Finite Group Databasebeta

← #16807184

Subgroups — #16807184

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131805C211yesmaximal, characteristic, complemented
2#13131803C211yesmaximal, characteristic, complemented
3#13131227C214yesmaximal, complemented
4#13131224C214yesmaximal, complemented
5C2×#11718233C211yesmaximal, characteristic, complemented
6#13131080C211yesmaximal, characteristic, complemented
7#13131078C211yesmaximal, characteristic, complemented
8C4×#88106C211yesmaximal, characteristic, complemented
9C2×#11718485C211yesmaximal, characteristic
10C2×#88204C411yescharacteristic
11C2×#88202C2211yescharacteristic
12C2×#88161C2211yescharacteristic
13#11719162—22no—
14#11719162C2214yescomplemented
15C2×#88106—22no—
16C2×#88106C2211yescharacteristic
17C2×#88106C2211yescharacteristic
18C2×#88106C2211yescharacteristic
19C2×#88106C2211yescharacteristic
20#11719096—22no—
21#11719096C2214yescomplemented
22D13⋊M32—22no—
23C2×C13×#104C411yescharacteristic
24C2×#88062C411yescharacteristic
25C2×#88045C411yescharacteristic
26C2×C4×#1055C2211yescharacteristic
27#11718485C412yes—
28#11718485C412yes—
29#11718485C2212yes—
30#11718485C2212yes—
31#11718304C2214yescomplemented
32#11718270C2214yescomplemented
33#11718233C2212yescomplemented
34#11718233C2212yescomplemented
35#11718231C2212yescomplemented
36C4×#6092C2212yescomplemented
37C2×C13×#41C2×C411yescharacteristic
38C2×#6127C2×C411yescharacteristic
39C2×C13×M16C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41#88204C812yes—
42#88204C812yes—
43#88204C2×C412yes—
44#88204C2×C412yes—
45#88202—21no—
46#88202—21no—
47#88202C2×C412yes—
48#88202C2312yes—
49C2×#6107C811yescharacteristic
50C2×#6106C811yescharacteristic
51C2×#6105C811yescharacteristic
52C2×#6104C811yescharacteristic
53C2×#6099—21no—
54C2×#6099C2×C411yescharacteristic
55C22×#1055—21no—
56C22×#1055C2×C411yescharacteristic
57C22×#1055C2311yescharacteristic
58#88161—21no—
59#88161—21no—
60#88161C2×C412yes—
61#88161C2312yes—
62C2×#6094—21no—
63C2×C8×D13—21no—
64#88106—21no—
65#88106—21no—
66#88106—21no—
67#88106—21no—
68#88106—24no—
69#88106D412yes—
70#88106D412yes—
71#88106C2312yes—
72#88106C2312yes—
73C2×#6092—21no—
74C2×#6092—21no—
75C2×#6092—24no—
76C2×#6092C2312yes—
77C2×#6092C2312yes—
78#88098—24no—
79D13⋊C16—24no—
80C13×#104C2×C412yes—
81C13×#104C2×C412yes—
82#88062C2×C412yes—
83#88062C2×C412yes—
84#88045C2×C412yes—
85#88045C2×C412yes—
86C4×#1055C2×C411yescharacteristic
87C4×#1055C2×C411yescharacteristic
88C4×#1055C2311yescharacteristic
89C4×#1055C2311yescharacteristic
90#33443—131nomaximal, Sylow
91C13×#41—21no—
92C13×#41—21no—
93C13×#41C2×C812yes—
94C13×#41C22×C412yes—
95C2×Q8×C13C2×C811yescharacteristic
96C2×D4×C13—21no—
97C2×D4×C13C2×C811yescharacteristic
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13C22×C411yescharacteristic
101C2×C22⋊D13—21no—
102#6127—21no—
103#6127—21no—
104#6127C2×C812yes—
105#6127C22×C412yes—
106C2×D52C2×C811yescharacteristic
107C2×C4×D13—21no—
108C2×Dic26C2×C811yescharacteristic
109C13×M16—21no—
110C13×M16C22×C412yes—
111C2×C8×C13—21no—
112C42×C13—21no—
113C42×C13C22×C411yescharacteristic
114C42×C13C22×C411yescharacteristic
115#6107C2×C812yes—
116#6107C2×C812yes—
117#6106C2×C812yes—
118#6106C2×C812yes—
119#6105C2×C812yes—
120#6105C2×C812yes—
121#6104C2×C812yes—
122#6104C2×C812yes—
123#6099—21no—
124#6099—22no—
