Finite Group Databasebeta

← #16726618

Subgroups — #16726618

Order 3328.

2564 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719455C211yesmaximal, characteristic
2D13×#568C212yesmaximal
3#13123447C211yesmaximal, characteristic, complemented
4#13123446C216yesmaximal, complemented
5#13123445C212yesmaximal, complemented
6#13123444C216yesmaximal, complemented
7C2×#11718554C216yesmaximal, complemented
8D13×#430C216yesmaximal, complemented
9C13×#2916C211yesmaximal, characteristic, complemented
10C2×#41×D13C2211yescharacteristic
11C13×#568C2212yes—
12C2×C13×#131C2211yescharacteristic
13#11719524C2212yes—
14C2×#88202C2211yescharacteristic
15#11719455—28no—
16#11719455C4116yes—
17D13×#131—28no—
18#11719450C22112yes—
19C2×#88161C2213yes—
20C2×M16×D13C22112yes—
21C2×M16×D13C2213yes—
22C2×#88155C2213yes—
23C22×#6094C2213yes—
24C13×#430C2216yescomplemented
25C2×C13×#108C2216yescomplemented
26#11718786C2216yescomplemented
27#11718785C22112yescomplemented
28C2×#88062C22112yescomplemented
29C2×#88059C2216yescomplemented
30#11718554C22112yes—
31#11718554C2214yes—
32#11718554C22112yescomplemented
33#11718554C22112yescomplemented
34D13×#108C22124yescomplemented
35C2×C13×#41C2311yescharacteristic
36#41×D13C2×C418yes—
37#41×D13D418yes—
38C2×#6131Q811yescharacteristic
39C2×Q8×D13Q811yescharacteristic
40C2×#6129Q813yes—
41C2×D4×D13Q813yes—
42C2×#6127C2313yes—
43C22×C4×D13C2313yes—
44C13×#131—28no—
45C13×#131C2×C418yes—
46C2×C13×M16C23112yes—
47C2×C13×M16C2313yes—
48C22×C8×C13C2313yes—
49#88202—28no—
50#88202C2×C418yes—
51C2×#6099C23112yes—
52C2×#6099C2313yes—
53C22×#1055C2313yes—
54#88161—224no—
55#88161C2×C4124yes—
56M16×D13—212no—
57M16×D13—212no—
58M16×D13C2×C4124yes—
59M16×D13C2318yes—
60M16×D13C23124yes—
61#88155—224no—
62#88155C2×C4124yes—
63C2×#6094—212no—
64C2×#6094C2×C4124yes—
65C2×#6094C2311yescharacteristic
66C2×#6094C2313yes—
67C2×#6094C2313yes—
68C2×#6094C2313yes—
69C2×C8×D13—212no—
70C2×C8×D13C2316yes—
71C13×#108C2314yes—
72C13×#108C23112yes—
73#88062C2318yes—
74#88062C23124yes—
75#88059C2314yes—
76#88059C23112yes—
77#60113—131nomaximal, Sylow
78C23×D13C2×Q813yes—
79C13×#41C22×C414yes—
80C13×#41C2×D414yes—
81C2×Q8×C13C2×Q811yescharacteristic
82C2×D4×C13C2×Q813yes—
83C22×C4×C13C2413yes—
84C2×C22⋊D13C2×Q816yes—
85C22×Dic13C2×Q813yes—
86#6131C4⋊C418yes—
87Q8×D13C4⋊C418yes—
88#6129C4⋊C4124yes—
89D4×D13C4⋊C4124yes—
90#6127C22×C4112yes—
91#6127C2×D4112yes—
92C2×D52C2×Q813yes—
93C2×C4×D13C22×C4112yes—
94C2×C4×D13C2×D4112yes—
95C2×C4×D13C2×Q813yes—
96C2×C4×D13C2×Q813yes—
97C2×C4×D13C2413yes—
98C2×C4×D13C2411yescharacteristic
99C2×Dic26C2×Q813yes—
100C13×M16—212no—
101C13×M16C22×C4112yes—
102C13×M16C2418yes—
103C2×C8×C13—212no—
104C2×C8×C13C22×C4112yes—
105C2×C8×C13C2413yes—
106C2×C8×C13C2411yescharacteristic
107#6099—212no—
108#6099C22×C4112yes—
