Finite Group Databasebeta

← C43×#19529 #24939546

Subgroups — C43×#19529 #24939546

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3230C211yesmaximal, characteristic, complemented
2C43×#3227C211yesmaximal, characteristic
3C43×#3216C211yesmaximal, characteristic
4C43×#2985C211yesmaximal, characteristic, complemented
5C43×#1698C212yesmaximal, complemented
6C43×#1692C212yesmaximal, complemented
7C43×#1678C212yesmaximal, complemented
8C43×#1672C212yesmaximal, complemented
9C43×#1572C211yesmaximal, characteristic, complemented
10C43×#1558C211yesmaximal, characteristic, complemented
11C43×#1553C211yesmaximal, characteristic
12C43×#533C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C2×C4⋊Q8×C43C2211yescharacteristic
15C43×#500—21no—
16C43×#498C2211yescharacteristic
17C43×#498C2211yescharacteristic
18C43×#497—21no—
19C43×#489—21no—
20C43×#487—21no—
21C43×#486C2211yescharacteristic
22C43×#486C2211yescharacteristic
23C43×#484—22no—
24C43×#481—22no—
25C43×#477C2212yes—
26C43×#477C2212yes—
27C43×#476—22no—
28C43×#462C2212yes—
29C43×#460C2212yes—
30C43×#452—22no—
31C43×#446—22no—
32C43×#446C2212yes—
33C8×Q8×C43C2212yes—
34C43×#433—22no—
35C43×#432C2211yescharacteristic
36C43×#432C2211yescharacteristic
37C43×#431C2211yescharacteristic
38C43×#431C2211yescharacteristic
39C43×#335C2212yes—
40C43×#334C2212yes—
41C43×#333C2212yes—
42C43×#333C2212yes—
43C43×#332C2212yes—
44C43×#331C2212yes—
45C2×#41×C43—21no—
46C22×Q8×C43—21no—
47C2×Q16×C43—22no—
48C2×SD16×C43—22no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43D411yescharacteristic
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43C2311yescharacteristic
55C4⋊Q8×C43C2311yescharacteristic
56C4⋊Q8×C43C2311yescharacteristic
57#127×C43C2311yescharacteristic
58#125×C43—21no—
59#124×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43D412yes—
62#121×C43—21no—
63#121×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43C2312yes—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43C2311yescharacteristic
72#107×C43—22no—
73#107×C43—22no—
74#106×C43—22no—
75#106×C43—22no—
76C4⋊C8×C43—22no—
77C4⋊C8×C43—22no—
78C4⋊C8×C43D412yes—
79C4⋊C8×C43C2312yes—
80C4⋊C8×C43C2312yes—
81C4⋊C8×C43C2312yes—
82#103×C43—22no—
83#103×C43—22no—
84#103×C43—22no—
85#102×C43—22no—
86#102×C43—22no—
87#102×C43—22no—
88C22⋊C8×C43—21no—
89C22⋊C8×C43—21no—
90C22⋊C8×C43—21no—
91C22⋊C8×C43D412yes—
92#97×C43—22no—
93#97×C43—21no—
94#97×C43—21no—
95C4×C8×C43—22no—
96C4×C8×C43—21no—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99#41×C43—82no—
100C2×Q8×C43—21no—
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43—21no—
104C2×Q8×C43—41no—
105C2×Q8×C43—82no—
106C2×Q8×C43C2×D412yes—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116Q16×C43—82no—
117SD16×C43—82no—
118C2×C8×C43—22no—
119C2×C8×C43—22no—
120C2×C8×C43—22no—
121C2×C8×C43C2×D412yes—
122C2×C8×C43C2×D412yes—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43C2×D412yes—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C42×C43—22no—
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C42×C43#4111yescharacteristic
144C42×C43C2411yescharacteristic
145C23×C43—41no—
146C23×C43#12111yescharacteristic
147Q8×C43—22no—
148Q8×C43—22no—
149Q8×C43—42no—
150Q8×C43—81no—
151Q8×C43—81no—
152Q8×C43—81no—
153Q8×C43—82no—
154D4×C43—42no—
155D4×C43—42no—
156D4×C43—81no—
157D4×C43—82no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—82no—
167C2×C4×C43—82no—
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C22×D411yescharacteristic
172C2×C4×C43C22×D411yescharacteristic
173C2×C4×C43C2×#4111yescharacteristic
174C8×C43—22no—
175C8×C43—22no—
176C8×C43—42no—
177C8×C43—42no—
178C8×C43—42no—
179#19529C4311yesmaximal, characteristic, direct product factor, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43C2×#12111yescharacteristic
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—42no—
192C4×C43—42no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43#57712yes—
197C4×C43#57812yes—
198#3230C2×C4311yescharacteristic, complemented
199#3227C2×C4311yescharacteristic
200#3216C2×C4311yescharacteristic
201#2985C2×C4311yescharacteristic, complemented
202#1698C2×C4312yescomplemented
203#1692C2×C4312yescomplemented
