Finite Group Databasebeta

← #25074068

Subgroups — #25074068

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148479C211yesmaximal, characteristic
2#19145543C211yesmaximal, characteristic, complemented
3#19144404C211yesmaximal, characteristic
4#19133869C214yesmaximal, complemented
5#19133862C214yesmaximal, complemented
6#19133267C211yesmaximal, characteristic, complemented
7#19133051C211yesmaximal, characteristic, complemented
8#19132978C211yesmaximal, characteristic
9C2×C43×#498C211yesmaximal, characteristic, complemented
10#14583624—21no—
11#14583624C2212yes—
12#14583623—21no—
13#14583623C2212yes—
14#14583584—22no—
15#14583584—22no—
16#14583510—22no—
17#14583473—21no—
18#14583456C2211yescharacteristic
19#14583454—21no—
20#14583454—21no—
21#14583377—21no—
22C4×#10621898C2211yescharacteristic
23#14583278—21no—
24#14583249—21no—
25#14583191—21no—
26#14583186—21no—
27#14583181C2212yes—
28#14583176C2212yes—
29#14583106C2214yes—
30#14583055—22no—
31#14582952C2211yescharacteristic
32#14582939—21no—
33#14582923C2211yescharacteristic
34#14582898—21no—
35#14582645C2214yes—
36#14582631C2212yes—
37#14582631C2214yes—
38#14582628C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C43×#498—22no—
42C43×#498C2214yes—
43C2×#106×C43—22no—
44C2×C4×C8×C43C2211yescharacteristic
45C2×#10621898D411yescharacteristic
46C2×#10621885—24no—
47C2×#10621877—21no—
48#13063325D411yescharacteristic
49#13063325D411yescharacteristic
50#13063323—22no—
51#13063320—24no—
52#13063320—24no—
53#13063317—21no—
54#13063316—22no—
55#13063316—22no—
56#13063315—24no—
57#13063315—24no—
58#13063314—22no—
59#13063308—24no—
60#13063305—22no—
61#13063305—22no—
62#13063304—21no—
63#13063304D412yes—
64#13063301—22no—
65#13063301—22no—
66Q8×Dic43—22no—
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70C4×Dic86—21no—
71C4×Dic86D411yescharacteristic
72C4×Dic86C2312yes—
73C4×Dic86C2311yescharacteristic
74#13063290—22no—
75#13063290—22no—
76C4×D172D411yescharacteristic
77C4×D172C2311yescharacteristic
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80#13063284—24no—
81#13063284—21no—
82#13063284D411yescharacteristic
83#13063283—22no—
84#13063283—22no—
85#13063282—21no—
86C42×D43—21no—
87#13063258—22no—
88#13063256—22no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2312yes—
91C4⋊(C43⋊C8)C2312yes—
92#13063249—24no—
93#13063248—22no—
94#13063245—22no—
95C22⋊(C43⋊C8)—21no—
96C4×C43⋊C8—21no—
97C22×Q8×C43—21no—
98C22×Q8×C43—21no—
99C22×C8×C43—21no—
100C4⋊Q8×C43—21no—
101C4⋊Q8×C43—21no—
102C4⋊Q8×C43—21no—
103C4⋊Q8×C43—21no—
104C4⋊Q8×C43—21no—
105C4⋊Q8×C43D412yes—
106C4⋊Q8×C43C2312yes—
107C4⋊Q8×C43C2312yes—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D412yes—
112C2×C42×C43C2311yescharacteristic
113#106×C43—28no—
114C4×C8×C43—21no—
115C4×C8×C43C2312yes—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—41no—
120C2×Q8×C43—42no—
121C2×Q8×C43—42no—
122C2×Q8×C43—82no—
123C22×C4×C43—22no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C2×C22⋊D43—21no—
129#10621898—22no—
130#10621898—22no—
131C2×D172C2×D411yescharacteristic
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×Dic86—21no—
136C2×Dic86C2×D411yescharacteristic
137C2×Dic86C2×D412yes—
138C2×C8×C43—24no—
139C2×C8×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43C2×D414yes—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2411yescharacteristic
