Finite Group Databasebeta

← C43×#8909 #24928926

Subgroups — C43×#8909 #24928926

Order 11008.

376 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
1Q8×M16×C43C211yesmaximal, characteristic
2C43×#1950C211yesmaximal, characteristic
3C43×#1566C211yesmaximal, characteristic
4C43×#1487C211yesmaximal, characteristic
5C2×C43×Q8⋊C8C211yesmaximal, characteristic
6C43×#1301C211yesmaximal, characteristic
7C43×#1278C211yesmaximal, characteristic
8C2×C4×Q8×C43C2211yescharacteristic
9C43×#446—21no—
10C43×#446—22no—
11C8×Q8×C43—21no—
12C43×#431C2211yescharacteristic
13C2×#108×C43—21no—
14C43×#423—21no—
15C43×#423C2211yescharacteristic
16C43×#423C2211yescharacteristic
17C2×C4⋊C8×C43C2211yescharacteristic
18C4×M16×C43—21no—
19C4×M16×C43C2211yescharacteristic
20C2×C4×C8×C43C2211yescharacteristic
21C43×#341—21no—
22C43×#334—22no—
23C43×Q8⋊C8—21no—
24C43×Q8⋊C8—21no—
25C43×Q8⋊C8C411yescharacteristic
26C43×Q8⋊C8C411yescharacteristic
27C43×Q8⋊C8C411yescharacteristic
28C43×Q8⋊C8C411yescharacteristic
29C22×Q8×C43Q811yescharacteristic
30C2×M16×C43—21no—
31C2×M16×C43—21no—
32C2×M16×C43D411yescharacteristic
33C2×M16×C43D411yescharacteristic
34C22×C8×C43—21no—
35C22×C8×C43—21no—
36C4×Q8×C43—21no—
37C4×Q8×C43—21no—
38C4×Q8×C43C2×C411yescharacteristic
39C4×Q8×C43C2×C411yescharacteristic
40C4×Q8×C43D411yescharacteristic
41C4×Q8×C43D411yescharacteristic
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43Q811yescharacteristic
44C2×C42×C43—21no—
45C2×C42×C43C2311yescharacteristic
46#108×C43—42no—
47C4⋊C8×C43—22no—
48C4⋊C8×C43—22no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43C2×C411yescharacteristic
55C4⋊C8×C43C2×C411yescharacteristic
56C4⋊C8×C43D412yes—
57C22⋊C8×C43—21no—
58#97×C43—22no—
59#97×C43—21no—
60C4×C8×C43—22no—
61C4×C8×C43—21no—
62C4×C8×C43—21no—
63C4×C8×C43—21no—
64C4×C8×C43C2×C411yescharacteristic
65C4×C8×C43C2×C411yescharacteristic
66C2×Q8×C43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43C4⋊C411yescharacteristic
70C2×Q8×C43C4⋊C411yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×Q811yescharacteristic
75C22×C4×C43#4111yescharacteristic
76M16×C43—21no—
77M16×C43—21no—
78M16×C43—21no—
79M16×C43—41no—
80M16×C43—41no—
81M16×C43—41no—
82M16×C43—41no—
83M16×C43SD1612yes—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—22no—
91C2×C8×C43—42no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43C4⋊C411yescharacteristic
102C4⋊C4×C43C4⋊C411yescharacteristic
103C42×C43—21no—
104C42×C43—21no—
105C42×C43—21no—
106C42×C43—21no—
107C42×C43C22×C411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111C23×C43C22⋊Q811yescharacteristic
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—42no—
116Q8×C43#10812yescomplemented
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—81no—
126C2×C4×C43C2×C4⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43C22⋊Q811yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C8×C43—22no—
137C8×C43—22no—
138C8×C43—41no—
139C8×C43—41no—
140C8×C43—41no—
141C8×C43—41no—
142C8×C43—42no—
143C8×C43—81no—
144C8×C43—81no—
145#8909C4311yesmaximal, characteristic, direct product factor, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#38511yescharacteristic
149C22×C43#47511yescharacteristic
150C22×C43#47911yescharacteristic
151C4×C43—21no—
152C4×C43—22no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#10811yescharacteristic
159C4×C43#43011yescharacteristic
160C4×C43C4×SD1611yescharacteristic
161C4×C43#44111yescharacteristic
162C4×C43#44811yescharacteristic
163C4×C43#45211yescharacteristic
164Q8×M16C2×C4311yescharacteristic
165#1950C2×C4311yescharacteristic
166#1566C2×C4311yescharacteristic
167#1487C2×C4311yescharacteristic
