Finite Group Databasebeta

← C43×#8574 #24928591

Subgroups — C43×#8574 #24928591

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C43C211yesmaximal, characteristic
2C43×#1797C211yesmaximal, characteristic
3C2×C43×#328C212yesmaximal
4C43×#1434C211yesmaximal, characteristic
5C43×#1294C212yesmaximal
6C2×C22⋊Q8×C43C2211yescharacteristic
7C2×C4×Q8×C43C411yescharacteristic, complemented
8C22×C42×C43C2211yescharacteristic
9C2×C4⋊C8×C43—21no—
10C2×C22⋊C8×C43C2212yes—
11C43×#391C411yescharacteristic, complemented
12C43×#389C411yescharacteristic, complemented
13C43×#387—21no—
14C43×#385—21no—
15C43×#380C2211yescharacteristic
16C4×C4⋊C4×C43—21no—
17C4×C4⋊C4×C43C411yescharacteristic, complemented
18C4×C22⋊C4×C43—21no—
19C2×#95×C43—21no—
20C2×#95×C43—21no—
21C2×#95×C43C2212yes—
22C43×#336—21no—
23C43×#328—24no—
24C22×Q8×C43C2×C411yescharacteristic
25C23×C4×C43—22no—
26C23×C4×C43D411yescharacteristic
27C23×C4×C43D411yescharacteristic
28C23×C4×C43C2311yescharacteristic
29C22×C8×C43—22no—
30C22⋊Q8×C43—21no—
31C22⋊Q8×C43—21no—
32C22⋊Q8×C43D412yes—
33C22⋊Q8×C43Q812yes—
34C4×Q8×C43—42no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C42×C43—21no—
44C2×C42×C43—21no—
45C2×C42×C43—42no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C4⋊C8×C43—42no—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53#95×C43—24no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—22no—
60#95×C43—22no—
61#95×C43—42no—
62C24×C43C2×D411yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43C4⋊C412yes—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—24no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—22no—
75C22×C4×C43—22no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—42no—
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×Q811yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C8×C43—42no—
97C2×C8×C43—42no—
98C2×C8×C43—42no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—42no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43C4⋊C412yes—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—42no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—41no—
113C42×C43—41no—
114C42×C43—42no—
115C42×C43—42no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43C2×C22⋊C411yescharacteristic
121C23×C43#12111yescharacteristic
122C23×C43C22⋊Q811yescharacteristic
123C23×C43#13512yes—
124C23×C43#13712yes—
125Q8×C43—42no—
126Q8×C43—42no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—44no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—44no—
154C2×C4×C43—44no—
155C2×C4×C43—44no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—82no—
163C2×C4×C43—82no—
164C2×C4×C43—82no—
165C2×C4×C43—82no—
166C2×C4×C43#9912yes—
167C2×C4×C43#10412yes—
168C2×C4×C43C2×C4⋊C411yescharacteristic
169C2×C4×C43#11711yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C22⋊Q811yescharacteristic
172C8×C43—82no—
173#8574C4311yesmaximal, characteristic, direct product factor, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—22no—
182C22×C43#38011yescharacteristic
183C22×C43C2×#9911yescharacteristic
184C22×C43#41011yescharacteristic
185C22×C43#41611yescharacteristic
186C22×C43#41911yescharacteristic
187C22×C43C2×#10411yescharacteristic
188C22×C43#42111yescharacteristic
189C22×C43#46412yes—
190C22×C43#47912yes—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—42no—
198C4×C43—42no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—84no—
202C4×C43—81no—
203C4×C43—81no—
204C4×C22⋊Q8C2×C4311yescharacteristic
205#1797C2×C4311yescharacteristic
206C2×#328C2×C4312yes—
207#1434C2×C4311yescharacteristic
208#1294C2×C4312yes—
209C2×C43—22no—
210C2×C43—22no—
211C2×C43#150011yescharacteristic
212C2×C43#150811yescharacteristic
213C2×C43#151511yescharacteristic
214C2×C43#151611yescharacteristic