125#6099—22no—
126#6099C22×C412yes—
127C2×#1055—21no—
128C2×#1055—22no—
129C2×#1055—22no—
130C2×#1055C2×C811yescharacteristic
131C2×#1055C2×C811yescharacteristic
132C2×#1055C2×C811yescharacteristic
133C2×#1055C2×C811yescharacteristic
134C2×#1055C22×C411yescharacteristic
135C2×#1055C22×C411yescharacteristic
136C2×#1055C22×C411yescharacteristic
137C2×#1055C2×D411yescharacteristic
138C2×#1055C2×D411yescharacteristic
139C2×#1055#4111yescharacteristic
140C2×#1055#4111yescharacteristic
141C2×#1055C2411yescharacteristic
142#6094—22no—
143#6094—22no—
144C8×D13—22no—
145C8×D13—22no—
146#6092—22no—
147#6092—22no—
148#6092—22no—
149#6092C2×D414yes—
150#3407—131no—
151#3407—131no—
152C2×#443—131no—
153#2171—134no—
154#2170—134no—
155C2×#364—131no—
156#2117—131no—
157#2117—131no—
158C4×M32—131no—
159C23×C13—21no—
160C23×C13#13111yescharacteristic
161C22×D13—21no—
162Q8×C13—21no—
163Q8×C13C22×C812yes—
164D4×C13—22no—
165D4×C13—22no—
166D4×C13—21no—
167D4×C13C22×C812yes—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—21no—
173C2×C4×C13—42no—
174C2×C4×C13C4×D411yescharacteristic
175C2×C4×C13C4×D411yescharacteristic
176C2×C4×C13C22×C811yescharacteristic
177C2×C4×C13C22×C811yescharacteristic
178C2×C4×C13#13111yescharacteristic
179C2×C4×C13C23×C411yescharacteristic
180C22⋊D13—22no—
181C22⋊D13—22no—
182C2×Dic13—21no—
183D52—21no—
184D52C22×C812yes—
185C4×D13—22no—
186C4×D13—22no—
187Dic26—21no—
188Dic26C22×C812yes—
189C8×C13—22no—
190#1055—22no—
191#1055C4×D411yescharacteristic
192#1055C4×D411yescharacteristic
193#1055C22×C811yescharacteristic
194#1055C22×C811yescharacteristic
195#1055C22×C811yescharacteristic
196#1055C22×C811yescharacteristic
197#1055C22×D411yescharacteristic
198#1055C2×#4111yescharacteristic
199C2×#135—131no—
200C2×#131—131no—
201C2×#131—131no—
202#504—134no—
203#504—134no—
204#504—262no—
205#504—262no—
206C2×M32—131no—
207C2×M32—131no—
208C2×M32—131no—
209C2×M32—131no—
210C2×M32—262no—
211C2×M32—262no—
212#443—132no—
213#443—132no—
214#443—132no—
215#443—132no—
216C2×#108—131no—
217C2×#104—131no—
218C2×#104#26111yescharacteristic
219C2×C4×C8—131no—
220#364—132no—
221#364—132no—
222#350—134no—
223#350—134no—
224#346—132no—
225C4×C16—132no—
226C22×C13—22no—
227C22×C13—41no—
228C22×C13—81no—
229C22×C13C8×D411yescharacteristic
230C22×C13C8×D411yescharacteristic
231C22×C13C2×#13111yescharacteristic
232C2×D13—22no—
233C2×D13—81no—
234C4×C13—22no—
235C4×C13—22no—
236C4×C13—41no—
237C4×C13C8×D411yescharacteristic
238C4×C13C8×D411yescharacteristic
239C4×C13C2×C4×D411yescharacteristic
240C4×C13C23×C811yescharacteristic
241Dic13—22no—
242C2×#41—131no—
243C2×#41C2×#26111yescharacteristic
244#135—132no—
245#135—132no—
246#135—132no—
247#135—132no—
248C2×Q16—131no—
249C2×SD16—131no—
250C2×SD16—131no—
251C2×D8—131no—
252#131—132no—
253#131—132no—
254#131—132no—
255#131—132no—
256#131—261no—
257#131—261no—
258#131—261no—
259#131—261no—
260C2×M16—131no—
261C2×M16—261no—
262C2×M16—261no—
263C2×M16C2×#26111yescharacteristic
264C22×C8—131no—
265C22×C8—131no—
266C22×C8—261no—
267C22×C8—261no—
268C2×C42C2×#26111yescharacteristic
269M32—132no—
270M32—132no—
271M32—132no—
272M32—132no—
273M32—264no—
274M32—264no—
275M32—261no—
276M32—261no—
277M32—261no—
278M32—261no—
279C2×C16—132no—
280C2×C16—132no—
281C2×C16—264no—
282C2×C16—264no—
283C2×C16—261no—
284C2×C16—261no—
