Finite Group Databasebeta

← C43×#60253 #24980270

Subgroups — C43×#60253 #24980270

Order 11008.

1702 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C43C211yesmaximal, characteristic
2C43×#2986C216yesmaximal, complemented
3C43×#2985C216yesmaximal, complemented
4C43×#2984C212yesmaximal, complemented
5C43×#2982C212yesmaximal, complemented
6Q8×M16×C43C211yesmaximal, characteristic, complemented
7C43×#2962C213yesmaximal, complemented
8C43×#2960C213yesmaximal, complemented
9C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
10C43×#2925C213yesmaximal
11C43×#2922C213yesmaximal
12Q82×C43C411yescharacteristic
13C43×#557C413yes—
14C43×#554C416yes—
15C43×#554C413yes—
16D4×Q8×C43C411yescharacteristic
17D4×Q8×C43C412yes—
18C43×#533C2213yes—
19C43×#533C2216yes—
20C4×#41×C43C2213yes—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×C4×Q8×C43C2212yes—
23C43×#446C2216yes—
24C43×#446C2216yes—
25C43×#446C2216yes—
26C43×#446C22112yes—
27C43×#446C2216yes—
28C8×Q8×C43C2211yescharacteristic
29C8×Q8×C43C2211yescharacteristic
30C8×Q8×C43C2213yes—
31C8×Q8×C43C2213yes—
32C8×Q8×C43C2216yes—
33C8×Q8×C43C2216yes—
34C8×Q8×C43C2216yes—
35C8×Q8×C43C2212yes—
36C43×#433C2216yes—
37C43×#433C2216yes—
38C43×#433C22112yes—
39C43×#432C2216yes—
40C43×#431C2216yes—
41C43×#431C2216yes—
42C43×#431C2216yes—
43C43×#424C2213yes—
44C43×#424C2213yes—
45C43×#423C2213yes—
46C2×C4⋊C8×C43C2213yes—
47C43×#408C2211yescharacteristic
48C43×#408C2213yes—
49C43×#405C2216yes—
50C4×M16×C43C2213yes—
51C2×C4×C8×C43C2213yes—
52C2×#41×C43C2311yescharacteristic
53C22×Q8×C43C2×C411yescharacteristic
54C22×Q8×C43C2×C412yes—
55C2×M16×C43C2311yescharacteristic
56C2×M16×C43C2313yes—
57C22×C8×C43C2311yescharacteristic
58C22×C8×C43C2313yes—
59C4⋊Q8×C43C2×C413yes—
60C4⋊Q8×C43C2×C416yes—
61C4⋊Q8×C43C2×C413yes—
62C4⋊Q8×C43C2×C416yes—
63#125×C43C2×C416yes—
64#125×C43C2×C4112yes—
65C22⋊Q8×C43C2×C416yes—
66C22⋊Q8×C43C2×C416yes—
67C22⋊Q8×C43C2×C416yes—
68C22⋊Q8×C43C2×C416yes—
69C22⋊Q8×C43C2×C4112yes—
70C4×Q8×C43C2×C411yescharacteristic
71C4×Q8×C43C2×C412yes—
72C4×Q8×C43C2×C413yes—
73C4×Q8×C43C2×C416yes—
74C4×Q8×C43C2×C413yes—
75C4×Q8×C43C2×C413yes—
76C4×Q8×C43C2311yescharacteristic
77C4×Q8×C43C2313yes—
78C4×Q8×C43C2316yes—
79C4×Q8×C43C2316yes—
80C4×D4×C43C2×C416yes—
81C4×D4×C43C2×C413yes—
82C4×D4×C43C2×C416yes—
83C4×D4×C43C2×C413yes—
84#117×C43C2313yes—
85#117×C43C2316yes—
86C2×C4⋊C4×C43C2×C413yes—
87C2×C4⋊C4×C43C2×C416yes—
88C2×C42×C43C2313yes—
89C2×C42×C43C2316yes—
90C4⋊C8×C43C2313yes—
91C4⋊C8×C43C2313yes—
92C4⋊C8×C43C2316yes—
93C4⋊C8×C43C2316yes—
94C4⋊C8×C43C2316yes—
95C4⋊C8×C43C2316yes—
96C4⋊C8×C43C2316yes—
97C4⋊C8×C43C2316yes—
98C4⋊C8×C43C2316yes—
99C22⋊C8×C43C2312yes—
100C22⋊C8×C43C2312yes—
101C22⋊C8×C43C2316yes—
102C22⋊C8×C43C2316yes—
103#97×C43C2316yes—
104#97×C43C23112yes—
105C4×C8×C43C2313yes—