204#1678C2×C4312yescomplemented
205#1672C2×C4312yescomplemented
206#1572C2×C4311yescharacteristic, complemented
207#1558C2×C4311yescharacteristic, complemented
208#1553C2×C4311yescharacteristic
209C2×C43—41no—
210C2×C43—161no—
211C2×C43#304411yescharacteristic
212C2×C43#305711yescharacteristic
213C2×C43#306811yescharacteristic
214#533C22×C4311yescharacteristic
215#532C22×C4311yescharacteristic
216C2×C4⋊Q8C22×C4311yescharacteristic
217#500—21no—
218#498C22×C4311yescharacteristic
219#498C22×C4311yescharacteristic
220#497—21no—
221#489—21no—
222#487—21no—
223#486C22×C4311yescharacteristic
224#486C22×C4311yescharacteristic
225#484—22no—
226#481—22no—
227#477C22×C4312yes—
228#477C22×C4312yes—
229#476—22no—
230#462C22×C4312yes—
231#460C22×C4312yes—
232#452—22no—
233#446—22no—
234#446C22×C4312yes—
235C8×Q8C22×C4312yes—
236#433—22no—
237#432C22×C4311yescharacteristic
238#432C22×C4311yescharacteristic
239#431C22×C4311yescharacteristic
240#431C22×C4311yescharacteristic
241#335C22×C4312yes—
242#334C22×C4312yes—
243#333C22×C4312yes—
244#333C22×C4312yes—
245#332C22×C4312yes—
246#331C22×C4312yes—
247C43#1952911yescharacteristic, direct product factor, Sylow
248C2×#41—21no—
249C22×Q8—21no—
250C2×Q16—22no—
251C2×SD16—22no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C4311yescharacteristic
256C4⋊Q8D4×C4311yescharacteristic
257C4⋊Q8C23×C4311yescharacteristic
258C4⋊Q8C23×C4311yescharacteristic
259C4⋊Q8C23×C4311yescharacteristic
260#127C23×C4311yescharacteristic
261#125—21no—
262#124—21no—
263C22⋊Q8—21no—
264C22⋊Q8D4×C4312yes—
265#121—21no—
266#121—21no—
267C4×Q8—21no—
268C4×Q8C23×C4312yes—
269C4×D4—21no—
270C4×D4—21no—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C23×C4311yescharacteristic
275#107—22no—
276#107—22no—
277#106—22no—
278#106—22no—
279C4⋊C8—22no—
280C4⋊C8—22no—
281C4⋊C8D4×C4312yes—
282C4⋊C8C23×C4312yes—
283C4⋊C8C23×C4312yes—
284C4⋊C8C23×C4312yes—
285#103—22no—
286#103—22no—
287#103—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8D4×C4312yes—
295#97—22no—
296#97—21no—
297#97—21no—
298C4×C8—22no—
299C4×C8—21no—
300C4×C8C23×C4311yescharacteristic
301C4×C8C23×C4311yescharacteristic
302#41—82no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—41no—
308C2×Q8—82no—
309C2×Q8C2×D4×C4312yes—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4C2×D4×C4311yescharacteristic
317C22×C4C2×D4×C4311yescharacteristic
318C22×C4#41×C4311yescharacteristic
319Q16—82no—
320SD16—82no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8C2×D4×C4312yes—
325C2×C8C2×D4×C4312yes—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4C2×D4×C4312yes—
340C22⋊C4—22no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—22no—
344C42C2×D4×C4311yescharacteristic
345C42C2×D4×C4311yescharacteristic
346C42#41×C4311yescharacteristic
347C42C24×C4311yescharacteristic
348C23—41no—
349C23#121×C4311yescharacteristic
350Q8—22no—
351Q8—22no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355Q8—81no—
356Q8—82no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—82no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4#121×C4311yescharacteristic
372C2×C4#121×C4311yescharacteristic
373C2×C4#121×C4311yescharacteristic
374C2×C4C22×D4×C4311yescharacteristic
375C2×C4C22×D4×C4311yescharacteristic
376C2×C4C2×#41×C4311yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22C2×#121×C4311yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4C43×#57712yes—
399C4C43×#57812yes—
400C2—41no—
401C2—161no—
402C2C43×#304411yescharacteristic
403C2C43×#305711yescharacteristic
404C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3230C2semidirect
4. C43×#2985C2semidirect
5. C43×#1698C2semidirect
6. C43×#1692C2semidirect
7. C43×#1678C2semidirect
8. C43×#1672C2semidirect
9. C43×#1572C2semidirect
10. C43×#1558C2semidirect
179. #19529C43direct (N × H)
198. #3230C2×C43semidirect
201. #2985C2×C43semidirect
202. #1698C2×C43semidirect
203. #1692C2×C43semidirect
204. #1678C2×C43semidirect
205. #1672C2×C43semidirect
206. #1572C2×C43semidirect
207. #1558C2×C43semidirect
247. C43#19529direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32302
C43×#32272
C43×#32162
C43×#29852
C43×#16982
C43×#16922
C43×#16782
C43×#16722
C43×#15722
C43×#15582
C43×#15532
#1952943