285#108—132no—
286#108—132no—
287#104—132no—
288#104—132no—
289#104C2×#26112yes—
290#104C2×#26112yes—
291C4×C8—131no—
292C4×C8—131no—
293C4×C8—131no—
294C4×C8—131no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—42no—
299C2×C13C2×C8×D411yescharacteristic
300D13—42no—
301#41—21no—
302#41—21no—
303#41—132no—
304#41—132no—
305#41—261no—
306#41—261no—
307#41D13⋊C812yes—
308#41C22×#26112yes—
309C2×Q8—131no—
310C2×Q8D13⋊C811yescharacteristic
311C2×D4—21no—
312C2×D4—131no—
313C2×D4—261no—
314C2×D4D13⋊C811yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—261no—
318C22×C4C22×#26111yescharacteristic
319Q16—132no—
320Q16—132no—
321SD16—132no—
322SD16—132no—
323SD16—132no—
324SD16—132no—
325D8—132no—
326D8—132no—
327M16—21no—
328M16—132no—
329M16—262no—
330M16—262no—
331M16—262no—
332M16—262no—
333M16—261no—
334M16C22×#26112yes—
335C2×C8—21no—
336C2×C8—131no—
337C2×C8—131no—
338C2×C8—131no—
339C2×C8—131no—
340C2×C8—131no—
341C2×C8—131no—
342C2×C8—131no—
343C2×C8—131no—
344C2×C8—131no—
345C2×C8—131no—
346C2×C8—131no—
347C2×C8—131no—
348C2×C8—262no—
349C2×C8—262no—
350C2×C8—262no—
351C2×C8—262no—
352C2×C8—261no—
353C42—21no—
354C42C22×#26111yescharacteristic
355C42C22×#26111yescharacteristic
356C16—134no—
357C16—262no—
358C16—262no—
359C16—262no—
360C13#3344311yescharacteristic, complemented, Sylow
361C23—21no—
362C23—261no—
363C23#8823811yescharacteristic
364Q8—21no—
365Q8—132no—
366Q8—261no—
367Q8C2×D13⋊C812yes—
368D4—22no—
369D4—22no—
370D4—21no—
371D4—132no—
372D4—262no—
373D4—262no—
374D4—261no—
375D4C2×D13⋊C812yes—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—261no—
383C2×C4—262no—
384C2×C4—262no—
385C2×C4C2×D13⋊C811yescharacteristic
386C2×C4C2×D13⋊C811yescharacteristic
387C2×C4#8823811yescharacteristic
388C2×C4D4×#26111yescharacteristic
389C2×C4D4×#26111yescharacteristic
390C2×C4C23×#26111yescharacteristic
391C8—22no—
392C8—131no—
393C8—131no—
394C8—131no—
395C8—131no—
396C8—131no—
397C8—131no—
398C8—131no—
399C8—131no—
400C8—262no—
401C22—22no—
402C22—41no—
403C22—81no—
404C22—262no—
405C22—1041no—
406C22#1171906311yescharacteristic
407C22#1171906311yescharacteristic
408C22C2×#8823811yescharacteristic
409C4—22no—
410C4—22no—
411C4—41no—
412C4—262no—
413C4#1171906311yescharacteristic
414C4#1171906311yescharacteristic
415C4C22×D13⋊C811yescharacteristic
416C4C2×D4×#26111yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—42no—
421C2—522no—
422C2C2×#1171906311yescharacteristic
subgroupG/H
centerC4C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C13×#104C4
socleC2×C13C2×C8×D4
prime radicalC2×#88204C4
cosocleC2×#1055C24
hypercenterC2×#104#261
hypocenterC13#33443
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #13131805C2semidirect
2. #13131803C2semidirect
3. #13131227C2semidirect
4. #13131224C2semidirect
5. C2×#11718233C2semidirect
6. #13131080C2semidirect
7. #13131078C2semidirect
8. C4×#88106C2semidirect
14. #11719162C22semidirect
21. #11719096C22semidirect
31. #11718304C22semidirect
32. #11718270C22semidirect
33. #11718233C22semidirect
34. #11718233C22semidirect
35. #11718231C22semidirect
36. C4×#6092C22semidirect
360. C13#33443semidirect

Maximal subgroups

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

subgroupindex
#131318052
#131318032
#131312272
#131312242
C2×#117182332
#131310802
#131310782
C4×#881062
C2×#117184852
#3344313