Finite Group Databasebeta

← #25080459

Subgroups — #25080459

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic
2#19144717C211yesmaximal, characteristic
3C2×Q8×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134051C212yesmaximal, complemented
5#19134041C212yesmaximal, complemented
6#19133975C212yesmaximal, complemented
7#19133945C212yesmaximal, complemented
8#19133356C211yesmaximal, characteristic, complemented
9#19133295C211yesmaximal, characteristic, complemented
10#19133291C211yesmaximal, characteristic
11C43×#3113C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13#14583295C2211yescharacteristic
14#14583273C2211yescharacteristic
15#14583249C2211yescharacteristic
16#14583247C2211yescharacteristic
17#14583212—21no—
18#14583194C2212yes—
19#14583130—21no—
20#14583130—21no—
21#14583099C2212yes—
22#14583038—21no—
23Q8×C43⋊C8—21no—
24Q8×C43⋊C8—21no—
25Q8×C43⋊C8C2212yes—
26Q8×C43⋊C8C2212yes—
27#14582997—22no—
28C4×#10621884—21no—
29C4×#10621884—21no—
30#14582956C2211yescharacteristic
31C2×C4⋊(C43⋊C8)—21no—
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×C4×C43⋊C8—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yes—
36#14582649C2212yes—
37#14582647C2212yes—
38#14582645C2212yes—
39#14582645C2212yes—
40#14582642C2212yes—
41C43×#533C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#483—21no—
44C43×#475C2212yes—
45C43×#462C2212yes—
46C43×#451—21no—
47C43×#441—22no—
48C43×#432C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621884—22no—
51C2×#10621884—21no—
52C2×#10621884—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8D411yescharacteristic
55C22×C43⋊C8D411yescharacteristic
56#13063325C2311yescharacteristic
57#13063322C2311yescharacteristic
58#13063313—21no—
59#13063299—21no—
60#13063299—21no—
61C4×D172—21no—
62C4×D172—21no—
63#13063258—22no—
64#13063256—21no—
65#13063256—21no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—22no—
68C4⋊(C43⋊C8)—22no—
69C4⋊(C43⋊C8)C2312yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063249—22no—
72#13063249—21no—
73#13063249—21no—
74#13063245—22no—
75#13063245—21no—
76#13063245—21no—
77C22⋊(C43⋊C8)—21no—
78#13063236—21no—
79C4×C43⋊C8—22no—
80C4×C43⋊C8—22no—
81C4×C43⋊C8D411yescharacteristic
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8C2311yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C22×Q8×C43D411yescharacteristic
86C2×Q16×C43—22no—
87C4⋊Q8×C43C2311yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89#125×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43D412yes—
97C4×Q8×C43C2312yes—
98#117×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#106×C43—22no—
104C4⋊C8×C43C2312yes—
105#103×C43—22no—
106#103×C43—22no—
107C22⋊C8×C43—21no—
108#97×C43—21no—
109C2×Q8×C43—24no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43C2×D412yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—41no—
120#10621898—82no—
121C2×D172—21no—
122C2×D172—21no—
123C2×D172—21no—
124C2×C4×D43—41no—
125C2×Dic86—21no—
126Q16×C43—44no—
127C2×C8×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43C2×D412yes—
138C22⋊C4×C43—41no—
139C42×C43—22no—
140C42×C43—22no—
141C42×C43—41no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43#4111yescharacteristic
145C42×C43C2411yescharacteristic
146#10621884—42no—
147#10621884—44no—
148#10621884—42no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—42no—
158C2×C43⋊C8C2×D411yescharacteristic
159C2×C43⋊C8C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C23×C43#12111yescharacteristic
163C22×D43—41no—
164Q8×C43—24no—
165Q8×C43—22no—
166Q8×C43—42no—
167Q8×C43—41no—
168Q8×C43—41no—
169Q8×C43#13514yes—
170C2×C4×C43—24no—
171C2×C4×C43—22no—
172C2×C4×C43—22no—
173C2×C4×C43—22no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—22no—
177C2×C4×C43—42no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43C22×D411yescharacteristic
184C2×C4×C43C22×D411yescharacteristic
185C2×C4×C43C2×#4111yescharacteristic
186C22⋊D43—82no—
187C2×Dic43—41no—
188D172—42no—
189D172—41no—
190D172—41no—
191D172—81no—
192C4×D43—82no—
193Dic86—81no—
194C8×C43—42no—
195C43⋊C8—21no—
196C43⋊C8—21no—
197C43⋊C8—21no—
198C43⋊C8—42no—
199C43⋊C8—42no—
200C43⋊C8#13712yes—
201#19263—431nomaximal, Sylow
202C22×C43—21no—
203C22×C43—21no—
204C22×C43#47112yes—
205C22×C43C2×#12111yescharacteristic
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—24no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—42no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43C2×#13512yes—
218C4×C43C2×#13711yescharacteristic
219C4×C43#57511yescharacteristic
220Dic43—81no—
221#3167—431no—
222#3113D4311yescharacteristic, complemented
