Finite Group Databasebeta

← #15779891

Subgroups — #15779891

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718804C211yesmaximal, characteristic
2#13116555C211yesmaximal, characteristic, complemented
3C2×#11718084C211yesmaximal, characteristic, complemented
4C2×#11718153C211yesmaximal, characteristic
5#13112944C211yesmaximal, characteristic, complemented
6#13112931C211yesmaximal, characteristic, complemented
7C13×#2913C211yesmaximal, characteristic
8C2×C13×#131C2211yescharacteristic
9C13×#520—21no—
10C2×#88205—21no—
11C22×Dic52C2211yescharacteristic
12C13×#428—21no—
13C13×#428—22no—
14C13×#427—21no—
15C13×#427C2211yescharacteristic
16C2×C13×#107—21no—
17C2×C13×#107C2211yescharacteristic
18#11718804—22no—
19#11718804C414yescomplemented
20C2×#88064—21no—
21C2×#88059C2211yescharacteristic
22C2×#88052C2211yescharacteristic
23C22×#6090C2211yescharacteristic
24#11718153—22no—
25#11718084—22no—
26#11718084—21no—
27#11718084—21no—
28C2×C13×#41D411yescharacteristic
29C22×Dic26—21no—
30C13×#131—21no—
31C13×#131—21no—
32C13×#131C2×C412yes—
33C13×#131D412yes—
34C2×C13×M16—21no—
35C2×C13×M16D411yescharacteristic
36C22×C8×C13—21no—
37C22×C8×C13C2311yescharacteristic
38C4×Q8×C13—41no—
39C4×D4×C13—42no—
40C4×D4×C13—41no—
41C13×#117—22no—
42C13×#117—21no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—21no—
45#88205—24no—
46#88205—42no—
47C2×#6107—41no—
48C2×#6105—41no—
49C2×#6099—21no—
50C2×Dic52—21no—
51C2×Dic52—21no—
52C2×Dic52—21no—
53C2×Dic52—21no—
54C2×Dic52—21no—
55C2×Dic52C2×C412yescomplemented
56C13×#107—22no—
57C13×#107—21no—
58C13×#107D411yescharacteristic
59C13×#107D412yes—
60C13×#107D411yescharacteristic
61C13×#106—22no—
62C13×#106—21no—
63#88064—24no—
64#88059—21no—
65#88059C2×C412yescomplemented
66#88052—21no—
67#88052—21no—
68C2×#6090—21no—
69C2×#6090—21no—
70C2×#6090—21no—
71C2×#6090—21no—
72#12997—131nomaximal, Sylow
73C13×#41—21no—
74C13×#41—21no—
75C13×#41C22⋊C412yes—
76C13×#41SD1612yes—
77C2×Q8×C13D811yescharacteristic
78C2×D4×C13—21no—
79C2×D4×C13D811yescharacteristic
80C22×C4×C13—21no—
81C22×C4×C13—42no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—41no—
85C2×Dic26—22no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C2×Dic26—41no—
91C13×M16—21no—
92C13×M16—22no—
93C13×M16—22no—
94C13×M16C22⋊C412yes—
95C2×C8×C13—21no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—41no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—41no—
111C42×C13—42no—
112C42×C13—41no—
113#6107—44no—
114#6105—44no—
115#6099—22no—
116#6099—41no—
117C2×#1055—41no—
118Dic52—22no—
119Dic52—22no—
120Dic52—41no—
121Dic52—41no—
122#6090—41no—
123#6090—41no—
124C2×#473—131no—
125#2913D1311yescharacteristic
126#2141—131no—
127C2×#358—131no—
128C2×#350—131no—
129#1387—131no—
130#1382—131no—
131C23×C13—21no—
132C23×C13AGL(1,ℤ/8)11yescharacteristic
133Q8×C13—21no—
134Q8×C13#10212yes—
135D4×C13—22no—
136D4×C13—22no—
137D4×C13—21no—
138D4×C13#10212yes—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—161no—
146C2×C4×C13—162no—
147C2×C4×C13C2×C22⋊C411yescharacteristic
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×D811yescharacteristic
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×Dic13—42no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156Dic26—42no—
157Dic26—42no—
158Dic26—81no—
159Dic26—81no—
160C8×C13—22no—
161C8×C13C4×D411yescharacteristic
162C8×C13C4×D411yescharacteristic
163C8×C13#12111yescharacteristic
164C8×C13#12111yescharacteristic
165#1055—42no—
166C2×#137—261no—
167C22×Q16—131no—
168C2×#131C2×D1311yescharacteristic
169#520—21no—
170C2×M32—131no—
171C22×C16—131no—
172#473—134no—
173#473—262no—
174C2×#108—131no—
175#428—21no—
176#428—22no—
177#427—21no—
178#427C2×D1311yescharacteristic
179C2×#107—21no—
180C2×#107C2×D1311yescharacteristic
181C2×#101—261no—
182#358—262no—
183#358—261no—
184#358—261no—
185#350—262no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—22no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13#41711yescharacteristic