152C22⋊Dic43—21no—
153C22⋊Dic43—22no—
154#10621885—84no—
155(C2×D43)⋊C4—24no—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—21no—
158(C2×D43)⋊C4—21no—
159C4⋊Dic43—24no—
160C4⋊Dic43—24no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43C2×D412yes—
165C4⋊Dic43C2×D411yescharacteristic
166C4⋊Dic43C2×D411yescharacteristic
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—21no—
170Dic43⋊C4—22no—
171Dic43⋊C4—21no—
172Dic43⋊C4—22no—
173C4×Dic43—24no—
174C4×Dic43—24no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—22no—
179#10621877—42no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43#12011yescharacteristic
183C22×D43—21no—
184Q8×C43—42no—
185Q8×C43—42no—
186Q8×C43—44no—
187Q8×C43—44no—
188Q8×C43—82no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—44no—
193C2×C4×C43—42no—
194C2×C4×C43—82no—
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43#13512yes—
199C2×C4×C43#13712yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—42no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—21no—
209D172—21no—
210D172—21no—
211C4×D43—42no—
212C4×D43—42no—
213C4×D43—42no—
214Dic86—21no—
215Dic86—21no—
216Dic86—24no—
217Dic86—42no—
218C8×C43—24no—
219C43⋊C8—42no—
220C43⋊C8—42no—
221#18655—431nomaximal, Sylow
222C22×C43—21no—
223C22×C43—21no—
224C22×C43#45212yes—
225C22×C43C2×#12011yescharacteristic
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—41no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—44no—
232C4×C43—82no—
233C4×C43#45212yes—
234C4×C43#45612yes—
235C4×C43C2×#13511yescharacteristic
236C4×C43C2×#13711yescharacteristic
237C4×C43#57712yes—
238Dic43—41no—
239Dic43—42no—
240Dic43—41no—
241Dic43—42no—
242Dic43—41no—
243#3509—431no—
244#3209—431no—
245C2×#498D4311yescharacteristic, complemented
246#3079—431no—
247#1653—434no—
248#1652—434no—
249#1546—431no—
250#1493—431no—
251#1476—431no—
252C2×C43—22no—
253C2×C43C2×#45211yescharacteristic
254C2×C43#301011yescharacteristic
255C2×C43C2×#45611yescharacteristic
256D43—81no—
257#557—432no—
258#557—861no—
259#556—432no—
260#556—861no—
261#552—862no—
262#552—862no—
263#541—862no—
264#536—861no—
265#533—431no—
266#533—861no—
267#533—861no—
268C2×C4⋊Q8C2×D4311yescharacteristic
269C2×C4⋊Q8C2×D4311yescharacteristic
270#519—861no—
271C4×#41—431no—
272#498—22no—
273#498C2×D4314yes—
274#494—861no—
275#487—861no—
276#477—861no—
277#476—861no—
278#475—432no—
279#474—432no—
280#462—434no—
281#451—862no—
282#431—431no—
283#428—861no—
284C2×#106—22no—
285#423—431no—
286#417—861no—
287C2×C4×C8C2×D4311yescharacteristic
288#332—434no—
289Q8⋊C8—434no—
290Q8⋊C8—432no—
291D4⋊C8—432no—
292C43#1865511yescharacteristic, complemented, Sylow
293C2×#41—431no—
294C22×Q8—21no—
295C22×Q8—21no—
296C2×Q16—864no—
297C2×M16—861no—
298C22×C8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—431no—
305C4⋊Q8—431no—
306C4⋊Q8—862no—
307C4⋊Q8C22⋊D4312yes—
308C4⋊Q8C22×D4312yes—
309C4⋊Q8C22×D4312yes—
310#126—864no—
311#126—864no—
312#125—862no—
313#125—862no—
314#125—864no—
315#125—864no—
316#125—861no—
317#124—862no—
318#123—864no—
319C22⋊Q8—432no—
320C22⋊Q8—862no—
321C22⋊Q8—862no—
322C22⋊Q8—862no—
323C22⋊Q8—862no—
324C22⋊Q8—861no—
325C4×Q8—431no—
326C4×Q8—431no—
327C4×Q8—432no—
328C4×Q8—862no—
329C4×Q8—862no—
330C4×Q8—862no—
331C4×Q8—862no—
332C4×Q8—862no—
333C4×Q8—862no—
334C4×Q8—861no—
335C4×D4—431no—
336C4×D4—431no—
337C4×D4—861no—
338C4×D4—861no—
