Finite Group Databasebeta

← #16790399

Subgroups — #16790399

Order 3328.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719162C211yesmaximal, characteristic, complemented
2C2×#11718304C211yesmaximal, characteristic, complemented
3C2×#11718304C211yesmaximal, characteristic, complemented
4#13131066C211yesmaximal, characteristic, complemented
5#13129881C211yesmaximal, characteristic, complemented
6#13129875C211yesmaximal, characteristic, complemented
7C2×#11718857C211yesmaximal, characteristic
8C2×C13×#135C411yescharacteristic
9C2×#88202C2211yescharacteristic
10C2×#88202C2211yescharacteristic
11#11719162—22no—
12#11719162—22no—
13C2×#88106—21no—
14C2×#88106C2211yescharacteristic
15C2×#88106C2211yescharacteristic
16C22×#6092—21no—
17C22×#6092C2211yescharacteristic
18C22×#6092C2211yescharacteristic
19C2×#88077C411yescharacteristic
20C2×#88077C411yescharacteristic
21#11718857—22no—
22#11718857—22no—
23C2×#88059C411yescharacteristic
24C2×C8×Dic13C2211yescharacteristic
25#11718304—22no—
26#11718304—22no—
27C22⋊#6092—21no—
28C22⋊#6092—21no—
29C2×C13×#41C2×C411yescharacteristic
30C2×C13×#41C2×C411yescharacteristic
31C13×#135—22no—
32C13×#135—22no—
33C2×C13×Q16C811yescharacteristic
34C2×C13×SD16C811yescharacteristic
35C2×C13×SD16C811yescharacteristic
36C2×C13×D8C811yescharacteristic
37C22×C8×C13C2×C411yescharacteristic
38#88202—21no—
39#88202—21no—
40#88202—21no—
41#88202—21no—
42#88202—21no—
43#88202—21no—
44#88202D412yes—
45#88202D412yes—
46C2×C4×Dic13C2×C411yescharacteristic
47C2×#6099—21no—
48C2×#6099—21no—
49C2×#6099C2×C411yescharacteristic
50C2×#6099C2×C411yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C22×#1055C2311yescharacteristic
54#88106—24no—
55#88106—21no—
56#88106—21no—
57#88106—21no—
58#88106D412yes—
59C2×#6092—24no—
60C2×#6092—21no—
61C2×#6092—21no—
62C2×#6092—21no—
63C2×#6092—21no—
64C2×#6092—21no—
65C2×#6092—21no—
66C2×#6092—21no—
67C2×#6092D411yescharacteristic
68C2×#6092D411yescharacteristic
69#88077—22no—
70#88077—22no—
71#88059—22no—
72C8×Dic13—21no—
73C8×Dic13—21no—
74#12980—131nomaximal, Sylow
75C13×#41—21no—
76C13×#41—21no—
77C13×#41—21no—
78C13×#41—21no—
79C13×#41—21no—
80C13×#41—21no—
81C13×#41C22⋊C412yes—
82C13×#41M1612yes—
83C2×Q8×C13C2×C811yescharacteristic
84C2×Q8×C13C2×C811yescharacteristic
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13C2×C811yescharacteristic
88C2×D4×C13C2×C811yescharacteristic
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13C22×C411yescharacteristic
92C22×Dic13—21no—
93C13×Q16—22no—
94C13×SD16—22no—
95C13×SD16—22no—
96C13×D8—22no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13C2×C811yescharacteristic
100C2×C8×C13C2×C811yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103#6099—21no—
104#6099—22no—
105#6099—22no—
106#6099—21no—
107#6099—21no—
108#6099—41no—
109#6099—41no—
110#6099C22⋊C412yes—
111C2×#1055—21no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055C2×D411yescharacteristic
118C2×#1055C2×D411yescharacteristic
119C2×#1055C2×D411yescharacteristic
120C2×#1055C2×D411yescharacteristic
121C2×#1055#4111yescharacteristic
122C2×#1055#4111yescharacteristic
123#6092—21no—
124#6092—22no—
125#6092—21no—
126#6092—41no—
127#6092—41no—
128C2×#504—131no—
129C2×#443—131no—
130C2×#350—131no—
131C2×#350—131no—
132#2113—131no—
133#1376—131no—
134#1374—131no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13#13111yescharacteristic
138Q8×C13—21no—
139Q8×C13—21no—
140Q8×C13—21no—
141Q8×C13C22⋊C812yes—
142D4×C13—22no—
143D4×C13—22no—
144D4×C13—21no—
145D4×C13—21no—
146D4×C13—21no—
147D4×C13—41no—
148D4×C13—41no—
149D4×C13C22⋊C812yes—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13C2×C22⋊C411yescharacteristic
157C2×C4×C13C4×D411yescharacteristic
158C2×C4×C13C4×D411yescharacteristic
159C2×C4×C13C22×C811yescharacteristic
160C2×C4×C13C2×M1611yescharacteristic
161C2×C4×C13#13111yescharacteristic
162C2×Dic13—22no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C8×C13—21no—
166C8×C13—21no—
167#1055—22no—
168#1055—41no—
169#1055#12011yescharacteristic
170#1055#12111yescharacteristic
171#1055#12111yescharacteristic
172#1055#12311yescharacteristic
173C2×#135#26111yescharacteristic
174C2×#131—131no—
175C2×#131—131no—
176#504—262no—
177#504—262no—
178C2×M32—131no—
179C2×M32—131no—
