemented
112C4⋊Dic13—82no—
113#6101—22no—
114#6101—22no—
115#6101—42no—
116C4×Dic13—42no—
117C4×Dic13—42no—
118C4×Dic13—41no—
119C4×Dic13—41no—
120C4×#123—131no—
121C2×#352—132no—
122#1800D1311yescharacteristic
123#1799—131no—
124#1390—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13C2×C4⋊C411yescharacteristic
135C23×C13#11711yescharacteristic
136C23×C13#12111yescharacteristic
137C23×C13C22⋊Q811yescharacteristic
138D4×C13—41no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—41no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—81no—
155C2×C4×C13#9911yescharacteristic
156C2×C4×C13#9911yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13C22⋊Q811yescharacteristic
159C2×Dic13—22no—
160C2×Dic13—22no—
161C2×Dic13—22no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—42no—
165C2×Dic13—41no—
166C2×Dic13—42no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—82no—
176C2×Dic13—82no—
177C2×Dic13—82no—
178C8×C13—82no—
179C2×#123—131no—
180C2×C4×D4C2×D1311yescharacteristic
181C22×C42—131no—
182#423—21no—
183C2×#100C2×D1312yes—
184C2×#99—132no—
185#388—261no—
186#387—261no—
187#386—131no—
188#385—131no—
189#381—131no—
190#380—261no—
191C4×C4⋊C4—261no—
192C4×C22⋊C4—131no—
193C4×C22⋊C4—261no—
194#352—264no—
195#343—21no—
196#342—261no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—42no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—81no—
213C22×C13#38011yescharacteristic
214C22×C13C2×#9911yescharacteristic
215C22×C13#41011yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13#35212yescomplemented
223Dic13—42no—
224Dic13—42no—
225Dic13—42no—
226Dic13—81no—
227Dic13—162no—
228C22×D4C22×D1311yescharacteristic
229C23×C4—131no—
230C23×C4—131no—
231C23×C4C4×D1311yescharacteristic
232C23×C4D5211yescharacteristic
233C2×M16—22no—
234#123—132no—
235#123—132no—
236#123—261no—
237#123—261no—
238C4×D4—41no—
239C4×D4—41no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—521no—
243C2×C4⋊C4C22⋊D1311yescharacteristic
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4—261no—
247C2×C22⋊C4—261no—
248C2×C22⋊C4—262no—
249C2×C22⋊C4C4×D1311yescharacteristic
250C2×C22⋊C4D5211yescharacteristic
251C2×C42—261no—
252C2×C42—261no—
253C2×C42—261no—
254C2×C42—521no—
255C2×C42—521no—
256C2×C42C22⋊D1311yescharacteristic
257C4⋊C8—41no—
258C4⋊C8—41no—
259#100—22no—
260#100—22no—
261#99—262no—
262#99—262no—
263#95—261no—
264#95—261no—
265#95—261no—
266#95—261no—
267#95—261no—
268#95—521no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—41no—
272C2×C13—41no—
273C2×C13—41no—
274C2×C13—41no—
275C2×C13#179911yescharacteristic
276C2×C13C2×#35211yescharacteristic
277C2×C13#212011yescharacteristic
278C24C2×C4×D1311yescharacteristic
279C24C2×D5211yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4D4×D1311yescharacteristic
283C2×D4#612911yescharacteristic
284C2×D4Q8×D1311yescharacteristic
285C2×D4#613111yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—132no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—261no—
297C22×C4—261no—
298C22×C4—522no—
299C22×C4—521no—
300C22×C4—521no—
301C22×C4—521no—
302C22×C4—522no—
303C22×C4#610311yescharacteristic
304C22×C4#610311yescharacteristic
305C22×C4#610311yescharacteristic
306C22×C4#610311yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308M16—42no—
309M16—42no—
310C2×C8—42no—
311C4⋊C4—41no—
312C4⋊C4—262no—
313C4⋊C4—262no—
314C4⋊C4—522no—
315C4⋊C4—1042no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—132no—
319C22⋊C4—261no—
320C22⋊C4—262no—
321C22⋊C4—262no—
322C22⋊C4—522no—
323C22⋊C4—521no—
324C22⋊C4—522no—
325C22⋊C4—522no—
326C42—21no—
327C42—21no—
328C42—522no—
329C42—522no—
330C42—521no—
331C42—521no—
332C13#1279411yescharacteristic, complemented, Sylow
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C4⋊C4×D1311yescharacteristic
342C23#8814611yescharacteristic
343C23#8814911yescharacteristic
344C23#8815111yescharacteristic
345C23C2×#610311yescharacteristic
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—262no—
364C2×C4—262no—
365C2×C4—262no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—522no—
375C2×C4—522no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—1042no—
380C2×C4—1042no—
381C2×C4—1042no—
382C2×C4#8804611yescharacteristic
383C2×C4#8804611yescharacteristic
384C2×C4#8819211yescharacteristic
385C2×C4#8820011yescharacteristic
386C8—82no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22C2×#8804611yescharacteristic
404C22#1171864811yescharacteristic
405C22#1171866711yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—522no—
413C4—522no—
414C4—522no—
415C4—1041no—
416C4—2082no—
417C4#1171806812yescomplemented
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—41no—
424C2#1311482111yescharacteristic
425C2C2×#1171806811yescharacteristic
426C2#1311647811yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1800C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1800D13
hypocenterC13#12794
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
8. C22×C4×Dic13C4semidirect
15. C4×C22⋊Dic13C4semidirect
17. #11718607C4semidirect
19. #11718604C4semidirect
95. C22×Dic13C4⋊C4semidirect
111. C22⋊Dic13C4⋊C4semidirect
222. C4×C13#352semidirect
332. C13#12794semidirect
417. C4#11718068semidirect

Maximal subgroups

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

subgroupindex
C4×#881892
C2×#117180682
#131148242
#131129552
C13×#18002
#1279413