Finite Group Databasebeta

← #24990001

Subgroups — #24990001

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136988C211yesmaximal, characteristic
2#19134358C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic
4#19132477C211yesmaximal, characteristic, complemented
5#19132477C211yesmaximal, characteristic, complemented
6#19132476C211yesmaximal, characteristic, complemented
7C43×#1295C211yesmaximal, characteristic, complemented
8C2×C42×D43C2211yescharacteristic
9C2×(C2×D43)⋊C8—21no—
10C2×(C2×D43)⋊C8—21no—
11C2×#13063236C2211yescharacteristic
12C2×#13063236C2211yescharacteristic
13#14582766—21no—
14#14582765C2211yescharacteristic
15#14582761—21no—
16#14582756C411yescharacteristic
17#14582756C411yescharacteristic
18C4⋊C4×Dic43C411yescharacteristic
19C4⋊C4×Dic43C411yescharacteristic
20#14582746—21no—
21#14582744—21no—
22#14582653—21no—
23#14582653—21no—
24C2×#97×C43C2211yescharacteristic
25C2×#97×C43C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C42×D43—21no—
42C42×D43—21no—
43C42×D43—21no—
44C42×D43—21no—
45(C2×D43)⋊C8—24no—
46(C2×D43)⋊C8—24no—
47#13063236—21no—
48#13063236—21no—
49#13063236—21no—
50#13063236—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C42×C43C2311yescharacteristic
62#97×C43—21no—
63#97×C43—21no—
64#97×C43—21no—
65#97×C43—21no—
66#95×C43—21no—
67#95×C43—21no—
68C23×D43C22⋊C411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C42×C43#4111yescharacteristic
100C42×C43#4111yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103(C2×D43)⋊C4—42no—
104(C2×D43)⋊C4—42no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—42no—
114C4×Dic43—42no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C23×C43C2×C22⋊C411yescharacteristic
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43#10412yes—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43#11711yescharacteristic
142C2×C4×C43#11711yescharacteristic
143C2×C4×C43#12311yescharacteristic
144C2×C4×C43#12311yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43#10412yes—
162C4×D43—42no—
163C4×D43—42no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—42no—
168C8×C43—42no—
169C8×C43—42no—
170C43⋊C8—42no—
171C43⋊C8—42no—
172#8720—431nomaximal, Sylow
173C22×C43#38111yescharacteristic
174C22×C43#41311yescharacteristic
175C22×C43#41311yescharacteristic
176C22×C43C2×#10411yescharacteristic
177C22×C43C2×#10411yescharacteristic
178C22×C43#42111yescharacteristic
179C22×C43#42111yescharacteristic
180C2×D43—22no—
181C2×D43—22no—
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—81no—
194C4×C43—81no—
195Dic43—22no—
196Dic43—41no—
197Dic43—41no—
198Dic43—81no—
199Dic43—81no—
200#2283—431no—
201#1749—431no—
202#1749—431no—
203#1295—431no—
204#1295—431no—
205#1295—431no—
206#1295D4311yescharacteristic, complemented
207C2×C43#152411yescharacteristic
208C2×C43#152911yescharacteristic
209C2×C43#153211yescharacteristic
210C2×C43#153511yescharacteristic
211C2×C43#182211yescharacteristic
212C2×C43#182611yescharacteristic
213C2×C43#182611yescharacteristic
214D43—42no—
215C22×C42—431no—
216C2×C22⋊C8—861no—
217C2×C22⋊C8—861no—
218C2×#97—431no—
219C2×#97—431no—
220C2×#97C2×D4311yescharacteristic
221C2×#97C2×D4311yescharacteristic
222#383—861no—
223#382—431no—
224#382C2×D4311yescharacteristic
225#381—861no—
226#380—431no—
227#380—431no—
228C4×C4⋊C4—431no—
229C4×C4⋊C4—431no—
230C4×C22⋊C4—861no—
231#376—861no—
232#336—861no—
233#336—861no—
234C43#872011yescharacteristic, complemented, Sylow
235C23×C4—431no—
236C23×C4—431no—
237C23×C4—431no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—861no—
241C22×C8—861no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4C4×D4311yescharacteristic
245C2×C4⋊C4C4×D4311yescharacteristic
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C42—431no—
249C2×C42—431no—
250C2×C42—431no—
251C2×C42—861no—
252C2×C42—861no—
253C2×C42—861no—
254C2×C42—861no—
255C2×C42—861no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258C22⋊C8—864no—
259C22⋊C8—864no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97—21no—
264#97—861no—
265#97—861no—
266#97—861no—
267#97—861no—
268#95—21no—
269#95—21no—
270#95—861no—
271#95—861no—
272#95—861no—
273#95—861no—
274#95—861no—
275#95—861no—
276C24—431no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4—1721no—
296C22×C4C2×C4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—1722no—
316C22⋊C4—1722no—
317C42—861no—
318C42—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42—861no—
323C42—1722no—
324C42—1722no—
325C42#1062189811yescharacteristic
326C42#1062189811yescharacteristic
327C42#1062190011yescharacteristic
328C42#1062190211yescharacteristic
329C23—432no—
330C23—861no—
331C23—861no—
332C23—861no—
333C23—861no—
334C23—861no—
335C23—861no—
336C23C22⋊C4×D4311yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—432no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4#1306328211yescharacteristic
371C2×C4#1306328311yescharacteristic
372C2×C4#1306330711yescharacteristic
373C2×C4#1306330711yescharacteristic
374C2×C4#1306331011yescharacteristic
375C2×C4#1306331011yescharacteristic
376C8—42no—
377C8—42no—
378C8—1722no—
379C8—1722no—
380C22—862no—
381C22—862no—
382C22—862no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22#1458276111yescharacteristic
388C22#1458288011yescharacteristic
389C22#1458288211yescharacteristic
390C22#104×D4311yescharacteristic
391C22#104×D4311yescharacteristic
392C22#1458291411yescharacteristic
393C22#1458291411yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—862no—
403C4—3441no—
404C4—3441no—
405C4—1721no—
406C4—1721no—
407C2—1722no—
408C2#1913318011yescharacteristic
409C2#1913320111yescharacteristic
410C2#1913321411yescharacteristic
411C2#1913322311yescharacteristic
412C2#1913467711yescharacteristic
413C2#1913469311yescharacteristic
414C2#1913469311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#8720
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. #19132477C2semidirect
5. #19132477C2semidirect
6. #19132476C2semidirect
7. C43×#1295C2semidirect
206. #1295D43semidirect
234. C43#8720semidirect

Maximal subgroups

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

subgroupindex
#191369882
#191343582
#191324772
#191324762
C43×#12952
#872043