Finite Group Databasebeta

← C43×#28826 #24948843

Subgroups — C43×#28826 #24948843

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3164C212yesmaximal
2C43×#3163C212yesmaximal
3C43×#2061C211yesmaximal, characteristic
4C43×#2061C211yesmaximal, characteristic
5C43×#2060C212yesmaximal
6C43×#1952C212yesmaximal
7C43×#1951C212yesmaximal
8C43×#1847C211yesmaximal, characteristic
9C43×#1773C212yesmaximal
10C43×#544C2211yescharacteristic
11C43×#544C2212yes—
12C43×#544C2211yescharacteristic
13C43×#501—22no—
14C43×#501—22no—
15C43×#501—22no—
16C43×#501—22no—
17C43×#500—22no—
18C43×#499—22no—
19C43×#499—22no—
20C43×#498—22no—
21C2×#108×C43C2212yes—
22C43×#428C2212yes—
23C43×#428C2212yes—
24C43×#428C2212yes—
25C43×#428C2212yes—
26C43×#427C2212yes—
27C2×#107×C43C2212yes—
28C2×#106×C43C2212yes—
29C43×#405C2212yes—
30C43×#405C2212yes—
31C2×#97×C43C2211yescharacteristic
32C43×#384C2211yescharacteristic
33C43×#382C2211yescharacteristic
34C43×#343C2211yescharacteristic
35C43×#343C2212yes—
36C43×#343C2211yescharacteristic
37C43×#339C2212yes—
38C43×#339C2212yes—
39C2×M16×C43C2312yes—
40C2×M16×C43C2312yes—
41C22×C8×C43C2312yes—
42C4⋊Q8×C43—22no—
43C4⋊Q8×C43—22no—
44C4⋊Q8×C43—22no—
45C4⋊Q8×C43—22no—
46#125×C43—22no—
47#125×C43—22no—
48#125×C43—22no—
49#125×C43—22no—
50C22⋊Q8×C43—41no—
51C22⋊Q8×C43—41no—
52C22⋊Q8×C43—42no—
53#117×C43C2312yes—
54#117×C43C2312yes—
55C2×C4⋊C4×C43—41no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C2×C4⋊C4×C43C2312yes—
59C2×C42×C43C2311yescharacteristic
60#108×C43Q818yescomplemented
61#107×C43—22no—
62#107×C43—22no—
63#107×C43—22no—
64#107×C43—22no—
65#107×C43—22no—
66#107×C43—22no—
67#107×C43D412yes—
68#107×C43D412yes—
69#106×C43—22no—
70#106×C43—22no—
71#106×C43—22no—
72#106×C43—22no—
73#106×C43—22no—
74#106×C43—22no—
75#106×C43D412yes—
76#106×C43D412yes—
77#97×C43—22no—
78#97×C43—22no—
79#97×C43Q814yescomplemented
80C4×C8×C43—22no—
81C4×C8×C43—22no—
82#95×C43—41no—
83C2×Q8×C43—41no—
84C2×Q8×C43—42no—
85C2×Q8×C43—41no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—22no—
90C22×C4×C43C2411yescharacteristic
91M16×C43—22no—
92M16×C43—22no—
93M16×C43C2×Q814yes—
94M16×C43C2×Q814yes—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43C2×D412yes—
98C2×C8×C43C2×D412yes—
99C2×C8×C43C2×Q814yes—
100C2×C8×C43C2×Q814yes—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—82no—
113C4⋊C4×C43C2×D412yes—
114C4⋊C4×C43C2×D412yes—
115C4⋊C4×C43C2×D412yes—
116C4⋊C4×C43C2×D412yes—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—22no—
119C42×C43—22no—
120C42×C43—22no—
121C42×C43—21no—
122C42×C43C2×Q812yes—
123C23×C43H(5,𝔽2)11yescharacteristic
124Q8×C43—162no—
125Q8×C43—161no—
126Q8×C43—161no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—82no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43C22×D412yes—
141C2×C4×C43C22×Q811yescharacteristic
142C2×C4×C43C22×Q812yes—
143C2×C4×C432−1+411yescharacteristic
144C8×C43—24no—
145C8×C43—24no—
146C8×C43C4⋊Q814yes—
147C8×C43C4⋊Q814yes—
148#28826C4311yesmaximal, characteristic, direct product factor, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#54411yescharacteristic
152C22×C43D4211yescharacteristic
153C22×C43Q8211yescharacteristic
154C4×C43—42no—
155C4×C43—42no—
156C4×C43—42no—
157C4×C43—42no—
158C4×C43—42no—
159C4×C43—82no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43C2×C4⋊Q812yes—
163C4×C43D4×Q812yes—
164#3164C2×C4312yes—
165#3163C2×C4312yes—
166#2061C2×C4311yescharacteristic
167#2061C2×C4311yescharacteristic