223#3112—431no—
224C2×C8×Q8—431no—
225#1684—432no—
226#1682—432no—
227#1672—432no—
228#1666—432no—
229#1568—431no—
230#1552—431no—
231#1551—431no—
232C2×C43—22no—
233C2×C43#303711yescharacteristic
234C2×C43#305011yescharacteristic
235C2×C43C2×#47111yescharacteristic
236D43—161no—
237#533C2×D4311yescharacteristic
238#532—431no—
239C2×C4×Q8C2×D4311yescharacteristic
240#498—431no—
241#492—431no—
242#487—431no—
243#486—431no—
244#483—21no—
245#480—861no—
246#477—432no—
247#475C2×D4312yes—
248#465—861no—
249#465—861no—
250#462C2×D4312yes—
251#460—432no—
252#451—21no—
253#448—861no—
254C8×Q8—432no—
255C8×Q8—432no—
256C8×Q8—861no—
257C8×Q8—861no—
258#441—22no—
259#440—862no—
260C4×SD16—861no—
261C4×SD16—861no—
262#432—431no—
263#432C2×D4311yescharacteristic
264C2×C4⋊C8—431no—
265C2×C4⋊C8—861no—
266C2×C4×C8—431no—
267C2×C4×C8—861no—
268#335—432no—
269#334—432no—
270#333—432no—
271#332—432no—
272#332—432no—
273#331—432no—
274C43#1926311yescharacteristic, complemented, Sylow
275C2×#41—861no—
276C22×Q8C22⋊D4311yescharacteristic
277C2×Q16—22no—
278C2×SD16—861no—
279C2×SD16—861no—
280C2×SD16—862no—
281C22×C8—431no—
282C22×C8—431no—
283C22×C8—861no—
284C4⋊Q8—431no—
285C4⋊Q8C22×D4311yescharacteristic
286C4⋊Q8C22×D4311yescharacteristic
287#127—431no—
288#125—21no—
289#124—861no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—861no—
293#121—861no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C22⋊D4312yes—
299C4×Q8C22×D4312yes—
300C4×D4—861no—
301C4×D4—861no—
302#117—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C22⋊D4311yescharacteristic
305C2×C42—21no—
306C2×C42C22×D4311yescharacteristic
307#107—862no—
308#106—22no—
309#106—861no—
310#106—861no—
311C4⋊C8—432no—
312C4⋊C8—432no—
313C4⋊C8—862no—
314C4⋊C8—862no—
315C4⋊C8—861no—
316C4⋊C8C22×D4312yes—
317#103—22no—
318#103—22no—
319#103—861no—
320#103—861no—
321#103—862no—
322#102—861no—
323#102—861no—
324#102—862no—
325C22⋊C8—21no—
326C22⋊C8—861no—
327#97—21no—
328#97—861no—
329C4×C8—431no—
330C4×C8—431no—
331C4×C8—431no—
332C4×C8—431no—
333C4×C8—862no—
334C4×C8—862no—
335#41—3442no—
336C2×Q8—24no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—861no—
341C2×Q8C2×C22⋊D4312yes—
342C2×D4—861no—
343C2×D4—861no—
344C2×D4—861no—
345C2×D4—1721no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—1721no—
349C22×C4D4×D4311yescharacteristic
350C22×C4#1062190011yescharacteristic
351C22×C4C2×C22⋊D4311yescharacteristic
352Q16—44no—
353SD16—1722no—
354SD16—1722no—
355SD16—1724no—
356C2×C8—22no—
357C2×C8—431no—
358C2×C8—431no—
359C2×C8—431no—
360C2×C8—431no—
361C2×C8—862no—
362C2×C8—862no—
363C2×C8—862no—
364C2×C8—1721no—
365C2×C8—1722no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4C2×C22⋊D4312yes—
378C22⋊C4—41no—
379C22⋊C4—1721no—
380C22⋊C4—1721no—
381C42—22no—
382C42—22no—
383C42—41no—
384C42D4×D4311yescharacteristic
385C42#1062190011yescharacteristic
386C42C2×C22⋊D4311yescharacteristic
387C42C23×D4311yescharacteristic
388C23—1721no—
389C23#1306329711yescharacteristic
390Q8—24no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—3441no—
396Q8#1306334514yes—
397D4—3441no—
398D4—3442no—
399D4—1722no—
400D4—1721no—
401D4—1721no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—3442no—
413C2×C4—1721no—
414C2×C4#1306329711yescharacteristic
415C2×C4#1306329711yescharacteristic
416C2×C4#1306329711yescharacteristic
417C2×C4C2×D4×D4311yescharacteristic
418C2×C4C22×C22⋊D4311yescharacteristic
419C2×C4C2×#1062190011yescharacteristic
420C8—42no—
421C8—432no—
422C8—861no—
423C8—861no—
424C8—861no—
425C8—1722no—
426C8—1722no—
427C22—21no—
428C22—21no—
429C22—3441no—
430C22—3441no—
431C22—3441no—
432C22#1458316412yes—
433C22C2×#1306329711yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—24no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—3441no—
443C4C2×#1306334512yes—
444C4#137×D4311yescharacteristic
445C4#1458369811yescharacteristic
446C2—22no—
447C2—6881no—
448C2#1914406411yescharacteristic
449C2#1914417311yescharacteristic
450C2C2×#1458316411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3113C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenter#3113D43
hypocenterC43#19263
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
3. C2×Q8×C43⋊C8C2semidirect
4. #19134051C2semidirect
5. #19134041C2semidirect
6. #19133975C2semidirect
7. #19133945C2semidirect
8. #19133356C2semidirect
9. #19133295C2semidirect
11. C43×#3113C2semidirect
222. #3113D43semidirect
274. C43#19263semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191447172
C2×Q8×C43⋊C82
#191340512
#191340412
#191339752
#191339452
#191333562
#191332952
#191332912
C43×#31132
#1926343