106C4×C8×C43C2313yes—
107C4×C8×C43C2313yes—
108C4×C8×C43C2313yes—
109C4×C8×C43C2316yes—
110C4×C8×C43C23112yes—
111#41×C43—22no—
112#41×C43—22no—
113C2×Q8×C43—24no—
114C2×Q8×C43—28no—
115C2×Q8×C43C22×C411yescharacteristic
116C2×Q8×C43C22×C413yes—
117C2×Q8×C43C22×C416yes—
118C2×Q8×C43C22×C416yes—
119C2×Q8×C43C22×C411yescharacteristic
120C2×D4×C43C22×C411yescharacteristic
121C2×D4×C43C22×C412yes—
122C22×C4×C43C22×C416yes—
123C22×C4×C43C22×C413yes—
124C22×C4×C43C22×C416yes—
125C22×C4×C43C22×C413yes—
126C22×C4×C43C2412yes—
127C22×C4×C43C2411yescharacteristic
128M16×C43—22no—
129M16×C43—26no—
130C2×C8×C43—26no—
131C2×C8×C43—22no—
132C2×C8×C43C2411yescharacteristic
133C2×C8×C43C2413yes—
134C2×C8×C43C2411yescharacteristic
135C2×C8×C43C2412yes—
136C2×C8×C43C2416yes—
137C2×C8×C43C2413yes—
138C4⋊C4×C43C22×C413yes—
139C4⋊C4×C43C22×C416yes—
140C4⋊C4×C43C22×C4112yes—
141C4⋊C4×C43C22×C413yes—
142C4⋊C4×C43C22×C416yes—
143C4⋊C4×C43C22×C416yes—
144C4⋊C4×C43C22×C416yes—
145C4⋊C4×C43C22×C413yes—
146C4⋊C4×C43C22×C413yes—
147C4⋊C4×C43C22×C4112yes—
148C4⋊C4×C43C22×C416yes—
149C22⋊C4×C43C22×C416yes—
150C22⋊C4×C43C22×C416yes—
151C22⋊C4×C43C22×C416yes—
152C42×C43C22×C416yes—
153C42×C43C22×C413yes—
154C42×C43C22×C416yes—
155C42×C43C22×C413yes—
156C42×C43C2413yes—
157C42×C43C2413yes—
158C42×C43C2416yes—
159C23×C43C23×C412yes—
160C23×C43C23×C411yescharacteristic
161Q8×C43—22no—
162Q8×C43—26no—
163Q8×C43—212no—
164Q8×C43—46no—
165Q8×C43#13114yes—
166D4×C43—24no—
167D4×C43—22no—
168C2×C4×C43—26no—
169C2×C4×C43—212no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—43no—
173C2×C4×C43—46no—
174C2×C4×C43C23×C412yes—
175C2×C4×C43C23×C413yes—
176C2×C4×C43C23×C416yes—
177C2×C4×C43C23×C413yes—
178C2×C4×C43C23×C416yes—
179C2×C4×C43C23×C413yes—
180C2×C4×C43C23×C411yescharacteristic
181C2×C4×C43C23×C413yes—
182C2×C4×C432−1+412yes—
183C2×C4×C432−1+412yes—
184C2×C4×C43C2511yescharacteristic
185C8×C43—23no—
186C8×C43—21no—
187C8×C43—21no—
188C8×C43—23no—
189C8×C43—22no—
190C8×C43—26no—
191#60253C4311yesmaximal, characteristic, direct product factor, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—22no—
195C22×C43—22no—
196C22×C43—22no—
197C22×C43#51912yes—
198C22×C43C24×C411yescharacteristic
199C4×C43—22no—
200C4×C43—23no—
201C4×C43—26no—
202C4×C43—23no—
203C4×C43—23no—
204C4×C43—26no—
205C4×C43#51912yes—
206C4×C43C2×#13116yes—
207C4×C43C2×2−1+411yescharacteristic
208C4×C43C2×2−1+411yescharacteristic
209Q8×#41C2×C4311yescharacteristic
210#2986C2×C4316yescomplemented
211#2985C2×C4316yescomplemented
212#2984C2×C4312yescomplemented
213#2982C2×C4312yescomplemented
214Q8×M16C2×C4311yescharacteristic, complemented
215#2962C2×C4313yescomplemented
216#2960C2×C4313yescomplemented
217C2×C8×Q8C2×C4311yescharacteristic, complemented
218#2925C2×C4313yes—
219#2922C2×C4313yes—
