Finite Group Databasebeta

← #24989368

Subgroups — #24989368

Order 11008.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134448C211yesmaximal, characteristic, complemented
2#19134448C211yesmaximal, characteristic, complemented
3C2×#14582639C212yesmaximal
4#19132476C212yesmaximal, complemented
5C4×#124×C43C211yesmaximal, characteristic
6C2×C4⋊(C43⋊C8)—21no—
7C2×C4⋊(C43⋊C8)—21no—
8C2×#13063236C2212yes—
9C2×#13063236C2212yes—
10#14582654—21no—
11#14582654—21no—
12#14582639—24no—
13C2×#124×C43C2211yescharacteristic
14C2×C4×Q8×C43C411yescharacteristic
15C2×C4×D4×C43C411yescharacteristic
16C43×#391C411yescharacteristic
17C43×#390C411yescharacteristic
18C43×#388—21no—
19C43×#388—21no—
20C43×#382C2211yescharacteristic
21C4×C22⋊C4×C43—21no—
22C4×C22⋊C4×C43—21no—
23C43×C43C2211yescharacteristic
24C22×C43⋊C8—22no—
25C22×C43⋊C8—22no—
26C4⋊(C43⋊C8)—24no—
27C4⋊(C43⋊C8)—24no—
28#13063236—22no—
29#13063236—22no—
30#13063236—22no—
31#13063236—22no—
32C22×Q8×C43C2×C411yescharacteristic
33C22×D4×C43C2×C411yescharacteristic
34C23×C4×C43—21no—
35#124×C43—21no—
36#124×C43—21no—
37#124×C43D412yes—
38#124×C43Q812yes—
39C4×Q8×C43—42no—
40C4×D4×C43—42no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C42×C43—21no—
50C2×C42×C43C2×C411yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61C24×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43C4⋊C412yes—
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43C4⋊C412yes—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—42no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86C22⋊C4×C43—22no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—22no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—42no—
91C22⋊C4×C43—42no—
92C22⋊C4×C43—42no—
93C42×C43—22no—
94C42×C43—22no—
95C42×C43—22no—
96C42×C43—41no—
97C42×C43—41no—
98C42×C43—41no—
99C42×C43—42no—
100C42×C43C2×D411yescharacteristic
101C42×C43C2×Q811yescharacteristic
102C42×C43#4111yescharacteristic
103C42×C43#4111yescharacteristic
104C2×C43⋊C8—24no—
105C2×C43⋊C8—24no—
106C2×C43⋊C8—42no—
107C2×C43⋊C8—42no—
108C2×C43⋊C8—42no—
109C2×C43⋊C8—42no—
110C23×C43—22no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118Q8×C43—42no—
119Q8×C43—42no—
120D4×C43—42no—
121D4×C43—42no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
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—21no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—84no—
147C2×C4×C43#10012yes—
148C2×C4×C43#10412yes—
149C2×C4×C43#10412yes—
150C2×C4×C43C2×C4⋊C411yescharacteristic
151C2×C4×C43#11711yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43C22⋊Q811yescharacteristic
155C2×C4×C43C22⋊Q811yescharacteristic
156C43⋊C8—44no—
157C43⋊C8—44no—
158#8581—431nomaximal, Sylow
159C22×C43—42no—
160C22×C43—42no—
161C22×C43—42no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43#38011yescharacteristic
167C22×C43C2×#10011yescharacteristic
168C22×C43#41311yescharacteristic
169C22×C43C2×#10411yescharacteristic
170C22×C43C2×#10411yescharacteristic
171C22×C43#42111yescharacteristic
172C22×C43#42111yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—42no—
183C4×C43—41no—
184C4×C43—81no—
185C4×C43—81no—
186C4×#124D4311yescharacteristic
187#1767—431no—
188#1767—431no—
189C2×#329—432no—
190#1295—432no—
191C2×C43—82no—
192C2×C43#152411yescharacteristic
193C2×C43#152711yescharacteristic
194C2×C43#153011yescharacteristic
195C2×C43#153511yescharacteristic
196C2×C43#180011yescharacteristic
197C2×C43#180611yescharacteristic
198C2×C43#180611yescharacteristic
199C2×#124C2×D4311yescharacteristic
