Finite Group Databasebeta

← C23×#12943 #19160569

Subgroups — C23×#12943 #19160569

Order 5888.

422 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
1C23×#2943C211yesmaximal, characteristic
2C23×#2159C211yesmaximal, characteristic, complemented
3C2×C23×#360C211yesmaximal, characteristic
4C23×#2139C211yesmaximal, characteristic
5C23×#1944C211yesmaximal, characteristic, complemented
6C23×#1386C211yesmaximal, characteristic, complemented
7C23×#1377C211yesmaximal, characteristic, complemented
8C2×C23×#135C2211yescharacteristic
9C4×#41×C23—21no—
10C2×C23×M32C2211yescharacteristic
11C2×C23×M32C2211yescharacteristic
12C23×#442—21no—
13C23×#441—21no—
14C23×#440—21no—
15C23×#440—21no—
16C23×#427C2211yescharacteristic
17C2×C23×#107C2211yescharacteristic
18C2×C23×#106C2211yescharacteristic
19C23×#416—21no—
20C2×C23×#97C2211yescharacteristic
21C23×#389—21no—
22C23×#367—21no—
23C23×#366—21no—
24C23×#360C414yescomplemented
25C23×#358—21no—
26C23×#357—21no—
27C23×#340—21no—
28C2×#41×C23—21no—
29C23×#135—21no—
30C23×#135—21no—
31C23×#135C2×C412yes—
32C23×#135Q812yes—
33C2×Q16×C23D411yescharacteristic
34C2×SD16×C23—21no—
35C2×D8×C23D411yescharacteristic
36C22×C8×C23D411yescharacteristic
37C22×C8×C23C2311yescharacteristic
38C4×Q8×C23—21no—
39C4×Q8×C23—21no—
40C4×D4×C23—21no—
41C4×D4×C23—21no—
42C4×D4×C23—41no—
43C4×D4×C23—41no—
44C23×#117—21no—
45C23×#117—41no—
46C2×C4⋊C4×C23—21no—
47C2×C4⋊C4×C23—21no—
48C2×C4⋊C4×C23—41no—
49C2×C42×C23—41no—
50C2×C42×C23D411yescharacteristic
51C23×M32—21no—
52C23×M32—21no—
53C23×M32—21no—
54C23×M32C2×C412yescomplemented
55C2×C16×C23—21no—
56C2×C16×C23—21no—
57C23×#107—21no—
58C23×#107—21no—
59C23×#107D411yescharacteristic
60C23×#107D411yescharacteristic
61C23×#106—21no—
62C23×#106—21no—
63C23×#106C2×C412yescomplemented
64C23×#103—21no—
65C23×#103—21no—
66C23×#102—21no—
67C23×#102—21no—
68C23×#97—21no—
69C23×#97—21no—
70C23×#95—41no—
71#41×C23—22no—
72#41×C23—22no—
73#41×C23—41no—
74#41×C23—41no—
75C2×Q8×C23—21no—
76C2×D4×C23—21no—
77C2×D4×C23—41no—
78C22×C4×C23—41no—
79C22×C4×C23—41no—
80C22×C4×C23—41no—
81C22×C4×C23—41no—
82C22×C4×C23—41no—
83C22×C4×C23D811yescharacteristic
84C22×C4×C23D811yescharacteristic
85C22×C4×C23C2×D411yescharacteristic
86Q16×C23—21no—
87Q16×C23C4⋊C412yescomplemented
88SD16×C23—22no—
89SD16×C23—22no—
90D8×C23—21no—
91D8×C23C4⋊C412yescomplemented
92C2×C8×C23—21no—
93C2×C8×C23—21no—
94C2×C8×C23—21no—
95C2×C8×C23C22×C411yescharacteristic
96C2×C8×C23C2×D411yescharacteristic
97C2×C8×C23C2×D411yescharacteristic
98C2×C8×C23C2×Q811yescharacteristic
99C2×C8×C23#4111yescharacteristic
100C2×C8×C23#4111yescharacteristic
101C4⋊C4×C23—22no—
102C4⋊C4×C23—21no—
103C4⋊C4×C23—21no—
104C4⋊C4×C23—41no—
105C4⋊C4×C23—41no—
106C4⋊C4×C23—41no—
107C4⋊C4×C23—41no—
108C4⋊C4×C23—41no—
109C4⋊C4×C23—82no—
110C22⋊C4×C23—41no—
111C22⋊C4×C23—41no—
112C22⋊C4×C23—41no—
113C42×C23—21no—
114C42×C23—21no—
115C42×C23—41no—
116C42×C23—41no—
117C42×C23—41no—