220C2×C43—22no—
221C2×C43—42no—
222C2×C43C2×#51911yescharacteristic
223C2×C43C22×#13111yescharacteristic
224C2×C43#357311yescharacteristic
225Q82C4×C4311yescharacteristic
226#557C4×C4313yes—
227#554C4×C4316yes—
228#554C4×C4313yes—
229D4×Q8C4×C4311yescharacteristic
230D4×Q8C4×C4312yes—
231#533C22×C4313yes—
232#533C22×C4316yes—
233C4×#41C22×C4313yes—
234C2×C4×Q8C22×C4311yescharacteristic
235C2×C4×Q8C22×C4312yes—
236#446C22×C4316yes—
237#446C22×C4316yes—
238#446C22×C4316yes—
239#446C22×C43112yes—
240#446C22×C4316yes—
241C8×Q8C22×C4311yescharacteristic
242C8×Q8C22×C4311yescharacteristic
243C8×Q8C22×C4313yes—
244C8×Q8C22×C4313yes—
245C8×Q8C22×C4316yes—
246C8×Q8C22×C4316yes—
247C8×Q8C22×C4316yes—
248C8×Q8C22×C4312yes—
249#433C22×C4316yes—
250#433C22×C4316yes—
251#433C22×C43112yes—
252#432C22×C4316yes—
253#431C22×C4316yes—
254#431C22×C4316yes—
255#431C22×C4316yes—
256#424C22×C4313yes—
257#424C22×C4313yes—
258#423C22×C4313yes—
259C2×C4⋊C8C22×C4313yes—
260#408C22×C4311yescharacteristic
261#408C22×C4313yes—
262#405C22×C4316yes—
263C4×M16C22×C4313yes—
264C2×C4×C8C22×C4313yes—
265C43#6025311yescharacteristic, direct product factor, Sylow
266C2×#41C23×C4311yescharacteristic
267C22×Q8C2×C4×C4311yescharacteristic
268C22×Q8C2×C4×C4312yes—
269C2×M16C23×C4311yescharacteristic
270C2×M16C23×C4313yes—
271C22×C8C23×C4311yescharacteristic
272C22×C8C23×C4313yes—
273C4⋊Q8C2×C4×C4313yes—
274C4⋊Q8C2×C4×C4316yes—
275C4⋊Q8C2×C4×C4313yes—
276C4⋊Q8C2×C4×C4316yes—
277#125C2×C4×C4316yes—
278#125C2×C4×C43112yes—
279C22⋊Q8C2×C4×C4316yes—
280C22⋊Q8C2×C4×C4316yes—
281C22⋊Q8C2×C4×C4316yes—
282C22⋊Q8C2×C4×C4316yes—
283C22⋊Q8C2×C4×C43112yes—
284C4×Q8C2×C4×C4311yescharacteristic
285C4×Q8C2×C4×C4312yes—
286C4×Q8C2×C4×C4313yes—
287C4×Q8C2×C4×C4316yes—
288C4×Q8C2×C4×C4313yes—
289C4×Q8C2×C4×C4313yes—
290C4×Q8C23×C4311yescharacteristic
291C4×Q8C23×C4313yes—
292C4×Q8C23×C4316yes—
293C4×Q8C23×C4316yes—
294C4×D4C2×C4×C4316yes—
295C4×D4C2×C4×C4313yes—
296C4×D4C2×C4×C4316yes—
297C4×D4C2×C4×C4313yes—
298#117C23×C4313yes—
299#117C23×C4316yes—
300C2×C4⋊C4C2×C4×C4313yes—
301C2×C4⋊C4C2×C4×C4316yes—
302C2×C42C23×C4313yes—
303C2×C42C23×C4316yes—
304C4⋊C8C23×C4313yes—
305C4⋊C8C23×C4313yes—
306C4⋊C8C23×C4316yes—
307C4⋊C8C23×C4316yes—
308C4⋊C8C23×C4316yes—
309C4⋊C8C23×C4316yes—
310C4⋊C8C23×C4316yes—
311C4⋊C8C23×C4316yes—
312C4⋊C8C23×C4316yes—
313C22⋊C8C23×C4312yes—
314C22⋊C8C23×C4312yes—
315C22⋊C8C23×C4316yes—
316C22⋊C8C23×C4316yes—
317#97C23×C4316yes—
318#97C23×C43112yes—
319C4×C8C23×C4313yes—
320C4×C8C23×C4313yes—
321C4×C8C23×C4313yes—
322C4×C8C23×C4313yes—
323C4×C8C23×C4316yes—
324C4×C8C23×C43112yes—
325#41—22no—
326#41—22no—
327C2×Q8—24no—
328C2×Q8—28no—
329C2×Q8C22×C4×C4313yes—
330C2×Q8C22×C4×C4316yes—
331C2×Q8C22×C4×C4311yescharacteristic
332C2×Q8C22×C4×C4316yes—
333C2×Q8C22×C4×C4311yescharacteristic
