Finite Group Databasebeta

← C53×#9433 #27216945

Subgroups — C53×#9433 #27216945

Order 13568.

440 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
1C53×#3141C211yesmaximal, characteristic
2C53×#2979C211yesmaximal, characteristic
3C53×#1560C211yesmaximal, characteristic
4C53×#1548C211yesmaximal, characteristic, complemented
5C53×#1546C211yesmaximal, characteristic, complemented
6C53×#1299C211yesmaximal, characteristic, complemented
7C53×#1299C211yesmaximal, characteristic, complemented
8C53×#532C2211yescharacteristic
9C2×C4⋊Q8×C53C2211yescharacteristic
10C53×#489C414yes—
11C53×#487—21no—
12C53×#486—21no—
13C53×#436—21no—
14C53×#436—21no—
15C8×D4×C53—21no—
16C8×D4×C53—21no—
17C53×#431C2211yescharacteristic
18C53×#431C2211yescharacteristic
19C53×#423C2211yescharacteristic
20C53×#423C2211yescharacteristic
21C53×#417—22no—
22C53×#408—22no—
23C4×M16×C53C2211yescharacteristic
24C53×#333—21no—
25C53×#333—21no—
26C53×#333—21no—
27C53×#332—21no—
28C53×#332—21no—
29C53×#331—21no—
30C2×#41×C53D412yes—
31C22×Q8×C53—21no—
32C2×M16×C53—22no—
33C2×M16×C53—21no—
34C2×M16×C53—21no—
35C2×M16×C53—21no—
36C22×C8×C53—22no—
37C4⋊Q8×C53—21no—
38C4⋊Q8×C53—21no—
39C4⋊Q8×C53—21no—
40C4⋊Q8×C53C2×C412yes—
41C4⋊Q8×C53D411yescharacteristic
42#127×C53D411yescharacteristic
43#124×C53C2×C412yes—
44#121×C53—21no—
45#121×C53—21no—
46C4×D4×C53—21no—
47C4×D4×C53—21no—
48C2×C4⋊C4×C53—21no—
49C2×C4⋊C4×C53—21no—
50C2×C42×C53C2311yescharacteristic
51C4⋊C8×C53—21no—
52C4⋊C8×C53—21no—
53C4⋊C8×C53—21no—
54C4⋊C8×C53—21no—
55C4⋊C8×C53D411yescharacteristic
56C4⋊C8×C53D411yescharacteristic
57C4⋊C8×C53D411yescharacteristic
58C4⋊C8×C53D411yescharacteristic
59#103×C53—24no—
60#102×C53—24no—
61C22⋊C8×C53—22no—
62C22⋊C8×C53—22no—
63C22⋊C8×C53—21no—
64C22⋊C8×C53—21no—
65#97×C53C2×C412yes—
66C4×C8×C53—21no—
67C4×C8×C53—21no—
68C4×C8×C53—21no—
69#41×C53—42no—
70#41×C53—42no—
71C2×Q8×C53—22no—
72C2×Q8×C53—41no—
73C2×Q8×C53—81no—
74C2×Q8×C53—81no—
75C2×Q8×C53C22⋊C412yes—
76C2×D4×C53—22no—
77C2×D4×C53—21no—
78C2×D4×C53—21no—
79C2×D4×C53C22⋊C412yes—
80C22×C4×C53—22no—
81C22×C4×C53—41no—
82C22×C4×C53C2×D411yescharacteristic
83C22×C4×C53#4111yescharacteristic
84C22×C4×C53#4111yescharacteristic
85M16×C53—41no—
86M16×C53—41no—
87M16×C53—82no—
88M16×C53—81no—
89M16×C53—81no—
90C2×C8×C53—22no—
91C2×C8×C53—21no—
92C2×C8×C53—21no—
93C2×C8×C53—21no—
94C2×C8×C53—21no—
95C2×C8×C53—41no—
96C2×C8×C53—41no—
97C2×C8×C53—82no—
98C4⋊C4×C53—21no—
99C4⋊C4×C53—21no—
100C4⋊C4×C53—22no—
101C4⋊C4×C53—22no—
102C4⋊C4×C53—41no—
103C4⋊C4×C53—41no—
104C22⋊C4×C53—22no—
105C22⋊C4×C53—22no—
106C42×C53C22×C411yescharacteristic
107C42×C53C2×D411yescharacteristic
108C42×C53C2×D411yescharacteristic
109C42×C53C2×D411yescharacteristic
110C23×C53—22no—
111C23×C53#12311yescharacteristic
112Q8×C53—42no—
113Q8×C53—82no—
114Q8×C53—81no—
115Q8×C53—81no—
116D4×C53—42no—
117D4×C53—41no—
118D4×C53—41no—
119D4×C53—41no—
120D4×C53—41no—
121D4×C53—82no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—22no—
129C2×C4×C53—42no—
130C2×C4×C53—42no—
131C2×C4×C53—42no—
132C2×C4×C53—82no—
133C2×C4×C53C2×C22⋊C411yescharacteristic
134C2×C4×C53C4×D411yescharacteristic
135C2×C4×C53C4×D411yescharacteristic
136C2×C4×C53#12011yescharacteristic
137C2×C4×C53#12111yescharacteristic
138C2×C4×C53#12111yescharacteristic
139C8×C53—42no—
140C8×C53—41no—
141C8×C53—41no—
142C8×C53—41no—
143C8×C53—41no—
144C8×C53—81no—
145C8×C53—81no—
146#9433C5311yesmaximal, characteristic, direct product factor, Sylow
147C22×C53—21no—
148C22×C53—21no—
149C22×C53—21no—
150C22×C53—42no—
151C22×C53—42no—
152C22×C53—42no—
153C22×C53#38611yescharacteristic
154C4×C53—21no—
155C4×C53—21no—
156C4×C53—21no—
157C4×C53—42no—
158C4×C53—82no—
159C4×C53#45511yescharacteristic
160C4×C53#45511yescharacteristic
161C4×C53#47111yescharacteristic
162C4×C53#47111yescharacteristic