118C16×C23—22no—
119C16×C23—41no—
120#12943C2311yesmaximal, characteristic, direct product factor, Sylow
121C23×C23—41no—
122C23×C23C2×D811yescharacteristic
123Q8×C23—22no—
124Q8×C23—41no—
125D4×C23—22no—
126D4×C23—42no—
127D4×C23—42no—
128D4×C23—41no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—41no—
132C2×C4×C23—42no—
133C2×C4×C23—42no—
134C2×C4×C23—41no—
135C2×C4×C23—41no—
136C2×C4×C23—42no—
137C2×C4×C23—41no—
138C2×C4×C23—41no—
139C2×C4×C23—82no—
140C2×C4×C23—82no—
141C2×C4×C23—81no—
142C2×C4×C23—81no—
143C2×C4×C23—81no—
144C2×C4×C23—81no—
145C2×C4×C23—81no—
146C2×C4×C23C4×D411yescharacteristic
147C2×C4×C23#12011yescharacteristic
148C2×C4×C23C22⋊Q811yescharacteristic
149C2×C4×C23#13511yescharacteristic
150C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C23#13711yescharacteristic
152C8×C23—41no—
153C8×C23C2×C4⋊C411yescharacteristic
154C8×C23C4×D411yescharacteristic
155C8×C23C22⋊Q811yescharacteristic
156C8×C23#12311yescharacteristic
157#2943C2×C2311yescharacteristic
158#2159C2×C2311yescharacteristic, complemented
159C2×#360C2×C2311yescharacteristic
160#2139C2×C2311yescharacteristic
161#1944C2×C2311yescharacteristic, complemented
162#1386C2×C2311yescharacteristic, complemented
163#1377C2×C2311yescharacteristic, complemented
164C22×C23—21no—
165C22×C23—21no—
166C22×C23—42no—
167C22×C23—81no—
168C22×C23—81no—
169C22×C23C4×D811yescharacteristic
170C22×C23#44711yescharacteristic
171C22×C23#47411yescharacteristic
172C4×C23—42no—
173C4×C23—41no—
174C4×C23—41no—
175C4×C23—82no—
176C4×C23—81no—
177C4×C23—81no—
178C4×C23—161no—
179C4×C23#38511yescharacteristic
180C4×C23#44011yescharacteristic
181C4×C23#45211yescharacteristic
182C4×C23#47811yescharacteristic
183C2×#135C22×C2311yescharacteristic
184C4×#41—21no—
185C2×M32C22×C2311yescharacteristic
186C2×M32C22×C2311yescharacteristic
187#442—21no—
188#441—21no—
189#440—21no—
190#440—21no—
191#427C22×C2311yescharacteristic
192C2×#107C22×C2311yescharacteristic
193C2×#106C22×C2311yescharacteristic
194#416—21no—
195C2×#97C22×C2311yescharacteristic
196#389—21no—
197#367—21no—
198#366—21no—
199#360C4×C2314yescomplemented
200#358—21no—
201#357—21no—
202#340—21no—
203C2×C23—21no—
204C2×C23—21no—
205C2×C23—82no—
206C2×C23#186211yescharacteristic
207C2×C23#219011yescharacteristic
208C2×C23#219111yescharacteristic
209C2×#41—21no—
210#135—21no—
211#135—21no—
212#135C2×C4×C2312yes—
213#135Q8×C2312yes—
214C2×Q16D4×C2311yescharacteristic
215C2×SD16—21no—
216C2×D8D4×C2311yescharacteristic
217C22×C8D4×C2311yescharacteristic
218C22×C8C23×C2311yescharacteristic
219C4×Q8—21no—
220C4×Q8—21no—
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—41no—
224C4×D4—41no—
225#117—21no—
226#117—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C42—41no—
231C2×C42D4×C2311yescharacteristic
232M32—21no—
233M32—21no—
234M32—21no—
235M32C2×C4×C2312yescomplemented
236C2×C16—21no—
237C2×C16—21no—
238#107—21no—
239#107—21no—
240#107D4×C2311yescharacteristic
