Finite Group Databasebeta

← #25007116

Subgroups — #25007116

Order 11008.

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

normal subgroups only

This group has 488 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#19140075C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic, complemented
3#19132621C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C2×C43×#343C211yesmaximal, characteristic, complemented
6C2×#13063299C411yescharacteristic
7#14582863—21no—
8#14582838C411yescharacteristic
9#14582838C2211yescharacteristic
10#14582816C411yescharacteristic
11#14582816C2211yescharacteristic
12#14582789—21no—
13#14582789—21no—
14#14582778—21no—
15#14582778—21no—
16C4×C22⋊Dic43C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×M16×C43—21no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C43×#343—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C2×#10621877—41no—
26#13063299—41no—
27#13063299—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C22⋊Dic43—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43—21no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—24no—
48C2×M16×C43—22no—
49C2×M16×C43—41no—
50C2×M16×C43—42no—
51C22×C8×C43—41no—
52C2×C4⋊C4×C43—41no—
53C2×C4⋊C4×C43—41no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C23×D43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
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—81no—
70C22×C4×C43—81no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×D172—41no—
85C2×D172—81no—
86M16×C43—24no—
87M16×C43—44no—
88M16×C43—42no—
89C2×C8×C43—44no—
90C2×C8×C43—42no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊Dic43—42no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—81no—
101(C2×D43)⋊C4—81no—
102C4⋊Dic43—41no—
103C4×Dic43—81no—
104#10621877—82no—
105C2×C43⋊C8—42no—
106C23×C43—22no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—41no—
110C23×C43#9911yescharacteristic
111C23×C43#9911yescharacteristic
112C23×C43C2×C22⋊C411yescharacteristic
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—42no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43#10412yes—
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C22⋊D43—82no—
144C22⋊D43—82no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154D172—82no—
155C8×C43—44no—
156C43⋊C8—82no—
157#11766—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43#35512yes—
168C22×C43C2×#9911yescharacteristic
169C22×C43#41711yescharacteristic
170C22×C43C2×#10411yescharacteristic
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—21no—
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—41no—
185Dic43—81no—
186Dic43—81no—
187Dic43—81no—
188#2591—431no—
189C2×#343D4311yescharacteristic, complemented
190#1463—431no—
191#1353—432no—
192#1345—432no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—22no—
196C2×C43—41no—
197C2×C43#150411yescharacteristic
198C2×C43#212111yescharacteristic
199C2×C43C2×#35511yescharacteristic
200D43—161no—
201C22×M16—21no—
202C2×#121—431no—
203C22×C4⋊C4C2×D4311yescharacteristic
204#407—861no—
205#400—431no—
206#400—431no—
207#394—431no—
208#394—431no—
209#388—861no—
210#388—861no—
211#386—861no—
212#386—861no—
213C4×C22⋊C4—431no—
214#343—21no—
215#343C2×D4312yes—
216#324—432no—
217#324—861no—
218C43#1176611yescharacteristic, complemented, Sylow
219C22×D4—431no—
220C22×D4—861no—
221C23×C4C4×D4311yescharacteristic
222C23×C4D17211yescharacteristic
223C23×C4C22⋊D4311yescharacteristic
224C2×M16—24no—
225C2×M16—22no—
226C2×M16—41no—
227C2×M16—42no—
228C2×M16—1721no—
229C22×C8—41no—
230#121—1721no—
231#121—1721no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4C4×D4311yescharacteristic
236C2×C4⋊C4D17211yescharacteristic
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C4⋊C4C22×D4311yescharacteristic
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C42—861no—
246C22⋊C8—862no—
247C22⋊C8—1721no—
248#95—431no—
249#95—431no—
250#95—861no—
251#95—861no—
252#95—861no—
253#95—861no—
254C24—861no—
255C24(C2×D43)⋊C411yescharacteristic
256C2×D4—3441no—
257C2×D4—1721no—
258C2×D4—1722no—
259C2×D4—1722no—
260C2×D4—1721no—
261C2×D4—1721no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4(C2×D43)⋊C411yescharacteristic
277C22×C4(C2×D43)⋊C411yescharacteristic
278C22×C4(C2×D43)⋊C411yescharacteristic
279C22×C4C2×C4×D4311yescharacteristic
280C22×C4C2×D17211yescharacteristic
281C22×C4C2×C22⋊D4311yescharacteristic
282M16—24no—
283M16—44no—
284M16—42no—
285M16—3442no—
286C2×C8—44no—
287C2×C8—42no—
288C2×C8—1722no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—1721no—
294C22⋊C4—3441no—
295C22⋊C4—3441no—
296C22⋊C4—1722no—
297C22⋊C4—1722no—
298C22⋊C4—1722no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C42—3441no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—41no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23#1306323911yescharacteristic
314C23#1306323911yescharacteristic
315C23C2×(C2×D43)⋊C411yescharacteristic
316D4—3442no—
317D4—3442no—
318D4—3442no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4#1306325312yes—
349C2×C4#1306335111yescharacteristic
350C2×C4#1306335611yescharacteristic
351C8—44no—
352C8—3442no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22—3441no—
369C22#1458269512yes—
370C22C2×#1306323911yescharacteristic
371C22#1458289811yescharacteristic
372C22C2×#1306325311yescharacteristic
373C4—21no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3441no—
381C4—3441no—
382C4—3441no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—6881no—
388C2#1913309711yescharacteristic
389C2#1913624211yescharacteristic
390C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC2×C43×#343C2
socleC22×C43C2×#99
prime radicalC2×#13063299C4
cosocleC2×C4⋊C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11766
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. #19132621C2semidirect
4. #19132597C2semidirect
5. C2×C43×#343C2semidirect
189. C2×#343D43semidirect
218. C43#11766semidirect

Maximal subgroups

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

subgroupindex
#191400752
#191329252
#191326212
#191325972
C2×C43×#3432
#1176643