334C2×D4C22×C4×C4312yes—
335C2×D4C22×C4×C4311yescharacteristic
336C22×C4C22×C4×C4316yes—
337C22×C4C22×C4×C4313yes—
338C22×C4C22×C4×C4316yes—
339C22×C4C22×C4×C4313yes—
340C22×C4C24×C4312yes—
341C22×C4C24×C4311yescharacteristic
342M16—22no—
343M16—26no—
344C2×C8—26no—
345C2×C8—22no—
346C2×C8C24×C4311yescharacteristic
347C2×C8C24×C4313yes—
348C2×C8C24×C4311yescharacteristic
349C2×C8C24×C4312yes—
350C2×C8C24×C4316yes—
351C2×C8C24×C4313yes—
352C4⋊C4C22×C4×C4313yes—
353C4⋊C4C22×C4×C4316yes—
354C4⋊C4C22×C4×C43112yes—
355C4⋊C4C22×C4×C4313yes—
356C4⋊C4C22×C4×C4316yes—
357C4⋊C4C22×C4×C4316yes—
358C4⋊C4C22×C4×C4316yes—
359C4⋊C4C22×C4×C4313yes—
360C4⋊C4C22×C4×C4313yes—
361C4⋊C4C22×C4×C43112yes—
362C4⋊C4C22×C4×C4316yes—
363C22⋊C4C22×C4×C4316yes—
364C22⋊C4C22×C4×C4316yes—
365C22⋊C4C22×C4×C4316yes—
366C42C22×C4×C4316yes—
367C42C22×C4×C4313yes—
368C42C22×C4×C4316yes—
369C42C22×C4×C4313yes—
370C42C24×C4313yes—
371C42C24×C4313yes—
372C42C24×C4316yes—
373C23C23×C4×C4312yes—
374C23C23×C4×C4311yescharacteristic
375Q8—22no—
376Q8—26no—
377Q8—212no—
378Q8—46no—
379Q8#131×C4314yes—
380D4—24no—
381D4—22no—
382C2×C4—26no—
383C2×C4—212no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—43no—
387C2×C4—46no—
388C2×C4C23×C4×C4312yes—
389C2×C4C23×C4×C4313yes—
390C2×C4C23×C4×C4316yes—
391C2×C4C23×C4×C4313yes—
392C2×C4C23×C4×C4316yes—
393C2×C4C23×C4×C4313yes—
394C2×C4C23×C4×C4311yescharacteristic
395C2×C4C23×C4×C4313yes—
396C2×C42−1+4×C4312yes—
397C2×C42−1+4×C4312yes—
398C2×C4C25×C4311yescharacteristic
399C8—23no—
400C8—21no—
401C8—21no—
402C8—23no—
403C8—22no—
404C8—26no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22C43×#51912yes—
411C22C24×C4×C4311yescharacteristic
412C4—22no—
413C4—23no—
414C4—26no—
415C4—23no—
416C4—23no—
417C4—26no—
418C4C43×#51912yes—
419C4C2×#131×C4316yes—
420C4C2×2−1+4×C4311yescharacteristic
421C4C2×2−1+4×C4311yescharacteristic
422C2—22no—
423C2—42no—
424C2C2×C43×#51911yescharacteristic
425C2C22×#131×C4311yescharacteristic
426C2C43×#357311yescharacteristic
subgroupG/H
centerC2×C4×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC2×#41×C43C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2986C2semidirect
3. C43×#2985C2semidirect
4. C43×#2984C2semidirect
5. C43×#2982C2semidirect
6. Q8×M16×C43C2semidirect
7. C43×#2962C2semidirect
8. C43×#2960C2semidirect
9. C2×C8×Q8×C43C2semidirect
191. #60253C43direct (N × H)
210. #2986C2×C43semidirect
211. #2985C2×C43semidirect
212. #2984C2×C43semidirect
213. #2982C2×C43semidirect
214. Q8×M16C2×C43semidirect
215. #2962C2×C43semidirect
216. #2960C2×C43semidirect
217. C2×C8×Q8C2×C43semidirect
265. C43#60253direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×#41×C432
C43×#29862
C43×#29852
C43×#29842
C43×#29822
Q8×M16×C432
C43×#29622
C43×#29602
C2×C8×Q8×C432
C43×#29252
C43×#29222
#6025343