168#2060C2×C4312yes—
169#1952C2×C4312yes—
170#1951C2×C4312yes—
171#1847C2×C4311yescharacteristic
172#1773C2×C4312yes—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#255111yescharacteristic
176C2×C43#328811yescharacteristic
177C2×C43#328911yescharacteristic
178#544C22×C4312yes—
179#544C22×C4311yescharacteristic
180#544C22×C4311yescharacteristic
181#501—22no—
182#501—22no—
183#501—22no—
184#501—22no—
185#500—22no—
186#499—22no—
187#499—22no—
188#498—22no—
189C2×#108C22×C4312yes—
190#428C22×C4312yes—
191#428C22×C4312yes—
192#428C22×C4312yes—
193#428C22×C4312yes—
194#427C22×C4312yes—
195C2×#107C22×C4312yes—
196C2×#106C22×C4312yes—
197#405C22×C4312yes—
198#405C22×C4312yes—
199C2×#97C22×C4311yescharacteristic
200#384C22×C4311yescharacteristic
201#382C22×C4311yescharacteristic
202#343C22×C4312yes—
203#343C22×C4311yescharacteristic
204#343C22×C4311yescharacteristic
205#339C22×C4312yes—
206#339C22×C4312yes—
207C43#2882611yescharacteristic, direct product factor, Sylow
208C2×M16C23×C4312yes—
209C2×M16C23×C4312yes—
210C22×C8C23×C4312yes—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215#125—22no—
216#125—22no—
217#125—22no—
218#125—22no—
219C22⋊Q8—41no—
220C22⋊Q8—41no—
221C22⋊Q8—42no—
222#117C23×C4312yes—
223#117C23×C4312yes—
224C2×C4⋊C4—41no—
225C2×C4⋊C4C23×C4311yescharacteristic
226C2×C4⋊C4C23×C4311yescharacteristic
227C2×C4⋊C4C23×C4312yes—
228C2×C42C23×C4311yescharacteristic
229#108Q8×C4318yescomplemented
230#107—22no—
231#107—22no—
232#107—22no—
233#107—22no—
234#107—22no—
235#107—22no—
236#107D4×C4312yes—
237#107D4×C4312yes—
238#106—22no—
239#106—22no—
240#106—22no—
241#106—22no—
242#106—22no—
243#106—22no—
244#106D4×C4312yes—
245#106D4×C4312yes—
246#97—22no—
247#97—22no—
248#97Q8×C4314yescomplemented
249C4×C8—22no—
250C4×C8—22no—
251#95—41no—
252C2×Q8—41no—
253C2×Q8—42no—
254C2×Q8—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4C24×C4311yescharacteristic
260M16—22no—
261M16—22no—
262M16C2×Q8×C4314yes—
263M16C2×Q8×C4314yes—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8C2×D4×C4312yes—
267C2×C8C2×D4×C4312yes—
268C2×C8C2×Q8×C4314yes—
269C2×C8C2×Q8×C4314yes—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—82no—
282C4⋊C4C2×D4×C4312yes—
283C4⋊C4C2×D4×C4312yes—
284C4⋊C4C2×D4×C4312yes—
285C4⋊C4C2×D4×C4312yes—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C42—22no—
289C42—22no—
290C42—21no—
291C42C2×Q8×C4312yes—
292C23H(5,𝔽2)×C4311yescharacteristic
293Q8—161no—
294Q8—162no—
295Q8—161no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C22×D4×C4312yes—
310C2×C4C22×Q8×C4311yescharacteristic
311C2×C4C22×Q8×C4312yes—
312C2×C42−1+4×C4311yescharacteristic
313C8—24no—
314C8—24no—
315C8C4⋊Q8×C4314yes—
316C8C4⋊Q8×C4314yes—
317C22—21no—
318C22—21no—
319C22C43×#54411yescharacteristic
320C22D42×C4311yescharacteristic
321C22Q82×C4311yescharacteristic
322C4—42no—
323C4—42no—
324C4—42no—
325C4—42no—
326C4—42no—
327C4—82no—
328C4—81no—
329C4—81no—
330C4C2×C4⋊Q8×C4312yes—
331C4D4×Q8×C4312yes—
332C2—21no—
333C2—21no—
334C2C43×#255111yescharacteristic
335C2C43×#328811yescharacteristic
336C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC23×C43H(5,𝔽2)
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
60. #108×C43Q8semidirect
79. #97×C43Q8semidirect
148. #28826C43direct (N × H)
207. C43#28826direct (N × H)
229. #108Q8×C43semidirect
248. #97Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31642
C43×#31632
C43×#20612
C43×#20602
C43×#19522
C43×#19512
C43×#18472
C43×#17732
#2882643