200C2×C4×Q8Dic4311yescharacteristic
201C2×C4×D4Dic4311yescharacteristic
202C2×C4⋊C8—861no—
203C2×C4⋊C8—861no—
204C2×#97—432no—
205C2×#97—432no—
206#391Dic4311yescharacteristic
207#390Dic4311yescharacteristic
208#388—21no—
209#388—21no—
210#382C2×D4311yescharacteristic
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213C43C2×D4311yescharacteristic
214#336—861no—
215#336—861no—
216#329—864no—
217C43#858111yescharacteristic, complemented, Sylow
218C22×Q8C2×Dic4311yescharacteristic
219C22×D4C2×Dic4311yescharacteristic
220C23×C4—21no—
221C22×C8—862no—
222C22×C8—862no—
223#124—21no—
224#124—21no—
225#124Dic8612yes—
226#124D17212yes—
227C4×Q8—42no—
228C4×D4—42no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×Dic4311yescharacteristic
231C2×C4⋊C4C2×Dic4311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—21no—
238C2×C42C2×Dic4311yescharacteristic
239C2×C42C2×Dic4311yescharacteristic
240C2×C42C22⋊D4311yescharacteristic
241C2×C42C22⋊D4311yescharacteristic
242C2×C42C22⋊D4311yescharacteristic
243C2×C42C22⋊D4311yescharacteristic
244C2×C42C22×D4311yescharacteristic
245C4⋊C8—864no—
246C4⋊C8—864no—
247#97—862no—
248#97—862no—
249#97—862no—
250#97—862no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8C4⋊Dic4312yes—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4C4⋊Dic4312yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C22⋊Dic4311yescharacteristic
271C22×C4C22⋊Dic4311yescharacteristic
272C22×C4C22⋊Dic4311yescharacteristic
273C22×C4C22⋊Dic4311yescharacteristic
274C22×C4C22×Dic4311yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277C2×C8—864no—
278C2×C8—864no—
279C2×C8—1722no—
280C2×C8—1722no—
281C2×C8—1722no—
282C2×C8—1722no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42C2×Dic8611yescharacteristic
301C42C2×D17211yescharacteristic
302C42#1062189811yescharacteristic
303C42#1062189811yescharacteristic
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C22⋊Dic4311yescharacteristic
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
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—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4#1306324212yes—
342C2×C4#1306325212yes—
343C2×C4#1306325212yes—
344C2×C4C2×C4⋊Dic4311yescharacteristic
345C2×C4#1306328411yescharacteristic
346C2×C4#1306329911yescharacteristic
347C2×C4#1306329911yescharacteristic
348C2×C4#1306330411yescharacteristic
349C2×C4#1306330411yescharacteristic
350C8—1724no—
351C8—1724no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#1458275911yescharacteristic
360C22C2×#1306324211yescharacteristic
361C22#1458288311yescharacteristic
362C22C2×#1306325211yescharacteristic
363C22C2×#1306325211yescharacteristic
364C22#1458291611yescharacteristic
365C22#1458291611yescharacteristic
366C4—22no—
367C4—22no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—42no—
377C4—81no—
378C4—81no—
379C2—82no—
380C2#1913318311yescharacteristic
381C2#1913319311yescharacteristic
382C2#1913320611yescharacteristic
383C2#1913322611yescharacteristic
384C2#1913458711yescharacteristic
385C2#1913461511yescharacteristic
386C2#1913461511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#124×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#124D43
hypocenterC43#8581
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #19134448C2semidirect
2. #19134448C2semidirect
4. #19132476C2semidirect
217. C43#8581semidirect

Maximal subgroups

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

subgroupindex
#191344482
C2×#145826392
#191324762
C4×#124×C432
#858143