Finite Group Databasebeta

← #25082089

Subgroups — #25082089

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145716C211yesmaximal, characteristic, complemented
2#19144050C211yesmaximal, characteristic
3#19143706C211yesmaximal, characteristic, complemented
4#19134041C212yesmaximal, complemented
5#19134034C212yesmaximal, complemented
6#19133987C212yesmaximal, complemented
7#19133982C212yesmaximal, complemented
8#19133371C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3039C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13#14583449C2211yescharacteristic
14#14583302C2212yes—
15#14583247C2212yes—
16#14583212—22no—
17#14583176—21no—
18#14583176—21no—
19#14583121—21no—
20#14583114—21no—
21#14583109C2211yescharacteristic
22#14583104C2211yescharacteristic
23#14583099C2211yescharacteristic
24#14583094C2211yescharacteristic
25Q8×C43⋊C8C2212yes—
26D4×C43⋊C8—22no—
27D4×C43⋊C8C2212yes—
28#14582952—21no—
29#14582952C2211yescharacteristic
30C2×C4⋊(C43⋊C8)—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582893—21no—
34#14582651C2212yes—
35#14582651C2212yes—
36#14582646C2212yes—
37#14582645C2212yes—
38#14582645C2212yes—
39#14582642C2212yes—
40C2×#137×C43—21no—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C4×#41×C43C2211yescharacteristic
43C43×#462—21no—
44C43×#462C2212yes—
45C43×#461—21no—
46C43×#461C2212yes—
47C43×#423C2211yescharacteristic
48C43×#419—21no—
49C2×#10621898—21no—
50#13063345—44no—
51C2×#10621885—21no—
52C2×#10621883—21no—
53C2×#10621884—21no—
54C2×#10621882—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—22no—
58#13063325C2311yescharacteristic
59#13063322C2311yescharacteristic
60#13063313—21no—
61#13063299—21no—
62#13063299—21no—
63C4×D172—21no—
64C4×D172—21no—
65#13063258—22no—
66#13063258—22no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—22no—
70C4⋊(C43⋊C8)D411yescharacteristic
71C4⋊(C43⋊C8)D411yescharacteristic
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75#13063248—21no—
76#13063248—21no—
77#13063245—21no—
78#13063245—21no—
79#13063245—22no—
80#13063245—22no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)D412yes—
83C4×C43⋊C8—22no—
84C4×C43⋊C8C2312yes—
85C2×#41×C43D411yescharacteristic
86C22×Q8×C43—21no—
87#137×C43—44no—
88C2×Q16×C43—22no—
89C2×SD16×C43—22no—
90C2×M16×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43C2312yes—
95C4×Q8×C43D411yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43D411yescharacteristic
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102#117×C43D411yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109#103×C43—22no—
110#103×C43—22no—
111#41×C43—22no—
112#41×C43D814yes—
113C2×Q8×C43—22no—
114C2×Q8×C43—41no—
115C2×Q8×C43—42no—
116C2×Q8×C43—42no—
117C2×Q8×C43C2×D411yescharacteristic
118C2×D4×C43—21no—
119C2×D4×C43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C2×C22⋊D43—41no—
128#10621898—42no—
129#10621898—42no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×C4×D43—41no—
134C2×Dic86—21no—
135Q16×C43—44no—
136SD16×C43—44no—
137M16×C43—42no—
138C2×C8×C43—22no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43C2×D411yescharacteristic
146C4⋊C4×C43C2×D411yescharacteristic
147C22⋊C4×C43—21no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C42×C43—21no—
151C42×C43—21no—
152C42×C43—21no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43#4111yescharacteristic
156C42×C43C2411yescharacteristic
157#10621885—42no—
158#10621884—42no—
159#10621883—42no—
160#10621882—42no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—42no—
169C2×C43⋊C8—82no—
170C2×C43⋊C8—81no—
171C2×C43⋊C8C2×D412yes—
172C2×C43⋊C8C2×D412yes—
173C23×C43—21no—
174C23×C43#12111yescharacteristic
175C22×D43—41no—
176Q8×C43—21no—
177Q8×C43—42no—
178Q8×C43—42no—
179Q8×C43—82no—
180Q8×C43C2×D812yes—
181D4×C43—24no—
182D4×C43—21no—
183D4×C43C2×D812yes—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—24no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—81no—
195C2×C4×C43—82no—
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43C2×D812yes—
200C2×C4×C43#13512yes—
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C2×#4111yescharacteristic
204C22⋊D43—82no—
205C2×Dic43—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209D172—41no—
210D172—81no—
211C4×D43—82no—
212Dic86—41no—
213Dic86—41no—
214C8×C43—42no—
215C43⋊C8—22no—
216C43⋊C8—22no—
217C43⋊C8—41no—
218C43⋊C8—41no—
219C43⋊C8—42no—
220#19416—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—22no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43#46612yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43—82no—
238C4×C43#46612yes—
239C4×C43C22×D811yescharacteristic
240C4×C43C2×#13511yescharacteristic
241C4×C43#57711yescharacteristic
242C4×C43#57811yescharacteristic
243Dic43—81no—
244#3226—431no—
245#3039D4311yescharacteristic, complemented
246#3035—431no—
247#2988—431no—
248#1682—432no—
249#1681—432no—
250#1674—432no—