241#107D4×C2311yescharacteristic
242#106—21no—
243#106—21no—
244#106C2×C4×C2312yescomplemented
245#103—21no—
246#103—21no—
247#102—21no—
248#102—21no—
249#97—21no—
250#97—21no—
251#95—41no—
252C23#1294311yescharacteristic, direct product factor, Sylow
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4D8×C2311yescharacteristic
266C22×C4D8×C2311yescharacteristic
267C22×C4C2×D4×C2311yescharacteristic
268Q16—21no—
269Q16C4⋊C4×C2312yescomplemented
270SD16—22no—
271SD16—22no—
272D8—21no—
273D8C4⋊C4×C2312yescomplemented
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8C22×C4×C2311yescharacteristic
278C2×C8C2×D4×C2311yescharacteristic
279C2×C8C2×D4×C2311yescharacteristic
280C2×C8C2×Q8×C2311yescharacteristic
281C2×C8#41×C2311yescharacteristic
282C2×C8#41×C2311yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—82no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—21no—
296C42—21no—
297C42—41no—
298C42—41no—
299C42—41no—
300C16—22no—
301C16—41no—
302C23—41no—
303C23C2×D8×C2311yescharacteristic
304Q8—22no—
305Q8—41no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C4×D4×C2311yescharacteristic
328C2×C4C23×#12011yescharacteristic
329C2×C4C23×C22⋊Q811yescharacteristic
330C2×C4C23×#13511yescharacteristic
331C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C23×#13711yescharacteristic
333C8—41no—
334C8C2×C4⋊C4×C2311yescharacteristic
335C8C4×D4×C2311yescharacteristic
336C8C23×C22⋊Q811yescharacteristic
337C8C23×#12311yescharacteristic
338C22—21no—
339C22—21no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22C4×D8×C2311yescharacteristic
344C22C23×#44711yescharacteristic
345C22C23×#47411yescharacteristic
346C4—41no—
347C4—41no—
348C4—42no—
349C4—82no—
350C4—81no—
351C4—81no—
352C4—161no—
353C4C23×#38511yescharacteristic
354C4C23×#44011yescharacteristic
355C4C23×#45211yescharacteristic
356C4C23×#47811yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C23×#186211yescharacteristic
361C2C23×#219011yescharacteristic
362C2C23×#219111yescharacteristic
subgroupG/H
center, socleC22×C23#447
commutatorC2×C8C22×C4×C23
Frattini, cosocleC22×C8C23×C23
prime radicalC2×C23×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×#97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2159C2semidirect
5. C23×#1944C2semidirect
6. C23×#1386C2semidirect
7. C23×#1377C2semidirect
24. C23×#360C4semidirect
54. C23×M32C2×C4semidirect
63. C23×#106C2×C4semidirect
87. Q16×C23C4⋊C4semidirect
91. D8×C23C4⋊C4semidirect
120. #12943C23direct (N × H)
158. #2159C2×C23semidirect
161. #1944C2×C23semidirect
162. #1386C2×C23semidirect
163. #1377C2×C23semidirect
199. #360C4×C23semidirect
235. M32C2×C4×C23semidirect
244. #106C2×C4×C23semidirect
252. C23#12943direct (N × H)
269. Q16C4⋊C4×C23semidirect
273. D8C4⋊C4×C23semidirect

Maximal subgroups

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

subgroupindex
C23×#29432
C23×#21592
C2×C23×#3602
C23×#21392
C23×#19442
C23×#13862
C23×#13772
#1294323