Finite Group Databasebeta

← #25007096

Subgroups — #25007096

Order 11008.

622 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137930C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic, complemented
3#19132624C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C2×C43×#343C211yesmaximal, characteristic, complemented
6C22×#10621898C411yescharacteristic
7C2×#13063308—21no—
8#14582863—21no—
9#14582819C411yescharacteristic
10#14582819C2211yescharacteristic
11#14582816C411yescharacteristic
12#14582816C2211yescharacteristic
13#14582778—21no—
14#14582770—21no—
15#14582770—21no—
16#14582762C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×M16×C43—21no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C43×#343—21no—
22C43×#343C2212yes—
23C2×#10621898—41no—
24C2×#10621898—41no—
25C2×#10621898—44no—
26C22×Dic86C2×C411yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C4×D43—21no—
30C2×#10621877—41no—
31#13063308—44no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—24no—
50C2×M16×C43—22no—
51C2×M16×C43—41no—
52C2×M16×C43—42no—
53C22×C8×C43—41no—
54C2×C4⋊C4×C43—41no—
55C2×C4⋊C4×C43—41no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C4⋊C4×C43C2311yescharacteristic
60C24×C43C22⋊C411yescharacteristic
61C23×D43—21no—
62C22×C4×C43—22no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—42no—
72C22×C4×C43—42no—
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—24no—
80C2×C22⋊D43—42no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86#10621898—44no—
87#10621898—44no—
88#10621898—44no—
89#10621898—44no—
90C2×D172—42no—
91C2×D172—41no—
92C2×C4×D43—42no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×Dic86—41no—
96C2×Dic86—42no—
97M16×C43—24no—
98M16×C43—44no—
99M16×C43—42no—
100C2×C8×C43—44no—
101C2×C8×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C22⋊Dic43—42no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—42no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112Dic43⋊C4—42no—
113Dic43⋊C4—42no—
114#10621877—82no—
115C2×C43⋊C8—42no—
116C23×C43—22no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—41no—
120C23×C43#9911yescharacteristic
121C23×C43#9911yescharacteristic
122C23×C43C2×C22⋊C411yescharacteristic
123C22×D43—22no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—81no—
150C2×C4×C43#10412yes—
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C22⋊D43—44no—
154C22⋊D43—44no—
155C2×Dic43—22no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164D172—42no—
165D172—42no—
166C4×D43—48no—
167Dic86—42no—
168Dic86—42no—
169C8×C43—44no—
170C43⋊C8—82no—
171#11762—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43AΣL(1,𝔽16)12yes—
182C22×C43C2×#9911yescharacteristic
183C22×C43#41711yescharacteristic
184C22×C43C2×#10411yescharacteristic
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—22no—
194C4×C43—21no—
195C4×C43—41no—
196C4×C43—41no—
197C4×C43—41no—
198C4×C43—41no—
199Dic43—42no—
200Dic43—81no—
201Dic43—81no—
202#2406—431no—
203C2×#343D4311yescharacteristic, complemented
204#1463—431no—
205#1354—432no—
206#1345—432no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—22no—
210C2×C43—41no—
211C2×C43#150411yescharacteristic
212C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C43#213311yescharacteristic
214D43—82no—
215C22×#41—431no—
216C22×M16—21no—
217C2×#123—861no—
218C22×C4⋊C4C2×D4311yescharacteristic
219#407—861no—
220#395—431no—
221#395—431no—
222#394—431no—
223#394—431no—
224#386—861no—
225#385—861no—
226#385—861no—
227#381—431no—
228#343—21no—
229#343C2×D4312yes—
230#324—432no—
231#324—861no—
232C43#1176211yescharacteristic, complemented, Sylow
233C2×#41—1721no—
234C2×#41—1721no—
235C2×#41—1724no—
236C22×Q8—431no—
237C22×D4—431no—
238C22×D4—861no—
239C23×C4—861no—
240C23×C4C4×D4311yescharacteristic
241C23×C4D17211yescharacteristic
242C23×C4C22⋊D4311yescharacteristic
243C2×M16—24no—
244C2×M16—22no—
245C2×M16—41no—
246C2×M16—42no—
247C2×M16—1721no—
248C22×C8—41no—
249#123—1724no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4—41no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4C4×D4311yescharacteristic
255C2×C4⋊C4D17211yescharacteristic
256C2×C4⋊C4C22⋊D4311yescharacteristic
257C2×C4⋊C4C22×D4311yescharacteristic
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—861no—
263C22⋊C8—862no—
264C22⋊C8—1721no—
265#95—431no—
266#95—431no—
267#95—861no—
268#95—861no—
269#95—861no—
270C24—861no—
271C24(C2×D43)⋊C411yescharacteristic
272#41—1724no—
273#41—1724no—
274#41—1724no—
275#41—1724no—
276C2×Q8—1721no—
277C2×Q8—1722no—
278C2×D4—864no—
279C2×D4—1721no—
280C2×D4—1722no—
281C2×D4—1722no—
282C2×D4—1721no—
283C2×D4—1721no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—1722no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4(C2×D43)⋊C411yescharacteristic
303C22×C4(C2×D43)⋊C411yescharacteristic
304C22×C4C2×C4×D4311yescharacteristic
305C22×C4C2×D17211yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307M16—24no—
308M16—44no—
309M16—42no—
310M16—3442no—
311C2×C8—44no—
312C2×C8—42no—
313C2×C8—1722no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—1722no—
319C4⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1722no—
322C22⋊C4—1722no—
323C22⋊C4—1722no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—41no—
330C23—862no—
331C23—1721no—
332C23—1721no—
333C23—1721no—
334C23—1721no—
335C23—1721no—
336C23—1721no—
337C23#1306323911yescharacteristic
338C23#1306323911yescharacteristic
339C23C2×(C2×D43)⋊C411yescharacteristic
340Q8—1722no—
341Q8—1722no—
342D4—1722no—
343D4—1722no—
344D4—1724no—
345D4—1724no—
346C2×C4—22no—
347C2×C4—22no—
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—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—862no—
367C2×C4—1728no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4#1306325312yes—
377C2×C4#1306335111yescharacteristic
378C2×C4#1306335611yescharacteristic
379C8—44no—
380C8—3442no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—3441no—
391C22—3441no—
392C22—3441no—
393C22—3441no—
394C22—1722no—
395C22—1722no—
396C22—1722no—
397C22#1458268712yes—
398C22C2×#1306323911yescharacteristic
399C22#1458289811yescharacteristic
400C22C2×#1306325311yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—3441no—
409C4—3441no—
410C4—1722no—
411C2—21no—
412C2—21no—
413C2—22no—
414C2—41no—
415C2—3442no—
416C2#1913309711yescharacteristic
417C2C2×#1458268711yescharacteristic
418C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC2×C43×#343C2
socleC22×C43C2×#99
prime radicalC22×#10621898C4
cosocleC2×C4⋊C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11762
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. #19132925C2semidirect
3. #19132624C2semidirect
4. #19132597C2semidirect
5. C2×C43×#343C2semidirect
203. C2×#343D43semidirect
232. C43#11762semidirect

Maximal subgroups

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

subgroupindex
#191379302
#191329252
#191326242
#191325972
C2×C43×#3432
#1176243