339#117—431no—
340#117—862no—
341#117—862no—
342#117—864no—
343#117—861no—
344#117—861no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4C22⋊D4312yes—
349C2×C42—861no—
350C2×C42C22×D4311yescharacteristic
351#107—862no—
352#106—28no—
353#106—862no—
354C4⋊C8—432no—
355C4⋊C8—432no—
356C4⋊C8—861no—
357#103—862no—
358#103—864no—
359#102—862no—
360C22⋊C8—861no—
361C4×C8—21no—
362C4×C8—861no—
363C4×C8C22×D4312yes—
364#41—862no—
365#41—862no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—41no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—82no—
373C2×Q8—431no—
374C2×Q8—432no—
375C2×Q8—861no—
376C2×D4—431no—
377C2×D4—861no—
378C22×C4—22no—
379C22×C4—41no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4—861no—
383C22×C4D4×D4311yescharacteristic
384C22×C4D4×D4311yescharacteristic
385C22×C4C2×C22⋊D4311yescharacteristic
386Q16—3444no—
387M16—1722no—
388C2×C8—24no—
389C2×C8—22no—
390C2×C8—862no—
391C2×C8—862no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—432no—
400C4⋊C4—431no—
401C4⋊C4—431no—
402C4⋊C4—864no—
403C4⋊C4—864no—
404C4⋊C4—864no—
405C4⋊C4—864no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—862no—
411C4⋊C4—861no—
412C4⋊C4—862no—
413C4⋊C4C2×C22⋊D4314yes—
414C22⋊C4—864no—
415C22⋊C4—864no—
416C22⋊C4—861no—
417C22⋊C4—862no—
418C22⋊C4—861no—
419C22⋊C4—861no—
420C42—864no—
421C42—864no—
422C42—861no—
423C42—861no—
424C42—861no—
425C42—862no—
426C42D4×D4311yescharacteristic
427C42D4×D4311yescharacteristic
428C42C2×C22⋊D4311yescharacteristic
429C42C23×D4311yescharacteristic
430C23—861no—
431C23#1306329311yescharacteristic
432Q8—44no—
433Q8—42no—
434Q8—42no—
435Q8—44no—
436Q8—82no—
437Q8—861no—
438Q8—861no—
439Q8—864no—
440Q8—1722no—
441D4—861no—
442D4—861no—
443D4—1722no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—82no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—862no—
453C2×C4—862no—
454C2×C4—861no—
455C2×C4—1722no—
456C2×C4—1722no—
457C2×C4—1722no—
458C2×C4#1306329311yescharacteristic
459C2×C4#1306329311yescharacteristic
460C2×C4#1306329311yescharacteristic
461C2×C4#1306334612yes—
462C2×C4#1306335412yes—
463C2×C4C2×D4×D4311yescharacteristic
464C2×C4C2×D4×D4311yescharacteristic
465C2×C4C22×C22⋊D4311yescharacteristic
466C8—24no—
467C8—1722no—
468C8—1722no—
469C22—21no—
470C22—21no—
471C22—1721no—
472C22—1721no—
473C22—1721no—
474C22#1458305812yes—
475C22C2×#1306329311yescharacteristic
476C4—21no—
477C4—21no—
478C4—44no—
479C4—82no—
480C4—1721no—
481C4—1722no—
482C4—1721no—
483C4—1721no—
484C4—1722no—
485C4#1458305812yes—
486C4#1458308112yes—
487C4C2×#1306334611yescharacteristic
488C4C2×#1306335411yescharacteristic
489C4#1458370512yes—
490C2—22no—
491C2—3441no—
492C2C2×#1458305811yescharacteristic
493C2#1914387711yescharacteristic
494C2C2×#1458308111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#498C2
socleC22×C43C2×#120
prime radicalC2×#10621898D4
hypercenterC2×#498D43
hypocenterC43#18655
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. #19145543C2semidirect
4. #19133869C2semidirect
5. #19133862C2semidirect
6. #19133267C2semidirect
7. #19133051C2semidirect
9. C2×C43×#498C2semidirect
245. C2×#498D43semidirect
292. C43#18655semidirect

Maximal subgroups

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

subgroupindex
#191484792
#191455432
#191444042
#191338692
#191338622
#191332672
#191330512
#191329782
C2×C43×#4982
#1865543