Finite Group Databasebeta

← D43×#1346 #25006792

Subgroups — D43×#1346 #25006792

Order 11008.

544 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#398×D43C211yesmaximal, characteristic
2#343×D43C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4⋊C4×D43—21no—
10C2×C4⋊C4×D43C411yescharacteristic
11C2×C4⋊C4×D43C2211yescharacteristic
12C22⋊C8×D43—21no—
13#14582833—21no—
14#14582832—21no—
15#14582831C411yescharacteristic
16#14582830C411yescharacteristic
17#14582829C2211yescharacteristic
18#95×D43—21no—
19#95×D43C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43—21no—
28C22×C4×D43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—41no—
34M16×D43—24no—
35M16×D43—42no—
36C2×C8×D43—41no—
37C2×C8×D43—41no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4C2×C411yescharacteristic
45C2×Dic43⋊C4D411yescharacteristic
46C4⋊C4×D43—41no—
47C4⋊C4×D43—41no—
48C4⋊C4×D43—41no—
49C4⋊C4×D43—41no—
50C4⋊C4×D43—42no—
51C4⋊C4×D43—42no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95C2×C411yescharacteristic
59C2×M16×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C4⋊C4×C43C2311yescharacteristic
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43C2×C411yescharacteristic
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—24no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—22no—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—42no—
91C2×C4×D43—42no—
92C2×C4×D43—42no—
93C2×C4×D43D812yes—
94C2×C4×D43SD1612yes—
95M16×C43—22no—
96M16×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—42no—
105C4⋊Dic43—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—42no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—42no—
112#10621877—22no—
113#10621877—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116#10621872—44no—
117C8×D43—44no—
118C8×D43—82no—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—22no—
121C22×D43—22no—
122C22×D43#9911yescharacteristic
123C22×D43#9911yescharacteristic
124C22×D43#10212yes—
125C22×D43#10412yes—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—22no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—22no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43#10212yes—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—22no—
157C4×D43—48no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—81no—
162C4×D43—82no—
163C4×D43—82no—
164C8×C43—42no—
165C8×C43—81no—
166C43⋊C8—42no—
167C43⋊C8—81no—
168C2×#1346—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43C2×#9911yescharacteristic
172C22×C43C2×#10211yescharacteristic
173C22×C43C2×#10411yescharacteristic
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—24no—
177C2×D43—24no—
178C2×D43#32712yes—
179C2×D43#32712yes—
180C2×D43#35212yes—
181C2×D43#35612yes—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—42no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—81no—
188Dic43—22no—
189Dic43—42no—
190Dic43—41no—
191Dic43—41no—
192Dic43—81no—
193C2×#398—431no—
194C2×#343—431no—
195C2×#324—431no—
196#1346—431no—
197#1346—431no—
198#1346—431no—
199#1346D4311yescharacteristic, direct product factor
200C2×C43—21no—
201C2×C43—21no—
202C2×C43C2×#32711yescharacteristic
203C2×C43C2×#35211yescharacteristic
204C2×C43C2×#35611yescharacteristic
205D43—22no—
206D43#134614yesdirect product factor
207C22×M16—861no—
208C22×C4⋊C4—431no—
209C22×C4⋊C4—431no—
210C22×C4⋊C4—861no—
211C2×C22⋊C8—861no—
212#398—431no—
213#398—431no—
214#398—431no—
215#398—861no—
216#398—861no—
217#398C2×D4311yescharacteristic
218C2×#95—431no—
219C2×#95—861no—
220#343—431no—
221#343—861no—
222#343C2×D4311yescharacteristic
223#324—431no—
224#324—861no—
225#324C2×D4311yescharacteristic
226C43C2×#134611yescharacteristic, complemented, Sylow
227C23×C4—431no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—861no—
231C23×C4—861no—
232C2×M16—21no—
233C2×M16—864no—
234C2×M16—861no—
235C2×M16—1721no—
236C2×M16—1722no—
237C22×C8—1721no—
238C22×C8—1721no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—1722no—
249C2×C4⋊C4—1722no—
250C2×C4⋊C4—1721no—
251C2×C4⋊C4—1721no—
252C2×C4⋊C4—1721no—
253C2×C4⋊C4—1721no—
254C2×C4⋊C4C4×D4311yescharacteristic
255C2×C4⋊C4C22×D4311yescharacteristic
256C22⋊C8—21no—
257C22⋊C8—861no—
258C22⋊C8—1721no—
259#95—21no—
260#95—431no—
261#95—861no—
262#95—861no—
263#95—861no—
264#95—861no—
265#95C4×D4311yescharacteristic
266C24—431no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—431no—
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—862no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—864no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—1722no—
285C22×C4—1721no—
286C22×C4—1721no—
287C22×C4—1722no—
288C22×C4—1722no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4—1722no—
292C22×C4C2×C4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295M16—22no—
296M16—41no—
297M16—862no—
298M16—1724no—
299M16—1721no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—3442no—
303C2×C8—1724no—
304C2×C8—1721no—
305C2×C8—1721no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1722no—
315C4⋊C4—1722no—
316C4⋊C4—1722no—
317C4⋊C4—1721no—
318C4⋊C4—1721no—
319C23—431no—
320C23—431no—
321C23—432no—
322C23—432no—
323C23—862no—
324C23—862no—
325C23C22⋊C4×D4311yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—432no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—862no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—3441no—
349C2×C4—3442no—
350C2×C4—3442no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1728no—
354C2×C4—1722no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4D8×D4311yescharacteristic
363C2×C4SD16×D4311yescharacteristic
364C8—42no—
365C8—81no—
366C8—3441no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—432no—
371C22—432no—
372C22—432no—
373C22—432no—
374C22—864no—
375C22—864no—
376C22—861no—
377C22—861no—
378C22#99×D4311yescharacteristic
379C22#102×D4311yescharacteristic
380C22#104×D4311yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—862no—
388C4—3441no—
389C4—1722no—
390C4—1721no—
391C4—1721no—
392C2—21no—
393C2—21no—
394C2—434no—
395C2—862no—
396C2#327×D4311yescharacteristic
397C2#352×D4311yescharacteristic
398C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43C2×#1346
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #19132602C2semidirect
5. #19132601C2semidirect
6. #19132600C2semidirect
7. C43×#1346C2semidirect
199. #1346D43direct (N × H)
206. D43#1346direct (N × H)
226. C43C2×#1346semidirect

Maximal subgroups

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

subgroupindex
#398×D432
#343×D432
#324×D432
#191326022
#191326012
#191326002
C43×#13462
C2×#134643