Finite Group Databasebeta

← #25073744

Subgroups — #25073744

Order 11008.

970 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#19148411C211yesmaximal, characteristic
2#19145746C211yesmaximal, characteristic, complemented
3#19144404C211yesmaximal, characteristic
4#19133733C214yesmaximal, complemented
5#19133726C214yesmaximal, complemented
6#19133276C211yesmaximal, characteristic, complemented
7#19133051C211yesmaximal, characteristic, complemented
8#19132978C211yesmaximal, characteristic
9C2×C43×#494C211yesmaximal, characteristic, complemented
10#14583629C2212yes—
11#14583624—21no—
12#14583610C2212yes—
13#14583604—22no—
14#14583564—21no—
15Q8×C22⋊D43—22no—
16#14583530—21no—
17#14583526—22no—
18#14583456C2211yescharacteristic
19#14583454—21no—
20C4⋊Q8×D43—21no—
21#14583380—21no—
22C4×#10621898C2211yescharacteristic
23#14583302—21no—
24#14583251—21no—
25#14583234—22no—
26#14583191C2214yes—
27#14583191C2212yes—
28#14583186C2212yes—
29#14583181—21no—
30#14583176—21no—
31#14582952C2211yescharacteristic
32#14582939—21no—
33#14582923C2211yescharacteristic
34#14582898—21no—
35#14582648C2214yes—
36#14582631C2214yes—
37#14582631C2212yes—
38#14582628C2212yes—
39C22×Q16×C43—22no—
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×C4⋊Q8×C43C2211yescharacteristic
42C43×#494—22no—
43C43×#494C2214yes—
44C2×C4×C8×C43C2211yescharacteristic
45C2×#10621898D411yescharacteristic
46C2×Q8×D43—22no—
47C2×#10621877—21no—
48#13063325D411yescharacteristic
49#13063325D411yescharacteristic
50#13063324—22no—
51#13063324—22no—
52#13063324—22no—
53#13063323—22no—
54#13063323—24no—
55#13063317—21no—
56#13063316—22no—
57#13063316—22no—
58#13063315—24no—
59#13063305—22no—
60#13063304—24no—
61#13063304—21no—
62#13063304D412yes—
63#13063303—24no—
64#13063301—22no—
65#13063301—24no—
66Q8×Dic43—22no—
67C4×Dic86—21no—
68C4×Dic86D411yescharacteristic
69C4×Dic86C2312yes—
70C4×Dic86C2311yescharacteristic
71#13063290—22no—
72#13063290—22no—
73C4×D172D411yescharacteristic
74C4×D172C2311yescharacteristic
75#13063287—22no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—21no—
78C4×C22⋊D43—21no—
79#13063284—21no—
80#13063284D411yescharacteristic
81#13063283—22no—
82#13063282—21no—
83C4⋊C4×D43—22no—
84C4⋊C4×D43—22no—
85C42×D43—21no—
86#13063258—24no—
87#13063258—22no—
88#13063256—22no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2312yes—
91C4⋊(C43⋊C8)C2312yes—
92#13063248—22no—
93#13063248—24no—
94#13063245—22no—
95C22⋊(C43⋊C8)—21no—
96C4×C43⋊C8—21no—
97C22×Q8×C43—21no—
98C22×Q8×C43D412yes—
99C2×Q16×C43—28no—
100C2×Q16×C43—48no—
101C22×C8×C43—21no—
102C4⋊Q8×C43—21no—
103C4⋊Q8×C43—21no—
104C4⋊Q8×C43—21no—
105C4⋊Q8×C43—21no—
106C4⋊Q8×C43—21no—
107C4⋊Q8×C43D412yes—
108C4⋊Q8×C43C2312yes—
109C4⋊Q8×C43C2312yes—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C4×C8×C43—21no—
116C4×C8×C43C2312yes—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—44no—
120C2×Q8×C43—44no—
121C2×Q8×C43—41no—
122C2×Q8×C43C2×D414yes—
123C22×C4×C43—22no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C2×C22⋊D43—21no—
129Q8×D43—84no—
130#10621898—22no—
131#10621898Q1614yescomplemented
132C2×D172C2×D411yescharacteristic
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—24no—
137C2×Dic86—21no—
138C2×Dic86—24no—
139C2×Dic86C2×D412yes—
140C2×Dic86C2×D411yescharacteristic
141Q16×C43—416no—
142C2×C8×C43—24no—
143C2×C8×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—41no—