163C4×C53#47211yescharacteristic
164C4×C53#47311yescharacteristic
165#3141C2×C5311yescharacteristic
166#2979C2×C5311yescharacteristic
167#1560C2×C5311yescharacteristic
168#1548C2×C5311yescharacteristic, complemented
169#1546C2×C5311yescharacteristic, complemented
170#1299C2×C5311yescharacteristic, complemented
171#1299C2×C5311yescharacteristic, complemented
172C2×C53—41no—
173C2×C53—82no—
174C2×C53#188511yescharacteristic
175C2×C53#190711yescharacteristic
176C2×C53#190811yescharacteristic
177#532C22×C5311yescharacteristic
178C2×C4⋊Q8C22×C5311yescharacteristic
179#489C4×C5314yes—
180#487—21no—
181#486—21no—
182#436—21no—
183#436—21no—
184C8×D4—21no—
185C8×D4—21no—
186#431C22×C5311yescharacteristic
187#431C22×C5311yescharacteristic
188#423C22×C5311yescharacteristic
189#423C22×C5311yescharacteristic
190#417—22no—
191#408—22no—
192C4×M16C22×C5311yescharacteristic
193#333—21no—
194#333—21no—
195#333—21no—
196#332—21no—
197#332—21no—
198#331—21no—
199C53#943311yescharacteristic, direct product factor, Sylow
200C2×#41D4×C5312yes—
201C22×Q8—21no—
202C2×M16—21no—
203C2×M16—22no—
204C2×M16—21no—
205C2×M16—21no—
206C22×C8—22no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8C2×C4×C5312yes—
211C4⋊Q8D4×C5311yescharacteristic
212#127D4×C5311yescharacteristic
213#124C2×C4×C5312yes—
214#121—21no—
215#121—21no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C42C23×C5311yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C5311yescharacteristic
226C4⋊C8D4×C5311yescharacteristic
227C4⋊C8D4×C5311yescharacteristic
228C4⋊C8D4×C5311yescharacteristic
229#103—24no—
230#102—24no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#97C2×C4×C5312yes—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239#41—42no—
240#41—42no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—81no—
245C2×Q8C22⋊C4×C5312yes—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊C4×C5312yes—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4C2×D4×C5311yescharacteristic
253C22×C4#41×C5311yescharacteristic
254C22×C4#41×C5311yescharacteristic
255M16—41no—
256M16—41no—
257M16—82no—
258M16—81no—
259M16—81no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—82no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C42C22×C4×C5311yescharacteristic
277C42C2×D4×C5311yescharacteristic
278C42C2×D4×C5311yescharacteristic
279C42C2×D4×C5311yescharacteristic
280C23—22no—
281C23#123×C5311yescharacteristic
282Q8—42no—
283Q8—82no—
284Q8—81no—
285Q8—81no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—82no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C5311yescharacteristic
304C2×C4C4×D4×C5311yescharacteristic
305C2×C4C4×D4×C5311yescharacteristic
306C2×C4#120×C5311yescharacteristic
307C2×C4#121×C5311yescharacteristic
308C2×C4#121×C5311yescharacteristic
309C8—42no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—41no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22C53×#38611yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4C53×#45511yescharacteristic
329C4C53×#45511yescharacteristic
330C4C53×#47111yescharacteristic
331C4C53×#47111yescharacteristic
332C4C53×#47211yescharacteristic
333C4C53×#47311yescharacteristic
334C2—41no—
335C2—82no—
336C2C53×#188511yescharacteristic
337C2C53×#190711yescharacteristic
338C2C53×#190811yescharacteristic
subgroupG/H
center, socleC22×C53#386
commutatorC42C22×C4×C53
Frattini, cosocleC2×C42C23×C53
prime radicalC53×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
4. C53×#1548C2semidirect
5. C53×#1546C2semidirect
6. C53×#1299C2semidirect
7. C53×#1299C2semidirect
146. #9433C53direct (N × H)
168. #1548C2×C53semidirect
169. #1546C2×C53semidirect
170. #1299C2×C53semidirect
171. #1299C2×C53semidirect
199. C53#9433direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#31412
C53×#29792
C53×#15602
C53×#15482
C53×#15462
C53×#12992
#943353