251#1673—432no—
252#1571—431no—
253#1547—431no—
254C2×#332—431no—
255C2×C43—22no—
256C2×C43—42no—
257C2×C43#304611yescharacteristic
258C2×C43C2×#46611yescharacteristic
259C2×C43#306911yescharacteristic
260D43—161no—
261C2×#137—21no—
262C2×#135—861no—
263#532—431no—
264C2×C4⋊Q8C2×D4311yescharacteristic
265C4×#41C2×D4311yescharacteristic
266#500—432no—
267#486—432no—
268#480—862no—
269#474—861no—
270#474—861no—
271#464—861no—
272#463—861no—
273#462—21no—
274#462—431no—
275#462C2×D4312yes—
276#461—21no—
277#461—431no—
278#461C2×D4312yes—
279#460—431no—
280#459—431no—
281C8×Q8—432no—
282C8×D4—432no—
283C8×D4—862no—
284#431—431no—
285#431—861no—
286#423C2×D4311yescharacteristic
287C2×C4⋊C8—431no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—861no—
290#419—21no—
291#416—861no—
292#335—432no—
293#335—432no—
294#332—432no—
295#332—432no—
296#332—432no—
297#331—432no—
298C43#1941611yescharacteristic, complemented, Sylow
299C2×#41—861no—
300C2×#41C22⋊D4311yescharacteristic
301C22×Q8—21no—
302#137—44no—
303#135—1724no—
304C2×Q16—22no—
305C2×Q16—861no—
306C2×SD16—22no—
307C2×SD16—861no—
308C2×SD16—861no—
309C2×D8—861no—
310C2×M16—21no—
311C22×C8—862no—
312C22×C8—861no—
313C22×C8—861no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—431no—
318C4⋊Q8C22×D4312yes—
319#127—431no—
320#124—861no—
321#121—861no—
322#121—861no—
323C4×Q8C22⋊D4311yescharacteristic
324C4×Q8C22×D4311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4C22⋊D4311yescharacteristic
330C4×D4C22×D4311yescharacteristic
331#117—21no—
332#117C22⋊D4311yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C42—21no—
336C2×C42C22×D4311yescharacteristic
337#107—862no—
338#107—862no—
339C4⋊C8—21no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—432no—
343C4⋊C8—431no—
344C4⋊C8—431no—
345C4⋊C8—862no—
346C4⋊C8—861no—
347C4⋊C8—861no—
348C4⋊C8C22×D4312yes—
349#103—22no—
350#103—22no—
351#103—861no—
352#103—861no—
353#102—862no—
354#102—862no—
355#102—861no—
356#102—861no—
357C22⋊C8—432no—
358C22⋊C8—862no—
359C4×C8—432no—
360C4×C8—862no—
361#41—22no—
362#41—1722no—
363#41—1722no—
364#41#1062188214yes—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—861no—
370C2×Q8C2×C22⋊D4311yescharacteristic
371C2×D4—21no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—861no—
375C2×D4—1721no—
376C2×D4C2×C22⋊D4311yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—1721no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385Q16—44no—
386Q16—1722no—
387SD16—44no—
388SD16—1722no—
389SD16—1722no—
390D8—1722no—
391M16—42no—
392C2×C8—22no—
393C2×C8—432no—
394C2×C8—432no—
395C2×C8—862no—
396C2×C8—861no—
397C2×C8—861no—
398C2×C8—3442no—
399C2×C8—3441no—
400C2×C8—1722no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4C2×C22⋊D4311yescharacteristic
410C4⋊C4C2×C22⋊D4311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42D4×D4311yescharacteristic
420C42#1062190011yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—21no—
424C23—1721no—
425C23#1306329711yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—42no—
429Q8—82no—
430Q8—1721no—
431Q8—1721no—
432Q8C2×#1062188212yes—
433D4—24no—
434D4—21no—
435D4—3441no—
436D4—3442no—
437D4—1721no—
438D4—1721no—
439D4—1721no—
440D4—1721no—
441D4C2×#1062188212yes—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—3442no—
455C2×C4—1721no—
456C2×C4#1306329711yescharacteristic
457C2×C4#1306329711yescharacteristic
458C2×C4#1306329711yescharacteristic
459C2×C4C2×#1062188212yes—
460C2×C4#1306334512yes—
461C2×C4C2×D4×D4311yescharacteristic
462C2×C4C22×C22⋊D4311yescharacteristic
463C2×C4C2×#1062190011yescharacteristic
464C8—42no—
465C8—862no—
466C8—862no—
467C8—1721no—
468C8—1721no—
469C8—1722no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—3441no—
476C22—3441no—
477C22—3441no—
478C22#1458313312yes—
479C22C2×#1306329711yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—82no—
487C4—3441no—
488C4#1458313312yes—
489C4C22×#1062188211yescharacteristic
490C4C2×#1306334511yescharacteristic
491C4#1458370811yescharacteristic
492C4#1458371511yescharacteristic
493C2—22no—
494C2—42no—
495C2—6881no—
496C2#1914414911yescharacteristic
497C2C2×#1458313311yescharacteristic
498C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3039C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#3039D43
hypocenterC43#19416
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. #19145716C2semidirect
3. #19143706C2semidirect
4. #19134041C2semidirect
5. #19134034C2semidirect
6. #19133987C2semidirect
7. #19133982C2semidirect
8. #19133371C2semidirect
9. #19133273C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3039C2semidirect
245. #3039D43semidirect
298. C43#19416semidirect

Maximal subgroups

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

subgroupindex
#191457162
#191440502
#191437062
#191340412
#191340342
#191339872
#191339822
#191333712
#191332732
C2×#145826452
C43×#30392
#1941643