Finite Group Databasebeta

← C43×#7753 #24927770

Subgroups — C43×#7753 #24927770

Order 11008.

504 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2732C211yesmaximal, characteristic
2C43×#2058C211yesmaximal, characteristic, complemented
3C43×#2024C211yesmaximal, characteristic, complemented
4C43×#2013C211yesmaximal, characteristic
5C43×#1272C211yesmaximal, characteristic, complemented
6C43×#1271C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic
8C22×SD16×C43—21no—
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×C22⋊Q8×C43—21no—
11C2×#106×C43—21no—
12C2×#103×C43—21no—
13C2×#103×C43—21no—
14C43×#399—21no—
15C43×#398—21no—
16C43×#396—21no—
17C43×#391C2211yescharacteristic
18C43×#390C2211yescharacteristic
19C43×#389C2211yescharacteristic
20C43×#386—21no—
21C43×#385—21no—
22C43×#340—21no—
23C43×#340—21no—
24C43×#336C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Q8×C43—21no—
28C22×Q8×C43D411yescharacteristic
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31C2×SD16×C43—42no—
32C2×SD16×C43—42no—
33C2×SD16×C43—42no—
34C22×C8×C43—21no—
35C22×C8×C43—21no—
36C22×C8×C43—21no—
37C4⋊Q8×C43—42no—
38C22⋊Q8×C43—42no—
39C22⋊Q8×C43—42no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C42×C43C2311yescharacteristic
56#106×C43—42no—
57#103×C43—42no—
58#103×C43—42no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63C24×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43SD1612yescomplemented
74C2×D4×C43—21no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43SD1612yes—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—81no—
86C22×C4×C43—81no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90SD16×C43—48no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—42no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—81no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—81no—
120C22⋊C4×C43—81no—
121C42×C43—41no—
122C23×C43—22no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43#12011yescharacteristic
130Q8×C43—42no—
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—81no—
134Q8×C43—81no—
135Q8×C43—81no—
136D4×C43—42no—
137D4×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—84no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43C2×SD1611yescharacteristic
164C2×C4×C43C2×SD1611yescharacteristic
165C2×C4×C43#13511yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43#13711yescharacteristic
168C2×C4×C43#13711yescharacteristic
169C8×C43—42no—
170C8×C43—42no—
171C8×C43—81no—
172#7753C4311yesmaximal, characteristic, direct product factor, Sylow
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43#44811yescharacteristic
181C22×C43#45011yescharacteristic
182C22×C43#45211yescharacteristic
183C22×C43#45311yescharacteristic
184C22×C43#45511yescharacteristic
185C22×C43#45611yescharacteristic
186C22×C43B(4,𝔽2)11yescharacteristic
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—42no—
194C4×C43—82no—
195C4×C43—81no—
196C4×C43—81no—
197C4×C43—81no—
198C4×C43—81no—
199#2732C2×C4311yescharacteristic
200#2058C2×C4311yescharacteristic, complemented
201#2024C2×C4311yescharacteristic, complemented
202#2013C2×C4311yescharacteristic
203#1272C2×C4311yescharacteristic, complemented
204#1271C2×C4311yescharacteristic, complemented
205#1270C2×C4311yescharacteristic
206C2×C43—82no—
207C2×C43#159611yescharacteristic
208C2×C43#160111yescharacteristic
209C2×C43#160311yescharacteristic
210C2×C43#163111yescharacteristic
211C2×C43#164311yescharacteristic
212C2×C43#165111yescharacteristic
213C2×C43#166111yescharacteristic
214C22×SD16—21no—
215C2×C4⋊Q8C22×C4311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×#106—21no—
218C2×#103—21no—
219C2×#103—21no—
220#399—21no—
221#398—21no—
222#396—21no—
223#391C22×C4311yescharacteristic
224#390C22×C4311yescharacteristic
225#389C22×C4311yescharacteristic
226#386—21no—
227#385—21no—
228#340—21no—
229#340—21no—
230#336C22×C4311yescharacteristic
231#336C22×C4311yescharacteristic
232#336C22×C4311yescharacteristic
233C43#775311yescharacteristic, direct product factor, Sylow
234C22×Q8—21no—
235C22×Q8D4×C4311yescharacteristic
236C22×D4D4×C4311yescharacteristic
237C23×C4—21no—
238C2×SD16—42no—
239C2×SD16—42no—
240C2×SD16—42no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4⋊Q8—42no—
245C22⋊Q8—42no—
246C22⋊Q8—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4D4×C4311yescharacteristic
254C2×C4⋊C4D4×C4311yescharacteristic
255C2×C4⋊C4D4×C4311yescharacteristic
256C2×C4⋊C4D4×C4311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42C23×C4311yescharacteristic
263#106—42no—
264#103—42no—
265#103—42no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8SD16×C4312yescomplemented
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4SD16×C4312yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4C2×D4×C4311yescharacteristic
295C22×C4C2×D4×C4311yescharacteristic
296C22×C4C2×D4×C4311yescharacteristic
297SD16—48no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C42—41no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#120×C4311yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—84no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C2×SD16×C4311yescharacteristic
371C2×C4C2×SD16×C4311yescharacteristic
372C2×C4#135×C4311yescharacteristic
373C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
374C2×C4#137×C4311yescharacteristic
375C2×C4#137×C4311yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C43×#44811yescharacteristic
387C22C43×#45011yescharacteristic
388C22C43×#45211yescharacteristic
389C22C43×#45311yescharacteristic
390C22C43×#45511yescharacteristic
391C22C43×#45611yescharacteristic
392C22C43×B(4,𝔽2)11yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—81no—
405C2—82no—
406C2C43×#159611yescharacteristic
407C2C43×#160111yescharacteristic
408C2C43×#160311yescharacteristic
409C2C43×#163111yescharacteristic
410C2C43×#164311yescharacteristic
411C2C43×#165111yescharacteristic
412C2C43×#166111yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2058C2semidirect
3. C43×#2024C2semidirect
5. C43×#1272C2semidirect
6. C43×#1271C2semidirect
73. C2×Q8×C43SD16semidirect
172. #7753C43direct (N × H)
200. #2058C2×C43semidirect
201. #2024C2×C43semidirect
203. #1272C2×C43semidirect
204. #1271C2×C43semidirect
233. C43#7753direct (N × H)
280. C2×Q8SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#27322
C43×#20582
C43×#20242
C43×#20132
C43×#12722
C43×#12712
C43×#12702
#775343