180C2×M32—261no—
181C22×C16—131no—
182C22×C16—131no—
183C22×C16—261no—
184#443—262no—
185#443—262no—
186C2×#108—131no—
187C2×#104—131no—
188C2×#104—131no—
189C2×C4×C8—131no—
190#350—262no—
191#350—262no—
192C22⋊C16—261no—
193C22⋊C16—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—22no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13#40811yescharacteristic
203C22×C13C8×D411yescharacteristic
204C22×C13#43511yescharacteristic
205C4×C13—22no—
206C4×C13—41no—
207C4×C13#38611yescharacteristic
208C4×C13C2×C22⋊C811yescharacteristic
209C4×C13C8×D411yescharacteristic
210C4×C13#43511yescharacteristic
211Dic13—42no—
212C2×#41C2×#26111yescharacteristic
213C2×#41C2×#26111yescharacteristic
214#135—22no—
215#135—22no—
216C2×Q16#105711yescharacteristic
217C2×SD16#105711yescharacteristic
218C2×SD16#105711yescharacteristic
219C2×D8#105711yescharacteristic
220#131—132no—
221#131—132no—
222#131—261no—
223#131—261no—
224#131—261no—
225#131—261no—
226#131—261no—
227#131—261no—
228C2×M16—131no—
229C2×M16—131no—
230C2×M16—261no—
231C2×M16—261no—
232C22×C8—131no—
233C22×C8—261no—
234C22×C8—261no—
235C22×C8C2×#26111yescharacteristic
236C2×C42—131no—
237M32—132no—
238M32—261no—
239M32—264no—
240M32—261no—
241M32—261no—
242C2×C16—131no—
243C2×C16—131no—
244C2×C16—261no—
245C2×C16—261no—
246C2×C16—261no—
247C2×C16—264no—
248C2×C16—261no—
249C2×C16—261no—
250C2×C16—261no—
251C2×C16—261no—
252#108—262no—
253#104—262no—
254#104—262no—
255C4×C8—261no—
256C4×C8—261no—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13—42no—
260C2×C13—81no—
261C2×C13#186911yescharacteristic
262C2×C13#217011yescharacteristic
263C2×C13#217111yescharacteristic
264#41—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268#41—21no—
269#41—21no—
270#41#612212yes—
271#41C22⋊#26112yes—
272C2×Q8C2×#105711yescharacteristic
273C2×Q8C2×#105711yescharacteristic
274C2×D4—21no—
275C2×D4—21no—
276C2×D4C2×#105711yescharacteristic
277C2×D4C2×#105711yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—261no—
281C22×C4C22×#26111yescharacteristic
282Q16—22no—
283SD16—22no—
284SD16—22no—
285D8—22no—
286M16—132no—
287M16—262no—
288M16—262no—
289M16—261no—
290M16—261no—
291M16—261no—
292M16—521no—
293M16—521no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—131no—
297C2×C8—131no—
298C2×C8—131no—
299C2×C8—131no—
300C2×C8—131no—
301C2×C8—131no—
302C2×C8—262no—
303C2×C8—262no—
304C2×C8—261no—
305C2×C8—261no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8C2×#105711yescharacteristic
309C2×C8C2×#105711yescharacteristic
310C42—261no—
311C42—261no—
312C16—261no—
313C16—261no—
314C16—262no—
315C16—521no—
316C16—521no—
317C13#1298011yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23#8823811yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8C22⋊#105712yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—41no—
331D4—41no—
332D4C22⋊#105712yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—262no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4#8823811yescharacteristic
343C2×C4D4×#26111yescharacteristic
344C2×C4D4×#26111yescharacteristic
345C2×C4C22×#105711yescharacteristic
346C2×C4C2×#612211yescharacteristic
347C2×C4C2×C22⋊#26111yescharacteristic
348C8—21no—
349C8—21no—
350C8—131no—
351C8—131no—
352C8—131no—
353C8—131no—
354C8—262no—
355C8—521no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22D4×#105711yescharacteristic
365C22#1171914411yescharacteristic
366C22#1171914611yescharacteristic
367C4—22no—
368C4—41no—
369C4—522no—
370C4D4×#105711yescharacteristic
371C4#1171914411yescharacteristic
372C4#1171915011yescharacteristic
373C4C2×C22⋊#105711yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2#1313080911yescharacteristic
379C2#1313122311yescharacteristic
380C2#1313122611yescharacteristic
subgroupG/H
centerC2×C4D4×#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#135C4
socleC22×C13C8×D4
cosocleC22×#1055C23
hypercenterC2×#135#261
hypocenterC13#12980
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11719162C2semidirect
2. C2×#11718304C2semidirect
3. C2×#11718304C2semidirect
4. #13131066C2semidirect
5. #13129881C2semidirect
6. #13129875C2semidirect
317. C13#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#117191622
C2×#117183042
#131310662
#131298812
#131298752
C2×#117188572
#1298013