192C22×C13#44711yescharacteristic
193C22×C13#48111yescharacteristic
194C4×C13—22no—
195C4×C13—82no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13#38611yescharacteristic
199C4×C13C2×#10211yescharacteristic
200C4×C13#44811yescharacteristic
201C4×C13#48011yescharacteristic
202Dic13—82no—
203C2×#41C22⋊D1311yescharacteristic
204C22×Q8—261no—
205#137—264no—
206#137—522no—
207C2×Q16—132no—
208C2×Q16—261no—
209C2×Q16—261no—
210C2×Q16—261no—
211C2×Q16—261no—
212C2×Q16—261no—
213C2×Q16—521no—
214C2×SD16—521no—
215#131—21no—
216#131—21no—
217#131C4×D1312yes—
218#131D5212yes—
219C2×M16—21no—
220C2×M16—261no—
221C2×M16C22⋊D1311yescharacteristic
222C22×C8—21no—
223C22×C8C22×D1311yescharacteristic
224C4×Q8—41no—
225C4×D4—42no—
226C4×D4—41no—
227#117—22no—
228#117—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231M32—261no—
232M32—261no—
233C2×C16—261no—
234C2×C16—261no—
235C2×C16—261no—
236C2×C16—261no—
237#108—132no—
238#108—261no—
239#107—22no—
240#107—21no—
241#107C22⋊D1311yescharacteristic
242#107C22⋊D1312yes—
243#107C22⋊D1311yescharacteristic
244#106—22no—
245#106—21no—
246#101—264no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—42no—
250C2×C13#187411yescharacteristic
251C2×C13#219411yescharacteristic
252C2×C13#219511yescharacteristic
253#41—21no—
254#41—21no—
255#41#610312yes—
256#41#610612yes—
257C2×Q8—262no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8—521no—
261C2×Q8—521no—
262C2×Q8—521no—
263C2×Q8#610411yescharacteristic
264C2×D4—21no—
265C2×D4#610411yescharacteristic
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—521no—
270C22×C4C2×C22⋊D1311yescharacteristic
271Q16—262no—
272Q16—262no—
273Q16—524no—
274Q16—521no—
275Q16—521no—
276SD16—524no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—262no—
281M16—521no—
282M16#610312yes—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—521no—
287C2×C8C2×C4×D1311yescharacteristic
288C2×C8C2×D5211yescharacteristic
289C2×C8#612711yescharacteristic
290C2×C8#612711yescharacteristic
291C2×C8C2×C22⋊D1311yescharacteristic
292C2×C8C2×C22⋊D1311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C42—42no—
301C42—41no—
302C16—521no—
303C16—521no—
304C13#1299711yescharacteristic, complemented, Sylow
305C23—21no—
306C23#8818611yescharacteristic
307Q8—21no—
308Q8—522no—
309Q8—522no—
310Q8—1041no—
311Q8—1041no—
312Q8#8804912yes—
313D4—22no—
314D4—22no—
315D4—21no—
316D4#8804912yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—161no—
324C2×C4—162no—
325C2×C4—522no—
326C2×C4—1041no—
327C2×C4—1041no—
328C2×C4C2×#610311yescharacteristic
329C2×C4#8818311yescharacteristic
330C2×C4C2×#610411yescharacteristic
331C2×C4C2×#610611yescharacteristic
332C2×C4#8819611yescharacteristic
333C2×C4#8820711yescharacteristic
334C8—22no—
335C8—522no—
336C8C4×C22⋊D1311yescharacteristic
337C8C4×C22⋊D1311yescharacteristic
338C8#8818411yescharacteristic
339C8#8818411yescharacteristic
340C22—21no—
341C22—21no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22#1171862711yescharacteristic
346C22#1171862911yescharacteristic
347C22#1171887811yescharacteristic
348C4—22no—
349C4—82no—
350C4—81no—
351C4—81no—
352C4—1042no—
353C4C2×#8804911yescharacteristic
354C4#1171862811yescharacteristic
355C4#1171887411yescharacteristic
356C4#1171888811yescharacteristic
357C2—21no—
358C2—21no—
359C2—42no—
360C2#1311515311yescharacteristic
361C2#1311680711yescharacteristic
362C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2913C2
socleC22×C13#447
prime radicalC2×C13×#41D4
cosocleC22×C8×C13C23
hypercenter#2913D13
hypocenterC13#12997
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #13116555C2semidirect
3. C2×#11718084C2semidirect
5. #13112944C2semidirect
6. #13112931C2semidirect
19. #11718804C4semidirect
55. C2×Dic52C2×C4semidirect
65. #88059C2×C4semidirect
304. C13#12997semidirect

Maximal subgroups

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

subgroupindex
C2×#117188042
#131165552
C2×#117180842
C2×#117181532
#131129442
#131129312
C13×#29132
#1299713