109#6099C2418yes—
110C2×#1055—212no—
111C2×#1055C22×C4112yes—
112C2×#1055C2413yes—
113C2×#1055C2411yescharacteristic
114#6094—28no—
115#6094—224no—
116#6094C22×C414yes—
117#6094C22×C4112yes—
118#6094C22×C4112yes—
119#6094C22×C4112yes—
120C8×D13—28no—
121C8×D13—224no—
122C8×D13C22×C4124yes—
123C2×#568—131no—
124C2×#568—132no—
125#2916—136no—
126#2916—136no—
127#2916—132no—
128#2916—131no—
129#2916D1311yescharacteristic, complemented
130C2×#430—136no—
131C2×#430—136no—
132C23×C13C22×Q813yes—
133C22×D13—83no—
134C22×D13C2×C4⋊C4112yes—
135C22×D13C22×Q811yescharacteristic
136C22×D13C22×Q813yes—
137Q8×C13C2×C4⋊C414yes—
138D4×C13C2×C4⋊C4112yes—
139C2×C4×C13C23×C416yes—
140C2×C4×C13C22×D416yes—
141C2×C4×C13C22×Q813yes—
142C2×C4×C13C2511yescharacteristic
143C22⋊D13C2×C4⋊C4124yes—
144C2×Dic13C2×C4⋊C4112yes—
145C2×Dic13C22×Q813yes—
146C2×Dic13C22×Q811yescharacteristic
147D52C2×C4⋊C4112yes—
148C4×D13C2×C4⋊C4112yes—
149C4×D13C2×C4⋊C4112yes—
150C4×D13C23×C416yes—
151C4×D13C23×C412yes—
152C4×D13C22×D412yes—
153C4×D13C22×D416yes—
154Dic26C2×C4⋊C4112yes—
155C8×C13—28no—
156C8×C13C23×C416yes—
157C8×C13C23×C412yes—
158#1055—28no—
159#1055C23×C416yes—
160#1055C23×C412yes—
161C22×#41—131no—
162#568—1316no—
163#568—132no—
164#568—1312no—
165#568—268no—
166#568C2×D1312yes—
167C2×#131—131no—
168C2×#131—133no—
169C2×#131—133no—
170C2×#131—268no—
171C2×#131C2×D1311yescharacteristic
172C22×M16—133no—
173C22×M16—133no—
174C22×M16—1312no—
175#430—1312no—
176#430—136no—
177#430—1312no—
178#430—134no—
179#430—1312no—
180#430—1312no—
181#430C2×D1316yescomplemented
182C2×#108—1312no—
183C2×#108—136no—
184C2×#108—1324no—
185C2×#108C2×D1316yescomplemented
186C22×C13—43no—
187C22×C13C22×C4⋊C416yes—
188C22×C13C23×Q811yescharacteristic
189C2×D13—41no—
190C2×D13—412no—
191C2×D13—43no—
192C2×D13C22×C4⋊C412yes—
193C2×D13C22×C4⋊C416yes—
194C4×C13C22×C4⋊C416yes—
195C4×C13C24×C411yescharacteristic
196C4×C13C23×D411yescharacteristic
197Dic13C22×C4⋊C416yes—
198Dic13C22×C4⋊C412yes—
199C2×#41—138no—
200C2×#41—138no—
201C2×#41—131no—
202C2×#41—133no—
203C2×#41—133no—
204C2×#41C22×D1311yescharacteristic
205C22×Q8—131no—
206C22×D4—133no—
207C23×C4—133no—
208#131—28no—
209#131—138no—
210#131—1324no—
211#131—1324no—
212#131—2624no—
213#131—2624no—
214#131—268no—
215#131C4×D1318yes—
216C2×M16—133no—
217C2×M16—1324no—
218C2×M16—1324no—
219C2×M16—133no—
220C2×M16—131no—
221C2×M16—133no—
222C2×M16—133no—
223C2×M16—1312no—
224C2×M16—138no—
225C2×M16—1324no—
226C2×M16—2612no—
227C2×M16—2612no—
228C2×M16—2612no—
229C2×M16C22×D13112yes—
230C2×M16C22×D1313yes—
231C22×C8—133no—
232C22×C8—136no—
233C22×C8—2612no—
234C22×C8C22×D1313yes—
235#108—138no—
236#108—1324no—
237#108—1312no—
238#108—134no—
239#108C22×D13112yes—
240#108C22×D1314yes—
241C2×C13—21no—
242C2×C13—26no—
243C2×C13C23×C4⋊C411yescharacteristic
244D13—22no—