168C2×Q8⋊C8C2×C4311yescharacteristic
169#1301C2×C4311yescharacteristic
170#1278C2×C4311yescharacteristic
171C2×C43—21no—
172C2×C43—21no—
173C2×C43#185511yescharacteristic
174C2×C43#186111yescharacteristic
175C2×C43#186511yescharacteristic
176C2×C4×Q8C22×C4311yescharacteristic
177#446—21no—
178#446—22no—
179C8×Q8—21no—
180#431C22×C4311yescharacteristic
181C2×#108—21no—
182#423—21no—
183#423C22×C4311yescharacteristic
184#423C22×C4311yescharacteristic
185C2×C4⋊C8C22×C4311yescharacteristic
186C4×M16—21no—
187C4×M16C22×C4311yescharacteristic
188C2×C4×C8C22×C4311yescharacteristic
189#341—21no—
190#334—22no—
191Q8⋊C8—21no—
192Q8⋊C8—21no—
193Q8⋊C8C4×C4311yescharacteristic
194Q8⋊C8C4×C4311yescharacteristic
195Q8⋊C8C4×C4311yescharacteristic
196Q8⋊C8C4×C4311yescharacteristic
197C43#890911yescharacteristic, direct product factor, Sylow
198C22×Q8Q8×C4311yescharacteristic
199C2×M16—21no—
200C2×M16—21no—
201C2×M16D4×C4311yescharacteristic
202C2×M16D4×C4311yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C2×C4×C4311yescharacteristic
208C4×Q8C2×C4×C4311yescharacteristic
209C4×Q8D4×C4311yescharacteristic
210C4×Q8D4×C4311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Q8×C4311yescharacteristic
213C2×C42—21no—
214C2×C42C23×C4311yescharacteristic
215#108—42no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8C2×C4×C4311yescharacteristic
224C4⋊C8C2×C4×C4311yescharacteristic
225C4⋊C8D4×C4312yes—
226C22⋊C8—21no—
227#97—22no—
228#97—21no—
229C4×C8—22no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8C2×C4×C4311yescharacteristic
234C4×C8C2×C4×C4311yescharacteristic
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8C4⋊C4×C4311yescharacteristic
239C2×Q8C4⋊C4×C4311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×D4×C4311yescharacteristic
243C22×C4C2×Q8×C4311yescharacteristic
244C22×C4#41×C4311yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16SD16×C4312yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4C4⋊C4×C4311yescharacteristic
271C4⋊C4C4⋊C4×C4311yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C22×C4×C4311yescharacteristic
277C42C2×D4×C4311yescharacteristic
278C42C2×D4×C4311yescharacteristic
279C42#41×C4311yescharacteristic
280C23C22⋊Q8×C4311yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#108×C4312yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×C4⋊C4×C4311yescharacteristic
296C2×C4C4×D4×C4311yescharacteristic
297C2×C4C4×D4×C4311yescharacteristic
298C2×C4#120×C4311yescharacteristic
299C2×C4C22⋊Q8×C4311yescharacteristic
300C2×C4#123×C4311yescharacteristic
301C2×C4C2×SD16×C4311yescharacteristic
302C2×C4#135×C4311yescharacteristic
303C2×C4#137×C4311yescharacteristic
304C2×C4#137×C4311yescharacteristic
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—42no—
312C8—81no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22C43×#38511yescharacteristic
317C22C43×#47511yescharacteristic
318C22C43×#47911yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#108×C4311yescharacteristic
327C4C43×#43011yescharacteristic
328C4C4×SD16×C4311yescharacteristic
329C4C43×#44111yescharacteristic
330C4C43×#44811yescharacteristic
331C4C43×#45211yescharacteristic
332C2—21no—
333C2—21no—
334C2C43×#185511yescharacteristic
335C2C43×#186111yescharacteristic
336C2C43×#186511yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#385
prime radicalC23×C43C22⋊Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
116. Q8×C43#108semidirect
145. #8909C43direct (N × H)
197. C43#8909direct (N × H)
285. Q8#108×C43semidirect

Maximal subgroups

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

subgroupindex
Q8×M16×C432
C43×#19502
C43×#15662
C43×#14872
C2×C43×Q8⋊C82
C43×#13012
C43×#12782
#890943