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2411yescharacteristic
156C22⋊Dic43—22no—
157C22⋊Dic43—21no—
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—21no—
160(C2×D43)⋊C4—21no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43C2×D411yescharacteristic
166C4⋊Dic43C2×D412yes—
167C4⋊Dic43C2×D411yescharacteristic
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—21no—
172Dic43⋊C4—22no—
173Dic43⋊C4—21no—
174Dic43⋊C4—22no—
175C4×Dic43—24no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—21no—
179C4×Dic43—22no—
180#10621877—42no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C23×C43#12011yescharacteristic
184C22×D43—21no—
185Q8×C43—44no—
186Q8×C43—44no—
187Q8×C43—44no—
188Q8×C43—82no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—42no—
193C2×C4×C43—82no—
194C2×C4×C43—82no—
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43C2×Q1612yes—
199C2×C4×C43#13712yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—24no—
204C2×Dic43—21no—
205C2×Dic43—22no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—22no—
209D172—21no—
210D172C2×Q1612yescomplemented
211C4×D43—24no—
212C4×D43—42no—
213C4×D43—42no—
214C4×D43—84no—
215Dic86—21no—
216Dic86—24no—
217Dic86—42no—
218Dic86—84no—
219Dic86C2×Q1612yescomplemented
220C8×C43—24no—
221C43⋊C8—42no—
222C43⋊C8—42no—
223#18623—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43#45112yes—
227C22×C43C2×#12011yescharacteristic
228C2×D43—22no—
229C2×D43—41no—
230C2×D43—41no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—44no—
234C4×C43—82no—
235C4×C43#45112yes—
236C4×C43#45312yes—
237C4×C43C22×Q1611yescharacteristic
238C4×C43C2×#13711yescharacteristic
239C4×C43#57812yes—
240Dic43—22no—
241Dic43—42no—
242Dic43—41no—
243Dic43—42no—
244Dic43—41no—
245#3503—431no—
246#3230—431no—
247C2×#494D4311yescharacteristic, complemented
248#3079—431no—
249#1633—434no—
250#1632—434no—
251#1548—431no—
252#1493—431no—
253#1476—431no—
254C2×C43—22no—
255C2×C43C2×#45111yescharacteristic
256C2×C43#301111yescharacteristic
257C2×C43C2×#45311yescharacteristic
258D43—42no—
259C22×Q16—22no—
260Q82—432no—
261#557—861no—
262#554—432no—
263#554—862no—
264D4×Q8—861no—
265D4×Q8—862no—
266#544—861no—
267#544—862no—
268#533—431no—
269#533—861no—
270C2×C4⋊Q8—861no—
271C2×C4⋊Q8C2×D4311yescharacteristic
272C2×C4⋊Q8C2×D4311yescharacteristic
273#520—861no—
274C4×#41—431no—
275#500—861no—
276#494—22no—
277#494C2×D4314yes—
278#487—861no—
279#484—862no—
280#477—432no—
281#477—434no—
282#476—432no—
283#475—861no—
284#474—861no—
285#431—431no—
286#428—861no—
287#423—431no—
288#417—861no—
289C2×C4×C8C2×D4311yescharacteristic
290#333—434no—
291Q8⋊C8—434no—
292Q8⋊C8—432no—
293D4⋊C8—432no—
294C43#1862311yescharacteristic, complemented, Sylow
295C2×#41—431no—
296C22×Q8—21no—
297C22×Q8—862no—
298C22×Q8C22⋊D4312yes—
299C2×Q16—28no—
300C2×Q16—48no—
301C2×M16—861no—
302C22×C8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—431no—
309C4⋊Q8—431no—
310C4⋊Q8—862no—
311C4⋊Q8—862no—
312C4⋊Q8—862no—
313C4⋊Q8—862no—
314C4⋊Q8—864no—
315C4⋊Q8C22⋊D4312yes—
316C4⋊Q8C22×D4312yes—
317C4⋊Q8C22×D4312yes—
318#125—862no—
319#125—862no—
320#125—864no—
321#125—861no—
322C22⋊Q8—432no—
323C22⋊Q8—862no—
324C22⋊Q8—864no—
325C22⋊Q8—864no—
326C22⋊Q8—862no—
327C22⋊Q8—864no—
328C22⋊Q8—861no—
329C4×Q8—431no—
330C4×Q8—431no—
331C4×Q8—432no—
332C4×Q8—862no—
333C4×Q8—862no—
334C4×Q8—862no—
335C4×Q8—861no—
336C4×D4—431no—
337C4×D4—431no—
338C4×D4—862no—