245D13—26no—
246C24—133no—
247#41—138no—
248#41—1324no—
249#41—1312no—
250#41—1312no—
251#41C2×C4×D1314yes—
252#41D4×D1314yes—
253C2×Q8—138no—
254C2×Q8—133no—
255C2×Q8Q8×D1311yescharacteristic
256C2×D4—136no—
257C2×D4—1324no—
258C2×D4—133no—
259C2×D4Q8×D1313yes—
260C22×C4—133no—
261C22×C4—1312no—
262C22×C4—1312no—
263C22×C4—133no—
264C22×C4—133no—
265C22×C4—133no—
266C22×C4—131no—
267C22×C4C23×D1313yes—
268M16—212no—
269M16—1312no—
270M16—1312no—
271M16—134no—
272M16—1312no—
273M16—1312no—
274M16—138no—
275M16—268no—
276M16—2624no—
277M16—2612no—
278M16C2×C4×D13112yes—
279M16C23×D1318yes—
280C2×C8—212no—
281C2×C8—1312no—
282C2×C8—131no—
283C2×C8—133no—
284C2×C8—1324no—
285C2×C8—268no—
286C2×C8—2624no—
287C2×C8—2612no—
288C2×C8C2×C4×D13112yes—
289C2×C8C23×D1313yes—
290C2×C8C23×D1311yescharacteristic
291C13#6011311yescharacteristic, complemented, Sylow
292C23—1312no—
293C23—131no—
294C23—133no—
295C23—1043no—
296C23C2×Q8×D1313yes—
297Q8—1312no—
298Q8C4⋊C4×D1314yes—
299D4—1324no—
300D4—1312no—
301D4C4⋊C4×D13112yes—
302C2×C4—1312no—
303C2×C4—131no—
304C2×C4—133no—
305C2×C4—1312no—
306C2×C4—1312no—
307C2×C4—136no—
308C2×C4—132no—
309C2×C4—132no—
310C2×C4—136no—
311C2×C4C22×C4×D1316yes—
312C2×C4C2×D4×D1316yes—
313C2×C4C2×Q8×D1313yes—
314C2×C4C24×D1311yescharacteristic
315C8—28no—
316C8—136no—
317C8—132no—
318C8—268no—
319C8C22×C4×D1316yes—
320C8C22×C4×D1312yes—
321C22—43no—
322C22—132no—
323C22—136no—
324C22—523no—
325C22—5212no—
326C22—521no—
327C22C2×C4⋊C4×D1316yes—
328C22C22×Q8×D1311yescharacteristic
329C4—132no—
330C4—136no—
331C4C2×C4⋊C4×D1316yes—
332C4C23×C4×D1311yescharacteristic
333C4C22×D4×D1311yescharacteristic
334C2—21no—
335C2—26no—
336C2—262no—
337C2—266no—
338C2C22×C4⋊C4×D1311yescharacteristic
subgroupG/H
centerC4C22×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC13×#2916C2
socleC2×C13C23×C4⋊C4
prime radicalC2×#41×D13C22
cosocleC2×C4×C13C25
hypercenter#2916D13
hypocenterC13#60113
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2916

Complements

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

NH ≅ G/Ntype
3. #13123447C2semidirect
4. #13123446C2semidirect
5. #13123445C2semidirect
6. #13123444C2semidirect
7. C2×#11718554C2semidirect
8. D13×#430C2semidirect
9. C13×#2916C2semidirect
24. C13×#430C22semidirect
25. C2×C13×#108C22semidirect
26. #11718786C22semidirect
27. #11718785C22semidirect
28. C2×#88062C22semidirect
29. C2×#88059C22semidirect
32. #11718554C22semidirect
33. #11718554C22semidirect
34. D13×#108C22semidirect
129. #2916D13semidirect
181. #430C2×D13semidirect
185. C2×#108C2×D13semidirect
291. C13#60113semidirect

Maximal subgroups

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

subgroupindex
C2×#117194552
D13×#5682
#131234472
#131234462
#131234452
#131234442
C2×#117185542
D13×#4302
C13×#29162
#6011313