215C2×C43#179911yescharacteristic
216C2×C43#180511yescharacteristic
217C2×C43#180611yescharacteristic
218C2×C22⋊Q8C22×C4311yescharacteristic
219C2×C4×Q8C4×C4311yescharacteristic, complemented
220C22×C42C22×C4311yescharacteristic
221C2×C4⋊C8—21no—
222C2×C22⋊C8C22×C4312yes—
223#391C4×C4311yescharacteristic, complemented
224#389C4×C4311yescharacteristic, complemented
225#387—21no—
226#385—21no—
227#380C22×C4311yescharacteristic
228C4×C4⋊C4—21no—
229C4×C4⋊C4C4×C4311yescharacteristic, complemented
230C4×C22⋊C4—21no—
231C2×#95—21no—
232C2×#95—21no—
233C2×#95C22×C4312yes—
234#336—21no—
235#328—24no—
236C43#857411yescharacteristic, direct product factor, Sylow
237C22×Q8C2×C4×C4311yescharacteristic
238C23×C4—22no—
239C23×C4D4×C4311yescharacteristic
240C23×C4D4×C4311yescharacteristic
241C23×C4C23×C4311yescharacteristic
242C22×C8—22no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8D4×C4312yes—
246C22⋊Q8Q8×C4312yes—
247C4×Q8—42no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C4311yescharacteristic
252C2×C4⋊C4C2×C4×C4311yescharacteristic
253C2×C4⋊C4C2×C4×C4311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—42no—
259C2×C42C2×C4×C4311yescharacteristic
260C2×C42C2×C4×C4311yescharacteristic
261C2×C42D4×C4311yescharacteristic
262C2×C42D4×C4311yescharacteristic
263C4⋊C8—42no—
264C22⋊C8—22no—
265C22⋊C8—22no—
266#95—24no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—22no—
273#95—22no—
274#95—42no—
275C24C2×D4×C4311yescharacteristic
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C4⋊C4×C4312yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4C22⋊C4×C4311yescharacteristic
300C22×C4C22⋊C4×C4311yescharacteristic
301C22×C4C22⋊C4×C4311yescharacteristic
302C22×C4C22⋊C4×C4311yescharacteristic
303C22×C4C22×C4×C4311yescharacteristic
304C22×C4C2×D4×C4311yescharacteristic
305C22×C4C2×D4×C4311yescharacteristic
306C22×C4C2×Q8×C4311yescharacteristic
307C22×C4#41×C4311yescharacteristic
308C22×C4#41×C4311yescharacteristic
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4C4⋊C4×C4312yes—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—42no—
323C42—22no—
324C42—22no—
325C42—41no—
326C42—41no—
327C42—42no—
328C42—42no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23C2×C22⋊C4×C4311yescharacteristic
334C23#121×C4311yescharacteristic
335C23C22⋊Q8×C4311yescharacteristic
336C23#135×C4312yes—
337C23#137×C4312yes—
338Q8—42no—
339Q8—42no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4#99×C4312yes—
380C2×C4#104×C4312yes—
381C2×C4C2×C4⋊C4×C4311yescharacteristic
382C2×C4#117×C4311yescharacteristic
383C2×C4#121×C4311yescharacteristic
384C2×C4C22⋊Q8×C4311yescharacteristic
385C8—82no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22C43×#38011yescharacteristic
395C22C2×#99×C4311yescharacteristic
396C22C43×#41011yescharacteristic
397C22C43×#41611yescharacteristic
398C22C43×#41911yescharacteristic
399C22C2×#104×C4311yescharacteristic
400C22C43×#42111yescharacteristic
401C22C43×#46412yes—
402C22C43×#47912yes—
403C4—22no—
404C4—22no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—42no—
412C4—42no—
413C4—84no—
414C4—81no—
415C4—81no—
416C2—22no—
417C2—22no—
418C2C43×#150011yescharacteristic
419C2C43×#150811yescharacteristic
420C2C43×#151511yescharacteristic
421C2C43×#151611yescharacteristic
422C2C43×#179911yescharacteristic
423C2C43×#180511yescharacteristic
424C2C43×#180611yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C43C4semidirect
11. C43×#391C4semidirect
12. C43×#389C4semidirect
17. C4×C4⋊C4×C43C4semidirect
173. #8574C43direct (N × H)
219. C2×C4×Q8C4×C43semidirect
223. #391C4×C43semidirect
224. #389C4×C43semidirect
229. C4×C4⋊C4C4×C43semidirect
236. C43#8574direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C432
C43×#17972
C2×C43×#3282
C43×#14342
C43×#12942
#857443