339C4×D4—864no—
340C4×D4—861no—
341C4×D4—861no—
342#117—431no—
343#117—862no—
344#117—861no—
345#117—861no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—862no—
351C2×C4⋊C4—862no—
352C2×C42—861no—
353C2×C42C22×D4311yescharacteristic
354#107—862no—
355#107—864no—
356#106—862no—
357C4⋊C8—432no—
358C4⋊C8—432no—
359C4⋊C8—861no—
360#103—862no—
361#103—864no—
362#102—862no—
363C22⋊C8—861no—
364C4×C8—21no—
365C4×C8—861no—
366C4×C8C22×D4312yes—
367#41—434no—
368#41—862no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—44no—
372C2×Q8—44no—
373C2×Q8—41no—
374C2×Q8—431no—
375C2×Q8—432no—
376C2×Q8—864no—
377C2×Q8—861no—
378C2×Q8—3444no—
379C2×Q8C2×C22⋊D4314yes—
380C2×D4—431no—
381C2×D4—861no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—864no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4D4×D4311yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4C2×C22⋊D4311yescharacteristic
391Q16—416no—
392M16—1722no—
393C2×C8—24no—
394C2×C8—22no—
395C2×C8—862no—
396C2×C8—862no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—432no—
407C4⋊C4—431no—
408C4⋊C4—864no—
409C4⋊C4—864no—
410C4⋊C4—864no—
411C4⋊C4—864no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—862no—
417C4⋊C4—861no—
418C4⋊C4—862no—
419C22⋊C4—864no—
420C22⋊C4—861no—
421C22⋊C4—862no—
422C22⋊C4—861no—
423C22⋊C4—861no—
424C42—864no—
425C42—861no—
426C42—861no—
427C42—861no—
428C42—862no—
429C42D4×D4311yescharacteristic
430C42D4×D4311yescharacteristic
431C42C2×C22⋊D4311yescharacteristic
432C42C23×D4311yescharacteristic
433C23—861no—
434C23#1306329311yescharacteristic
435Q8—44no—
436Q8—44no—
437Q8—44no—
438Q8—82no—
439Q8—432no—
440Q8—861no—
441Q8—864no—
442Q8—3444no—
443Q8—1722no—
444D4—432no—
445D4—864no—
446D4—861no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—861no—
454C2×C4—864no—
455C2×C4—862no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—862no—
459C2×C4—3444no—
460C2×C4—1722no—
461C2×C4—1722no—
462C2×C4#1306329311yescharacteristic
463C2×C4#1306329311yescharacteristic
464C2×C4#1306329311yescharacteristic
465C2×C4Q16×D4312yes—
466C2×C4#1306335712yes—
467C2×C4C2×D4×D4311yescharacteristic
468C2×C4C2×D4×D4311yescharacteristic
469C2×C4C22×C22⋊D4311yescharacteristic
470C8—24no—
471C8—1722no—
472C8—1722no—
473C22—21no—
474C22—21no—
475C22—862no—
476C22—1721no—
477C22—1721no—
478C22#1458305312yes—
479C22C2×#1306329311yescharacteristic
480C4—21no—
481C4—21no—
482C4—44no—
483C4—82no—
484C4—862no—
485C4—1721no—
486C4—1722no—
487C4—1722no—
488C4—1721no—
489C4#1458305312yes—
490C4#1458306612yes—
491C4C2×Q16×D4311yescharacteristic
492C4C2×#1306335711yescharacteristic
493C4#1458371212yes—
494C2—22no—
495C2—1722no—
496C2C2×#1458305311yescharacteristic
497C2#1914388611yescharacteristic
498C2C2×#1458306611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#494C2
socleC22×C43C2×#120
prime radicalC2×#10621898D4
hypercenterC2×#494D43
hypocenterC43#18623
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
2. #19145746C2semidirect
4. #19133733C2semidirect
5. #19133726C2semidirect
6. #19133276C2semidirect
7. #19133051C2semidirect
9. C2×C43×#494C2semidirect
131. #10621898Q16semidirect
210. D172C2×Q16semidirect
219. Dic86C2×Q16semidirect
247. C2×#494D43semidirect
294. C43#18623semidirect

Maximal subgroups

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

subgroupindex
#191484112
#191457462
#191444042
#191337332
#191337262
#191332762
#191330512
#191329782
C2×C43×#4942
#1862343